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Patterns and individual-based modeling of spatial competition within two main components of neotropical mangrove ecosystems [Elektronische Ressource] / Cyril Piou

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Patterns and individual-basedmodeling of spatial competition withintwo main components of Neotropicalmangrove ecosystems.Doctoral thesisCyril PiouSubmitted to the Faculty 2 (Biology & Chemistry),in partial fulfillment of the requirements for the degree ofDoctor of Natural Sciences (Dr. rer. nat.)Evaluators:PD Dr. Uta BergerProf. Dr. Ulrich Saint-PaulAdditional examinators:Dr. Ilka Candy FellerProf. Dr. Juliane FilserFebruary 2007iiiiiTo my Parents, Martha and my future baby...ivPrefaceI have “really” started being interested in Ecology as a scientific topic in2002 with my field trip in Belize for my master thesis. There, I fall in lovewith the amazing environment of mangroves. But particularly, I felt as anecologist during that time because I started to convert my natural curiosityinto a scientific process of sampling and data analysis, dealing with plantsinteracting with and within their environment. During the many hours spentin Belizean mangroves, I liked imagining possible processes that drove thearchitectures of single trees or structure of the forest itself. I guess it is partlyfrom these times as well that comes my interest for modeling and statisticaltools trying to unraveling the hidden. I have been very influenced duringthis first experience by the own passion of Candy for the mangroves, as wellas the inputs of Uta in imagining processes with her KiWi model...

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Published 01 January 2007
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Patternsandindividual-based
modelingofspatialcompetitionwithin
twomaincomponentsofNeotropical
ecosystems.evmangro

DoCyrilctoralPiouthesis

SubmittedtotheFaculty2(Biology&Chemistry),
inpartialfulfillmentoftherequirementsforthedegreeof
DoctorofNaturalSciences(Dr.rer.nat.)

aluators:EvergerBUtaDr.PDProf.Dr.UlrichSaint-Paul

xaminators:eAdditionalDr.IlkaCandyFeller
FilserJulianeDr.Prof.

2007bruaryeF

ii

oT

my

ents,Par

Martha

and

ym

efutur

iii

aby...b

iv

Preface

I2002havewith“mreally”yfieldstartedtripibnBeingelizeinforterestedmyinmasterEcologythesis.asaThere,scientIfificallintopiclovine
withecologisttheaduringmazingthatentimevironmenbtecauseofImangrostartedvets.ocButonveprtmyarticularlynatural,Ifceltauriositsayn
inintoateractingscienwithtificproandcwessithinofstheiramplingenvandironmendatat.aDuringnalysis,themdealinganyhwithoursspplanentts
inarcBelizeanhitecturesmofangrosingleves,treesIlikoredstructureimaginingoftpheossibleforestproitself.cessesIguessthatitdroisvepartlythe
tofromolsthesetryingttoimesunraasvwellelingthatthecomeshidden.myIinhavterestebforeenmvoerydelinginfluencedandstatisticalduring
thisfirstexperiencebytheownpassionofCandyforthemangroves,aswell
astheinputsofUtainimaginingprocesseswithherKiWimodel...Once
themasterthesiswasfinishedin2003,Iwasluckyandhappytohavethe
supportofUtaandProfessorSaint-PaultogetapositionofPhDstudentin
theMADAMprojecttodevelopamodeloncrabmovements.However,you
willseeinthefirstpartofthepresentthesis,thatIdidnotfocusonlyon
hadcrabstartedecologyin...BelizeMyoPhDnmbangroecameveafconoresttinuationdynamicandaddedimprotovtheemennewtsofewhatxcitingI
topicofUcidescordatus...
ThejumpintothePhDthesismighthavebeenabitfast,andthefirst
experienceoffieldworkinBrazilwasquitehard.Butwiththemoralsupport
ofMartha,myParents,CandyandUta,IthinkIwentthroughsomevery
richpersonalexperiencesandfinallyobtainedinterestingfindings...Atmy
returnfromBrazil,UtaandIproposedtohaveanewexperienceonthefield
tofewinvemontstigatehslater,morethisonttimeheamobitvebmenetttersofcprepared,rabsabasedndonwiththeamoasterbservastionstudenIt
hadoriginmofademostduringofthethedfiatarsteonxptheedition.spatialBeforedistributionthissecondofctriprabs,IthatwlearnedasaCtt++he
anddevelopedthefirstversionsoftheIBUmodel...Iwasnotconvincedat
firstsomehothatwtheIBUonewtouldhatrbringeallybimpelievortaneditnitmadditionalorethanminformation.yself,andVolkfinishederwtaso

v

vi

PREFECA

convincemeofthepotential...Theexperienceoftryingtounderstandpat-
ternswithonlyhypothesesonsomehiddenprocesseswasquitechallenging
andfinallysuccessful.ParticularlynowthatIhavedoneasecondstudywith
IBU(Chapter8),Irealizeevenmorethepotentialforfuturetheoretical,but
orks.wappliedalsoFromthedevelopmentandtryingtofitIBUtothefieldpatternswasborn
theneedofdevelopingtheapproachofPOMIC.Thiswasactuallyanother
bigexperienceandpersonaladvancement.Ihadnotmuchknowledgeon
likelihoodmethodsorinformationcriterion.However,fewweeksafterenter-
ingintothistopic,appearedtomethepossibilitythatonecouldestimate
thelikelihoodofanon-linearstochasticmodel,whichmakePOMICinterest-
ingandparalleledtothefamousAkaikeinformationcriterion.Ihavebeen
veryoftendoubtingaboutthemathematicalreliabilityofthe“newmethod”
createdwithit.Afteraskingmanyspecialists,Ibecamequiteconvincedof
itspotential.Andfinallynoneofthesespecialistsfoundthatsomethingwas
wronginthePOMICapproach...SoIjusthavetohopenowthatitwillbe
ofhelptootherindividual-basedmodelers...
InparalleloftheUcidescordatusandPOMICstudies,Ihadalsobeen
workingontheforestdynamicpartandtheKiWimodel.Iwroteandpub-
lishedmyfirstpaper(animportanteventinthelifeofanecologist)withthe
bighelpofCandyandUtaduringmyfirstyearofPhD.Itispresentedhere
becauseitfitsparticularlywellwiththeotherpapersonmangroveforest
dynamic,butthemostimportantpart(thefieldwork)wasdoneduringmy
master.Theoriginsoftheworkonsimulatingtheinfluenceofhurricanes
onmangroveforestdiversitywerealsocomingfrommymaster.However,
inthepaperpresentedhere(Chapter4),mostoftheworkwasdoneduring
thelastthreeyears.Thelastchapterofthefirstpartonmangroveforest
dynamic(Chapter5)wasthenaconnectionbetweenmynewexperienceof
tuningmodels(comingfromtheIBUmodel)andpattern-orientedmodeling
usingthePOMICapproach,sothatitcouldbeseenasparalleltothelast
chapterofthecrabpart.
Finally,theentireworkIhavedoneduring3years(exceptthedevelop-
mentofPOMIC)wasmostlyturningaroundonespecialaspect:theobserva-
tionandunderstandingofpatternshypothesizedtobebecauseof“competi-
tion”...Humansoftenbelievethatcompetitionisoneofthemostimportant
naturalforceatthebaseofanyrelationships,andparticularlyfortheirown
ones.Iwouldlikenottobelieveinthisdirection,andIhavealwaysbeen
quiteattractedtothetopic.Iwouldhavelikedtotrytodemonstratethat
competition-basedrelationshipsisnotthesolutionforhumanpopulations.I
amafraidmyecologicalworkwillneverdemonstratethat...Atleastnotat
allinthisPhDthesis.Butatlast,Icancomfortmyselfwiththeassessment

vii

oftheroleofcompetitiononotherpopulationsandcommunities...Ihave
orientedthecompilationofmyarticlestocoverdifferentaspectsofcompeti-
tionandtheexpressionofitundersomefewpatterns.Youwillrealizethat
Itreatedofinterandintra-specificcompetitioninthetwopartsofthethesis
respectively,andalsodiscussedwiththechapter8ofasymmetricandsym-
metriccompetition.Eveniffarfrombeingexhaustive,Icoveredinteresting
partsofcompetitionsituationinmangroveecosystems.Finally,itleadsme
toapropositionoflookingatcompetitionwithaprobabilisticapproachthat
Ipresentintheconclusionschapter.Letseehowthisideacompeteagainst
other...

nevIerwhanavtetaorrivfinishedttohistheprefacepresentwiththesisanwacithoutknowthehledgemenelpoftmpanartyp.Ieople.wouldI
willstartwithUtaBergerwhosupportedmeinallstepsandadvisedme
alwaysfrankly.IhavealsoabigdebttoCandyFellerwithhertransferof
passionforthemangrovesandconstantsupportonalltheecologicalpartsof
mywork.VolkerGrimmisthenthethird,butnotlessimportant,“mentor”
leathatstfinorthatparticular...IacmonindebtvincedtomethatProfessorIBUUlricwhorks,SainIt-Phavaul,etowhothankmadehimtheseat
forthreeaycceptingearspotossible.evaluateIwomyuldwolikerk,alsoandtoHthankeidemarieWProfessorolterandJulianneJonathanFilser
Montalvotobeonmydefensecommittee.
ThereisalotofpeoplethathelpedmeforsomestudiesandthatIwould
liketothankwarmly:KarenDieleforthefieldworkinBrazilandintroduc-
tiontoUcidescordatus,HannoHildenbrandtforhistalentonmakingC++
programmingsmarter,MarceloProtazioforhisexplanationsongeostatis-
tics,MarcTaJonathanylorandMonGtalvonzalooforOlivhisares-JohnsonmathematicalforfadvisoryruitfulforthediscussionsPOMIConmanpart,y
ecologicaltopics,CoralieD’LimaandUlfMehligforthesharedexperiencein
Brazilianmangroves,SenhorManuel,DomingosdeAraujoandAldodeMelo
forthehelpinfieldworkinBrazil,andFaustinoChiandthepeopleofthe
InstituteStern-PirlotofMalsoarinehelpedStudiesmeforimprothevwingorktheinBEelize.nglishofMarcpartsTaofylortheandthesis.Amanda
andEvIenwoifuldtheylikebetolievtehanktheymyarenparenottsosfmoruchtheirinvoclvedonstanintit,lovIeathinkndsupptheyort.do,
ToalltherestofmyfamillyandfriendsnotyetmentionedIthankthem
alsoforsupportingmeinmanyways.Andfinally,Ihavetoconfessthat
MarthaLilianaFontalvoHerazomademehappyandabletoworkonthis
waPhDyofhduringelp.allShe’llthecontthreeinueytoears.makIeammeveryhappy,gratefulallofwingormeherltoovbeaecomendvafatherrious
insomefewmonths...

viii

APREFEC

tsentCon

Preface

tsentCon

FiguresofList

ofListblesaT

ductiontroinGeneral11.1Modelinginecology........................
1.2Competitioninecology......................
1.3Neotropicalmangroves......................
1.3.1Generalities........................
1.3.2The“trees”component..................
1.3.3The“grazers”component................
1.4Objectivesandpresentationofthethesis............
1.4.1Generalandmethodologicalobjectives.........
1.4.2Specificobjectives.....................
1.4.3Administrativepresentationofthethesis........
.............................eferencesR1.5

v

xiii

xvii

xx

125111121315151610242

2Proposinganinformationcriterionforindividualbasedmodel
92selection2.1Abstract..............................30
2.2Introduction............................31
2.3ActualtoolsofPOM.......................33
2.4AninformationcriterionforPOM................36
2.4.1Background........................36
2.4.2Proposition........................38
2.4.3Derivedstatisticsforstronginference..........39
2.4.4Derivedstatisticsforinversemodeling.........41

ix

CONTENTSx2.5ExampleofApplication......................41
2.5.1DescriptionofSIMOVIM.................42
2.5.2Inversemodelingphase..................44
2.5.3Stronginferencephase..................46
2.6Discussion.............................47
2.7Acknowledgements........................50
2.92.8RAppeferencesendices.........................................................5503
2.9.1AppendixA........................53
2.9.32.9.2AppAppendixendixCB................................................5566
2.9.4AppendixD........................58
IInterspecificcompetitioninCaribbeanmangrove
36forests3ZonationpatternsofBelizeanoffshoremangroveforests41
3y.e1arsAabstfterractacatastrophic..............................hurricane6656
3.2Introduction............................67
3.3Methods..............................69
33..33..12SFtouredsytamreeaasaurnedmseitnetss......................................7609
3.3.3Physical-chemicalsurvey.................70
3.3.4Indicatorsofdestructionlevel..............72
3.3.5Dataanalysis.......................73
3.4Results...............................74
3.4.1Forestmeasurements...................74
3.4.2Physical-chemicalmeasurements.............74
3.4.3Indicatorsofdestructionlevel..............77
3.4.4Statisticalanalyses....................80
3.5Discussion.............................81
3.6Acknowledgments.........................83
3.7References.............................83
4Modelingtheeffectofhurricanedisturbancesonmangrove
forestdiversity87
4.1Abstract..............................88
4.2Introduction............................89
4.3Methods..............................90

CONTENTSxi4.3.1KiWimodelgeneralsettings...............90
4.3.2Settingsofinterspecificcompetitionparameters....92
4.3.3Effectsofabioticconditions...............94
4.3.4Effectsofperturbationregimes.............95
4.4Results...............................96
4.4.24.4.1SFirstecondeexercise:xercise:effectseffectsofoafpbioticcerturbationonditionsregimes...........9967
4.5Discussion.............................102
4.6Acknowledgements........................105
4.84.7RAppeferencesendices.........................................................110057
4.8.1AppendixA........................107
4.8.2AppendixB........................110
5Importanceofabioticgradientsonmangrovezonationpat-
terns:asimulationexperiment113
5.1Abstract..............................114
5.2Introduction............................115
5.3Methods..............................118
5.3.1TheKiWimodel.....................118
5.3.2Simulationsandanalysis.................124
5.4Results...............................128
5.5Discussion.............................130
5.6Acknowledgements........................134
5.7References.............................134
IIIntraspecificcompetitioninNorthBrazilianUcides
cordatuspopulations137
6Spatialstructureofaleaf-removingcrabpopulationina
mangroveofNorth-Brazil139
6.1Abstract..............................140
6.2Introduction............................141
6.3Methods..............................143
6.3.1Studyarea.........................143
6.3.2Noteonthesamplingofburrowsasproxyofcrabpop-
6.3.3ulaSpatialtiondistribution...........................atsmallscale............114444
6.3.4Habitatheterogeneityeffectoncrabpopulationatlarge
scale............................145

CONTENTSxii6.4Re6.3.5sultsSpatial...............................distributionatlargescale............114487
6.4.1Burrowsasproxyofcrabpopulation..........148
6.4.2Spatialdistributionatsmallscale............148
6.4.3Habitatheterogeneityeffectoncrabpopulation....151
6.4.4Spatialdistributionatlargescale............154
6.5Discussion.............................155
6.6Acknowledgements........................160
6.7References.............................160
7Simulatingcrypticmovementsofamangrovecrab:recovery
phenomenaaftersmallscalefishery163
77..12IAnbtsrtordauccttion..........................................................116654
7.3Fieldexperiments.........................167
7.3.1Methods..........................167
7.3.2Results...........................168
7.47T.4h.e1IBUDesmcoridpetlion..................................................116699
7.4.2Modelanalysis......................176
7.5Results...............................178
7.5.1Nullmodel........................178
7.67D.i5s.c2ussiFoOnNmodel.....................................................118803
7.7Acknowledgements........................188
7.8References.............................188
8Tatestinginindividual-levtraspeelcifictoreproducephenomenologicalpopulation-levcompeeltitionpatternsmodelsof
amangrovecrab193
8.1Abstract..............................194
8.2Introduction............................195
8.3Methods..............................198
88..33..12TSihmeuIlBatUionmsodel..............................................129083
8.3.3Analysisofgoodnessoffittothepatterns.......205
8.4Results...............................207
8.5Discussion.............................209
8.5.1Modelstructureandsymmetryofcompetition.....210
8.5.2Differencesinmethodsanalyzingthereproductionof
population-levelpatterns.................213

CONTENTS

xiii

8.5.3Competitionatindividuallevelandinferringonindi-
vidualbehavior......................214
8.6Acknowledgements........................216
8.88.7RAppeferencesendices.........................................................221186
8.8.18.8.2AppAppendixendixAB................................................221198

GeneralDiscussionandConclusions

225

2259.1Organizationofthischapter...................226
9.2DiscussiononPartI.......................226
9.2.1Generalcontributions...................226
9.2.2Aboutinterspecificcompetition.............227
9.2.3Outlook..........................228
9.3DiscussiononPartII.......................229
9.3.1Generalcontributions...................229
9.3.2Furtherimplications...................230
9.3.3Outlook..........................231
9.4Discussiononecologicalmodeling................232
9.4.1Onindividual-basedmodeling..............232
9.4.2Onpattern-orientedmodeling..............234
9.4.3OntheuseofPOMIC..................235
9.5Integratingtheecologicallessons................236
9.5.1Generalconclusions....................236
9.5.2Concludingoninter-andintra-specificcompetitions..238
9.5.3Proposition........................239
9.6References.............................244

xiv

CONTENTS

FiguresofList

1.11.21.3

2.12.22.3

1.32.3.334.33.5

4.14.24.34.44.54.6

dPifferesenrenttaationrticloefsthegeneral..........................topicsandmethodscoveredbythe17
TTheoreticalheoreticalframewframeworkorkooffttheheobobjectivjectivesesofofthethefirstsecondpartpart......1219

Spatialdistributionoftheoreticalindividualsafter50daysin
theirenclosure...........................42
tionFittingtoantheestimatorhistogramofoftheobservasamplingtionofXprobabilit.y...........densityfunc-54
Fittinganestimatorofthesimulationresultsprobabilityden-
sityfunctiontothehistogramofobservationofYwithaden-
sitykernelestimator........................55

TurneffeAtollandCalabashCay................71
Mangroveforeststructureofthedifferentsites.........75
Nutrientuseefficiencyresults..................78
Resorptionefficiencyresults...................78
TreesDBHclassdistribution...................79

ISDHvariationsaccordingtosalinityandrelativenutrient
availability............................97
Dynamicalvariationsofthetwocompetitionparameteriza-
tionswithselectedabioticscenariosinIVandISDH......98
DynamicalvariationsinIVandISDHwithdifferentpertuba-
tionregimes............................99
MedianISDHvariationsaccordingtoperturbationfrequency
andintensity...........................100
MedianISDHvariationsaccordingtoperturbationfrequency
forselectedcase..........................101
Appendix-Belizeandbh-densitydataandaandbparameter-
izationofRhizophoramangle(black)andAvicenniagerminans109

xv

xvi

4.74.8

5.15.25.35.4

6.16.26.36.46.56.66.7

7.12.77.37.47.5

FIGURESOFLIST

Appendix-CARICOMPdbh-densitydataandgeneralaand
bparameterization........................
Appendix-PatternsofsystemresponseinmedianISDHvari-
ationstopertubationregimes..................

Schemeofrepartitionofthehypothesesoffactorsaffecting
mangrovespecieszonationpatterns...............
Annualproductionofpotentialrecruitsofasingletreeaccord-
ingtoitsdiameteratbreastheight...............
Sub-modelsofprobabilitytosettledependingonthespecies
andthemaximumtidalrange..................
FieldobservedbasalareasandbestKiWisimulationresults
perspeciesandzonesofthefoursitesofCalabashCay....

Relationshipbetweensizesof310burrowentrancesandsizes
ofUcidescordatuscapturedinthem..............
Spatialpointpatternanalysisofburrowentrancesonnon-
rootedareas.............................
Spatialpointpatternanalysisofburrowentrancesandprop
rootpositiononaRhizophoramanglerootedarea........
Numberandmediansizeofburrowsdependingontheneigh-
boringtreespecies.........................
Numberandmediansizeofburrowsdependingonaqualitative
descriptionofpneumatophoresoccupations...........
Numberofburrowspersquaremeterdependingontheele-
vation,R.mangleproprootcoverageandPARpercentage
reachingthesquaremetermeasured...............
Spatialpointpatternanalysisofburrowentrancesaggregation
alongthethreetransects......................

Proportionofoccupiedburrowsthroughtimeafterthefishing
experiment.............................
SnapshootofIBUmodelinterface................
Effectsofαdev,cRmoveandcdisaponthereproductionofthe
recoverypatterns.........................
EffectsofPmoveandPstoponthereproductionoftherecovery
patterns..............................
Effectofthescalingparametertotransformcompetitionin-
tensitytoadditionalprobabilityofmovementonthemean
totalerrorofdeviationwiththesecondtypeofmodel.....

011211

611021221231

841941051151251351551

961371971810181

LISTOF7.6

7.7

8.18.2

91.9.29.3

FIGURESMeantotalerroragainstvarianceoftotalerrorintherepro-
ductionoftherecoverypatternfortheparameterizationsof
thesecondmodeltypeandselectedparameterizationofthe
firstmodeltype..........................
Recoverypatternsofthemostrealisticandbestfittingparam-
eterizationsforthetwotypeofmodels.............

Rmoeprodelforductionthisofthepatternreco(vRMeryZOaIfterwithfisherya=10of)the...........mostrealistic
Rwitheprotheductionmostofrtheealisticspatialmodelfordistributionthisppatternattern(atRMsmallFONscalewith
a=10)...............................
ChangeofinterpretationofFON................
PDifferenrobabilistictprrobabilisticepresenintationtoferpretationindividual...............treeinteractions..

.

.

xvii

281481

029

012224412
243

xviii

LISTOFFIGURES

blesaTofList1.1Termsdefiningthepossibletypesofinteractionsamong2or-
ganisms..............................8
1.2Presentationofthearticles....................23
2.1sTionestedsofvtaheluesSIoMfOtVheIMmoparametersdels.included.................inthedifferentver-44
2.3Appendix-ResultsofSIMOVIMmodelforparameterization
ofP2.................................st58
2.52.4AppAppendixendix--RResultsesultsooff21ndSSIIMMOOVVIIMMmmooddeell......................5599
2.6Appendix-Resultsof3rdSIMOVIMmodel...........60
2.7Appendix-Resultsof4thSIMOVIMmodel...........61
3.1Physicochemicalmeasurementsresultspersitesandzones...77
3.2Factorloadingsofnutrientusevariablesfactoranalysis....77
3.3Univariatetestsofsignificanceandsummaryofparametersof
thegeneralregressionmodel....................80
4.1uGserodiwthnthaendKiWispatialmodcel.ompetition.....................species-specificparameters93
5.1Species-specificparametersusedintheKiWimodel.......125
5.2Sub-modelsandparametervaried................126
5.3SiteAresults...........................129
5.4SiteBresults...........................129
55..56SSiitteeCDrreessuullttss......................................................113310
6.1Meanoccupiedburrownumbersandsizesofburrowentrance
pertransects............................151
6.2ResultsofGeneralRegressionModelwithbackwardstepwise
selection...............................154
xix

xx

1.77.2

8.18.28.38.4

8.5

LISTOFATBLESParametersandinitializationvaluesfortheIBUmodel....172
Descriptionsandvaluesofparameterstestedwiththetwomodels176

ParametervaluesofconstantsCinequations.........
ParametersenteringinthefourtypesofsimulationsofIBU.
Descriptionofpatterns......................
Resultsofeachmodelofindicatorsofgoodnessoffitforeach
pattern...............................
Resultsofeachmodelinoverallindicatorsofgoodnessoffit.

ofgoodnessoffit.

.

.

102202402802211

Chapter

General

1

rotni

duction

1

2

DUCTIONONTRIGENERAL

Thistopicsinmgeneralywiork:ntroEcologicalductionmoshalldeling,pCresenomptegeneraltitionaandspMectsangroofvethreemecosys-ain
tems.Inthefirstsection,Ipresentwhatecologicalmodelingis,whatitmay
helptodoandwhatareindividual-basedmodelsandthepattern-oriented
modelingapproach.InthesecondsectionIexplainwhatisgenerallyunder-
stootheoriesdunderanalyzingthetheconceptroleofocfiompnteer-atitionndinintra-specology,ecificpresencomptsomeetitionandexamplesarrivoef
towhatcouldbetheroleofindividual-basedmodelsinthesetheories.In
tthewotmhirdainscompection,onenIptsoresenfNteotropicalgeneralitiesomangrofmveangros:v(1)eethecosystemstreecommandunitfoycusaondn
particularlythethreemainspeciesfoundinCaribbeanmangroveforests;(2)
thegrazerscommunityandparticularlytheleaf-removingcrabUcidescor-
datus.InthelastsectionofthisgeneralintroductionIpresentthegeneral
andpartsmofethothedologicalthesisobdealingjectiveseacofhthewithtahesisspandecificthescomppecificonentobofjectivNesoeotropicalftwo
womangrorks,vthees.fInundingsthisandlastthesection,peopleIinalsovolvedpreseninteacthehfollotempwingoralchframeapter.ofmy

1.1TheWhysandHowsofecological
deling?mo

Thescienceofecologytriestounderstandinteractionsoflivingorganisms
otheramongtsciences,hemselvecomsandbineswithtwotheirmainhabitatapproach(Haecesofkelanalysis:1866).Eocologybserv,aationsmanandy
expdescriberimenedtbyation.theThefirst.lOatterbservsahouldtionsoidenfntifyaturaltheprosystemscessesshouldleadingbetoaccompa-patterns
niedofstatistical,experimentalandtheoreticaltoolstoavoidthatecology
stamanysyattfindingshelevgelofenerallynaturalconfirmedhistory.wTithheexpdescriptiverimentseapndartofthereafterecologyleadsacceptedto
asself-thinninggeneralcruleoncepts.(YodaT1he963)planintplantsuccessionecology,oconceptrthe(Cowlespredator-prey1901)taypndestheof
inecologyteractions,are(Vexamplesolterra1of926,largelyLotka1932acceptedinTowconceptsnsendedevteal.loped2003)aifternaobser-nimal
vaTheytions,areusefulmathematicalinthedescriptionsunderstandingandofexpdynamicserimenotfalrtestsesourcesatofminanyterestscales.for
humans,aswellasgenerallyitheunderstandingofnaturalsystems.
However,manyecologicalconceptsaredebated.Theproblemsmightbe
tofirsttounderstanddescribeallthethemosthphenomenaolisticallybepohindssiblethem.thenTheaturalcouplingpatternsofandsdescriptiveconde

ECOLOGYINMODELING1.1.

3

andexperimentalecologyworksatsmalllevelofintegration(e.g.individual
orpopulationlevel)orsmallspatialortemporalscalesbutmightnotalways
atlargescales.Whenthescaleofintegrationistoolarge(e.g.atcommunity
ormacroecologicalscale)orthespatialortemporalframeoftheprocesses
implicatedistoowide,descriptiveecologycanleadtointerestinghypotheses
butexperimentalecologymaybelessconvincingorfeasible.Suchsituations
tendtohappenforhypothesesoriginatedafterlargescaleobservations.A
goodexampleofthisistheintermediatedisturbancehypothesis(“IDH”,
Connel1978).Obviously,theIDHcouldforexamplebeexperimentallytested
onplankton(Fl¨oderandMosser1999)orevenbedmussels(Lenzetal.
2004).However,whenspeakingofsystemswithmuchlargerregeneration
timeorspatialrange(suchastropicalforests),experimentsaregenerally
onlypartiallyreproducingtheentirerangeofpossibilitiesunderlyingthe
hypothesis.TheIDHisthereforenoyetacceptedbyallecologists,and
particularlythosewhofocusonlargescalequestions(e.g.seeargumentations
onMackeyandCurrie2001,SheilandBurslem2003,Sheaetal.2004).
ThediscussionaroundtheIDHisoneofmanyexamplesdemonstratingthe
difficultiesofexperimentallyassessinganhypothesisonlargescale.Insuch
cases,the“simulationpart”ofecologicalmodelingcouldenterintoplay
andbringimportantinputs.Iwilldefinenowwhatismeantbyecological
modeling,andwhatisgenerallyunderstoodunderthespecific“simulation
part”.Ecologicalmodelingcouldbedefinedasthecreationofconceptualor
mathematicalmodelstosynthesizeacquiredknowledgeandillustrateortest
hypothesesoftheecologicalscience.Thisdefinitionisverybroadbecause
weneedtoincorporatemanydifferenttypesofmodels:conceptualmodels
(canbeadiagram,sometheoreticalequationsorevenaspecificformulation
ofahypothesis),statisticalmodels(generallydevelopedtoanalyzedataand
testifthesedatasupportafocushypothesis),flowmodels(describingthe
flowofenergyormatteramongcompartmentsofafocussystemassumedto
beundersteadystate)anddynamicmodels.Theyareaimingatthesame
generalobjectives:combiningpreviouslyacquiredknowledgetogofurther
onunderstanding.Dynamicmodelsaregenerallyfocusingonthedescrip-
tionofdynamicsofpopulation,speciesassemblageorcommunity.Theycan
haveanadditionalaimnotpossiblewiththeotherecologicalmodelingap-
proaches:thepredictionoffuturetrendsinthefocussystem.Withinthese
dynamicmodels,modelsusingcomputersimulationsconstitutethe“simu-
lationpart”ofecologicalmodelingmentionedearlier.Thesemodelscanbe
goingfromasimpleequationdescribingjustapopulationinteractingwith
itsenvironment,uptoamodelwithstructureddescriptionofdifferenttypes
ofindividualsinvariouspopulationsofacommunityanddescribingtheir

4

DUCTIONONTRIGENERAL

intrinsicinteractionsaswellaswiththeenvironment.Thecomplexityof
dynamicmodelsdependsonthepurposeofthemodelandtherebytheneed
ofpredictionpower,theneedofprecision,theknowledgesynthesizedwith
themodel,theproblematicassessedinrelationtothisknowledgeandthe
timeallocatedtothedevelopmentofthemodel.
GrimmandRailsback(2005)arguethatecologyandbiologyingeneral
stilllackstrongmathematicaltoolstohavethecapacitytoproveaslogically
aspossiblespecificcharacteristicsofnaturalsystems.Withthedevelopment
ofcomputerbasedmodelsinthelast30-40years,algorithmandmathemati-
calapproachesincreasedtremendouslyincomplexityinresponsetotheneed
ofunderstandingofcomplexityofnaturalsystems.Specifically,bottom-up
dynamicalmodelingapproacheshavebeendevelopingalotduringthelast
20yearsbasedontheideathatasystemisnotjustasumoftheparts.
Withthesebottom-upmodels,ecologistsorganizeandsimulatethesystem
offocusincompartmentsofidenticallevelofintegrationtounderstandphe-
nomenonathigherlevelofintegration.Inparticular,theindividual-based
modeling(IBM,oralsocalledagent-basedmodelingABM)approachfollows
thisframeworkandhelpedinunderstandingemergentpropertiesofcomplex
systemssuchaspopulationorcommunitiesoutofthecharacteristics,be-
haviorandinteractionsofpartsofthissystem,namelyindividualorganisms
(Brecklingetal.2005,DeAngelisandMooij.2005,Grimmetal.2005).

Studiesusingindividual-basedmodelinghaveincreasedlinearlyinthelast
20yearswithnumberofpublicationspassingfrom1to150publications/yr
blieveteweenthat1990thesetandools2004couldeven(DeAngelisbecomeandtheMofoij,undamen2005).tsoSfaomemocompletelydelersbnewe-
2005).approachHotowever,ecologyandtraditionalcreatetecologistsheirowcnalltintheoriesoq(uestionGrimmtheandRreliabilitailsbacyokf,
thesemodelsbecauseoftheirinternalcomplexity,theirlackofverifications
results.againstnTheseaturalcriticsconditions,leadtahendIBMthedsevelopometimesers,toandobhighsottom-uppecificitmoyofdelerstheirin
(POM).general,toThedevoebjlopectivaneaoftdditionalhePOMaspproactrategyhinamedstopincreaseattern-orienthetedreliabilitmodyelingof
prothemoductiondelofandtsomeoudoseascumenovteralleddevpatternselopmenofatsobystem,jectiveodescribfanedIaBMtthedifferenre-t
lev1996,els,andWiegandassumingetal.2they003,areGtherimmresultsandoBfsergerpecific2003,proGcessesrimmet(Grimmal.2et005).al.
TheschoolofthoughtofPOMdoesnotgenerallyusetheterm“emergent
scprophoolerties”oftothoughdtescrib(e.g.etheirBrecklingpatterns.etal.This2005).termisHoweusedver,oftenemergenbyatnotherprop-

ECOLOGYNICOMPETITION1.2.

5

ertiesarehighlevelpatternsultimately.Andwhenalreadydescribedfrom
fieldstrategy.studies,ThethesePOMesmergentrategytphropasebertiesenshoulddescribbedeawithmainafrocusigorousoftheprotoPOMcol
includingfoursteps(Wiegandetal.2003):(1)“aggregationofindividual-
basedbiologicalinformation”forthemodelconstruction,(2)“determination
ofternandparameterthevsimalues”,ulated(3)pattern“systematicproducedcbyomparisonthemboetdwel”eenandthe(4)o“bservedsecondarypat-
tofieldpredictions”.observInations,thetewoitherlastofsfocteps,uss(pattern,ystematicstepc3)oomparisonrnon-inoftmenodtionalelresults(part
ofthesecondarypredictions,step4),shouldleadtotheincreaseinreliability
ofthemodelthatbottom-upmodelersneededandwerelookingforwiththe
POMapproach.ThetwofirststepsassuretheIBMorABMtoincorporate
atlow-levhigherellevelsinformation(e.g.bethathaisviorofleadingtoindividualtheefishmergenftormingpropaefishrtiesscorhopolatternswhen
grouped,e.g.Reynolds1987).

1.2Thecompetitionconceptinecology
Inecology,theconceptofcompetitioncomesfromtheconceptofresource
limitationthatorganismsfaceinnaturalsituations.Bothconceptsoflim-
itationofresourcesandcompetitionwerefundamentalontheelaboration
ofecologicaltheoriesasearlyasforDarwin(1859)andhis“strugglefor
life”concept.Limitationofresourcesisamajorlinkbetweentheorganisms
andtheirenvironment.Withoutsuchlimitations,onecouldimaginethat
apopulationwouldgrowtowardaninfinitesize.Limitationofresources
canhappenmainlythroughtwotypesoffactors:abiotic(comingfromthe
physical-chemicalenvironment),orbiotic.Competitionentersintoplayas
oneofthemajorbioticresponsestolimitedresourcesandmayaddfurther
limitationpressure.Assuch,thecompetitionconceptintegratesalltypesof
interactionsamongorganismsthatlimitinsomewayoneormoreresources
tooneorallorganisms.ThisdefinitionisclosetotheoneKeddy(2001)
proposes,andalthoughhewasfarfrombeingthefirsttogiveadefinition
(probablyClementsetal.1929),Iwillsticktohis:
“Competitionwillbedefinedasthenegativeeffectswhichone
organismhasuponanotherbyconsuming,orcontrollingaccess
to,aresourcethatislimitedinavailability.”
Thisdefinitionisdisputable,buttriestointegrateasmanyaspectsaspossible
tobegeneralenoughbutnottoovagueeither.Specifically,thisdefinition
hat:timplies

6

DUCTIONONTRIGENERAL

•competitionisaninteraction;
•competitionoccursprimarilyamongindividualorganisms;
•competitionleadstoanegativeeffectonatleastoneoftheseorganisms;
•competitionisalwaysforaresource(i.e.aresourceultimatelymediates
eraction).tnithe

However,thedefinitionintentionallyleavesroomforthemultipleaspects
ofKeddycomp2001).etitioncThefionsideredrstaspinecteistcologyhekind(alloffolloresourceswingtobedescriptionsconsidered.accordingTheseto
resourcescanbeanythingnecessaryfortheecologicalsuccessoftheorgan-
ismsinconsiderations:food,mates,nutrients,space,light,etc...Theycan
beconstant,seasonalorvariableintime,spatiallyhomogeneousorheteroge-
theneous,typmesofultipleorganismorunique,cconsidered:omplemeniftheytaryareoroefssenidenttial.icalTspheecies,secondwesasppeakectofis
inthirdtraspaespcificectiscompthemecetition;hanismsifnotbywewshicpehaktheofinnegativterspeecificeffectocompccurs.etition.ItcanThebe
throughdirectinteractionssuchasfighting,territorialbehaviororpoison-
ing.happTeninghisisthenthroughtdefinedheuseas“ofincommonterferencercompesourcesietition”.sdIefinedndirectas“compexploitationetition
compmetrictoetition”.aTsymmetricheresultscompoftetition.heeffectsThelareatteralsoreferstconsideredoastoituationseparatewheresaym-n
organismfeelscompetitioneffectsnotvaryingproportionallytothesizesof
theothercompetingorganisms.
discussedThedamongescriptioneacologistsndthe(useetilite.g.yoBftircheh1957,conceptHarpofceromp1961,etitionEkscwahmitsoftenand
canBrecklingunderstand1994).hoBwutkimpeepingortantinmighmindtbtheerthistesourceypeofinlimitationteractiondaefinition,mongoneor-
ganismsanditsimplicationonecosystemsfunctioning.Keddy(2001)makes
theporganismsaralleltobetthewgeenracompvitationaletitionforceasoinnetofhethefframewundamenorkoftalNforcesewtonianphconnectingysics.
mHeustatestualism.thatAftertheathreenalyzingthefundamenptotenaltialforcesaretheoreticalcompinettition,eractionsparedationmongtwando
Iworganismsouldnot(orspimplifyopulation)intberactionelongingforcestoanamongidenticalindividualsecosystemasof(Tonlyablethree1.1),
alizekinds.theHowimpever,ortanceloookingftheattheconceptrofcesource-mediatedompetition.intAparteractions,fromonecneutralismanre-
petition,(theoreticallyallotherrarecforasesoofrganismsinteractingbelongingorganismstothesamethroughcecosystem)ommonrandesourcescom-

ECOLOGYNICOMPETITION1.2.

7

areformingthegroupofso-called“positiveinteractions”.Thesearetradi-
tionallygeneralizedtoincludecommensalism,facilitationandmutualismand
thelasttwoarefrequentlyindistinctlyusedasinterchangeable.Theseposi-
tiveinteractionsareunderhighinterestbypresentecologists(e.g.Kennedy
andSousa2006,Brunoetal.inpress).
Oneoftheoriginalandstillmostimportantquestionbringinginterest
tothewayorganismsinteractswasthedescriptionsofsomanydifferent
speciesandthequestiontounderstandwhyitisso(e.g.Hutchinson1959).
Inthiscontext,competitionwasofmainfocusforthedevelopmentofevo-
lutiontheoryandspeciationthroughnaturalselectionproposedbyDarwin
(1859).Morespecifically,studyingtheprocessesofinterspecificcompetition
wasthoughtveryearlytobefundamentalfortheobjectiveofexplaining
speciescoexistence.Earlytheoreticalworksonthesequestionsdeveloped
theLotka-Volterra’scompetitionequations(Volterra1926,Lotka1932in
Townsendetal.2003)andarrivedtothe“competitiveexclusionprinciple”,
alsoknownas“Gause’sprinciple”(1934inTilman1982).Thisprinciple
statesthatwhentwocompetingspeciescoexistinstableenvironment,they
areinasituationofnichedifferentiation,andifthisdifferentiationdoesnot
existtheyareinatemporalnon-equilibriumthatwillalwaysend-upbythe
exclusionofonebytheother.Thisprinciplewasusefultounderstandanddif-
ferentiatebetweenthefundamentalnicheandtherealizednicheofaspecies
(Townsendetal.2003).However,theGause’sprinciplehasbeenrevised
alotmainlybecauseofmanyobservationsofspeciescoexistencecasesnot
accordingwithit(Townsendetal.2003).Tociteonlyfewtheoreticalworks
aroundtheseaspects,Levin(1970)forexamplefocusedonthetemporal
aspectandproposedtoconsiderthelackofnichedifferentiationasperiodic
equilibriumsituations.Tilman(1982)proposedaresource-basedinterspecific
competitionapproachthatforsimplesituationsgavecomparableresultsto
theresultsoftheLotka-Volterramodel,butthenallowedalsotodifferentiate
theimportanceofspatialdistributionofresources(e.g.Tilman1994).The
understandingthattemporalandspatialvariationsinresourcesavailability
wereimportantforexplainingspeciescoexistenceinsupposedinterspecific
competitionsituationorientedecologiststolookmoreatquestionsaround
how“resourcepartitioning”occuramongcompetingspecies.ThisledBarot
andGignoux(2004)toevenconsiderthat“spaceandtimearetheultimate
resources”toconsiderinexplainingplantspeciescoexistence.Inrecentyears,
theconcernsofspaceheterogeneity,temporalvariabilityandresources-based
approachescreatedabranchofecologyconcerningnon-equilibriumdynam-
ics(e.g.Rohde2005).Ultimately,non-equilibriumhypothesesandrecent
coexistencestudiesproposedthatinterspecificcompetitionismuchlessim-
portantthanoriginallybelievedinexplainingtheobservationofhighnumber

8

DUCTIONONTRIGENERAL

Table1.1:Typesofinteractionsamong2organisms(orpopulations)(1and2)
belongingtothesameecosystem.Definedaccordingtotheeffectcomingoutofthis
relationforeachorganism(positive(+),negative(-)ornoeffect(=))anddepending
onthemediatoroftheinteraction:throughoneexternalresource(ER),manyre-
sources(MR)orbecause1isresourceof2(1R)).Notethatreproductionisnotincluded
becauseobviouslynotpossibleamongeverycoupleoforganismsanecosystemcanpresent.
EffectEffectMediatorDefinitionofExamples
on1on2interaction
++ERorMRFacilitationTwoplantscreatingamicro-
awaclimaticy1995)conditions(e.g.Call-
++1RMutualismorCyanobacteriaoncorals(e.g.
symbiosisRaietal.2002)
−+MRCompetitionforTreegrowingbetterwith
oneresourceandthenutrientsfixedbyunder-
facilitationorstoryplantalthoughthelat-
commensalismontercouldgrowbetterwithout
another(ForERtheshadowofthetree
ssible?)oimp−+1RPredation,Trophicinteractions
parasitism=+ERorMRCommensalismLarvaeusingresourcesatdif-
ferentdecaystages(Heard
1994)=+1RCommensalismAtree(1)hostingacarnivo-
2)(eciessprous−−ERorMRCompetitionTreesinaforest,animalsun-
condi-resourceimitedlder...etctions,−−1RSynnecrosis(rare)Parasitekillingitshostbefore
ductioneprorits−=ERorMRTotalasymmetricAtree(2)shadingaseedling
competition(1)thatdoesnotaccessthere-
(sometimescalledsourcesofthetree
Amensalism)==ERorMRNeutralism(rare)
=or−=1RTheoretically
ssibleoimp

−==−−−−−

=r=o−

+1++=

==

RMRorER1RMRorER1RERorMR

MRorERR1

ECOLOGYNICOMPETITION1.2.

9

ofspeciesincoexistence.Atlast,allthesetheoriesandmanyexperimental
studiesarrivedtodifferentiatebetweenthepotentialofactionofinterspecific
competitionanditsrealimportance(Townsendetal.2003),whichappear
nottobethesame.
Intraspecificcompetitionwasacceptedinecologicalconceptsasearlyas
theinterspecificone.However,thefocusquestionswereobviouslydifferent
andnotsofundamental.Veryearly,theroleofintraspecificcompetition
inpopulations’structureswasintegratedintheoriesofpopulationbiology.
Forexample,thelogisticgrowthmodelsusedinmanyfisheryorpopulation
biologymodelsassumeintraspecificcompetitionwiththecarryingcapacity
factor.Thereby,itisgenerallyacceptedthatintraspecificcompetitionex-
plainstherelationshipamongdensityandpercapitaavailableresourcein
somespecificcases(Keddy2001).Forexample,itisacceptedtobeatthe
originoftheself-thinningphenomenonobservedinmanyplantandsessile
organismpopulations.Theself-thinningtheory,oralsocalled“-3/2law”,
assumesthatthedensityofapopulationofapproximatelyeven-agedsessile
organismsisrelatedtothemeanbiomassofindividualswithaconstantpower
factor(α).Itassumesalsothatthisrelationshipisobservablewithdynami-
calfollowupofastand’sgrowth(MeanBiomass=Constant×densityα,
whereα=−3/2,Yoda1963,seealsoreviewsofLonsdale1990ortheoretical
representationreviewofReynoldsandFord2005).Althoughthevalueof
thepowerfactoroftheself-thinningrelationshipisdiscussed(e.g.Weller
1987),thecompetitionforresourceandparticularlycompetitionforspaceis
widelyacceptedasmainfactorattheoriginofthisphenomenon.Relatively
early(e.g.Klomp1964)thecompetitionforspacewasseenasamajorpart
ofintraspecificinteractions.Doingso,spacewasseenasaresource,asit
waslatelyacceptedontheinterspecificlevel.Intraspecificcompetitionstud-
iesalsoanalyzedthetypeofeffectproducedbycompetition:symmetricor
asymmetric.Alotofstudiestheorizedaroundtheeffectofthesedifferent
typesofcompetitions,particularlyinplantsystems,onthesizedistribu-
tionandgrowthpatternsandwaysofpartitionresources(e.g.seereview
SchwinningandWeiner1998).Manystudiesfocusedonintraspecificcompe-
titiontoevaluateitsrelativeimportanceagainstinterspecificcompetitionin
populationstructures(manyexamplesgiveninKeddy2001,p21).Thiscan
beeasilyassessedwhenusingtheLotka-Volterracompetitionequationsand
comparingtheimportanceoftheparametersrelatedtointer-orintra-specific
competition(seeTownsendetal.2003,p199).Butultimately,theaccep-
tanceofintraspecificcompetitionwasmuchlessdebatedthanfortherole
ofinterspecificcompetitioninshapingcommunities.Manystudieslooked
attheinfluenceofintraspecificcompetitiononsizedistributionpatternsin-
sidepopulations(e.g.inKlomp1964).Andintraspecificcompetitioncould

10

DUCTIONONTRIGENERAL

differentheoreticallytstagesshapoeaprganisms”opulationastheinstructureterspinecificgeneralcomptermetitionofw“coasebelievxistenceedtofo
influencecommunities.Thesedifferencesofacceptancecouldcomefromthe
easyAdditionallyobserv,tationsheofdifferenceorganismsofusingresource-usedcommonorrevenesourcestualatresourcesimilarpartitioninglife-stages.
vbaetwtionseenandco-spthusecificcanbeorganismsmoreeofasilydifferentincludedlife-stageininaretraspalsoecificcommontheoriesobser-than
theresourcepartitioningquestionsatinterspecificquestions.

Tocaricaturizethesituationoftheconceptsofinter-andintra-specific
competitioninecology,Iseethefirstasproducingmanytheoriesthattried
tobedemonstratedbyobservations,whilethesecondisbasedonobserva-
tionsleadingtomanytheories.Thisrelativecontradictorysituationcould
showthatstudieslookingattheinterspecificleveloftenforgottheintrin-
sicimportanceofindividualsandresourcesinthecompetitiondefinition:
competition(interorintra)happenbetweenindividualsprimarily,andre-
sourcesarethevectorsofanycompetitionforce.Andparticularly,therecent
awarenessofimportanceofspaceasanultimateresource(BarotandGig-
noux2004)demonstratedthenecessityofinterspecificcompetitionstudies
tocomebackattheindividual-level.Assumingthatthephenomenahap-
peningattheindividuallevelaretransmittedathigherintegrationlevelas
emergentproperties,interspecificcompetitiontheoriesshouldlookfurther
inthisdirection.Thesetheorieswouldlearnprobablymorefromthere-
sultsofemergentpropertiescomingfromindividual-levelinteractionsand
couldbeillustratedandcomparedwithemergentpropertiesofsystemsin-
cludingonlyintraspecificcompetition.Already,somerecentstudieslooked
afterspeciescoexistencequestionsintegratingthespatialandtemporalas-
pectsofresourcepartitioningatindividualleveltoinferoncommunitylevel
patterns(e.g.Pachepskyetal.2001).Additionally,severalindividual-based
modelingstudieslookedattheimplicationsofspatialcompetitiononpopu-
lationstructures(e.g.PacalaandSilander1985,Weineretal.2001,Berger
andHildenbrandt2003).Thefastincreaseinbottom-upmodelingcapacities
andsimulationapproachesshouldallowlookingfurtherinthecoexistence
questionswithaprocess-basedperspective.

1.3.NEOTROPICALMANGROVES

11

1.3MaincomponentsofNeotropicalmangrove
ecosystems

Generalities1.3.1“Mangroves”canrefereithertotheindividualtreesandshrubsgrowingin
theintertidalzonesoftropicalandsubtropicalcoastlinecreatingtreeassem-
blages,ortotheassemblageofthesetreesitself(toavoidconfusion,usually
referredtoasmangroveforest).Amangroveecosystemisgenerallycon-
sideredasanecotoneamongthelargerecosystemsthatareopenseaand
terrestrialland.Mangroveecosystemsarethereforenotreally“closed”in
termoffluxesofenergyastheoriginalecosystemdefinitionimplies.Itis
generallyacceptedthatamangroveecosystemincludes:theorganismsliving
inatropicalforestedintertidalarea(i.e.themangroveforestareaandadja-
centwaters),theirinteractions,thephysicalenvironmentandthephysical-
chemicalfactorsinfluencingtheseorganisms.Thedistributionofmangrove
ecosystemsaroundtheworldisapproximatelybetween30◦Nand30◦S.The
southernmostextremepointofdistributionisfoundinAustraliaat38◦45’S
(Duke1992),whilethenorthernmostisinBermudaat32◦20’N(Saenger
2002).Thesedistributionsarecorrelatedwiththewinterpositionofeither
theseawatertemperatureisothermof24◦C(Barth1982)ortheisothermof
16◦Cofairtemperature(Chapman1977),assumedasmainfactorslimiting
growthofmangrovetreesinextremeareas.Mangroveecosystemscovermore
than105km2worldwide(Bunt1992).
Twomainbiogeographicalareasaredifferentiated:theIndo-West-Pacific
hemisphere(IWP),andtheAtlantic-East-Pacifichemisphere(AEP).Al-
thoughthetwohemisphereshavealmostequivalentspatialextent(Bunt
1992,Duke1992),themangrovetreespeciesonIWParemuchmorenumer-
ous(40to58speciesdependingonauthors)thantheAEPones(only8to12
species).TheNeotropicalmangrovesaremorespecificallyreferringtoman-
grovesfoundontheAmericancontinentsalthoughtheyareapproximately
thesametreespeciesthanthosefoundonwesternAfrica.
Althoughthetreesgrowingonintertidalareashavetocopewithsaline
environmentortidalfluctuationsofabioticenvironment,onaglobalscale
mangrovesareamongthemostproductiveecosystemsonearth(Bunt1992).
However,manyvariationsintermofproductivityandecosystemfunction
havebeennoted.Thegeomorphologicalsettings,inputsofnutrientsand
rainfalldeterminedifferenttypesofproductivityandfunctioningandthereby
eventualtransferoforganicmattertoadjacentmarineecosystems(Jenner-
jahnandIttekkot2002).Intermofprimaryproductionalone,someman-

12

DUCTIONONTRIGENERAL

groveareasaremoreproductivethanneighboringtropicalforests(Saenger
most2002).impTheortanptrimarypartofproanductionextensivandefsoodtandingwebincorpbiomassoofratingthebotreesthismarinethe
andterrestrialorganisms(Alongi2002).

1.3.2The“trees”component
Besidefixingnutrientsandbeingatthebaseofthefoodweb,mangrove
treesalsostabilizethesedimentsandprovidephysicalhabitatspresenting
sevtidaleralrootsystem,micro-systems:belowcganoproundy,rotrunkots.andEacnhon-inmicro-systemundatedahaserialanrooassots,inciatedter-
onecommofounittheryofprimarymicro-system.andMangrosecondaryvetreesconsumersareurelativsuallyelyfounddistinctonfromshelteredthe
areas,awayfromstrongwaveactionsalthoughtheymightalsobecapable
oftheyreducingconstitutewavecanbenergyeofman(Mazdayetdifferenal.tf1997ormsinthatSaengercanbec2002).lassifiedTheafccord-orests
ingSnedactokertheirp1974:hyovesiographicrwash,andfringe,srivtructuralerine,basin,attributeshummo(describckandeddbywarfLugo),theirand
physical-chemicalenvironment(soilstypes,tidalrange,etc...),theirgeo-
morphologicalsettings(river-dominated,tide-dominated,barriers,lagoon,
spalluvialeciesencounplains,teered)tc..(.)seeorSaengertheir2phy002).tosioTcheseiologyneedsof(describingcthelassificationsgroupandof
theactualdiversityofformsillustratethehighplasticityandphysiological
capacitiesofthefewmangrovetreespecies(seeBall1988).
Mangroveforestsarehighlydynamic,presentingmanydifferentadapta-
protionscessestosprecificelatedtosituations.thelifeThehistoryconceptofofindividualforestdtreesynamicsandtheincludesevolutionalltheof
thetreeassemblagethroughtime.Anexampleofdynamicalconceptcan
bethespeciesdominancesuccession.Itwasatfirstbelievedtobelinked
tosionalandandlbuildingand-buildingcapacityconceptsofmweangrorevinestensiv(Daelyvis1940).discussedThe(e.g.spLeciesugos1ucces-980,
zonationJohnstonepatterns.1983)andItappearsparticularlynowintrhatlelationtand-buildingothedoobservesanottionseemofsptoeciesbe
asppatternsecificity(Smithofm1angro992).veTfheorests,speciesandnotsuccessionattheoconceptriginowfasspethenciesoftenzonationat-
tributedtochangesinabioticconditions(Tomlinson1986),andrarelylinked
toinFortersptheecificCaribbcompeanmetitionangro(vseees,tBallhethree1980,mainBergerspeetciesal.(2R006).hizophoramangle,
AvicenniagerminansandLagunculariaracemosa)havedifferentcapacities
ctohdealaracteristicswithinstressesan(McKeeindividual-based1995c).sChenimulationandmTwilleyodel,(r1998)eproducedincludedobservthesea-

1.3.NEOTROPICALMANGROVES

13

tionsofbasalareaofFlorida,andobtainedspeciesdominancesuccession
occurringover500yrs.However,thesesimulationsassumedphasesoflarge
proportionoftreesofidenticalspeciesdyingtogetherbecauseofidentical
ages(whatisgenerallynamedsenescenceofastand).Duke(2001)adapted
atheoreticalmodel(Jim´enezetal.1985,Fromardetal.1998)toanalyze
mangroveforestdynamicsasawhole(irrelevantoftheplace),includingthe
gapdynamicconcept.Theresultsofthismodelhypothesizethatsenescence
phaseswouldrarelyhappeninmangroveforests,inaccordancetomanyob-
servations(Duke2001)buttheoreticallyincontrasttothemodelofChen
andTwilley(1998).Butfinally,Fromardetal.(2004)documentedsenescing
phasestooccuratlargescaleonthecoastofFrenchGuyana,mainlydriven
byerosion,andre-adaptedthetheoreticalmodeltoincludelargescalegeo-
phenomena.morphologicalThesedifferencesoftheoriesofdynamicsobservedbydifferentmangrove
ecologistscouldbeseenasdifferentdynamicalpathwaysthatmangrove
forestscantakeingeneralandintheNeotropicalmangrovesinparticular.
Thesepathwaysmightbedependentonfrequencyoflargescaledisturbances
(erosionorhurricanes),smallscaledisturbances(gapformation)andgrowth
conditions(nutrient,temperatureandlightconditionsareforexamplemore
favorableinBrazilorFrenchGuyanacomparedtoFloridaforthesamesetof
species).Thesegrowthconditionscouldthenbethemainfactorssupporting
ornotstronginterspecificcompetitionleadingtotheobservationofsucces-
sionatfast(lessthandecade,asinBergeretal.2006)orslowspeed(more
thancentury,asinChenandTwilley1998).

1.3.3The“grazers”component
Trophicmodelingstudiesshowedthatthemainpartoftheprimarypro-
ductioninNeotropicalmangroveecosystemsiseitherlargelyconsumedby
primaryconsumersorganisms(e.g.Wolffetal.2000)orexportedoffshore
toneighboringecosystems(e.g.Vega-CendejasandArregu´ın-S´anchez2001).
Theconsumptionpathwayisgenerallyassumedasdrivenbylargebenthic
communitiesofcrabsorsnails(e.g.Wolffetal.2000,ProffitandDevlin
2005).Directgrazingonthetreesbycrabs(e.g.Aratuspisonii,Beeveretal.
1979)orinsects(e.g.Feller1995,FellerandMatthis1997,FellerandMcKee
the1999,floSwsaurofeetanergyl.i1999)nNwereeotropicalalsoobservmangroedves.andcAnotherouldbepathofwimpayisortancetheode-n
compositionofleaf-litterprimaryproductionthroughbacteria(Alongi2002).
Allrecyclingthesechpathwaaracteristicysoffateofofmangrotrees’ves,biomassandtareherebytheinfluencinggeneraltherroleetenoftiontheseor
ecosystems.

14

DUCTIONONTRIGENERAL

InNeotropicalmangroves,themainprimaryconsumersofbenthiccom-
munityinfluencingtheenergypathwaysseemstobeeitherthesemi-terrestrial
crabUcidescordatus,shownasofparticularlyhighecologicalimportancein
NorthBrazil(Wolffetal.2000,KochandWolff,2002,Schoriesetal.2003,
Nordhausetal.2006),Equator(Twilleyetal.1997)andtheDominicanRe-
public(GeraldesandCalventi1983)oreventuallyasnailspeciesMelampus
coffeusasinFlorida(ProffitandDevlin2005).Thesetwopotentiallyhigh
primaryconsumersareshowingamuchlowerspeciesrichnessthantheben-
thicgrazerscommunityofsesarmidcrabsfoundintheIWPbiogeographic
area(e.g.SkovandHartnoll2002).Thismightbeexplainedbythelowertree
speciesrichnessandtherebylowerdiversityoffoodsourcesintheNeotropics.
ThebiologyofUcidescordatus(Linnaeus1763,orUcidescordatuscorda-
tusontheAtlanticsideandUcidescordatusoccidentalisonthePacificside)
wasrecentlystudiedinmoredetails.Twilleyetal(1997)forEcuadorand
Nordhausetal.(2006)forBrazildemonstratedwiththeroleofthisspecies
theoriginalmisbeliefthatNeotropicalmangroveshadleaf-litterprocessing
pathwaysbasedondetrituswhiletheIWPoneswerebasedongrazingbyde-
capodcrabs(McIvorandSmith1995).ForBrazilinparticular,manystudies
oftheMADAMproject(Bergeretal.1999)illustrateditsimportanteconom-
icalrole(GlaserandDiele2004),itskeyroleinecosystemstructure(Wolffet
al.2000,KochandWolff2002)andecosystemfunction(Schoriesetal.2003,
Nordhausetal.2006).Ucidescordatusisaslowgrowingspecies(Dieleet
al.2005)feedingpreferentiallyonRhizophoramangleleavesfallingfromthe
trees(Nordhaus2004),anddoesnotseemtohavedirectcompetitorsforthis
resourcewithinthebenthiccommunity(KochandWolff2002).Itcreates
deepburrowsonthesedimentwhereitstaysinsidemostofitstime,orstand
close-byoutsidewaitingforleavestofall(Nordhaus2004).Thiscrabpopu-
lationappearstobefoodlimitedontheCaet´ePeninsula(Nordhaus2004),
a140km2mangrovepeninsula,focusareaoftheMADAMproject.Intraspe-
cificcompetition,atleastinterferencecompetition,isbelievedtohappen
frombehavioralandfeedingstrategiesobservations(Nordhaus2004).This
populationissubjecttoahighfishingpressure,hypothesizedatfirsttobe
leadingtoover-fishingsituation(Wolffetal.2000),butlaterobservedas
relativelystableandanywayfarfromthreateningbiologicalsustainability
(Dieleetal.2005).Thisismainlyduetothetraditionalfishingtechniques
ofthecrabcollectorsofthisareaandthemaininterestofthemarketfor
largemalesmucholderthansexualmaturity(Dieleetal.2005).Another
interestingaspectofthefishingtechniquesisthepossibilitytodistinguishin
thefavoritefishinggroundsthataretheRhizophoramangleforests,fishing
areaswherethecrabcollectorscanaccessandpullthecrabsoutoftheirbur-
rows,andnon-fishedareasthatcrabcollectorscannotaccessbecauseoftoo

1.4.OBJECTIVESANDPRESENTATIONOFTHETHESIS15

highrootdensities(Dieleetal.2005).Thesesituationswerehypothesizedas
producingbuffersystemsalsoavoidingentiredepletionoflargemalestocks
inRhizophoramangleforests(Diele2000).

1.4Objectivesandpresentationofthethesis

1.4.1Generalandmethodologicalobjectives
Thegeneralcontextofthepresentthesisistoinvestigatetheimportance
ofcompetitionasafactorstructuringecologicalcommunitiesandpopula-
tions.Morespecifically,Iexpectthatcompetitionforspaceattheindividual
levelcouldshapespatialandeventuallytemporalpatternsofcommunityand
populationstructure.Consideringthatinter-andintra-specificcompetition
couldbebothanalyzedfromanindividual-basedperspective,Iaminter-
estedinpossibleparallelsbetweenthetworolesofspatialcompetitionin
structuringrespectivelycommunitiesandpopulations.

Iselectedforthispurposetwosystems,oneateachlevel:(1)theCaribbean
mangrovetreecommunitytostudyinterspecificcompetitionand(2)the
NorthBrazilianpopulationofthemangrovecrabUcidescordatustoana-
lyzetheroleofintraspecificcompetition.Twodifferentpartscorresponding
tothesetwosystemsunderanalysisaretreatedwithagroupof3articles
each(Chapters3to5and6to8respectively,seeFig.1.1).Thefirstar-
ticleofeachpartpresentsafieldstudyonspatialpatternsofinterestfor
eachsystem:oneatcommunitylevel(lookingatthespatialdistributionof
species)andoneatpopulationlevel(lookingatthespatialdistributionof
individuals).Thefollowingtwoarticlesofeachpartanalyzewiththehelpof
individual-basedmodels(seeFig.1.1)theroleofcompetition,andspecifi-
callyspatialcompetition,forthereproductionofthespatialpatternsandthe
observation(orreproduction)oftemporalpatterns(seeFig.1.1forchapters
usingthepattern-orientedmodelingapproach).Thegeneralobjectivecan
s:asummarizedebStudywiththehelpofindividual-basedmodelingtheimportance
ofcompetitionamongindividualsforthespatialorganizationof
twomajorcomponentsofNeotropicalmangroves.
Eachparthasneverthelessspecificobjectivesinrelationtotheecologyofthe
focussystems.Thesespecificobjectivesareinparallelsinceenteringunder
thegeneralobjective.Ageneraldiscussionandconclusion(Chapter9)comes
backtothesespecificandgeneralobjectivesandlooksatpossibleparallels

16

DUCTIONONTRIGENERAL

betweeninterspecificandintraspecificcompetitionrolesintherespective
shapingofcommunitiesandpopulations.

Assaidabove,Iapplythepattern-orientedmodelingapproachformost
individual-basedmodelingstudies.Onthismethodologicalaspect,thepresent
thesishasalsotheobjective:
Develop,evaluateanduseacriterionbasedoninformationtheory
fortheevaluationofmodelsinqualityofpatternreproduction.
Themotivationsofdevelopmentandthe“pattern-orientedmodelinginforma-
tioncriterion”(POMIC)arepresentedinChapter2.ItisusedinChapters
6and8,andindirectlycomparedtoothermethodsinChapter8(seeFig.
1.1).

1.4.2Specificobjectives
PartI.InterspecificcompetitioninCaribbeanmangroveforests.
TheCaribbeanmangrovesareofparticularinterestforstudyinginterspe-
cificcompetitionsincethesecommunitiesshowonlythreetofourtrue-species
ofmangrovetrees.Thisobviouslywouldnothelponansweringthegeneral
question“whysomanyspecies?”seenabove,butthefactorsallowingor
notlocalcoexistenceofthesethreespeciescouldbeseenaseasiertoinves-
tigateatindividuallevelthanifthesystemwouldcompriseseveraltensof
spscaleecies.disturbancesCaribbeansucmhangroasvhuesarerricanesaanddditionallytropicalfrequentstorms,lywdisturbhichedmbakyetlargehe
studyofsecondaryrecoverydynamicpossibleandofimportance.Patterns
ofzonationandsuccessionofspeciesdominancewereobserved(e.g.McKee
1995a,b,Ball1980),hypothesizingthatinterspecificcompetitionforspace
mightbeamajorfactoronstructuringthesetreecommunities.Additionally,
withthesamesetofspecies,datafromFromardetal.(1998)showedthat
theself-thinningdynamicwasobservable,whichisrelativelyrarefortropi-
calforests(Saenger2002).Thus,competitionforspaceishappeningamong
ecies.sptheseofindividualsAnotheradvantageinstudyingthisgroupoftreespeciesisthattwo
individual-basedmodelsarealreadyparameterizedforthem:FORMAN
(ChenandTwilley1998),andKiWi(BergerandHildenbrandt2000).The
KiWimodel,aspatially-explicitindividual-basedmodel,wasdevelopeddur-
ingtheMADAMproject(BergerandHildenbrandt2000).Thismodelhas
thecharacteristicofsimulatingcompetitionforspaceamongindividualsat
theindividuallevel(whileatthegaplevelinChenandTwilley’s).Thus,

1.4.OBJECTIVESANDPRESENTATIONOFTHETHESIS

individual-basedandtternsaPmodelingofspatialcompetition
withintwomaincomponentsof
ecosystems.evmangroNeotropical

17

ComponentofLevelofspatial
assubNeotropicaljectofmaangronalysisvescompetitionofinterest
forestsCaribbeanmangrove✲ChapPatertr3I.,4,5✲Interspecific
poUcidespulationcordatus✲ChapPatertr6II,7.,8✲Intraspecific

Approachofecologicalmodelingused
Individual-basedmodeling✲Chapter4,5,7,8

Pastrategyttern-orien(withtedPOmoMICdeling∗)✲Chapter2∗,5∗,7,8∗

FieldsamplingforspatialSpatialpatternreproduced
patternanalysiswithindividual-basedmodel:
Species-level,✲Chapter3✲Chapter5
amplingstransectpoinIndividual-levt-patternel,analysis✲Chapter6✲Chapter8

Figurearticles1.1:(referencedPresenbyCtationhapterofntheumgbers)eneralofthetopicspresenandtmthesis.ethodscoveredbythedifferent

18

DUCTIONONTRIGENERAL

theKiWimodelisaperfecttoolforthestudyofinfluenceofinterspecific
spatialcompetitionattheindividuallevelontheproductionofspatialand
patterns.oraltemp

Ifocusinthispartonthetypicalspatialpatternofspecieszonation,and
analyzethetemporalpatternofsuccessionunderthegeneralquestionof
theintermediatedisturbancehypothesis(Fig1.2).Thesesuccessionand
inzonationtertidalarea.patternsThearesppecificatternsobofjectivmeangroofvtehistreepartspcaneciesbcoesexistenceummarizedinaasgiveto:n
Studytheimportanceofabioticfactorsandinterspecificspatial
compsuccessionetitionandhappzeonationningatpatternsindividual-levinCearibblaseanpromcessesangrovefexplainingorests.

Inthispart,Chapter31focusesondocumenting4patternsofzonation
aroundaBelizeanoffshoremangroveisland,CalabashCay,andinvestigate
thepossibleroleofalargescaledisturbanceontheheterogeneityofspecies
dominanceofzoneswithinthezonationpatternsofthe4sites.Thereby,
Itrytoanalyzefactorsexplainingthecoexistenceofspeciesinsomezones
whileotherzonesaremono-specific.Chapter4analyzesdeeperwiththe
KiWimodelthepossiblefactorsinfluencingspeciesdiversity(intermofhet-
erogeneityofdominance)inCaribbeanmangrovestands.Chapter4also
looksatthefactorsinfluencingspeciessuccessionandtheimplicationofsuc-
cessioninobservingintermediatedisturbancehypothesispattern(Connell
1978).Chapter5investigatesthespecificroleofabioticfactorsonthezona-
tionpatternsdescribedinChapter3,assumingthatinterspecificcompetition
forspaceoccursatindividuallevel.

PartII.IntraspecificcompetitioninNorthBrazilian
Ucidescordatuspopulations
ThesituationofUcidescordatus,astheonlyinvertebratespeciesusing
leaf-litterfallingfromthetreesinthebenthiccommunityofNorth-Brazilian
mangroves(KochandWolff2002),makesitaperfectmodelspeciestoana-
lyzeintraspecificcompetitioneffectsonpopulationstructurewithouthaving
toconsideralsointerspecificcompetition.ResultsoftheMADAMproject
studiesonthemangrovesoftheCaet´epeninsulaprovidesmuchinformation
onU.cordatuspopulationstructure,life-cycle(Wessels1999,Diele2000,
1NotethatthefieldworkandanalysesofthisChapterweredoneduringmyMSc.
studies

1.4.OBJECTIVESANDPRESENTATIONOFTHETHESIS

PartI.Interspecificcompetitionin
Caribbeanmangroveforests.

19

Figure1.2:Theoreticalframeworkoftheobjectivesofthefirstpartofthepresentthesis:
“Studytheimportanceofabioticfactorsandinterspecificspatialcompetitionhappening
atindividual-levelasprocessesexplainingsuccessionandzonationpatternsinCaribbean
mangroveforests”.NotethattheQuestionsarepartofthetheoreticalframeworkas
directionofinvestigation,notasquestiontobeentirelyanswered.

Dieleetal.2005),behavior(Nordhaus2004,Nordhausetal.2006),and
Itwecologicalasorbservoleed(Wasolffhavetingal.as2000,patialKochanddistributionWolfv2002,aryingScinhoriessizeetandal.densit2003).y
namicalaccordingasptoectsohabitatfptypopulationes(Wesselsstructure1999,areDiele2particularly000,intNordhauseresting2004).tostudyDy-
totheseareasunderstandhavehobweenfishedharvestedareasbayrehumans.recolonizedCrabbycollectorsindividualrepcrabsortedrwhenela-
tivelyconstantrecolonizationtime(personalcommunications,Diele).The

20

GENERALDUCTIONONTRI

thebufferoriginmecohftanismshistempproporalosedbpatternyofpreviousrecoverystudieswhic(hDielewas2ho000),wevemighrntotbeana-at
lyzedthoroughlysofar(onlyasmallexperimentinDiele2000).Thespatially
structuredpopulationandtherecoveryofharvestedareasareindicatorsthat
individualcrabschangeburrows.Thus,studyingthemovementsofthecrabs
wouldgiveinterestinginputsfortheprocessesattheoriginsofthehypoth-
esizedspatialortemporalpatterns.
dividualsIntraspeitherecificforinburroterferencewsorcompforfooetitiondwas(Nordhausobserved2004).tohEappenxploitationamongcom-in-
ptheectitionrabsforappRearedhizophortoabefomangleodlealimitedvesw(aslessNordhausevident2004).butalsoBothpoinssibleterferencesince
andcompeetitionxploitationforcspaceompebytitiontheinthisindividuals.speciesIfocouldcusobnetheconsideredsecondtpartogetheroftheas
mopresenvetmenttshesisofoU.nscortudyingdatus,theandimpacttherebofyitsthisinspatialtraspecificdistributioncompandetitionrecoonvtehery
patterns(Fig.1.3).Thespecificobjectiveofthispartisto:
Studyindividualstheimpasproortancecessofinexplainingtraspecificrecoveryspatialandcsomppatialetitiondistributionamong
patternsinNorthBrazilianUcidescordatuspopulations.
Intionsthisofpart,individualsChapter6withinaimsR.atdomanglecumentingdominatedthesandpatialLpatternsagunculariaofracdistribu-emosa
dominatedforests.Itlooksattheindividuals’spatialdistributiononsmall
(<10m)andlargescale(>10m)andpotentialabioticandbioticfactorsinflu-
encingthelatter.Anindividual-basedmodelispresentedinChapter7:the
Individual-BasedUcidesorIBU.Itwasdevelopedwiththepattern-oriented
modelingapproachfocusingontwopatternsofrecoveryaftersmallscalefish-
erydocumentedalsoinChapter7.Theaimofthischapterwastoanalyze
theburrorolews.ofinChaptertrasp8ecificusesalsocomptheetitionIBUinmothedel.Itdecisionfocusofonacrabstnalyzingoleavtheertheirole
bofehaviorasymmetricofcrabscompleadingetitiontoandthespatialdistanceofpatternresourcesatsmallcompscaleetedforobservonedtonhe
Chapter8andtherecoverypatternsofChapter7.

1.4.3Administrativepresentationofthethesis
DifferentpartsofthepresentthesiswerewrittenasarticlessinceOctober
2003.Thereby,thethesisisacumulativedocumentof7articles(Chapter
2to8)integratedwithageneralintroduction(thepresentchapter)anda
generaldiscussionandconclusion(Chapter9).TheChapter3fieldworkand
analysiswasdoneduringmyISATECmasterthesis(UniversityofBremen),

1.4.OBJECTIVESANDPRESENTATIONOFTHETHESIS

PartII.IntraspecificcompetitioninNorth
BrazilianUcidescordatuspopulations

21

Figure1.3:Theoreticalframeworkoftheobjectivesofthesecondpartofthepresent
thesis:“Studytheimportanceofintraspecificspatialcompetitionamongindividualsas
processexplainingrecoveryandspatialdistributionpatternsinNorthBrazilianUcides
cordatuspopulations”.NotethattheQuestionsarepartofthetheoreticalframeworkas
directionofinvestigation,notasquestiontobeentirelyanswered.

bebutlievtheediatwrticleaspresennecessarytedhtoerewincludeasitrewohererkedasduringfieldbactheklastground3yofearstheafindrstI
part.pleAll(seethewPreface)orkswandouldpnotharticularlyavebteenhepossibleco-authorswithoutofthet7hehelparticles.ofImanydescribpeo-e
inarticle,Tableits1.2ctheorresprespondingectivechpapterarticipationsnumberofaendachcfundingo-author,sourcethetitleaccordingofeactoh
themainyearsofwork.InadditiontothedescribedresponsibilitiesinTable

22

GENERALNTRIODUCTION1.2,allco-authorsparticipatedinelaborationofconceptsanddiscussionson
ideasoftherespectiveworks.
ThemainfundingofthisthesiswastheMADAMproject(MAngrove
DynamicsAndManagement),abilateralcooperationbetweentheCenterfor
TropicalMarineEcology(ZMT)attheUniversityofBremen,Germanyand
theFederalUniversityofPar´a(UFPa)inBel´em,Brazil,andfinancedbythe
BrazilianEducationNandationalResearcRhesearch(BMBF)Councilundert(CNPq)hecodeandthe03F0154A,GermanwhichsMinistryupportedfor
meandmyfieldworkfromthe1stofOctober2003tothe31stofDecember
2005.ThePUME(PUfferMEchanismus)projectwasgrantedtoDr.Uta
andBergertbyheoreticaltheDwFoGrksunderfromthetheco1stdeofBEJanuary1960/2-1,2006fortothefinancing31stofmypDecemositionber
2006.TheZMTfinanceddirectlycomputersandothermaterialfacilities,
and4additionalmonthsformyposition.

1.4.OBJECTIVESANDPRESENTATIONOFTHETHESIS23

Modelingtheeffectofhur-
man-ondisturbancesricanegroveforestdiversity

4

Table1.2:Titlesofthearticlesconstitutingthepresentthesiswithcorresponding
Chapternumber,abriefdescriptionoftheinvolvementsofeachco-authorsandthe
mainfundingsourcesandyearofworkcorresponding(PUMEwasaDFGproject(BE
1960/2-1),MADAMwasaCNPq-BMBFproject(03F0154A),andtheNSFfundings
weregrantedtoI.C.Fellerforthefieldworkandsampleanalyzes(DEB-9981535).)
ArticletitleChapterDescriptionsofresponsibilitiesFundings
ear)(yProposinganinformationcri-2IdevelopedthePOMICandwrotethePUME
moteriondelsforelectionindividualbasedthemaniudea’sscript.devUtaelopmenBergertandpforarticipatedthewrit-in(2006)
ingZonationpatternsofBelizean3Ididthefieldwork,theanalysisandtheNSF
offshoremangroveforests41mainpartofthewriting.CandyFeller(2002-
yearsafteracatastrophichur-participatedinfieldworkdevelopment2004)
ricaneandinthewriting.UtaBergerpar-
ticipatedinthewriting.FaustinoChi
helpedforthefieldwork.
Modelingtheeffectofhur-4Ididthesimulations,theanalysisandMADAM
ricanedisturbancesonman-themainpartofthewriting.UtaBerger(2003-
groveforestdiversityparticipatedintheanalysisandwrit-2005)
ing.HannoHildenbrandthelpedinthe
simulationanddevelopedtheideapre-
sentedinAppendixA.CandyFellerpar-
ticipatedinthewriting.
Importanceofabioticgradi-5Ididthesimulations,analysisandtheMADAM
entsonmangrovezonationmainpartofthewriting.UtaBerger&PUME
patterns:asimulationexperi-participatedinthewriting.Candy(2005-
mentFellerparticipatedintheidea’sdevel-2006)
.topmenSpatialstructureofaleaf-6Ididthefieldwork,theanalysisandtheMADAM
removingcrabpopulationinamainpartofthewriting.UtaBerger(2003-
mangroveofNorth-BrazilandCandyFellerparticipatedinthe2005)
writing.Simulatingcrypticmovements7Idevelopedthemodel,didthesimula-MADAM
ofamangrovecrab:recoverytions,theanalysisandthemainpart(2003-
phenomenaaftersmallscaleofthewriting.UtaBergerandVolker2006)
fisheryGrimmparticipatedintheanalysisand
writing.KarenDieleparticipatedinthe
writing.HannoHildenbrandthelpedfor
thedevelopmentofthemodel.Coralie
D’Limadidapartofthefieldwork.
Testingintraspecificphe-8Ididthesimulations,theanalysisandPUME
nomenologicalcompetitionthewriting.(2006)

Importanceofabioticgradi-
entsonmangrovezonation
patterns:asimulationexperi-
tmenSpatialstructureofaleaf-
removingcrabpopulationina
North-BrazilofevmangroSimulatingcrypticmovements
ofamangrovecrab:recovery
phenomenaaftersmallscale
fishery

Testingintraspecificphe-
titioneompcnomenologicalmodelsatindividual-levelto
reproducepopulation-level
patternsofamangrovecrab

567

8

24

eferencesR1.5

DUCTIONONTRIGENERAL

Alongi,D.M.2002.Presentstateandfutureoftheworld’smangroveforests.Environmental
29:331-349.tionaConservBall,M.C.1980.PatternsofsecondarysuccessioninamangroveforestinsouthernFlorida.
44:226-235.Berlin)(OecologiaBall,M.C.1988.Ecophysiologyofmangroves.Trees2:129-142.
Barot,S.,andGignoux,J.2004.Mechanismspromotingplantcoexistence:canallthe
proposedprocessesbereconciled?Oikos106:185-192.
Barth,H.1982.Thebiogeographyofmangroves.Pages85-110In:D.N.SenandK.S.
Rajpurohit,editors.ContributionstotheEcologyofHalophytes,TaskforVegetation
Science.DrW.Junk,TheHague.
Beever,J.W.,Simberloff,D.,andKing,L.L.1979.Herbivoryandpredationbythemangrove
crab,Aratuspisonii.Oecologia43:317-328.
Berger,U.,andHildenbrandt,H.2000.Anewapproachtospatiallyexplicitmodelling
offorestdynamics:spacing,ageingandneighbourhoodcompetitionofmangrovetrees.
EcologicalModelling132:287-302.
Berger,U.,andHildenbrandt,H.2003.Thestrengthofcompetitionamongindividualtrees
andthebiomass-densitytrajectoriesofthecohort.PlantEcology167:89-96.
Berger,U.,Adams,M.,Grimm,V.,andHildenbrandt,H.2006.Moldellingsecondarysuc-
cessionofneotropicalmangroves:Causesandconsequencesofgrowthreductioninpioneer
species.PerspectivesinPlantEcology,EvolutionandSystematics7:243-252.
Berger,U.,Glaser,M.,Koch,B.,Krause,G.,Ruben,L.,Saint-Paul,U.,Schories,D.,and
Wolff,M.1999.Anintegratedapproachtomangrovedynamicsandmanagement.Journal
ofCoastalConservation5:125-134.
Birch,L.C.1957.Themeaningsofcompetition.TheAmericanNaturalist91:5-18.
Breckling,B.,M¨uller,F.,Reuter,H.,H¨olker,F.,andFr¨anzle,O.2005.Emergentproperties
inindividual-basedecologicalmodels-introducingcasestudiesinanecosystemresearch
context.EcologicalModelling186:376-388.
Bruno,J.F.,Stachowicz,J.J.,andBertness,M.D.inpress.Inclusionoffacilitationinto
ecologicaltheory.TRENDSinEcologyandEvolution.
Bunt,J.S.1992.Introduction.In:A.I.RobertsonandD.M.Alongi,editors.Tropical
MangroveEcosystems.AmericanGeophysicalUnion,Washington,DC,USA.
Callaway,R.M.1995.Positiveinteractionsamongplants.Botanicalreview61:306-349.
Chapman,V.J.1977.Introduction.Pages1-29In:V.J.Chapman,editor.Ecosystemsof
theworld.1.Wetcoastalecosystems.ElsevierScientificPublishingCompany,Amster-
dam.Chen,R.,andTwilley,R.R.1998.Agapdynamicmodelofmangroveforestdevelopment
alonggradientsofsoilsalinityandnutrientresources.JournalofEcology86:37-51.
Clements,F.E.,Weaver,J.E.,andHanson,H.C.1929.Plantcompetition:ananalysisof
communityfunctions.CarnegieInstitutionofWashington,WashingtonD.C.
Connell,J.H.1978.Diversityintropicalrainforestsandcoralreefs.Science199:1302-1310.
Cowles,H.C.1901.ThephysiographicecologyofChicagoandvicinity:Astudyofthe
origin,development,andclassificationofplantsocieties.BotanicalGazette31:73-108.
Darwin,C.R.1859.Ontheoriginofspeciesbymeansofnaturalselection;or,thepreser-
vationoffavoredracesinthestruggleforlife.JohnMurray,London,
Davis,J.H.1940.TheecologyandgeologicroleofmangrovesinFlorida,Publicationsof
theCarnegieInstitutePublicationnumber517,Washington,D.C.

REFERENCES1.5.

25

DeAngelis,D.L.,andMooij,W.M.2005.Individual-basedmodelingofecologicaland
evolutionaryprocesses.AnnualReviewofEcologyEvolutionandSystematics36:147-168.
Diele,K.2000.LifehistoryandpopulationstructureoftheexploitedmangrovecrabUcides
cordatuscordatus(L.)(Decapoda:Brachyura)intheCaet´eestuary,NorthBrazil.PhD
Thesis,ZMTContribution9,Bremen,Germany.
Diele,K.,Koch,V.,andSaint-Paul,U.2005.Populationstructure,catchcompositionand
CPUEoftheartisanallyharvestedmangrovecrabUcidescordatus(Ocypodidae)inthe
Caete´estuary,NorthBrazil:Indicationsforoverfishing?AquaticLivingResources18:169-
178.Duke,N.C.1992.MangroveFloristicsandBiogeography.In:A.I.RobertsonandD.M.
Alongi,editors.TropicalMangroveEcosystems.AmericanGeophysicalUnion,Washing-
D.C.ton,Duke,N.C.2001.Gapcreationandregenerativeprocessedrivingdiversityandstructureof
mangroveecosystems.WetlandsEcologyandManagement9:257-269.
Ekschmitt,K.,andBreckling,B.1994.Competitionandcoexistence:thecontributionof
modellingtotheformationofecologicalconcepts.EcologicalModelling75/76:71-82.
Feller,I.C.1995.EffectsofnutrientenrichmentongrowthandherbivoryofdwarfRhizophora
mangleL.(redmangrove).Biotropica28:13-22.
Feller,I.C.,andMathis,W.N.1997.Primaryherbivorybywood-boringinsectsalongan
architecturalgradientofRhizophoramangle.Biotropica29:440-451.
Feller,I.C.,andMcKee,K.L.1999.SmallGapCreationinBelizeanMangroveForestsby
aWood-BoringInsect.Biotropica31:607-617.
Fl¨oder,S.,andSommer,U.1999.Diversityinplanktoniccommunities:Anexperimentaltest
oftheintermediatedisturbancehypothesis.LimnologyandOceanography44:1114-1119.
Fromard,F.,Vega,C.,andProisy,C.2004.Halfacenturyofdynamiccoastalchange
affectingmangroveshorelinesofFrenchGuiana.Acasestudybasedonremotesensing
dataanalysesandfieldsurveys.MarineGeology208:265-280.
Fromard,F.,Puig,H.,Mougin,E.,Marty,G.,Betoulle,J.L.,andCadamuro,L.1998.
Structure,above-groundbiomassanddynamicsofmangroveecosystems:newdatafrom
FrenchGuyana.Oecologia115:39-53.
Geraldes,M.G.d.,andCalventi,I.B.d.1983.Estudiosexperimentalesparaelmanten-
imientoencautiveriodelcangrejoUcidescordatus.CienciaInteramericana23:41-53.
Glaser,M.,andDiele,K.2004.Asymmetricoutcomes:assessingcentralaspectsofthe
biological,economicandsocialsustainabilityofamangrovecrabfishery,Ucidescordatus
(Ocypodidae),inNorthBrazil.EcologicalEconomics49:361-373.
Grimm,V.,andBerger,U.2003.Seeingthewoodforthetrees,andviceversa:pattern-
orientedecologicalmodelling.Pages411-428In:L.SeurontandP.G.Strutton,editors.
HandbookofScalingMethodsinAquaticEcology:Measurement,Analysis,Simulation.
CRCPress,BocaRaton.
Grimm,V.,andRailsback,S.F.2005.Individual-basedmodelingandecology.Princetown
UniversityPress,Princeton,N.J.,480pp.
Grimm,V.,Frank,K.,Jeltsch,F.,Brandl,R.,Uchmanski,J.,andWissel,C.1996.Pattern-
orientedmodellinginpopulationecology.TheScienceoftheTotalEnvironment183:151-
166.Grimm,V.,Revilla,E.,Berger,U.,Jeltsch,F.,Mooij,W.M.,Railsback,S.F.,Thulke,
H.-H.,Weiner,J.,Wiegand,T.,andDeAngelis,D.L.2005.Pattern-orientedmodelingof
agent-basedcomplexsystems:lessonsfromecology.Science310:987-991.
Haeckel,E.1866.GenerelleMorphologiedesOrganismen:AllgemeineGrundz¨ugederor-
ganischenFormen-wissenschaft,mechanischbegr¨undetdurchdievonCharlesDarwinre-

26

NTRIGENERALDUCTIONO

Berlin.eimer,RDescendenz-Theorie.formirteHarper,J.L.1961.Approachestothestudyofplantcompetition.SymposiaoftheSociety
forExperimentalBiology15:1-39.
Heard,S.B.1994.Pitcher-plantmidgesandmosquitoes:aprocessingchaincommensalism.
75:1647-1660.EcologyHutchinson,G.E.1959.HomagetoSantaRosaliaorwhyaretheresomanykindsofanimals?
93:145-159.NaturalistmericanATheJennerjahn,T.C.,andIttekkot,V.2002.Relevanceofmangrovesfortheproductionand
depositionoforganicmatteralongtropicalcontinentalmargins.Naturwissenchaften89:23-
30.Jim´enez,J.A.,Lugo,A.E.,andCintr´on,G.1985.TreemortalityinMangroveforests.
17:177-185.BiotropicaJohnstone,I.M.1983.Successioninzonedmangrovecommunities:whereistheclimax?In:
H.J.Teas,editor.Tasksforvegetationscience.Dr.W.JunkPublishers,TheHague.
Keddy,P.A.2001.Competition(2ndedition).KluwerAcademicsPublishers,Dordrecht.
Kennedy,P.G.,andSousa,W.P.2006.ForestencroachmentintoaCaliforniangrass-
land:examiningthesimultaneouseffectsoffacilitationandcompetitionontreeseedling
148:464-474.Oecologiat.recruitmenKlomp,H.1964.Intraspecificcompetitionandtheregulationofinsectnumbers.Annual
ReviewofEntomology9:17-40.
Koch,V.,andWolff,M.2002.Energybudgetandecologicalroleofmangroveepibenthosin
theCaete´estuary,NorthBrazil.MarineEcologyProgressSeries228:119-130.
Lenz,M.,Molis,M.,andWahl,M.2004.Testingtheintermediatedisturbancehypothesis:
responseoffoulingcommunitiestovariouslevelsofemersionintensity.MarineEcology
278:53-65.eriesSProgressLevin,S.A.1970.Communityequilibriaandstability,andanextensionofthecompetitive
exclusionprinciple.TheAmericanNaturalist104:413-423.
Lonsdale,W.M.1990.Theself-thinningrule:deadoralive?Ecology71:1373-1388.
Lugo,A.E.1980.Mangroveecosystems:successionalorsteadystate?Biotropica12:65-72.
Lugo,A.E.,andSnedaker,S.C.1974.Theecologyofmangroves.AnnualReviewofEcology
5.ystematicsSandMackey,R.L.,andCurrie,D.J.2001.TheDiversity-DisturbanceRelationship:Isitgener-
allystrongandpeaked?Ecology82:3479-3492.
Mazda,Y.,Wolanski,E.,King,B.,Sasa,A.,Ohtsuka,D.,andMagi,M.1997.Mangroves
asacoastalprotectionfromwavesintheTongKingdelta,Vietnam.MangrovesandSalt
:127-135.1MarshesMcIvor,C.C.,andSmithIII,T.J.1995.Differencesinthecrabfaunaofmangroveareas
ataSouthwestFloridaandaNortheastAustralialocation:Implicationsforleaflitter
processing.Estuaries18:591-597.
McKee,K.L.1995a.MangrovespeciesdistributionandpropagulepredationinBelize:An
exceptiontothedominance-predationhypothesis.Biotropica27:334-345.
McKee,K.L.1995b.SeedlingrecruitmentpatternsinaBelizeanmangroveforest:effectsof
establishmentabilityandphysico-chemicalfactors.Oecologia101:448-460.
McKee,K.L.1995c.Interspecificvariationingrowth,biomasspartitioning,anddefensive
characteristicsofneotropicalmangroveseedlings:Responsetolightandnutrientavailabil-
ity.AmericanJournalofBotany82:299-307.
Nordhaus,I.2004.Feedingecologyofthesemi-terrestrialcrabUcidescordatuscordatus
(Decapoda:Brachyura)inamangroveforestinnorthernBrazil.PhDThesis,ZMTcon-
tribution18,Bremen,Germany.

REFERENCES1.5.

27

Nordhaus,I.,Wolff,M.,andDiele,K.2006.Litterprocessingandpopulationfoodintakeof
themangrovecrabUcidescordatusinahighintertidalforestinnorthernBrazil.Estuarine,
CoastalandShelfScience67:239-250.
Pacala,S.W.,andSilander,J.A.J.1985.Neighborhoodmodelsofplantpopulationdy-
namics.1Single-speciesmodelsofannuals.TheAmericanNaturalist125:385-411.
Pachepsky,E.,Crawford,J.W.,Bown,J.L.,andSquire,G.2001.Towardsageneraltheory
ofbiodiversity.Nature410:923-926.
Proffitt,C.E.,andDevlin,D.J.2005.GrazingbytheintertidalgastropodMelampuscoffeus
greatlyincreasesmangroveleaflitterdegradationrates.MarineEcologyProgressSeries
296:209-218.Rai,A.N.,Bergman,B.,andRasmussen,U.2002.CyanobacteriainSymbiosis.Kluwer
AcademicPublishers,Dordrecht.
Reynolds,C.W.1987.Flocks,herdsandschools:adistributedbehavioralmodel.Computer
21:25-34.GraphicsReynolds,J.H.,andFord,D.E.2005.Improvingcompetitionrepresentationintheoretical
modelsofself-thinning:acriticalreview.JournalofEcology93:362-372.
Rohde,K.2005.Nonequilibriumecology.CambridgeUniversityPress,Cambridge.
Saenger,P.2002.Mangroveecology,silvicultureandconservation.KluwerAcademicsPub-
lishers,Dordrecht.
Saur,E.,Imbert,D.,Etienne,J.,andMian,D.1999.Insectherbivoryonmangroveleaves
inGuadeloupe:effectsonbiomassandmineralcontent.Hydrobiologia413:89-93.
Schories,D.,Barletta-Bergan,A.,Barletta,M.,Krumme,U.,Mehling,U.,andRademaker,
V.2003.Thekeystoneroleofleaf-removingcrabsinmangroveforestsofNorthBrazil.
WetlandsEcologyandManagement11:243-255.
Schwinning,S.,andWeiner,J.1998.Mechanismsdeterminingthedegreeofsizeasymmetry
incompetitionamongplants.Oecologia113:447-455.
Shea,K.,Roxburgh,S.H.,andRauschert,E.S.J.2004.Movingfrompatterntoprocess:
coexistencemechanismsunderintermediatedisturbanceregimes.EcologyLetters7.
Sheil,D.2001.Long-termobservationsofrainforestsuccession,treediversityandresponses
todisturbance.PlantEcology155:183-199.
Skov,M.W.,andHartnoll,R.G.2002.Paradoxicalselectivefeedingonalow-nutrientdiet:
whydomangrovecrabseatleaves?Oecologia131:1-7.
SmithIII,T.J.1992.ForestStructure.In:A.I.RobertsonandD.M.Alongi,editors.
TropicalMangroveEcosystems.AmericanGeophysicalUnion,Washington,DC.
Tilman,D.1982.Resourcecompetitionandcommunitystructure.PrincetonUniversity
NJ.Princeton,Press,Tilman,D.1994.Competitionandbiodiversityinspatiallystructuredhabitats.Ecology
75:2-16.Tomlinson,P.B.1986.Thebotanyofmangroves.CambridgeUniversityPress,Cambridge,
413.Townsend,C.R.,Begon,M.,andHarper,J.L.2003.Essentialsofecology(2ndedition).
BlackwellPublishing,Oxford.
Twilley,R.R.,Pozo,M.,Garcia,V.H.,Rivera-Manory,V.H.,Zambrano,R.,andBodero,A.
1997.LitterdynamicsinriverinemangroveforestsintheGuayasRiverestuary,Ecuador.
111:109-122.OecologiaVega-Cendejas,M.E.,andArregu`ın-S`anchez,F.2001.Energyfluxesinamangroveecosys-
temfromacoastallagooninYucatanPeninsula,Mexico.EcologicalModelling137:119-
133.

28

GENERALNTRIODUCTIONWeiner,J.,Stoll,P.,Muller-Landau,H.,andJasentuliyana,A.2001.Theeffectsofdensity,
spatialpattern,andcompetitivesymmetryonsizevariationinsimulatedplantpopula-
tions.TheAmericanNaturalist158:438-450.
Weller,D.E.1987.Areevaluationofthe-3/2powerruleofplantself-thinning.Ecological
57:23-43.MonographsWe(Ocypssels,oL.didae)1999.inUndertersucMhangroungenvevzuronr¨Bragan¸aumlicca,henPVar´a,erbreitungBrasilien.bodenlebDiplomaenderthesis,LandkrabbUniversiteny
ofBonn,Germany.
forWiegand,revT.,ealingJheltsciddenh,iF.,Hanski,nformation:I.,aakndeyforGrimm,V.reconciling2003.eUsingcologicalptheoryattern-orienandtedmoapplication.deling
100:209-222.soOikWolff,M.,Koch,V.,andIsaac,V.2000.AtrophicflowmodeloftheCaet´emangroveestuary
(NorthBrazil)withconsiderationsforthesustainableuseofitsresources.Estuarine,
CoastalandShelfScience50:789-803.
Yoda,K.,Kira,T.,Ogawa,H.,andHozumi,K.1963.IntraspecificCompetitionamong
HigherPlants.XI:Self-ThinninginOvercrowdedPureStandsunderCultivatedandNat-
uralConditions.J.OsakaCityUniversityInst.Polytech.

Chapter

2

osingProp

criterion

mo

del

na

orf

nformationi

individual

elections

29

asedb

2CHAPTER30Proposinganinformationcriterionfor
individualbasedmodelselection

Piou,Cyril12&Berger,Uta1
Partsofthischapterwillbesubmittedasanarticlewithanidenticaltitle

bstractA2.1Agent-BasedandIndividual-BasedModels(ABM/IBMs)havebeenim-
provedpattern-orienintqualitedymoanddelingreliabilit(POM).yinTherPecentOMyeproparswosesithanguidelinesapproactohdevcalledelop
mocallydelshowtryingwellttohereproABM/IBMsducepatternsreprooducebservtedhem.onthePOMfieldstudiesandtuestsedgsystemati-enerally
traditionalmethodsofgoodnessoffitsuchasthesumofsquaresevaluation
or“handmade”comparisonsoffittingerrorsandvariations.
Modelselectionisalsoanewstatisticalapproachinecologythatassesses
morethantwohypothesesatthetimeagainstasetoffielddata.Thetools
usedforthispurposeareusuallyinformationcriterionsuchastheAkaike’s
InformationCriterion(AIC).Thesearebasedoninformationtheoryandhelp
doinginferenceinamultimodelcontext.
Althoughbothapproachesfocusontheexplanationofpatternsbyeval-
uatingcriteriatheandptheotentialPOMwasunderlyingsofarpronevercesses,done.theTlinkhisbestudytweenproptheosesaninformationinfor-
momationdelingcriterioninformationformodelcriterion:selectionPOiMnIaC)POMusingcontextsimilar(theprinciplespattern-orienthanttedhe
ofAIC.patternsWetodescribbeefihotted.wtoWecalculatepresentdPOerivMIedCforstatisticsdifferenthatttypcanesbeandcnumalculatedbers
withPOMICandhelpindoingstronginferencefromasetofABM/IBMs,
inorveallorsewmcodeling.alculatingWelikielihollustrateodthemaximizeduseofPOparameterMICvwithaluesaisnaimplecontextexampleof
ofconcludeapplication.thattheWeusediscussofthethePOpMIrecautionsCgivesandtoaPdvOManatagesnewofpoPOtentMIialCo,afnin-d
ferenceontheunderstandingof“behaviors”ofindividualpartofcomplex
systems.eadaptivKeyWords:agent-basedandindividual-basedmodeling,pattern-
12CenCorrespteroforndingTaropicaluthor:MarineEcyril.piou@zmcology,Ft-bremen.deahrenheitstrasse6,23859Bremen,Germany

ODUCTIONINTR2.2.

31

orientedmodeling,informationtheory,Akaike’sinformationcrite-
rion.

2.2Introduction

Theuseinsocialsciencesandecologyofagentandindividual-basedmod-
els(ABM/IBMs)startedabout20yearsagoandincreasedquicklywiththe
developmentofcomputationcapacities(Grimm1999).Thegeneralcriticsof
inthethefirstaIBMspplicationweretotcobeoncreteeitherptoroblems,oortheoreticaltobeotrootoocomplexsimpleatondbeunreliablereliable
inmocasedelingof(POM)necessaryapproachgeneralizationswasthentodevewiderlopehdtoorizons.countTheper-balanceattern-orienthesecrit-ted
icsbydevelopingandtestingIBMwiththeobjectivetoreproducepatterns
observWiegandedinetnal.ature2003,(GrimmGrimmetetal.al.12996,005).TRailsbachekfirst,2purp001,oseBrangofePOMtal.was2002,to
develop,scaleandparameterizeIBMsaccordingtothereproductionofnatu-
ralpuncertainatternsty(ande.g.selectionWiegandofetbaestl.1998).parameterThesetsmethocandsbeofrcallededucing“inverseparametermod-
eling”(Grimmetal.2005)torefertotheidenticalmethodsusedinother
themoPdelingOMapproacexerciseh,t(e.g.sogethertatisticalwithoorneoflineartheomoriginaldeling).onesAofsecondindividual-basedpurposeof
moagainstdelingnwaturalastotestpatternsdifferenobservtehdypatothesishigheroifnptroegrationcessesatleveanl.Thisindividualwasclevalledel
byGrimmetal.(2005)the“stronginference”procedure.Thissecondpart
ofPOMcouldbeparalleledtothemodelselectionproceduresusingdifferent
statisticalmodelsandinformationcriteriatocreateacontextofmultimodel
inference.Multimodelinference(or“modelselection”dependingonauthors)isused
more2004).andItspmorerincipleoftenistoinconfronnaturaltsevesciencesralworking(reviewhybpyothesisJohnsonatatandimeOmland,against
asetofdata.Inthisprocedure,oneshouldformulatedifferentverbalhy-
ptooeactheseshfirst,statisticalexpressmodelthemandendupmathematicallydoing,ginferenceiveaingooeitherdnessofstronglyfitindicatorselect-
ingThus,onethishypapproacothesish’sorkphilosopheepingayisetstoofconcludeplausibleaboutonesawithsetofdifferenmosttlikwelyeighphe-ts.
thenomenamostlikelyinfluencingone.Mfocusultimodata,delinferencealthoughcontsometimesrastswitithctheouldarrivclassicaletomethoselectd
inofterest.testingaGnullenerallyhypotothesismaketotheacceptoinference,rrejectthetheaapproaclternativhusesehypoinformationthesisof
criteriatorankthestatisticalmodelsfittingempiricaldata.Inparticular

32

2CHAPTER

theAkaike’sinformationcriterion(AIC)anditsderivative(Akaike1973,
1974,Bozdogan1987)consideringbothgoodnessoffitandstatisticalmodel
complexityarethepreferredcriteria.TheAICwasdevelopedtoextendthe
likelihoodratiotestapproachtomultimodelsituationsaddinganincreasing
biasformorecomplexmodelsfitwithamaximumlikelihoodestimator:
AIC(k)=−2logLθˆk+2k(2.1)
function,andLθˆkisthelikelihoodoftheparameters’maximumlikelihood
wherekisthenumberofparametersinthemodel,logisanaturallogarithm
estimatesofthestatisticalmodelgiventhedatatobefit.Therationaleisto
penalizeoverparameterizationwiththe+2kpartandfindacompromising
wellfittingandasparsimoniousaspossiblemodel.Thisinformationcriterion
anditsderivativehavebeenusedwidelyinmodelselectionandelaborationin
manyothersciences(e.g.geophysics:Hipel1981,pharmaceutics:Yamaoka
etal.1978).Innaturalsciencesitisparticularlyusedinthecomparisonof
non-nestedmodelsinmark-recapturestudies(e.g.Huggins1991,Lebreton
etal.1992,Andersonetal.1994,Caswelletal.1999,Yoccozetal.2001,
LangtimmandBeck2003)andmodelselectionofDNAsequenceevolution
(e.g.Posada2001,2003).Ithasalsobeenusedindifferentcasesofstatistical
modelsselectionofdispersion(e.g.Doncasteretal.1997)andselectionof
differenttypesofautoregressivemodelsofpopulationvariations(e.g.Hansen
etal.1999,Postetal.2002).
DespitethesimilarityofpurposeofmultimodelinferenceandPOM,there
isstillalackofequivalenttoolstotheAICforthepattern-orientedapproach
forIBMs.Theexpressionofalikelihoodfunctiontoiteratedeterministi-
callythevaluesofparametersofcomplexsimulationmodelslimitedtheap-
proach.Particularly,parameterslinkedtoindividualbehaviorsimplemented
inacomplexIBMarealmostimpossibletoestimatewithsuchfunctions
consideringpatternsobservedatahigherintegrationlevelasdatatobefit
(e.g.populationspatialdistributionpatternsemergingfromthebehaviorand
interactionsofindividuals).Therefore,likelihoodestimatorfunctionswere
rarelydevelopedfornon-linearmodelssuchasindividualbasedorothertypes
ofbottom-uprule-basedmodels.Inonlyonecasetestingasimpledispersion
IBM,MoojandDeAngelis(2003)usedlikelihoodfunctionstofindthepa-
rameters’maximumlikelihoodestimatedescribingindividualbehavior,but
inthiscasefittingpatternsalsoatindividuallevel.Withoutmaximizedlike-
lihoodestimatesfortheparametersusedinamodel,theassumptionsofthe
AICandderivedinformationcriteriadonotstand.Weneedconsequently
tothinkabouthowtoapplytheprinciplesoftheAICapproachsouseful
intraditionalmultimodelinferencesothatIBMsdevelopedfortheanaly-
sisandunderstandingofemergentpropertiesappearingincomplexadaptive

2.3.ACTUALTOOLSOFPOM

33

systemscanbeanalyzedwiththestrategyofthemodelselectionprocedure.
Sofar,somestudiesusedstatisticaltoolssuchasdeviationmethodsforthe
parameterizationphaseofindividual-basedmodels(e.g.Wiegandetal.1998,
2003,2004Kramer-Schadtetal.2004),andarrivedtoverycoherentresults.
However,tothebestofourknowledgethesecondphaseofmodelselection
andinferencefromthemhasgenerallybeendonebyqualitativecriteria(e.g.
Bergeretal.2006),rarelywithmathematicaltools(e.g.Wiegandetal.
2004),andneverwithindicatorsofgoodnessoffitbasedoninformation
.theoryTheobjectivesofthisstudyistoproposeapattern-orientedmodeling
informationcriterion(POMIC)forinversemodelingand/orstronginference
appliedtoABM/IBMsinordertounderstandacomplexadaptivesystemby
reproductionofmultiplepatterns.AlthoughourmainfocusisonIBMs
inecology,thiscriterionwouldapplyforanybottom-uprule-basedmodel
developedwithinaPOMcontext.Wefirstpresentthetoolsalreadyexisting
andusedinPOMstudiesforinversemodelingandinferenceonmultiple
modelstoillustratetheneedofaninformationtheoreticbasedapproach.
Secondly,weexplainthemaininformationtheoreticprincipleoftheAICto
proposeadaptationsandnewassumptionsforthePOMICinordertohaveit
basedonsimilarprinciple.Thenwerecommendderivedstatisticsthatcanbe
extrapolatedfromtheuseofAICtotheuseofPOMICforstronginference
andforinversemodelingparameterization.Anexampleofapplicationis
presentedwithasimplecaseofIBMdevelopedtounderstandtheindividual
behaviorbehindemergentpropertiesofasimplesystem.Finally,wediscuss
theadvantagesofPOMIContheotherindicatorsofgoodnessoffitandits
generalpotentialforfuturepattern-orientedmodelingstudies.

2.3Actualtoolsofpattern-oriented
delingmo

Intheoriginaldefinitionofpattern-orientedmodeling(Grimmetal.1996),
thepatternsoffocuswereconsideredasinformationcomingfromnaturalsys-
thetemspthatattern-orienunderlinedtedmaohdypelingothesisapproacofphrocess.sincetHohenwevwer,erethegpeneralizedatternsutosedaniny
fromkindoffieldinformationobservationsnotanddirectlytheunderlyingincludablehinyptheomthesisodelaspectparameterswassomehocomingw
puttoasecondimportance.Inthiscontext,Wiegandetal.(2003)proposed
aofpattern-orienindividual-basedtedmodbiologicalelingprotocolinformation”whichfforollowsthe4msodteps:el(1)construction,“aggregation(2)

34

2CHAPTER

“determinationofparametervalues”,(3)“systematiccomparisonbetween
(4)the“observsecondaryedpatternpredictions”.andtheTsimhethirdulatedsptepatternincludesprowducedhatcbyouldthebmeodel”paralleledand
tomighantb“ineversemoindividual-levdeling”elbehaphase,viorasalthoughwellasthefochigher-levuselpatternspiatterns.nthisFromprotoctheol
wayWiegandetal.describedthesecondarypredictions,somemightalsobe
calledemergentproperties(e.g.Brecklingetal.2005)orpopulation-level
differenpatterns.tmTohduelss,ltheeading“strongtotheseinference”poonpulation-levindividualelbpatternsehaviorisparoppartosedofwthisith
protocol’sfourthstep.Inboththeinversemodelingpartandthestrongin-
istoferenceestimatepartofhothewpwelltattern-orienhemodelstedmfitodtheelingfieldoapproacbservha,antions.importanDifferenttasptoeoctls
existtodoso.
modelTheffiromrsttsheimpledifferentanalysesgraphicalarevisualoutputaofssessmensimtsulationsbycselectingomparedthetobtesthe
fieldobservations.Grimm(2002)proposedtocallthistypeofassessmentthe
bevisualassimpledebuggingastryingprocedure.freelyAtdifferenthetbpeginningarameterizationsofmodeldandevaelopmenlgorithmst,itcandan
shouldobservefollothewrsesultsomeccoherenoherence.tcriteriaInafurtherndthearnalysis,esultssthehouldpalsoarameterbeanalyzedselection
morethoroughlyandcanleadtographsortableshowingtheirproximity
tomofielddelsinobservecologyations.(e.g.ThisJiseltschusedetaal.lot1997,withThulkindividualeetabl.ased1999,orRailsbacgrid-basedk
andHarvey2002,Groeneveldetal.2002,Eisingeretal.2005,Bergeretal.
2006).Visualdebuggingisparticularlyusefulforpreliminaryanalysisand
tobuildingthemodphaseselerofadecisionsimandulationlackmoofdel.pHorecisionwever,forathesesystematicmethodsaresubcomparisonject
toselectamongaparameterizationset,ortodoinferenceonhypotheses
proposedbydifferentmodels.
Fdeviationorthem“inethovdsersetomoestimatedeling”shotep,wfarWiegandeachetal.(parameterization2003)propisosedfromtotheuse
thefieldspacepatterns.,theLetacorresppatternondingbedefinedempiricalbythemeasuremenobservatstionsXi==1x1,,x22······nxnin,
andthesimulationresultsofonereplicatedonewithaprocess-basedmodel
bemeasuremendefinedbtybYy:=y1,y2···yn.Thedeviation(d)iscalculatedforeach

di=xi−yi(2.2)
Themeansquareddeviation(MSD)isoneofthecriteriaderivedfromthe

2.3.ACTUALTOOLSOFPOM

deviation:

35

nMSD=1(xi−yi)2(2.3)
n=1iKobayashiandUsSalam(2000)decomposedtheMSDinseveralcomponents
linkedtothecorrelationanalysisparameters,allowingverifyingwhereisthe
majorpartofthedeviationofasimulationresultscomingfrom.Gauchetal.
(2003)proposedanotherdecompositiontosolvetheproblemsoflinksamong
thecomponentsofKobayashiandSalamandallowabettercomparisonof
modelsastoknowwhichpartistheleastrobusttoreproducetheempirical
data.However,alltheseconsiderationswereusuallynottakenintoaccount
byIBMdevelopers,usingmostofthetimetherootmeansquareddeviation
(RMSD)asacriterion(e.g.Jamiesonetal.1998,Wiegandetal.1998,
2004,Kramer-Schadtetal.2004,Chapter6)toworkwiththeactualdistance
betweenthesimulationresultsandtheempiricalmeasurements:
nnRMSD=1(xi−yi)2(2.4)
=1iThesetechniquesallowanestimationofthedevianceofthesimulationre-
sultstothefocuspattern.Theobjectiveistominimizethisdeviancewhen
processingafinetuningofamodel(e.g.Wiegandetal.1998).Whencon-
sideringmreplicatesofasimulationmodel,theobjectiveistominimizethe
sumorthemeanofthesedeviancesasindicatorsoftheerrorofthemodel
(e.g.Wiegandetal.2004).However,thiswaydoesnotconsiderthevariance
oftheerroramongreplicates.Asolutionistotrytominimizeboththeerror
expressedbytheseindicatorsandthevariance(e.g.Chapter6).
Ingeneral,theuseofthedeviationmethodsiscombinedwithathreshold
criteriacomingfromassumptions(e.g.Wiegandetal.1998)orrandomiza-
tionoffielddata(e.g.Wiegandetal.2004)toevaluateifthesimulation
resultsareacceptable.Thisleadstobinaryresultsastoacceptornotapa-
rameterizationforitscapacitytoreproducefieldpatterns.Otherstatistics
thanadeviationmethodcanleadtothesebinaryresults.Thecomparisons
amongthefielddatarangesofvariationandsimulationresultsrangemight
beone.Statistically,thiscouldbedoneforexamplewithaWilcoxonsigned
rankedtest(asinHigginsetal.2001).Usinganybinarycriteria,thebest
parameterizationswouldbetheoneswithallpatternsreproduced.Forthe
“stronginference”partitispossibletogeneralizethesebinarycriteriato
selectthebestmodelsastheonesreproducingallpatterns.However,at
thislevel,thequantitativegoodnessoffitofonegoodmodelcomparedto
anotherisnotkept,andthestronginferenceisthenonlyqualitativeeven

36

2CHAPTER

ifseveralmodelscontradicteachothers.Insuchcase,estimatingrelative
scoresobtainedforthedifferentpatternsallowattributingaglobalscoreto
eachmodelbutthevarianceishardertointroduce.Andwhendealingwith
differenttypeofpatternsuchascombinationoftemporalseriesandspatial
distribution,thisscoringanalysisareevengettingmorecomplexbecause
dealingwithdifferentmeasurementtypesandunits.Alikelihoodmeasure
insteadofadistancemeasurewouldhelpsolvingtheseproblems.
Drechsler(2000)introducedtheconceptoflikelihoodforselectionof
modelparameterizationswithasimpleapproachbasedalsoontherank-
ingofsimulationresults.However,hedidnotconsiderdifferentcomplexity
ofmodelsandthelikelihoodestimateswherenotbasedoninformationthe-
ories.MooijandDeAngelis(2003)didapplyaninformation-theory-based
likelihoodcalculationontheestimationandreliabilityestimationofparame-
tersofthreemodelsofdifferentcomplexity.Buttheirpatternsoffocuswere
atindividuallevel,i.e.atthesamelevelthantheirparameters.Anadapta-
tionoftheAICapproachusinglikelihoodfortheassessmentatalllevelof
goodnessoffitwasthenbelievedtoallowthesecomparisonsofmodelsfitto
severalpatternsandconsideringforeachofthemtheerrorandthevariance
oferrorofthesimulationresults.Theinterestingaspectofthisadaptation
wouldalsobetobeabletousethesameapproachfortheinversemodeling
part.inferencetrongsand

2.4Aninformationcriterionfor
delingmoedtpattern-orien

kgroundacB2.4.1OneminimizeoftthehemainKullbackprinciples-LeibleroftheinformationAICdevdivelopmenergencetbet(Bozdoganweenthe1987)“istruth”to
andgencet(heI)imosadelssessedincbetwonsideration.eenthetrueThedistributionKullbackd-Leiblerescribiedbyanformationprobabilitdiver-y
functionf(x)ofavariableoffocusxandthepredicteddistributiondescribed
byaprobabilityfunctiong(x)ofastatisticalmodeldescribingthevariations
that:soxof

∞+I(f(x);g(x))=−∞f(x)logfg((xx))dx(2.5)
=+∞f(x)logf(x)dx−+∞f(x)logg(x)dx
−∞−∞

2.4.ANINFORMATIONCRITERIONFORPOM

37

Thisfunctionisconsideredaslossfunctionofdoingstatisticalmodelingin
theAICdevelopment(seeBozdogan1987,BurnhamandAnderson2002).
ofAkaaiksetatisticalsuggestedmothedeluwsehicofh2p×I(farameters(x);gw(xere))pasanreviouslyestimatorestimatedofthewithqualitay
vamaximlueofumthelikpelihoarameterodgivestimatorenthe(i.e.dataatonbeefit).quationSincerfeturningurtherthemassumptionsostlikelyof
forthetAheICarebparameters,asedonwethenaeedtossumptionreconsidertousetahemaximapproacumhlikandelihocodannotaestimatorpply
directlytheAICtorule-basedmodels.

Statisticalmodelsconsiderapossibleparametersetθinfluencingthefo-
ofcusvparametersariable.Aθ∗ICassumedinfluencingthatthetthisruesetofdistributionparametersofthewasfocuspartvofariablethesetx.
Focusingonbottom-uprule-basedmodels,notonlyparametersmighthave
aninfluenceonxbutalsoprocesses.Thisterminologicaldifferenceimplies
thatwecomparemodelswithdifferentalgorithmscorrespondingtodifferent
hypothesesofprocessesorindividualbehaviorinthespecialcaseofIBMs,
vaandntnageotofobthisviouslyapproacwithhisdifferenthattntheumsbersamplingorvaproluescessesofp(Z)arameters.influencingAnad-the
sampleoutcomecanbeconsidered.Byincorporatingthesamplingprocesses
inarule-basedmodel,acomparisonofmodeloutcomesandfieldsamplecan
bedonewithatleastoneknowncommonunderlyinginfluencingprocess.
Thiscanbecomparedtothe“virtualecologist”procedureusedindifferent
IBMstudies(e.g.Bergeretal.1999,Wiegandetal.2003).Inouropinion,
sothepthatdataattern-orienprotedducedmobdyelingmodelsapproacarehreallyshouldalwcomparableaystoconsiderfieldtphispatterns.oint
sampleAssumingthatdistribution,theeweffectcanofnowsamplingcompareisthethespameoredictednmodeldistributionoutcomesoftandhe
modeldescribedbyaprobabilityfunctiong(x|θ)(whereθaretheprocesses
simulatedintherule-basedmodel)withthesamplingdistributiondescribed
byaprobabilityfunctionb(x|θ∗)(whereθ∗areallthep∗rocessesthatinflu-
encedtheoutcomeofthesampledvariable),withbothθandθincludingZ.
Thetheticallattertruepprobabilitrobabilityfyunctiondistributionwouldfbeunctiontakenfa(sx|aθn∗∗i)(whndicatorereθof∗∗thearehallypo-the
processesinfluencingthetruedistribution),whichisnotassessableother-
wiseinanykindofmodeling(statisticalorbottom-up)sincetheprocessesor
parametersbehindthedataareassumedunknownfromthebeginningand
havetobeanalyzedbytheprocedure.TheKullback-Leiblerinformation
divmodelergenceobutcomeetweenthedistributionsamplingcanthenprobabilitbeusedyasadistributionlossfandunctiontheofrourule-basedrule-

38

2CHAPTER

basedpattern-orientedmodelingapproach.Theequation2.5willbecome:
+∞+∞
I(b(x|θ∗);g(x|θ))=−∞b(x|θ∗)logb(x|θ∗)dx−−∞b(x|θ∗)logg(x|θ)dx
=−H(b(x|θ∗);b(x|θ∗))+H(b(x|θ∗);g(x|θ))(2.6)
Thefirstpartoftherighthandsideofequation2.6isthenegativeShannon
entropyofthesampleprobabilitydistribution−H(b(x|θ∗);b(x|θ∗))=−H(b(x|θ∗))
andisconstant.Thus,comparingseveralmodels,theoneshowingthelowest
cross-entropyH(b(x|θ∗);g(x|θ))willhavethelowestinformationdivergence.
Onceestimatedthetwoprobabilityfunctionsb(x|θ∗)andg(x|θ),wecould
thenusethecross-entropyasanindicatorofgoodnessoffitofthemodelto
thefocuspattern.

sitionoropP2.4.2Letassumeanindividual-basedstochasticmodeldevelopedtoreproduce
thenobservationsofthecontinuousvariablexover,withcorrespond-
ingempiricalmeasurementsX=x1,x2···xn.Thesimulationresultsofone
replicateofthemodelwithidenticalsamplingprocess(withidenticalnum-
berofobservations)areY=y1,y2···yn.Afunction(b(x))givingthe
probabilityofobservationofx∗canbeassumed(AppendixA-page53)and
consideredasestimateofb(x|θ)sothat:
b(x|θ∗)>0foranyx∈X
b(nx|θ∗)=0∗foranyx∈]−∞;Xmin[or]Xmax;+∞;[
andi=1b(xi|θ)=1
whereXminandXmaxaretheminimumandmaximumobservedfieldvalues
ofxrespectively.Aprobabilityfunctiong(y)(oranestimatorofit)should
befittothesimulationsresultsYsothatitisdefinedover,andcanthen
estimateg(x|θ).WedescribeinAppendixA(page53)howtoestimatethese
probabilityfunctions,andinAppendixB(page56)thespecialcaseofn=1.
Wepropose,outofequation2.6(seeAppendixC-page56formath-
ematicalargumentation)anestimatorofgoodnessoffitofYtoX,the
pattern-orientedmodelinginformationcriterion(POMIC)withthefollow-
ula:forming

nPOMIC=−1b(xi|θ∗)log(g(xi|θ))
n=1i

(2.7)

2.4.ANINFORMATIONCRITERIONFORPOM39
ThisPOMICvalueshouldgotowards0asg(x|θ)isgettingtowardb(x|θ∗),
i.e.YisclosetobeX.Iftherangeofthevaluesofg(x|θ)>0incor-
poratetherange[Xmin;Xmax]thenPOMICisanumericalvalue<∞.
Iftherange[Xmin;Xmax]doesnotincorporateg(x|θ)=0thenforsome
x∈[Xmin;Xmax],andPOMICcouldbeassumedtobeinfinite.
WithSreplicatesofthemodelanalysis,thedistributionshouldbeesti-
matedforeachreplicatessothateachwillhaveaparticularestimatorof
g(x|θ)≡gs(x|θ).Thegoodnessoffitofthemodelcouldthenbecalculated
with:SnPOMIC=−1b(xi|θ∗)1log(gs(xi|θ))(2.8)
ni=1Ss=1
Inthiscase,thelargerSis,themoreprecisetheestimationofthegoodness
offitwouldbe.
Inthespecialcasethatthepatternofconsiderationisgivenbyonlyoneobser-
vationofonevariablexuniqueobs,wecouldassumethatb(xuniqueobs|θ∗)=1
andthereforethePOMICwouldbegivenby:
POMIC=−loggAllSxuniqueobs|θ(2.9)
wheregAllSisaprobabilityfunctionfittotheresultsoftheuniqueobservation
ofSreplicatesoftheIBM(seeAppendixB-page56).
Inthecaseofastudywithseveralmodelsdevelopedtoreproducemultiple
patterns,aftertheassessmentofgoodnessoffitofsinglepatterns,thestrong
inferenceonthemodelsfittingallpatternsmightneedacriterionincluding
thegoodnessoffitofallpatternstogether.Consideringϕpatternsp(ofequal
importance),eachoftheseppatterndescribedbypdifferentindependent
variables,withforeachvariablenp,jobservations,thePOMICwouldbe:
ϕ⎛pnp,jS⎞
ϕp=1pj=1np,ji=1Ss=1
POMIC=−1⎝11bp,j(xi|θ∗)1log(gp,j,s(xi|θ))⎠
(2.10)ThePOMICisanestimatoroftheKullback-Leiblerdivergencebetweenthe
modelandthesampledistributionpatterns.Thestatisticsusedintraditional
modelselectionprocedureswiththeAICcanthenbeappliedaswelltothe
POMIC(thefollowingarederivedfromBurnhamandAnderson,2002).

2.4.3Derivedstatisticsforstronginference
offit.ThefiSincerststhetatisticPOMderivICe,dafsromtheanAIC,doinformationesnothavcriterionerealistunitsheanddifferencescould

40

2CHAPTER

rangewidely,interpretingaPOMICvaluemakesonlysensebycomparing
ittootherPOMICvaluesofmodelsfittothesamesamples.Thuswecan
usethedifferencesΔiasforAIC:
Δi=POMICi−POMICmin(2.11)
wherePOMICministhesmallestPOMICvalueofthemodelsetR.TheΔi
canbeinterpretedas“strengthofevidence”(BurnhamandAnderson,2002)
wherethebestmodelwillhaveΔi=0,andtheotherhaveΔi>0.Following
therulesofthumbofBurnhamandAnderson(2002)wecanproposethe
followingfordifferentmodels:
•withΔi≤1,themodelshavesubstantialevidence,
•with2≤Δi≤4,themodelshaveconsiderablylessevidence,
•withΔi>5,themodelshaveessentiallynoevidence.
Theseconduseistherelativelikelihoodofeachmodelgiventhedataandthe
setofmodelstested(R).ThiscanbecalculatedfromthePOMICdifferences
as:L(modeli|data,R)=exp(−Δi)(2.12)
Fromthisrelativelikelihoodestimator,pairsofmodelsjandhcanbecom-
paredwithanevidenceratioER:
ER=L(modelj|data,R)/L(modelh|data,R)
=exp(−Δj)/exp(−Δh)(2.13)
=exp(POMICh−POMICj)
whichinformabouttherelativeevidenceofmodelhtomodelj.
ThemostimportantandhandypartistheequivalenttotheAkaikeweights,
withatnormalizethemodellikelihoodssuchthattheysumto1:
exp(−Δi)
wi=rR=1exp(−Δr)(2.14)
Thesegiveweightsofevidenceinfavorofeachmodeliandcanbeseenasthe
probabilitythatitisthebestmodelamongthesetRofmodelstested.So,if
thebestmodelwiissothatwi>0.9wecouldsaythatwith90%confidence
thisisthebestmodelwehavetoreproducetheprocessesthatinfluenced
thevariablexsothatweobservedthepatterngivenbythedata.Inother
cases,stronginferencewouldbedonebyunderstandingwhichmodelscould
bereproducingtheprocessesthatdrovetheobservedpatterns,andwhich
otherareunlikelytohavebeen.

2.5.EXAMPLEOFAPPLICATION

41

2.4.4Derivedstatisticsforinversemodeling
AnotherimportantuseofAkaikeweightsisformodelaveraging.Model
averagingforthecaseofindividual-basedmodelsinapattern-orientedmod-
ofelingPOM,approaci.e.hfindwotheuldbestcomefibacttingktoparameterconsideringvalues.theiLetnvaersessumemoonedelingmodpartel
structureincludingtheprocessesθwithoneunknownparameterk.Testing
wsevoulderalvathenluesgivofeskaagainstsetRtheofsampledifferentdatamodproelsjducingustwtheithpatternsdifferentofpintarame-erest
terizations.ThePOMICandderivedAkaikeweightscouldbecalculated
asdescribedearlier.Ifthebestfittingparameterizationisnotoneofthe
extremetestedvaluesofk,thenonecouldaveragethevaluestofindamaxi-
mizedlikelihoodestimateofk≡kˆasfollows(fromBurnhamandAnderson,
2002):

Rkˆ=wi×ki
=1i

(2.15)

Withavariancegivenby:
⎡⎤2
vaˆrkˆ=⎣Rwivar(k)i+ki−kˆ21/2⎦(2.16)
=1iwherevar(k)iwouldbeapotentialvarianceoftheparameterkapriori
implementedinthemodeli.
Ideally,thisapproachcouldevenbeeffectuatedtomultipleparameters
situations.ThissequenceofinversemodelingcouldenhancealotthePOM
approachifappliedforthedifferenttypeofmodelswithdifferentunderlying
hypothesisofprocessesbeforeasequenceofstronginferenceonthem.

ApplicationofxampleE2.5Forthisexampleofapplicationweproposetoconsideratheoreticalex-
perimentthatcouldbeconductedonindividualsofanimaginaryspeciesin
anenclosedsquareareaof100by100m.Theseindividualswouldhavetwo
possiblestatuses:activeorinactive.Fromthebiologyoftheseindividuals
wewouldnotknowhowtheactiveindividualsactuallymoveorinteractwith
theirneighbors,butwewouldknowthattheinactivestatuswouldbefor4
days.Leavingrandomlydistributed25individualsatthebeginningofthe
experimentwewouldobserveduring50daysthattheproportionofmoving
individualswouldalwaysbe0.5standarddeviationof0.1.Afterthese50

42

2CHAPTER

days,thespatialorganizationanalyzedwiththeL-ripleyfunction(Besagon
ualsRipleyof1977)10m(woFig.uld2sho.1).waAnsignificanindividualtrbegularasedmodistancedelcbetouldweenbetheconstructedindivid-
mowithvingthePOMindividualsapproacandrhtoegularreprooducerganizationtheseatfterwo50pdaatternsys.Wofepfiroprstodrtionescribofe
asimplemodeltoanalyzethissituation:theSIMOVIM(SImpleMOVement
IndividualModel).Secondly,wedescribetheapplicationofthePOMICfor
aansinvtrongerseminferenceodelingproanalysis.cedure.Andfinally,weshowhowtousePOMICfor

Figure2.1:Spatialdistributionoftheoreticalindividualsafter50daysintheirenclosure.
a)individualsrepresentedwithrespectivexandyaxisofpositionsand2statusesof
active/inactive(black/emptyrespectively).b)L-Ripleyanalysis(BesagonRipley1977)
wheretheblacklineistheLfunctionofthemapa)andthedashedlinesareconfidence
envelopecreatedwith999Monte-Carlorandomizationofthe25individuals’positions.

2.5.1Descriptionofasimpleindividualmovementmodel
IM)V(SIMOInthispartwedescribetheSIMOVIMmodelfollowingtheODDprotocol
(Grimmetal,2006).Firstwegiveanoverviewdescription(purpose,state
variablesandprocesses),thenwepresentthedesignconceptsandfinallythe
details(initialization,input,sub-models).
ThepurposeoftheSIMOVIMmodelwastotesthypothesisofmovement
ofindividualsleadingtoaregulardistributionafter50timesteps.The
statevariablesdescribingtheindividualswerethepositionandthestatuses

2.5.EXAMPLEOFAPPLICATION

43

(active-inactive)allowingtheindividualtomoveornot.Thesimulation
areawasasquareof100by100mwithreflectiveboundaries.Thestatus
ofeachindividualwascheckedateachtimestep,andeventuallychanged
accordingtotwoprobabilities(P1=0.25andP2,Table2.1)fromonetothe
otherstatus(inactivetoactiveandactivetoinactiverespectively).Active
individualswerethenmovedwithagivenfunctionofmovementdepending
onthesub-modelinuse(randommovement,attractedmovement,repulsed
movement,attractedandrepulsedmovement).
TheSIMOVIMmodelreproducedanemergentpropertyofspatialorga-
nizationdependingonthesub-modelofmovementinuse.Theproportion
ofindividualsmovingperday(hereafterreferredtoasPM)wasalsotested
againsttheassumedpatternofobservationdescribedearlier(afixedseries
PMobsof50normallydistributedrandomnumbersofmean0.5andstan-
darddeviationof0.1),butwasobviouslyforcedbytheratioP1/P2.Inall
exceptthefirstmovementsub-models,theindividualssensedtheirneighbors
intheselectionofitsclosestone.Thechangeofstatuswasstochastically
determined.Eachtimesteps,thefrequencyofmovementandproportion
ofinactiveindividualswererecorded.Thespatialorganizationwasonly
assessedafter50timesteps.Atinitialization,theindividualswereplaced
randomlyonthesimulatedareaandtheirstatusrandomlyassignedwitha
ratioof1:1forinactive/activeindividuals.Noinputwasattributedtothe
modelafterthisinitialization.Thefirstsub-modelofmovementwassimulat-
ingarandomwalk(SIMOVIMversion1).Thenewpositionoftheindividual
wasassignedwiththefollowingformula:
xxrand1
yt+1=yt+rand2(2.17)
whererand1andrand2weretwouniformrandomnumberbetween−MaxMovD
and+MaxMovD(Table2.1).Thesecondsub-modelsimulatedattraction
ofindividualsuntilagiventhreshold(SIMOVIMversion2).Foreachin-
dividual,firsttheclosestneighborwasfoundandifitsdistance(Dist)was
aboveMaxNeighD(Table2.1),thenewpositionwasgivenas:
(2.18)+=xx(xclosest−xFocus)×MaxDiMstovD
yFocust+1yFocust(yclosest−yFocus)×MaxDiMstovD
wherexclosestandyclosestwerethecoordinatesoftheclosestneighbor.Ifthe
distanceDistwasbelowMaxNeighDthefocusindividualmadearandom
movementasin(2.17).Thethirdsub-modelsimulatedrepulsionbetween
individualsuntilagiventhreshold(SIMOVIMversion3).Foreachindi-
vidual,theclosestneighborwasfoundandifitsdistance(Dist)wasbelow

44

2CHAPTER

Table2.1:Testedvaluesoftheparametersincludedinthedifferentversionsofthe
SIMOVIMmodels.
ModelParameterofMaximumdistanceThresholdof
versionsprobabilitytoofmovementinoneinteractionwiththe
(sub-changestatusP2directionclosestneighbor
models)activetoinactive(MaxMovD)(MaxNeighD)
10.05to0.50.5to20-
20.05to0.50.5to202to25
30.05to0.50.5to202to25
40.05to0.50.5to202to25

MaxNeighDthenewpositionwasgivenas:
xx(xFocus−xclosest)×MaxDiMsotvD

yFocust+1=yFocust+(yFocus−yclosest)×MaxDiMstovD(2.19)
IfthedistanceDistwasaboveMaxNeighD,thefocusindividualwasset
tomakearandommovementasin(2.17).Thefourthsub-modelsimulated
bothrepulsionandattraction,usingthetwoequations(2.18)and(2.19)in
casesofdistancewiththeclosestneighboraboveandbelowtheMaxNeighD
respectively(SIMOVIMversion4).

2.5.2UsingPOMICforinversemodeling
parameterizationsdMethoTheparameterspresentedintable2.1wereassumedunknownforthebiol-
ogyofourtheoreticalindividuals.Thefirstpatterntobereproducedwasthe
proportionofindividualsmovingperday(PM).Thiswasnotpossiblyin-
fluencedbytheMaxMovDandMaxNeighDparametersinSIMOVIM.We
thereforetested20differentvaluesofP2with1000replicatesofSIMOVIM

2.5.EXAMPLEOFAPPLICATION

45

withthefirstmovementsub-modelandafixMaxMovD=10.Foreach
replicatejweconsideredtheobservationofPMofeachdaytoreproducea
vthatectorapof50robabilitobservyfationsunctionPMofsiappmje=arancePMsofimj,PM1,PvaMsluesimwj,2as···createdPMsifmorj,50eac,sho
observreplicateation(gjt(ofPMPM|P2o))bs,outweocfaalculatedhistogramtheofthisprobabilitPMysbi(mPMjvobsector.t|samplFore)teacoh
hationve2.8tobservocedalculatethePMtheobsPOtvMaIlueCvafromluestheforseacample.hWparameterethenPa:ppliedequa-
2POMIC=−150b(PMobst|sample)×
50=1t10001j=11000log(gj(PMobst|P2))(2.20)
Wtionse2.11calculatedandthe2.14Δirespandectivwievlya.luesAoutmaximofuthem2lik0PelihoOMICodvaestimatelueswithandevqua-ari-
anceofPwasthencomputedfollowingequations2.15and2.16.Thesecond
patternt2obereproducedwasthespatialorganizationanalyzedwiththeL-
Ripleyfunction.Eachmodelversionwastestedwith100replicatesofeach
thattheparameterization70Lobs(rp)ovaluesssibilitiesalong(Tathebler2.1)axisandofwtheithpPattern2=0.25.measuremenWeatwssumedere
independentvariableswitheachaspecificprobabilitydistribution.Thus,for
eachrweusedthe100replicateresultstoconstructaprobabilityfunction
gWr(eL(r)applied|modelfor)teacohevarvluatealuethetheperobabilitquationy2.9torandeprosduceummedthethemLobst(or)ovbtainalue.
theoverallPOMICvalue:
POMIC=−701r70=1log(gr(Lobs(r)|MoxMovD,MaxNeighD,sub−model))
(2.21)Weequationsthen2.11calculatedandt2.14heΔrespiandectivweilyv.aTluesheformaximeachummolikveelihomenotdsub-moestimatesdelawndith
vationsrian2ce.15ofandMax2.16.MovIDnbandothcMaasesxNeitheghgD(xw|eremodel)fcomputedunctionsfollowerewingcreatedequa-
cwithadensitykernelestimatoroftheRsoftware(RDevelopmentCoreTeam
tofit2006)anappliedhistogramtotofheprobabilitconsideredyofvoectorXccurrence.ofsimulationresultsandscaled

ResultsThePOMICvaluesvariedbetween1.5and0.3forthedifferentvalues
ofP2.Thebestfittingparameter(i.e.thesmallerPOMICvalue)was

46

2CHAPTER

foundwithP2=0.2,buttheweightscalculationshowedthatnocasehad
aprobability>0.07tobethecorrectparametervalue(AppendixD,Table
2.3).TheaveragingofP2withtheweightsofevidencegaveanestimateof
P2MLE=0.234±0.11.Thisrangeofvariationincludetheexpectedvalueof
P2=P1=0.25sothattheoriginal50%proportionofactiveindividualsof
startstayoverthe50days.Theaveragingishowevernotleadingexactlyto
thisexpectedvaluebecauseofthesmallnumberofobservationsperreplicates
50).=n(ForthefirstSIMOVIMversion,withthesub-modelofrandomwalk,
thedifferenttestedvaluesofMaxMovDshowedinfinitevaluesofPOMIC
(AppendixD,page59).Thismeantthatnoparameterizationcasefitted
correctlythespatialorganizationpattern,whichwasexpectablesincethe
movementwasspatiallyrandom.ForthesecondSIMOVIMversion,with
thesub-modelofattractionwalk,allthecombinationoftestedvaluesof
MaxMovDandMaxNeighDshowedinfinitevaluesofPOMIC(Appendix
D,page59).Thismeantthatnoparameterizationfittedcorrectlythespatial
attern.porganizationForthethirdSIMOVIMversion,withthesub-modelofrepulsionwalk,the
bestparameterizationwasfoundwithaPOMIC=1.166,MaxMovD=2
andMaxNeighD=10(AppendixD,page60).TheaveragingofMaxMovD
andMaxNeighDwiththeweightsofevidencegaveestimatesofMaxMovDMLE=
4.88±3.27andMaxNeighDMLE=10.14±1.59.
ForthefourthSIMOVIMversion,withthesubmodelofrepulsionand
attractionwalk,thebestparameterizationwasfoundwithaPOMIC=
1.426,MaxMovD=6andMaxNeighD=15(AppendixD,page60).
TheaveragingofMaxMovDandMaxNeighDwiththeweightsofevidence
gaveestimatesofMaxMovDMLE=7.42±1.79andMaxNeighDMLE=
18.16±1.85.
2.5.3UsingPOMICforstronginference
onindividualbehavior
sdMethoThedifferentSIMOVIMversionswerenowknownastoreproducethe
secondpatternofspatialdistributionornot.Weusedonlythethirdand
fourthversionforthisexampleofstronginferencesincethetwofirstonewere
knownnottoreproducethefieldpatternofspatialdistribution.However,
toeffectuatearealstudywithstronginference,weshouldbetestingawider
setofpotentialmodelsreproducingrelativelywellthefieldpatterns.
Werun100replicatesofeachSIMOVIMversions(3or4)withstochastic

DISCUSSION2.6.

47

valuesofP2,MaxMovDandMaxNeighDaroundtheaveragesfoundinthe
previouspartandwiththeirrespectivestandarddeviation(P2MLE=0.234±
0.11;forversion3:MaxMovDMLE=4.88±3.27andMaxNeighDMLE=
10.14±1.59;forversion4:MaxMovDMLE=7.42±1.79andMaxNeighDMLE=
18.16±1.85).TheoverallPOMICforthefitofthetwopatternswerethen
s:acalculatedPOMIC=−501t50=1b(PMobst|sample)10001j=11000log(gj(PMobst|P2))
−170r70=1log(gr(Lobs(r)|sub−model))/2(2.22)
WecalculatedtheΔiandwivaluesforthe2movementsub-modelswith
equations2.11and2.14respectively.

Results-ConclusionsTheSIMOVIMversions3and4withthebestfittedparametersleadto
POMICvaluesof0.956and0.996respectively.Thedifferencesamongthem
beingsosmall(<0.1),theweightsofevidencewere0.52and0.48respec-
tively.Thisindicatedthattheversion3ofSIMOVIMwiththesub-model
ofrepulsionwalkandtheversion4withthesub-modelofrepulsionandat-
tractionwalkwerealmostidenticallylikelytobereproducingthebehavior
individuals.heoreticaltourofHowever,thestronginferenceoutofthisexercisewasthattherepulsion
issurelyhappeningtoarriveatthereproductionoftheconsideredpatterns.
Themodelversionswithoutrepulsiondidnotreproducethespatialdistri-
butionpattern.Theadditionofattractiontotherepulsionprocessdidnot
enhancethefit,nordiditdecreaseitsubstantially.Thus,itcouldnotbe
discardedasabiologicalprocesshappeninginadditiontorepulsion.But
followinganOckham’sRazorprincipleofusingtheleastcomplexmodelfor
anequivalentpayoffastoreproducereality(definedastheMedawarZone
byGrimmetal.2005),theuseoftheversion4insteadofversion3would
besuperfluousifonewantstoworkonfurtheraspectofthispopulationwith
theSIMOVIMmodel.

iscussionD2.6Wedescribedandappliedanewtooladaptedfrominformationtheoryfor
evaluatingthegoodnessoffitofstochasticrule-basedmodelsforwhicha
deterministicequationofmaximumlikelihoodestimatesoftheparameters

48

2CHAPTER

cannotbecomputed.Thisconditionparticularlyappliestoagent-basedand
individual-basedmodelsthataretryingtoreproducefieldobservationsat
higherintegrationlevel.Wehaveproposedalsoasetofderivedstatisticsto
estimateevidenceweightsandmaximizedlikelihoodestimatesofparameters
thatweredemonstratedinourexampletobeusefulforstronginferenceand
inversemodelingrespectively.

AbouttheparsimonyofmodelsassessedbyPOMIC
Thereasoningofcheckingover-parameterizationofstatisticalmodelswith
AICandofABM/IBMswithPOMIChaveidenticalobjectives:increasethe
model’spredictability(orpayoff)withincreasecomplexityuntilthiscom-
plexityincreasedoesnotincreasepayoff.Consideringastatisticalmodel
includingrandomand/ornon-randomparameters,theirnumbermightin-
creasefitcapacitybutmightalsoleadtoanincreaseofvariabilitythatat
somegivenpointdoesnotfavortheoverallfit.Modelselectioncriteria
suchasAIC(actuallyoftenreplacedbymorecomplexone),useanover-
parameterizationpenalizationincludingthenumberofparametersinthe
formula.Thesecriteriacanthenindicateeasilyifitisworthtoincreasethe
numberofrandom/non-randomparametersornot.InthePOMcontext,
theobjectivebeingthesame,theinterestwastodetermineatwhichpoint
thefitincreaseisnotworththeincreaseofcomplexity.Wedemonstrated
withourSIMOVIMexamplethatusingthePOMICallows,withaninfor-
mationtheoreticbasis,todosuchconclusions.Thenumberofparameters
orprocessesisnotinPOMICbutbecauseitisanestimateofaKullback-
Leibler(K-L)distanceastheAIC,thegoodnessoffitdifferencesandweight
ofevidencesallowustodiscardornotamorecomplexmodelapplyingthe
famousOckham’sRazzor.Consequently,thefactthatthenumberofpa-
rametersorprocessesofthemodelassessedwithPOMICdoesnotenterin
thePOMICformuladoesnotrestrictourapproachtobeabletocheckfor
modelparsimony.

AbouttheprecautionstousePOMIC
Ob(Burnhamviouslya,ndweshouldAndersonstretc2002)htthehePOfactMIthatCvasaluesforccanomparingonlybeAICvcomparedalues
amongmodelstestedagainststrictlyidenticalsetoffielddata.Additionally
thesameprobabilityfunctionestimatesforthefielddatadescribingthepat-
ternsestimatesshouldofbteheused,simandulationthesresultsamewsayhouldofbecalculatingapplied.thepAnotherrobabilityfprecaution,unction
whichwasrarelyconsideredinpattern-orientedmodelingstudies,istohavea

2.6.DISCUSSION

49

samplingdesignprocesswithinthemodelthatreproducesthedesignusedin
tanthetfield.assumptionsThislastoutoftprecautionhisisremarkessential(particularlytoPOtMheIConetsinceouwseethemsadeimpamplingor-
thisdistributionideasfhouldunctionalsobaseagoappliedodwhenindicatorusingoftheothertruegoodnessdistribution).offitHowindicatorsever,
suchasmean-squaredeviationorregressions,becausesampledfielddatanot
influencedbythesamplingtechniquearealmostinexistent.Actually,this
orscienconsiderationtistsuissedalsotooneofinformationthemaintheoriesadvawillncesofseeourtheaPOpproacMIh.CSastatistician“only”a
roughappliedatoanpplicationyosituationftheofK-Lcomparingdistance.twoThefK-Lunctions.distanceWeiarenghereeneralccouldomparingbe
aprobabilitydistributionfunctionwithanother,thefirstbeingthesample
advthatawnceeitrysttohatrweproeduce,includedthethesecondsamplingbeingprothecesssimtoulationobtaintheresults.simButulationthe
results,sothatwearereallycomparinghowwellourmodelreproducesthe
sampledistribution.Thiswastoourknowledgeneverdoneinagent-based
orindividual-basedmodelingwithinorwithoutapattern-orientedmodeling
ork.framew

Abouttheinverse-modelingwithPOMIC

fromInvetherse-mogoodnessdelingofisfittheeresultsxerciseofosfimulationsestimatingwithunknodifferenwnmotpdelparameterarametersval-
ues.criteriaOneissthehort-cutmodelavsometimeseragingdofoneinsparameterstatisticalovermosetsdelingofmusingodelswithinformationdif-
ferentstructurebutincludingalltheparametersinfocus.Werecommend
This,stronglymainlyagainstbecausethispinrothecessescasemighoftAnotbeBM/IBMsalwaytsuunedsingwaithpthearameterPOMinIanC.
idenpatternticalofwfaoycusandinasthereforeamemintanner.eractMowithdeloptherarametersparameterswithidentinfluencingicalnamesthe
anddistancebiologicalthresholdpurpoofseint(e.g.eractioninSIMOwithVtheIMcthelosestManxeighNebiogrhiDnmisodtheelvmeaximrsionum2
to(e.g.4)MamighxtNnoteighhaDvethedeterminesametheumathematicalseofrandom/effectindifferenattractiontmoordrelveepulsionrsion
walkmaximizedinthelikelihodifferenodtSIMOestimates.VIMvTheersions)modelaandvcaneragingwthereforeouldbehavinethisdifferencaset
misleading.completely

50

2CHAPTER

ConclusionslikTheelihooPOdMandICwiseightsbasedofmoondelsgivinformationenthedatatheoryandandthecansetofthereforetestedmocomputedels.
Thisallowstodostronginferenceonasetofmodels,butalso(andeventually
behigherfore)inptegrationarameterizationlevel.avTheseearagingspectsforgAivetoBM/IBMstherepropattern-orienducingtedmpatternsodelingat
approachanimportantimprovement.Whileassessingadatasetwithaset
ofstatisticalmodelandAICislookingforthemostlikelyinterconnection
ofparameters(sometimesrepresentingprocesses),developinganABM/IBM
usingthePOMapproachwithPOMICcouldbecomparedtofindingthe
actualemergen“btehapropvertior”y.ofThisindividualnewmpethoartsd,thattogetherleadtowithahigheradaptationintofegrationnewtolevoelsl
sucandhastheindividual-basedParetoevomolveodelingfKomdeveurolopeetdail.na(2006)POMcwillontextdefinitelyanewgpivoetenatgenialt
ofinferenceontheunderstandingof“behaviors”ofindividualpartofcom-
plexadaptivesystems.

2.7Acknowledgements
ThediscussionfirsttahatuthorledwtoishttheotideahankoftryingparticularlytoWapplyernerAICWtoosnioktheforPOMtheoconriginaltext
andJonathanMontalvoformathematicalverifications.Wearealsothankful
vtoeVrsionolkoerfthisGrimmmanuandscript.ThorstenThisworkWiegandwasfortfinancedheirundercommentthesoDFnaGnperoarlierject
(PUME).1960/2-1BE

eferencesR2.8

Akaike,H.1973.Informationtheoryandanextensionofthemaximumlikelihoodprinciple.-
In:Petrov,B.N.andCsaki,B.F.(eds.),Secondinternationalsymposiumoninformation
theory.-AdademiaiKiado,pp.267-281.
Akaike,H.1974.Anewlookatthestatisticalmodelidentification.-IEEETransactionson
AutomaticControl19:716-723.
Anderson,D.R.,Burnham,K.P.andWhite,G.C.1994.AICmodelselectioninoverdis-
persedcapture-recapturedata.-Ecology75:1780-1793.
Berger,U.,Adams,M.,Grimm,V.andHildenbrandt,H.2006.Moldellingsecondarysuc-
cessionofneotropicalmangroves:Causesandconsequencesofgrowthreductioninpioneer
species.-PerspectivesinPlantEcology,EvolutionandSystematics7:243-252.

2.8.REFERENCES

51

Berger,U.,Wagner,G.andWolff,W.F.1999.Virtualbiologistsobservevirtualgrasshop-
pers:anassessmentofdifferentmobilityparametersfortheanalysisofmovementpatterns.
-EcologicalModelling115:119-127.
Bozdogan,H.1987.ModelselectionandAkaike’sinformationcriterion(AIC):thegeneral
theoryanditsanalyticalextensions.-Psychometrika52:345-370.
Brang,P.,Courbeaud,B.,Fischer,A.,Kissling-N¨af,I.,Pettenella,D.,Sch¨onenberger,W.,
Sp¨ork,J.andGrimm,V.2002.Developingindicatorsforthesustainablemanagementof
mountainforestsusingamodellingapproach.-ForestPolicyandEconomics4:113-123.
Breckling,B.,M¨uller,F.,Reuter,H.,H¨olker,F.andFr¨anzle,O.2005.Emergentproperties
inindividual-basedecologicalmodels-introducingcasestudiesinanecosystemresearch
context.-EcologicalModelling186:376-388.
Burnham,K.P.andAnderson,D.R.2002.Modelselectionandmultimodelinference:A
practicalinformation-theoreticapproach(2ndedition).-SpringerVerlag.
Caswell,H.,Fujiwara,M.andBrault,S.1999.Decliningsurvivalprobabilitythreatensthe
NorthAtlanticrightwhale.-ProceedingsoftheNationalAcademyofScienceofUSA96:
3308-3313.Doncaster,C.P.,Clobert,J.,Doligez,B.,Gustafsson,L.andDanchin,E.1997.Balanced
dispersalbetweenspatiallyvaryinglocalpopulations:analternativetothesource-sink
model.-TheAmericanNaturalist150:425-445.
Drechsler,M.2000.Amodel-baseddecisionaidforspeciesprotectionunderuncertainty.-
Biologicalconservation94:23-30.
Eisinger,D.,Thulke,H.-H.,Selhorst,T.andMller,T.2005.Emergencyvaccinationofrabies
underlimitedresourcescombatingorcontaining?-BMCInfectiousDiseases5:10.
Gauch,H.G.,Hwang,J.T.G.andFick,G.W.2003.Modelevaluationbycomparisonof
model-basedpredictionsandmeasuredvalues.-AgronomyJournal95:1442-1446.
Grimm,V.1999.Tenyearsofindividual-basedmodellinginecology:whathavewelearned
andwhatcouldwelearninthefuture?-EcologicalModelling115:129-148.
Grimm,V.2002.Visualdebugging:awayofanalyzing,understandingandcommunicating
bottom-upsimulationmodelsinecology.-Naturalresourcemodeling15:23-38.
Grimm,V.,Berger,U.,Bastiansen,F.,Eliassen,S.,Ginot,V.,Giske,J.,Goss-Custard,
J.,Grand,T.,Heinz,S.,Huse,G.,Huth,A.,Jepsen,J.U.,Jorgensen,C.,Mooij,W.
M.,Mueller,B.,Pe’er,G.,Piou,C.,Railsback,S.F.,Robbins,A.M.,Robbins,M.M.,
Rossmanith,E.,Rger,N.,Strand,E.,Souissi,S.,Stillman,R.A.,Vabo,R.,Visser,U.and
DeAngelis,D.L.2006.Astandardprotocolfordescribingindividual-basedandagent-
basedmodels.-EcologicalModelling198:115-126.
Grimm,V.,Frank,K.,Jeltsch,F.,Brandl,R.,Uchmanski,J.andWissel,C.1996.Pattern-
orientedmodellinginpopulationecology.-TheScienceoftheTotalEnvironment183:
151-166.Grimm,V.,Revilla,E.,Berger,U.,Jeltsch,F.,Mooij,W.M.,Railsback,S.F.,Thulke,
H.-H.,Weiner,J.,Wiegand,T.andDeAngelis,D.L.2005.Pattern-orientedmodelingof
agent-basedcomplexsystems:lessonsfromecology.-Science310:987-991.
Groeneveld,J.,Enright,N.J.,Lamont,B.B.andWissel,C.2002.Aspatialmodelofcoexis-
tenceamongthreeBanksiaspeciesalongatopographicgradientinfire-proneshrublands.
-JournalofEcology90:762-774.
Hansen,T.F.,Stenseth,N.C.andHenttonen,H.1999.Multiannualvolecyclesandpopu-
lationregulationduringlongwinters:ananalysisofseasonaldensitydependence.-The
129-139.154:NaturalistAmericanHiggins,S.I.,Richardson,D.M.andCowling,R.M.2001.Validationofaspatialsimulation
modelofaspreadingalienplantpopulation.-JournalofAppliedEcology38:571-584.

52

2CHAPTER

Hipel,K.W.1981.GeophysicalmodeldiscriminationusingtheAkaikeinformationcriterion.
-IEEETransactionsonAutomaticControl26:358-378.
Huggins,R.M.1991.Somepracticalaspectsofaconditionallikelihoodapproachtocapture
experiments.-Biometrics47:725-732.
Jamieson,P.D.,Porter,J.R.,Goudriaan,J.,Ritchie,J.T.,vanKeulen,H.andStol,W.
1998.AcomparisonofthemodelsAFRCWHEAT2,CERES-Wheat,Sirius,SUCROS2and
SWHEATwithmeasurementsfromwheatgroanunderdrought.-FieldCropsResearch
23-44.55:Jeltsch,F.,Mller,T.,Grimm,V.,Wissel,C.andBrandl,R.1997.Patternformation
triggeredbyrareevents:lessonsfromthespreadofrabies.-ProceedingsoftheRoyal
SocietyofLondonB264:495-503.
Johnson,J.B.andOmland,K.S.2004.Modelselectioninecologyandevolution.-TRENDS
inEcologyandEvolution19:101-108.
Kobayashi,K.andUsSalam,M.2000.Comparingsimulatedandmeasuredvaluesusing
meanssquareddeviationanditscomponents.-AgronomyJournal92:345-352.
Komuro,R.,Ford,D.E.andReynolds,J.H.2006.Theuseofmulti-criteriaassessmentin
developingaprocessmodel.-EcologicalModelling197:320-330.
Kramer-Schadt,S.,Revilla,E.,Wiegand,T.andBreitenmoser,U.2004.Fragmentedland-
scapes,roadmortalityandpatchconnectivity:modellinginfluencesonthedispersalof
Eurasianlynx.-JournalofAppliedEcology41:711-723.
Langtimm,C.A.andBeck,C.A.2003.Lowersurvivalprobabilitiesforadultfloridamana-
teesinyearswithintensecoastalstorms.-EcologicalApplications13:257-268.
Lebreton,J.-D.,Burnham,K.P.,Clobert,J.andAnderson,D.R.1992.Modelingsurvival
andtestingbiologicalhypothesesusingmarkedanimals:aunifiedapproachwithcase
studies.-EcologicalMonographs62:67-118.
Mooij,W.M.andDeAngelis,D.L.2003.Uncertaintyinspatiallyexplicitanimaldispersal
models.-EcologicalApplications13:794-805.
Posada,D.2003.Selectingmodelsofevolution.-In:Salemi,M.andVandamme,A.-M.
(eds.),Thephylogenetichandbook.CambridgeUniversityPress,pp.256-282.
Posada,D.andCrandall,K.2001.Selectingmodelsofnucleotidesubstitution:anapplication
tohumanimmunodeficiencyvirus1(HIV-1).-MolecularBiologyandEvolution18:897-
906.Post,E.,Stenseth,N.C.,Peterson,R.O.,Vucetich,J.A.andEllis,A.M.2002.Phase
dependenceandpopulationcyclesinlarge-mammalpredator-preysystem.-Ecology83:
2997-3002.Railsback,S.F.2001.Conceptsfromcomplexadaptivesystemsasaframeworkforindividual-
basedmodelling.-EcologicalModelling139:47-62.
Railsback,S.F.andHarvey,B.C.2002.Analysisofhabitat-selectionrulesusingan
individual-basedmodel.-Ecology83:1817-1830.
Ripley,B.D.1977.ModellingSpatialPatterns.-JournaloftheRoyalStatisticalSociety.
SeriesB(Methodological)39:172-212.
Thulke,H.-H.,Grimm,V.,Mller,T.,Staubach,C.,Tischendorf,L.,Wissel,C.andJeltsch,
F.1999.Frompatterntopractice:ascaling-downstrategyforspatiallyexplicitmodelling
illustratedbythespreadandcontrolofrabies.-EcologicalModelling117:179-202.
Wiegand,T.,Jeltsch,F.,Hanski,I.andGrimm,V.2003.Usingpattern-orientedmodeling
forrevealinghiddeninformation:akeyforreconcilingecologicaltheoryandapplication.
-Oikos100:209-222.
Wiegand,T.,Moloney,K.A.andMilton,S.J.1998.PopulationDynamics,Disturbance,
andPatternEvolution:IdentifyingtheFundamentalScalesofOrganizationinaModel

APPENDICES2.9.

53

Ecosystem.-TheAmericanNaturalist152:321-337.
Wiegand,T.,Revilla,E.andKnauer,F.2004.Dealingwithuncertaintyinspatiallyexplicit
populationmodels.-BiodiversityandConservation13:53-78.
Yamaoka,K.,Nakagawa,T.andUno,T.1978.ApplicationofAkaike’sinformationcriterion
(AIC)intheevaluationoflinearpharmacokineticequations.-JournalofPharmacokinetics
andBiopharmaceutics6:165-175.
Yoccoz,N.G.,Stenseth,N.C.,Henttonen,H.andPr´evot-Julliard,A.-C.2001.Effectsof
foodadditionontheseasonaldensity-dependentstructureofbankvoleClethrionomys
glareoluspopulations.-JournalofAppliedEcology70:713-720.

endicesppA2.9AendixppA2.9.1∗andWethedescribmodelerhereesultshowptoerobabilitstimateyftheunctionsamplingg(x|θ).probabilitLetayfssumeaunctionsrb(ule-basedx|θ)
x,stowcithhasticcorrespmodeldondingevelopedempiricaltomreproduceeasurementhetsnXobserv=xa1,xtions2···ofxnt.heTvheariablesim-
(withulationidentresultsicalonfuomneberofreplicateobservofathetions)moaredelYw=ithy1iden,y2t···icalyn.samplingprocess
Estimatingthesamplingprobabilityfunctionofn>1fieldobser-
tionsavWecandrawahistogramofprobabilityofobservationofvaluesofxfrom
themeasurementsXwithNbcategoriesdefinedbyavectorofintervals
B=[Xmin;B2[,[B2;B3[···[BNb;Xmax]whereeachintervalisofwidthΔB.
Afunctionofprobabilityofobservationofx(b(x))canbeassumedasthe
contin∗uousupperlineofthishistogramandcouldbeconsideredasestimate
ofb(x|θ)(Fig.2.2),sothat:
b(x|θ∗)>0foranyx∈X
b(nx|θ∗)=0∗foranyx∈]−∞;Xmin[or]Xmax;+∞;[
andi=1b(xi|θ)=1
Practically,theb(xi|θ∗)oftheobservationxiwillbeevaluatedasthenumber
ofassumedobservianttionsheof“BacXwithinkground”thepartsamethatctheategoryntobservhanaxitionsdividedofourbyn.sampleSincewewree
b(ourxi|eθn∗t)ire=1tunivoasersesurtoetbheatbrepro(xi|θ∗duced)wbouldybtheehamvoedasel,awreealnpeedtherobabilitsumyfofunctionthese
berespectingestimatedtheasKdescribolmogoroedvinathexioms.folloFortwinghisforreasonthemothisdelb(xr)fesultunctionprobabilitcannoty
function.

54

2CHAPTER

Figure2.2:Fittinganestimatorofthesamplingprobabilitydensityfunctiontothe
histogramofobservationofX.

Estimatingthemodelresultsprobabilityfunction

ΔBUsingthantheforstheamenumprobabilitberyNbfofunctioncategoriesofthefiandeldtrheesults,sametheintervsimalulationwidth
resultsYcanbealsousedtoconstructahistogramofprobabilityofobser-
vationsofy.Asabove,theupperlineofthishistogramcouldbeconsid-
eredasanestimateofg(y).However,usingsuchestimateastheprobabil-
ityfunctiong(x|θ)wouldrestrictaPOMICvalue<∞onlyinacaseof
[nXmin;increase.Xmax]T∈o[Yobtainmin;Yamaxw],iderrwhicangehiswhereguncomfortably(x|θ)>0(harderleadingtotoobtainPOasMItheC
vatogramlues<so∞)thataitconistinmoreuouslikelyfunctionreturningg(y)c>ould0forbeallfitxtoofXthe.Fporrobabilitexample,yhis-in
thecasethatweknowthatthesimulationresultsareknowntobenormally
distributed,wecanuseascaledprobabilitydensityfunctionofthenormal
distribution(pdfnormal)fittedtooursimulationresults.Togetanestimatorof
theneedpdfonlynormtoal(x)vcalculatealueofthethemfieaneldofdtatahegsimivenulationthemodresultsel(Y¯),parameterization,theirstandardwe
ofodeviationccurrence(SDiYn).theWesimcanutlationhenuseresultsthisdatapdfnorset:malandscaleittoprobability

g(x|θ)=pdfnormal×ScalingP
1(x−Y¯)2
=SDY√2πexp−2×SDY2×ScalingP(2.23)

APPENDICES2.9.

whereScalingPisaparametercalculatedas:

ScalingP=max(gh(x))/max(pdfnormal(x))

55

(2.24)

wheregh(x)isthefunctionfittothehistogramdescribedabove,andmax(.)
returnthemaximumvalueofbothfunctions.Thiswayofestimatingthe
probabilityfunctionisactuallyvalidforanydistributionsofsimulationre-
sultsknowntofollowanotherspecificdistributionofwhichtheprobability
densityfunctioncanbecalculated.Insuchcase,thepdfofthespecificdis-
tributioncanbeusedinsteadofpdfnormalinequations2.23and2.24.

toFiguretheh2.3:istogramFittingofanobservationestimatorofYoftwithheasimduensitlationykernelresultspestimator.robabilitydensityfunction

Ifwedonothaveaprioriknowledgeonthetypeofdistributionsofour
simulationsresults,werecommendthentouseakerneldensityestimatorof
yvalueswithabandwidthBWsothatBW=ΔB/2;andscaledownthese
densityestimatestotheprobabilitiesobservedinthehistogramofYwiththe
sametechniqueasinequation2.24.Thesetransformedprobability-density
valueswillbetheestimateofg(x|θ)foronereplicate(Fig.2.3).Toestimate
thelikelihoodtofindaspecificxivalueofthefielddatasetgiventhemodel
parameterization,wewillestimateitastheg(xclosest|θ)valuewherexclosestis
theclosestxvaluetoxi.Forthisreason,thedensitykernelestimatorshould
haveaBWnottoobigtoreducetheapproximationerrorofthismethod.

2CHAPTER

2CHAPTER56BendixppA2.9.2Estimatingthesamplingprobabilityfunctionofn=1fieldobser-
tionavAssumingfore.g.thatwewanttoreproduceapatternofaspatialor
temporalvariableofwhichthevaluesareconsideredindependent.Wewould
assumeeachobservationasanindependentvariableofonly1observationthat
shouldbereproducedbyourIBM.Identicallytothefirstcaseofappendix
A(page53),weneedthesumofb(xi|θ∗)tobe∗equalto1,andsincen=1,
wecouldassumethatb(xuniqueobservation|θ)=1.
Estimatingthemodelresultsprobabilityfunctionreproducingn=
ationobservfield1Thesimulationresultshouldproduceonlyonevalueofyperreplicate
Y=y.Thelikelihoodtoproduceaprecisexvaluegiventhemodelhasthen
tobecalculatedoutofthereplicatesresults.LetassumetheSreplicates
produceavectorTofuniqueobservationsperreplicatesT=Y1,Y2···YS,the
likelihoodfunctionofourmodelwillthenbecometheprobabilityfunctionfit
tothevectorTasdescribedinAppendixA(page53)forthesimulationresult
probabilityfunctionestimationdependingifweknowornotofanunderlying
distributiontypeforT.

CendixppA2.9.3Wewanttodevelopanunbiasedestimatorofgoodnessoffitofrule-based
modelsincludingtheprocessesθleadingtothedistributionfunctiongofx
againstasampledistributionfunctionbofxinfluencedbytheprocessesθ∗.
Weassumeaslossfunctionofdoingthismodelingexercise,theKullback-
Leibler(K-L)distancebetweenbothdistributions:
I(b(x|θ∗);g(x|θ))=+∞b(x|θ∗)logb(x|θ∗)dx−+∞b(x|θ∗)logg(x|θ)dx
−∞−∞=−H(b(x|θ∗);b(x|θ∗))+H(b(x|θ∗);g(x|θ))(2.25)
=Eb{logb(x|θ∗)}−Eb{logg(x|θ)}
wheretheexpectations(functionsE)aretakenwithrespecttothesample
distributionfunctionb,whichissupposedheretorepresentthetruth.Since
thefirsttermofthesumisconstantforourmodelingexercise,theK-L
distancecanbesummarizedas:
I(b(x|θ∗);g(x|θ))=constant−Eb{logg(x|θ)}(2.26)

2.9.APPENDICES

57

sincewehave
−H(b(x|θ∗);b(x|θ∗))=constant
IntheAICorotherinformationcriteriatheexpectationofloglikelihoodof
themodelElogg(x|θ)tofitthedataistakenwithrespecttothetruedistri-
bution.Inthesecases,thedatasetisusedtoestimatetheparameterswith
themaximumlikelihoodestimate(MLE)functionrelatedtothemodeltobe
fit,andalsotoestimatethegoodnessoffitoftherespectivemodel(Bozdogan
1987,BurnhamandAnderson2002).Consequently,theparameterdistance
ofθfromθ∗canbeestimateddependingonthetypeofmodels,thenumber
ofparameterskinθ,thenumberoffieldobservationsnandthecovariance
amongparameters.Theapproachconsiderthenasriskfunctionofdoing
modelingtheexpectedK-Ldistancewithrespecttothetruedistribution,
andthisdistanceofθfromθ∗canindicatethebiasfactorbfofthegeneral
biascorrectedinformationcriterion(BCIC,Bozdogan2000):
BCIC=−2logL(θˆ)+2n×bf(2.27)
whereL(θˆ)isthemaximumlikelihoodofthemodel.
Inourapproach,theprocessesandparameterswithinthemarenotesti-
matedwithamaximumlikelihoodfunctionconsideringthedatatobefitto.
SothesebiasesbfcannotbeestimatedandthewholeapproachoftheAIC
andotherinformationcriteriadoesnotapply.Butwewanttofitthemodel
topatternsthatgenerallywerealreadyseenasofinterestandthereforewedo
notintendtoguessthetruedistributionfunction,butbettertoestimatethe
qualityofourmodelsincomparisontoanexpressionofthistruedistribution
givenbythesampledistribution.SocomingbacktotheK-Ldistanceasloss
function,anditsexpectationwithrespecttothetruedistributionastherisk
function,fromequation2.26wehave:
Ef{I(b(x|θ∗);g(x|θ))}=Ef{constant}−Ef{Eb{logg(x|θ)}}(2.28)
TheEf{Eb{logg(x|θ)}}expectationwithrespecttothetrueandsample
distributioncanthenbeassumedtobeequaltoEb{logg(x|θ)}onlyinre-
specttothesampledistributionifweassumethat:(1)thesampleisagood
representationofthetruthand(2)redoingthismodelingexerciseshouldlead
tothesamemodels,i.e.thepattern-orientedmodelingprotocol(Wiegandet
al.2003)waswellfollowed.Also,sinceEf{constant}isconstant,wehave
tominimizeanestimatorofgoodnessoffitgivenby:
Estimator=C−Eb{logg(x|θ)}
n=C−b(x|θ∗)logg(x|θ)(2.29)
=1i

2.29)(

58

2CHAPTER

ThisleadsustoapreliminarypropositionofPOMICthatshouldbemini-
mized:

nPOMIC=−b(xi|θ∗)log(g(xi|θ))(2.30)
=1iAndingeneral,tobeabletotransportthePOMICfromonecaseofdata
fittingtoanotherindependentlyofthen,wedividePOMICbyn:
nPOMIC=−1b(xi|θ∗)log(g(xi|θ))(2.31)
n=1iDendixppA2.9.4ThisappendixpresentthedetailedresultsoftheSIMOVIMinversemod-
phases.eling

Table2.3:Resultsoftheinversemodelingparameterizationtestsoftheparameterof
probabilityofindividualstochangestatusfrominactivetoactive(P2)(inbold,theresult-
ingbestfittingP2valueaccordingtoPOMIC;initalictheexpectedbestP2valueof0.25).
P2POMICΔi(Eq2.11)wi(Eq2.14)
.20)2(Eq0.050.0250.4380.5630.1080.2330.0550.049
0.10.07500.419.3780.0890.0480.0570.059
0.150.1250.3460.3510.0210.0160.0610.061
0.20.17500.338.3300.0080.0000.0610.062
0.250.2250.3440.35500.014.0250.0610.060
0.30.27500.393.4350.1050.0630.0560.058
0.350.3250.4970.5870.1670.2570.0520.048
0.40.37500.641.7240.3940.3110.0420.045
0.0370.5170.8470.4250.450.4751.0091.1830.6790.8530.0310.026
0.0191.187.51710.5

2.9.APPENDICES

59

Tamaximbleum2.4:movedResultsdoistancefthe(MainvexMrseovmDo)dforelingthepfirstvarameterizationersionoftSIMOestsofVIM.theparameterof
MaxMovDPOMICΔi(Eq2.11)wi(Eq2.14)
.21)2(Eq10.5iinfinitenfinite--0.0000.000
21.5iinfinitenfinite--0.0000.000
64iinfinitenfinite--0.0000.000
0.000-nfinitei80.000-infinite101520infiniteinfinite--0.0000.000

Table2.5:Resultsoftheinversemodelingparameterizationtestsoftheparameter
ofneighbmaximor(umMaxmoNveeidghdD)fistanceorthe(sMaxecondMovvDersion)andofSIMOthresholdVIM.inAntyperactionarameterwithcomthebcinationlosest
ledtoidenticalresults.
MaxMovDMaxNeighDPOMICΔi(Eq2.11)wi(Eq2.14)
.21)2(Eq10.525infiniteinfinite--0.0000.000
21.5180iinfinitenfinite--00.000.000
412infinite-0.000
615infinite-0.000
8101208iinfinitenfinite--00.000.000
20152522infiniteinfinite--0.0000.000

Δi(Eq2.11)wi(Eq2.14)
0.000-0.000-0.000-.0000-.0000-.0000-.0000-0.000-0.000-0.000-

2CHAPTER60Table2.6:Resultsoftheinversemodelingparameterizationtestsoftheparameter
ofneighbmaximor(umMaxmoNveeidghdD)fistanceorthe(tMahirdxMvoevDrsion)aofndSIMOthresholdVIM.interactionwiththeclosest
MaxMovDMaxNeighDPOMICΔi(Eq2.11)wi(Eq2.14)
.21)2(Eq21.5110011.330.1660.1640.0000.0770.065
1101.3860.2200.062
4101.3890.2230.061
10.518011.410.4440.2440.2770.0600.058
42881.4791.4500.3120.2840.0560.058
46110211.493.5340.3270.3680.0550.053
86110211.557.5420.3910.3760.0520.053
0.0480.4781.64410100.0460.5101.67612150.0460.5141.680121081.521211.734.6840.5680.5170.0440.046
810115522.167.3281.1621.0010.0240.028
0.0092.1853.3512010Allothercombinationsinfinite-0.000

2.9.APPENDICES61

Table2.7:Resultsoftheinversemodelingparameterizationtestsoftheparameter
ofmaximummoveddistance(MaxMovD)andthresholdinteractionwiththeclosest
neighbor(MaxNeighD)forthefourthversionofSIMOVIM.

DovxMaM684106108610810theroAll

hDigeaxNM5181511881200202222225inationsbcom

P(EqOM2I.21)C
1.426.4781.58011.623.63811.889.9451.32322.436.89023.318infinite

.11)2(EqΔi0.0000.0510.1540.1970.2120.4630.5190.8971.0101.4631.891-

.14)2(Eqwi0.1470.1390.1260.1210.1190.0920.0870.0600.0530.0340.0220.000

62

CHAPTER2

Intersp

Caribb

trPa

cifice

ean

I

comp

etition

angromev

63

ni

orestsf

Chapter

Zonation

offshore

yarse

3

patterns

evangrom

ftera

rricaneuh

a

of

Belizean

orestsf

atastrophicc

65

41

66

3CHAPTER

ZonationpatternsofBelizeanoffshore
mangroveforests41yearsaftera
urricanehcatastrophic

Piou,Cyril12;Feller,IlkaC.3;Berger,Uta1;&Chi,Faustino4
AuthorPosting.cAssociationforTropicalBiologyandConservation(ATBC)
2006.Thisistheauthor’sversionofthework.Itispostedherebypermissionof
theATBCforpersonaluse,notforredistribution.Thedefinitiveversionwas
publishedinBiotropica,38(3):365-374.
/doi:10.1111/j.1744-7429.2006.00156.xghttp://dx.doi.or

bstractA3.1

Mangrovesarepronetoreceivefrequentlythefullbruntofhurricanesand
tropicalstorms.Theextentofdestructionandearlyregenerationarewidely
studied.Thepurposeofthisstudywastoaddalong-termviewofmangrove
regenerationandassessthepotentialeffectsonmangrovehorizontalzonation
patternsofcatastrophicdestruction.Hattie,aCategoryFivehurricane,hit
theBelizeancoastin1961.ItpasseddirectlyovertheTurneffeAtollwhere
ourstudyarea,CalabashCay,islocated.Atfoursitesofthisisland,man-
groveforeststructurewasanalyzedalongtransectsparalleltotheshoreline
withinzonesdelineatedbyspeciesdominanceandtree-height.Wepropose
anindexbasedontheSimpsonindexofdiversitytoexpresschangesinthe
heterogeneityofthespeciesdominance.Physical-chemicalparametersand
nutrientavailabilitywerealsomeasured.Thedestructionlevelswereesti-
matedbyanalysisofthedistributionofdiameteratbreastheightsofthe
biggertreesintheinlandzones.Variationsinspeciesdominanceamong
sitesandzonescouldbeexplainedbyinteractionsofvariousfactors.We
alsofoundthatthedifferentlevelsofdestructionbetweenthetwosidesof
theislandhadasignificanteffectoncurrentpatternsofspeciesandstruc-
turalzonationatCalabash.Weconcludethatdisturbanceregimeingeneral
shouldbeconsideredasafactorpotentiallyinfluencingmangrovehorizontal

12CenterforTropicalMarineEcology,Fahrenheitstrasse6,23859Bremen,Germany
Correspondingauthor:cyril.piou@zmt-bremen.de
34InstituteSmithsonianofMEnarineSvironmentudies,talUnivResearcersithyCenoftBer,elize,POBPOoxBo28,x990,EdgewaBelizeter,MDCity,B21037,elizeUSA

ODUCTIONINTR3.2.

zonationpatterns.

67

bances;KeywLagords:unculAarviicaraenniacemosa;lgerminansong-term;Belize;regeneration;hurricanemdangroistur-ve
forestgeneity;Tudynamics;rneffeARhtoll;izophorzaonationmpangle;atterns.speciesdominancehetero-

3.2Introduction
Mangroveforestslinemostoftheworld’stropicalandsubtropicalcoast-
lines.canesaInndthistropicalcoastalstorms,pwosition,hicharemangroafvesrequenrteceivfeormtheoffulldisturbancebruntofinhtheseurri-
latitudes.Treemortality,treespeciesresistance,andearlyforestrecovery
Vermeerimmediately1963,folloStowingddarthu1963,rricaneBardsleydestruction1984,havRotheb1een992,widelySmithetstudiedal.(1994,e.g.,
Roth1997,Imbertetal.1998,Sherman&Fahey2001,Baldwinetal.2001,
Imbert2002).Ratesofhurricane-relatedmortalityinmangrovesforestsare
significantlyhigherthanforanyothertropicalforests(comparedinBaldwin
etal.analyzed2001;theseeimpactsalsoofImtbehesertetal.destructions1998).onSomerecosystemecentfstudiesunctionshasvucehaalsos
peteatal.2005)formationwithin(Cahotheondetecadeal.follo2004)wingorwhuoodyrricanes.debrisInaconccumtrast,ulationfew(Kraussstudies
Inhavethesexaminedtudiescthearriedoutlong-termintrheecoveCaribbryean,patternsresults(e.g.,ofspSmithecies&Dukresistancee1987).to
hurricanesarecontradictory.Forinstance,accordingtoRoth,Smith,and
RImbehizophorrta(Rothm1angle992,istheSmithleeasttal.resistan1994,ttIomhberturricaneetal.1998,destruction.ImbertHow2ev002)er,
ShermanandFahey(2001)foundthatAvicenniagerminansistheleastre-
etsistanal.t.(1994),RegardingandBtheraldwinelativeteal.imp(2001)ortancefofoundtreeasize,higherRothprobabilit(1992),yofSmithde-
structionforintermediateandhighersizeclasses.Otherstudieshaveshown
eitheraninversepattern(e.g.,Imbertetal.1998),ornodifferenceindamage
amongsizeclasses(e.g.,Sherman&Fahey2001).
Theextentofforestdamagedependsontheintensityofthehurricane.
Category(www.nhc.noaa.goOneorTv)woshuhouldrricanesgenerallyontheSinflictlessaffir-SimpsondamagetHurricanehanCScaleategories
depThreeendingtoFivone.siteNevexpeosure.rtheless,Forthepeexample,rcenItagembofert(dead2002)atreesndcanShermanalsovaandry
Faheyshoreline.(2001)(seefoundalsothee.g.,highestRothlev1992,elsImofbertetdisturbanceal.1in998).zonesBcaldwinlosetoettheal.

68

3CHAPTER

(2001)reportedalsothatthedifferencesinlevelsofdestructionattwosites
inFloridadependedontheirrelativepositionwithinthepathoftheeye
ofHurricaneAndrew.AtTurneffeAtoll,Stoddart(1963)describedthatthe
mangroveforestsonmanysmallwindwardislandswerecompletelydestroyed
byHurricaneHattie,aCategoryFivestormthatstruckBelizeinOctober
1961,whileinsidetheatollthevegetationdamagewerelessimportant.
Delayedmortalityisanothersourceofvariationinhurricanedamage.
Somemangrovetreesareabletocoppice(e.g.,A.germinansandLaguncu-
lariaracemosa)andusetheirpre-hurricanereservestocreatenewtissues
andfoliage(Tomlinson1986).However,ifthesetreesareseverelydamaged,
theydonotlivemuchmorethan2yrafterthehurricane(seee.g.Sherman&
Fahey2001).Thedelayedmortalityisnotashighinmangrovesasinother
tropicalforests(Imbertetal.1998).Furthermore,mangroveforestsappear
lessresistantbutmuchmoreresilientthanothertropicalforests.Imbertet
al.(1998)suggestedthatnoCaribbeanmangrovespeciesarepioneerswhen
comparedtorainforests.However,mangrovespeciesapparentlypresentdif-
ferentadaptationsforre-colonizationstrategiesandwindresistance(Roth
1992),relatingtheeffectsofhurricanestothemangrovedynamicsandstruc-
ture.Toourknowledge,nostudieshaveyetdocumentedthelong-termeffectsof
hurricanesonthehorizontalzonationpatternsofmangroveforests.Suchpat-
ternsmayrefertostructuralcharacteristics(structuralzonation)orspecies
dominance(specieszonation).Structuralzonationdescribesbandsparal-
leltotheshoredifferingintreedensity,canopyheightortreediameters.
Specieszonationexpresseszonessuccessivelyencounteredfromoffshoreto
inlandwithdifferentmonospecificcompositionorparticularassociationsof
fewtreespecies.Severalhypotheseshavebeenexpressedtoexplainthephe-
nomenadrivingthesepatterns:plantsuccession(Davis1940),geomorpho-
logicalfactors(Thom1967),differentialdispersalofpropagules(Rabinovitz
1978),differentialpredationonpropagules(Smith1987),interspecificcompe-
tition(Ball1980)andspecies-specificphysiologicaladaptationstogradients
(Macnae1968,forreviewseeSmith1992).InBelize,differentialpredation
onpropagulesisnotresponsiblefordifferencesinspecieszonation(McKee
1995a).McKee(1993)foundthatphysiologicaladaptationsbestexplain
zonationpatternsinBelizeanmangroves.Togetherwiththespecies-specific
physiologicaladaptationstogradientsofsalinityandtidalinfluence,nutrient
availabilityplaysanimportantroleinCaribbeanmangrovezonation(Feller
003).2al.etThemainobjectiveofthisstudywastodeterminewhetherperturba-
tionssuchashurricanesinteractwithotherpossibleexplanatoryphenomena
mentionedabovetohaveaneffectonthesehorizontalzonationpatternsin

METHODS3.3.

69

mangroveecosystems.Thesecondaimwastodocumentthelong-termeffects
oflarge-scaledestructiononforeststructureandtoproposesomerecovery
pathwayscenarios.TheoffshoreBelizeanmangroveislandsinTurneffeAtoll
providedanideallocationfortheseinvestigationssincetheywerepreviously
destroyedbyHurricaneHattiemorethan40yrago,andtheoccurrenceof
onlyfourtreespeciesprovidesaparticularbutrelativelysimpleforestsys-
tem.

dsethoM3.33.3.1Studyareaandsites
ThisstudywasconductedatCalabashCay(alsosometimesreferredasthe
Tu“MainrneffeCAtoll,alabashoneCaoyf”tohefathree“CalabashBelizeanCaays”tollsgroup),(Fig.3on.1).theItiseasternlocatedsideap-of
profromxtheimatelym34ainland.kmeastCalabashoftheCaMyisaesoAmericanlmost2kBmlarrierongaReefndabandoutab1outkm50atkmits
wawidesttersbpyoinat.sItmallcreekincludesonantheinnernorthlagoendonotfhattheislinkislandedto(Fig.the3T.1).Iturneffeislagofringedon
btheyemangroasternvesside.onaTllheitstidalinnerraangendisoutermicrotidalcoasts(wavitheragetherangeexception<30ofcm)partaofnd
isclassifiedasmixedsemidiurnal.
drysTheeasons.climateTheisannutropicalaltorainfallrsubtropical,angeisbweloithwcthelearly2020distinctmmperrainyyearandof
airBelizetempCiteyraturesbutabvoaryvef1rom5003m2◦mC(iC.nsPiou,ummerp(ers.Marchobs.).toSAveptemerageber)mtoaxim28◦umC
intheswintameermon(OctobthlyertopatternFebruary).from24Av◦Cterageo20◦C.minimTheumctemplimateiseraturesvinfluencedarywithby
coldfronts(or“Northerns”)comingfromNorthAmericaduringthewinter
monincreaseths.tBheetoweenccurrenceJulyofandheaNovyvemrainber,andhustrongrricanestointhecatastrophicCaribbeanwinds.Region
On31October1961,HurricaneHattie,aCategoryFivehurricane,hit
wtheestBsouth-welizeanecstoast.overTTheueyrneffeeofAttollhishuwithrricanewindswoevnterfrom260keastm/hr.Tnorth-eastheinten-to
hsity,umanwhindabitationsdirection,andwavmeostaoction,ftheandtmangrohevestormforestssurgeofCdestroalabashyedaCllay.ofAthec-
smallcordingitslandoS∼to300ddartmto(1963)windwwhoardvofisitedCTualabashrneffeCaiyn,1was962,BigcompletelyCalabash,cleareda
ofsevanerityymofangrodvesestructionbyfHattie.romeBastasedtowonestStowasddart’sexpecteddescription,formaangrogveradienftorestin

70

3CHAPTER

atCalabashCay.Specifically,Stoddart(1963)describedthatdefoliationof
mangrovestandswaslesssevereandregenerationwasalreadyoccurringin
theinteriorpartofTurneffeAtollbyearly1962.CalabashCayhasalarge
innerlagoon,whichisconsideredanaturalshelterbythelocalpopulation.
Thewaveactionandthetidalhurricanesurgewereweakerinsidethein-
nerlagoonthanoutside.Sincethehumansettlementsweredestroyedand
notrebuiltafterHattie,theregenerationofthemangroveforestsofCalabash
Caywasnotinfluencedbyanyanthropogenicactivitiessince1962.Although
tropicalstormsandlightningstrikescouldhaveinducedthedeathofindi-
vidualtrees,nootherhurricanesorcatastrophicperturbationshaveaffected
substantiallytheCalabashmangrovessinceHattie.Thegradientofdistur-
bancehypothesizedbyStoddart(1963)inarelativelyshortdistancearound
Calabashmakesthisareaidealforthemainobjectiveofthisstudy.
FourstudysiteswereselectedaroundCalabashalongtheproposeddistur-
bancegradient.ThesesiteswerelabeledAtoD(Fig.3.1).Allsitesextended
fromthefringingmangroveforestalongthewater’sedgetothehighintertidal
marginwherebuttonwood(Conocarpuserectus)thicketsdominatedadjacent
totheuplandterrestrialforest.Preliminarysurveyswereconductedtode-
terminezoneswithinthesesitesdependingonboththeapparentstructural
andspecieszonationpatterns.SiteAwaslocatedonthenortheastsideof
Calabashwherefourzonesweredefinedfromtheshorelineinland.SiteBwas
locatedonthenorthernmostpointofCalabashandfourzonesweredefined.
SiteCwassituatedonthenorthwestsideofCalabashandextendedfrom
OrchidCreektotheuplandareawithsixdifferentzones.SiteDwaslocated
ontheeastsideoftheinnerlagoonandhadthreemixedzones.

3.3.2Forestmeasurements
Meandiameteratbreastheight(DBH),treeheight,density,andspecies
frequenciesweremeasuredbythepointcenteredquartermethod(PCQM)
transectslaidwithineachzoneofeachsitebetweenNovember2002and
February2003.Inordernottomeasurethesametreetwice,thedistance
betweenpointsofthePCQMtransectsvariedbetween2minthedwarf
areasto12mintallbasinforests.EachofthePCQMtransectsconsistedof
21pointsforarepresentativemeasurementofthestudiedarea(Cintr´on&
1984).ellivhaeffer-NoSc

3.3.3Physical-chemicalsurvey
PSystemorewataterthreesalinitydifferenandtppHerioweds:re24-30measuredNovemwithbera2002,YSI6c-9556FeMbruaryulti-Prob2003,e-

METHODS3.3.

71

loFigurecalization3.1:ofTtheusrneffeitesA(motolldifiedwithfromHurricaneGarcia&HattieeHoltermannyespath1998).andCalabashCaywith

and27February2003.Tidalmeasurementsweremade13-22February2003.
Tidetablesandseveralovernightmeasurementsinarowwereusedtoesti-
mateaFebruarymaximumtidallevelforeachstation.Ayearlymaximum
tidallevelwascomputedbyextrapolationoftheseFebruarymaximumtidal
levelsinconjunctionwiththeyearlytidetables.Theslopeoftheelevation
changewithineachzonewasalsocalculatedwiththefollowingformula:

slope=H3−H1×100
Dist1−3

3.1)(

hace

whereH1andH3weretherelativeelevationofthefirstandlastpointofeach
zone,respectively,andDist1−3wasthedistancebetweenthesetwopoints.
Asameasureofsitefertility,thenutrientresorptionefficiencyandleaf
biomassproductionperunitofnutrientwerecalculatedasanindirectwayto
determinetrendsofnutrientavailability,asdescribedinFelleretal.(1999).
Leaveswerecollected20-22February2003.Ineachzonewherepresent,

72

CHAPTER3

fourpairwassamplescompofotsedhreeoftoafivematurepairsleafofleaandvesaofR.ready-to-fallmanglewesenescenretharvleafested.fromA
thesametwig.Digitalimagesandimageanalysissoftware(SigmaScanPro
4.0)wereusedtomeasureleafarea.Allsampleswereoven-driedat70◦C,
wenitrogenighed,(N)andgandroundtophosphoruspass(P)throughconcena0.38mmtrationsinmeshthescreen.greenWandesenescenmeasuredt
leavesandcalculatednutrientresorptionefficiencyandbiomassproduction
perunitofnutrientinvestedforeachexperimentaltree.Resorptionefficiency
(RE)wascalculatedasthepercentageofNandPrecoveredfromsenescing
leavesbeforeleaffall(ChapinIII&VanCleve1989):
NorP(mg.cm−2)greenleaves−NorP(mg.cm−2)senescentleaves
100=RE×NorP(mg.cm−2)greenleaves
(3.2)

Biomassproductionperunitofnutrientwascalculatedastheinverseofthe
nutrientconcentrationinsenescentleaves(nutrientuseefficiency,NUEing
biomass/gNorP).

3.3.4Indicatorsofdestructionlevel
Nodirectinformationwasavailabletoestimatedifferencesofmangrove
destructionamongsitesduringHurricaneHattie.Therefore,anindirect
measurementwasnecessarytoextrapolatefromthestandingtreesconsid-
eredolderthan41yrtocompareanestimateddestructionlevelamongthe
foursites.Fromtheseestimates,aqualitativevariableof“complete”or
“incompletedestruction”wasattributedtoeachsite.
Inthemostinlandmangrovezone,namedherehinterlandzone,ofthe
foursites,belt-transectsof60mlongand10mwidthwereestablished.The
hinterlandzoneswerechosentomakecertainthatthetreesmeasuredwere
inacomparablephysical-chemicalsituation.Withinthesebelt-transects,all
treeswithDBHmorethan20cmweremeasured.Thedistributionpatterns
oftheselargetreeswereusedtodetectextraordinaryoldorlargetreesseen
asoutliersintherightsideofthedistribution.Theseoutlierswerethenused
asproxiesofdestructionlevelsofthefourdifferentsites,assumingthatthey
representthetreesolderthan41yr.
Inthefringe(i.e.,thefirstzonealongthewater’sedge)anddwarfzones
ofsiteC,atreeagingtechniquewasadaptedfromDukeandPinz´on(1992)
basedonleafscarproductiontoestimatethepossibledestructionlevelofthis
forest.AnestimationofleafscarsproducedbydwarfR.mangleofTurneffe
Atollwas4.1scarsperyear(I.C.Feller,unpublisheddata).Thisnumber

METHODS3.3.

73

wasroundedto5tokeepanerrorrangeandarobustestimateoftreeage.
Leafscarswerecountedfromthetopmostapicalleavestothebottomofthe
treesforallstemspresentinthree1×1mplots.Stemsfromanindividual
treehavingmorethan205scarswereconsideredtobeolderthan41yr.The
percentageoftrees>41yrwascalculatedfromthesemeasurements.

nalysisaataD3.3.5eachTheofthePCQMfourrspesultsecieswpeererzuonesedatsodcescribalculateedinanCinimptr´onortanceandvNoaluevelli(IV)f(1984).or
IVwasbasedonrelativedensity,relativedominanceandrelativefrequency
ofeachspecies.Consequently,thesumoftheIVofallfourspecieswas
equalto300foreachzone.TosummarizetheIVvariationbetweenzones
ofandspsiteseciesandtodominanceconsiderhalleterogeneitspeciesya(tIthe)bsameasedtime,onwtheedfevolloelopwingedanequation,index
HSDadaptedfromthereciprocalindexofSimpson(Hill1973):
1)(300300−×ISDH=iq=1(IVi×(IVi−1))(3.3)
whereIViistheimportancevalueofthespeciesiandqthenumberofspecies.
Iiscomparabletoaspeciesdiversityindexofsecondorderofentropy
beSDHcauseitwouldincreasewithahighernumberofspeciesbutgivemore
wtheeighrtelativtoetheimpeveortancennessoinfsIVpe.ciesTheinindextermofwasforestusedbestructurecauseitinsteadincorpoofratesthe
nofunmubmerbofersofindividuals.individuals,Thubsutdalsoominanceofcspacehangeowccupiedouldbynoteoachnlyspbeeacies.question
vestigatetNon-parametricherelationshipsSpearmanbetwReenthecorrelationphysical-canalyseshemicalwerefactorsconductedtincludingoin-
thenutrientavailabilityindicatorsandthedifferentforeststructurevariables
(excludingISDH).Afactoranalysiswithprincipalcomponentextractionand
nvuatrienrimaxtrvaotationriables.wasScorescarriedoftheoutttwoogroupprincipallinearfactorscorrelationswereausedmongastheexplana-four
thetoryvvaariationriablesfoforthetheIfSDHurther,ageneralanalyses.linearToinvmodelestigateatnalysisheufactorssingTypeinfluencingVde-
compositionwasused,followedbyageneralregressionmodelanalysiswith
backwardstepwiseselectionofvariables.Thefollowingcontinuousindepen-
dentvariableswereconsideredforbothanalyses:meanrecordedsalinity,
trienmaximtuusemtandidalrlevesorptionel,meanpH,efficiencies.slope,Theandqtheualitativtwoesvynariabletheticoffactorsdestructionofnu-
wasalsousedascategoricalfactorintheseanalyses.TheISDHandslope

74

3CHAPTER

valuesweresquareroot(arcsin(x/4)+constant)transformedtogetcloserto
.ynormalit

esultsR3.4

3.4.1Forestmeasurements
ThecanopyheightandDBHatallsitesshowedgeneralincreasesfromthe
fringezonetothehinterland(Fig.3.2).However,theresultingstructural
zonationpatternsamongsitesweredifferent.Forexample,treesatsiteC
weredwarfovera60mwideareafollowedbya15mtallforestwhereas
treesatsiteAwererelativelyhomogeneousacrosstheforest.Anothermain
differenceamongthesiteswasseeninthespecieszonationpattern(Fig.
3.2).Asageneralpattern,R.mangledominatedthefringezoneofallsites.
ThebasinzoneswereoccupiedmainlybyA.germinansinsitesB,Cand
D.ThesesitesweredominatedbyL.racemosainthehinterlandzones.In
contrast,R.manglewasdominantinallzonesatsiteA.
Speciesdominanceheterogeneity(ISDH)variedsignificantlyamongzones
andsites(Fig.3.2).SitesCandDweremoreheterogeneousthansitesA
andB.ThepuredominanceofR.mangleinthezones1and2ofsiteAwas
notfoundinotherpartsoftheislandexceptinthefringeandthefirstdwarf
zoneofsiteC.Also,theonlypureareaofA.germinanswasfoundonsite
B.Anherbaceousspecies,Batismaritima,wasfoundonbothsidesofthe
islandandindifferentzonetypes.

3.4.2Physical-chemicalmeasurements
maximTheusmalinitsyalinitieswaswererelativmelyeasuredinhomogeneousA.atgerminanssiteAbasins(Tableatsite3.1).B,CTahend
vD.aluesTheofsminimiteAumandvaBlueswewreererneutralecordedattinhehinfringeterlandandzhinonesofterland,allsites.andsThelighptlyH
lowerinthecentralzonesprobablylinkedtoanoxicconditions(Table3.1).
ForsitesCandD,pHvaluesweregenerallyincreasingtowardthehinterland
zones.InsitesAandB,thefirstandlastzoneshadhigherslopevalues
hadicomparedngteneralothethecensametralpzones,atternwhicwhereashweretheatoplmostographycompletelywasmflat.orevSitearyingD
atsiteC(Table3.1).
Nitrogenuseefficiency(NUE−N)variedslightly,leadingtofewsig-
onificanccurredtinsdifferencesiteC,pamongarticularlyzonesintheanddwsitesarfz(Fig.ones.3.3).PhosphorusTheusehighestvefficiencyalues

3.4.TRESULS75

Figure3.2:Mangroveforeststructureofthedifferentsites(A−Drespectively).Zones
arenamedaccordingtopositionandtypeofstructure(*indicatepresenceofBatismar-
itimaontheground).ISDHvaluesindicatethecorrespondingIndexofspeciesdominance
heterogeneity.Piechartsshowthespeciescomposition.Linegraphsshowtreesmean
DBH,meancanopyheightperzone(errorbarsrepresentstandarddeviations),andprofile
ofmaximumheightoftidallevelatequinoxesspringhightide(incmaboveground).

76

Figure

.23

ued.intcon

CHAPTER3

RESUL3.4.ST

77

Tasalinitbley±3.1:SD,Pheysicoxpressedchemicalinpmracticaleasuremensalinittsryesultsunitsp(erpsu);sitesmandeanzpHones.±(VSD;aluesS=areslopmeeanof
zoneground,Zonesin%.)123456
SiteAppsuH37.96.6±±0.20.4636.9.4±±0.051.537.76.4±±0.12.0737.0.0±±0.43.3
S1.20.1-0.061.8
SiteBppsuH6.738.9±±0.60.96.845.1±±0.38646.0.5±±0.110.6639.6.9±±0.210.9
S1.950.03-0.120.7
SiteCppsuH6.640.5±±0.12.7644.9.6±±0.32.8646.1.7±±0.25.0639.7.5±±0.15.1642.0.8±±0.39.0722.8.1±±0.19.1
S0.250.330.170.1-0.21.4
SiteDppsuH6.540.6±±0.26.3644.7.9±±0.16.5721.6.3±±0.25.1
2.07.700.9S

(NUE−P)wasalsoveryhighinthesedwarfzonesofsiteC.Forallsites,
NUE−NandNUE−Pweregenerallyhigherinzone1anddecreasedgo-
inglandward.TherewerenosignificantdifferencesinNresorptionefficiency
(RE−N)amongthesites(Fig.3.4).SimilartopatternsofNUE−N
andNUE−P,Presorptionefficiency(RE−P)washighestinthedwarf
zonesandwithlowestvaluesintheinlandzonesatsitesB,CandD(Fig.
3.4).ThevariationsinNUEandREamongthesitesandzonesweresyn-
thesizedwithfactoranalysis(Table3.2),whichconfirmstightcorrelationof
bothNUE−Nand−PandRE−P.
Table3.2:Factorloadingsofnutrientusevariablesfactoranalysiswithprincipalcom-
ponentextractionmethodandvarimaxrotation(markedloadingsare>0.70).
Factor1Factor2
NUENUE−−PN0.9580.738-0.0980.490
0.9780.023NRE−0.1530.901PRE−Eigenvalues2.2731.230
Prop.ofTotalVar.0.5680.307

3.4.3Indicatorsofdestructionlevel
IndistributionthebeltofDtransectsBHofofttreeshe>hin20terlandcmzonesdecreasedofsitescontAinanduouslyB,thegoingtofrequencyward

78

3CHAPTER

Figurephosphorus3.3:(Rfilledhbizophorars)ainmgramsangleoleafcvesreatednutrienleatveusebeiomass/gfficiencyofofNnoritrogenP((errorwhitebarsbars)=SandE).
Thex-axisrepresentsthedifferentsitesandzonenumbers.Lettersshowthehomogeneous
groups(PosthocanalysisSheffe´test).

Figure3.4:Rhizophoramangleleavesresorptionefficiencyofnitrogen(whitebars)and
sitesphosphorusandzone(fillednubmbars)ers.inpeLettersrcenstagehowt(errorhebars=homogeneousSE).Tgheroupsx-axis(PosthorepresenctstheanalysisdifferenSheffte´
test).

RESUL3.4.ST

79

biggersizeclasses(Fig.3.5).HoweverinthehinterlandzonesofsitesC
andD,thedistributionincludedafewoutlierswithDBH>55cm.The
conlargesttinuoustreesindecrease,sitesAprovandidedBehadvidenceDBHthat<t37hecm,treeswinhicthhosetsitesogetherhadwithgrowtnhe
ofDBHsubsequenoftstoitesCaHurricanendDwasHattie.disconOnttinheuouscontberarytw,teenhe45cmfrequencyand55cm.distributionThe
fewlargetreesattheendofthedistributionsurvivedHattieandwerethus
of>41dwarfyrold.treeswereAdditionally>41,yr.inzones1and2atsiteC,morethan61percent

Figure3.5:TreesDBHclassdistribution(onlyDBH>20cm)inthelastzoneofeach
sites(SiteA:blackfilled;SiteB:white;SiteC:horizontalstripes;andSiteD:vertical
s).estrip

AlltheseobservationssuggestthatHattiecausedcompletedestruction
ofthemangroveforestatsitesAandB,whereasremnantsoftheoriginal
forestsstillexistedacrosstheforestsatsitesCandD,indicatingincomplete
destruction.Thisinformationwasusedtogenerateadummyvariableoftwo
destructionlevels:forsitesAandB,0=completedestructionduringHattie,
forsitesCandD,1=incompletedestructionduringHattie.

80

CHAPTER3

analysestatisticalS3.4.4TheSpearmancorrelationanalysesshowedthattheimportancevalues
(IV)ofR.manglewerenegativelycorrelatedtothepHandpositivelyto
NUEcorrelated−N,toNUENUE−−PN,andNUERE−−PP.andIVREsof−A.Pbutpgerminansositivewlyeretothenegativmeaxi-ly
mumaximmrumecordedtidalslevalinitely.andIVpsoositivfL.elyractotemosahewslopereeandnegativpH.elyIVsocorrelatedfC.ertoetctushe
weNUEre−negativN,elyNUE−correlatedPandtotREhe−Pmaximbutumptoidalsitivellyevel,tothethesmeanlopeandsalinitpy,H
(SpNUEe−armanPcandREorrelation−Pwtest,ereP<negativ0.05elyinallcorrelatedcases).withDBHAdditionallyandtreeNUEheigh−Nt,
andpositivelycorrelatedwithtreedensity(Spearmancorrelationtest,p
<0.01inallcases).
Thegenerallinearmodelconstructedwithallthevariablesdidnotex-
plainsignificantlyvariationsoftheindexofspeciesdominanceheterogeneity
(ISDH)(testwholeGLMmodelvs.residual,MultipleR=0.812,F=2.483,
p=0.102).However,withinthismodel,thedestructionindicatordummy
vaF=5.158,riablehadap=0.049).significanNoneteofffecttheonothetherIvSDaHriables(GLM(i.e.,univsalinitariatey,tidalsignificance;level,
pH,slope,andnutrientavailabilityfactors)hadasignificantinfluenceon
theISDH.Onthecontrary,thegeneralregressionmodelconstructedwitha
backwardstepwiseselectionandselectingthedestructionindicatordummy
variableandthefirstfactorofnutrientavailabilityindicator(Table3.3),ex-
plainedasignificantproportionofthevarianceofISDH(testwholeGRM
modelvs.residual,MultipleR=0.718,F=7.450,p=0.006).

Table3.3:Univariatetestsofsignificanceandsummaryofparametersofthegeneral
regressionmodelwithbackwardstepwiseselectionofexplanatoryvariablesontheISDH
variations(markedfactorsaresignificantatp<0.05).
SSdfMSFpParameterStdError
Intercept0.73510.7351.5150.239-0.2080.169
MaximumTidalLevelPooled0
MeanSalinityPooled0
MeanpHPooled0
SlopePooled0
Factor1Nutrients3.93413.9348.1130.013-0.5590.196
Factor2NutrientsPooled0
Destruction4.20314.2038.6670.011-0.5020.170
0.48514.7896Error

DISCUSSION3.5.

iscussionD3.5

81

Forestmeasurementsresultsshowedclearlydifferenthorizontalzonation
patternsatCalabashCay.Firstly,thestructuralzonationpatternindicated
byDBH,treeheight,andforestdensitydifferedateachsite.Correlation
analysessuggestedthatthesepatternswererelatedtoNuseefficiency,P
useefficiency,andPresorptionefficiency.AccordingtothefindingsofFeller
(1995)andFelleretal.(2002,2003),thesevalueswereindicativeofnutrient
availability.Thespecieszonationpatternswerealsoclearlydifferentfrom
sitestosites.Rhizophoramanglewasmoredominantinlownutrientavail-
abilityandacidicareas.Similarly,Avicenniagerminansdominatedmorein
highsalinityandhighnutrientavailabilityareas,andLagunculariaracemosa
inhigherintertidal,steeperandmoreneutraltobasiczones.Therestriction
ofC.erectusonlyinthehinterlandzonesdemonstratedtheadaptationof
thisspeciestorarelyinundatedareas(Tomlinson1986).Thesetrendsfit
wellwithotherstudiesintheCaribbean.Theysuggestedthatdifferencesin
propagulesdispersal(Rabinovitz1978,Jim´enez&Sauter1991),geomorpho-
logicalfactors(Thom1967),aswellasphysiologicaladaptationstogradients
acrosstheintertidalzone(Macnae1968,ore.g.,McKee1995a,McKee1995b)
wereinteractingfactorsdrivingzonationpatternsinCalabashCay.
AccordingtoStoddart(1963),thevegetationofinnerpartsofTurneffe
waslessdamagedbyHurricaneHattiethanthevegetationofoutersites.
Bothproxiesusedtoindicatedestructionlevelsinthisstudysupportedthis
observation41yearslater:thedistributionsofalltreeswithdbh>20cm
showedthatnooldtrees(rightsideoutliers)existedintheseawardsitesA
andB,butsomebighollow,remnanttreesolderthan41yrwerefoundin
theinnersitesCandD.Secondly,thenumberofscarsindicatingtheageof
dwarftreesalsoshowedincompletedestructioninashelteredpositiononthe
westsideofCalabash.Thepercentofdwarftreesolderthan41yrsuggested
thatthedwarfmangrovesofCalabashCaywerethetreesthatbestresisted
HurricaneHattie.Thesefindingswereconsistentwithotherobservations
fromtheCaribbean(Smithetal.1994,Lugo1997)andAustralia(Bardsley
1984).DuringHattie,thehighwaterlevelduetothestormsurgewouldhave
coveredthesesmallindividuals,preventingthemfrombeingblowndownby
strongwinds.Ifthesetreeshadbeenexposedtowaveaction,itislikelythat
theywouldhavebeenkilledasthefringingzonesofmosthurricane-destroyed
sites(e.g.Imbert2002).Thus,thesurvivabilityofthedwarftreesmakes
thempotentialsourcesofpropagulesforre-colonizationprocessesafterlarge
rturbations.epTheindexofspeciesdominanceheterogeneity(ISDH)showeddifferences
amongzonesandsites.Oneofthegeneraltrendsforeachsitewasthatthe

82

3CHAPTER

hinterlandzonehadthemaximumISDHvalue.Thistrendresultedfrom
thehigherpossibilityoffindingpureR.mangleorA.germinansstandsin
thelowerintertidalzonesthaninthehinterlandwhereL.racemosawasfre-
quentlymixedwithC.erectus.Besidetheseintra-sitevariations,theISDH
attheeastsideoftheisland(i.e.,theexposedpartthatsustainedthemost
damagefromHattie)wasmorehomogeneousthanthewestside(sheltered
part).OurstatisticalresultswiththeGLMmodelshowedtheimportance
ofthedestructionindicatortotheseforestheterogeneitydifferences.The
GRMmodelalsoincludedthefactorsindicatingnutrientavailability,which
couldberelatedtotwoaspectsofforestheterogeneity.First,Puseefficiency
andresorptionefficiencyincreasedfromthefringetotheupperzones,as
didtheISDH.Second,NuseefficiencywashighestatsiteswhereR.man-
gledominated,leadingtoalowISDH.Theserelationshipssupportedthe
hypothesisthatnutrientavailabilitywasimportanttospeciesdominance.
Yet,onlythemodelincludingboththenutrientavailabilityandthede-
structionindicatorexplainedthedifferencesofforestheterogeneitybetween
thetwosidesofCalabash.Theseresultssuggestedthatforestdynamicsat
CalabashwereinfluencedbytheremnantforestthatsurvivedHattie.Apos-
siblescenariowasthatthesurvivingA.germinansandL.racemosaaswell
asthedwarfR.mangletreesonthewesternsideoftheislandservedasa
reservoirforpropagulesonthenearbyareas.Incombinationwithexternal
propagules,thiscouldhaveresultedinarelativelyrapidre-colonizationof
Calabash.Successionmodifiedbythepresenceofthelargertreesmighthave
increasedthespatialpatchinessbycompetitioneffects.Weobservedthat
someR.mangletreesdevelopedasanunderstoryinA.germinansbasins
attheshelteredsites,whichindicatedthatthiscomplexphenomenonwas
notfinishedyet.Rhizophoramanglemayeventuallyout-competethetwo
otherspeciesinsomezones.Incontrast,ontheeasternsites,successionand
out-competitionprobablyhappenedaccordingtothespeciescharacteristics
toabioticconditions.Thiswouldhaveledtomorehomogeneouszoneswith
clearerpartitioningofthespeciesalongtheintertidal.TheexampleofCal-
abashCayhavingthemostheterogeneoussitesontheleastdestroyedsites
exceptforthedwarfareaswascontradictorytowhatBaldwinetal.(2001)
predictedforBiscayneBay(Florida).However,theirobservationsofthe
regenerationofmangrovesiteswereonly7yrafterHurricaneAndrew,and
illustratedtheinfluenceofseveralherbaceousspeciesontheearlyregenera-
tionpathways.TheherbaceousspeciespresentinCalabashCaywerefound
inbothheterogeneousandhomogeneousforest.Ourstudywasconsistentto
Imbert(2002)whofoundthatthenumberofsurvivingtreesinfluencedthe
recoverypathwaysandsuccession.Allthesestudiesshowedthatremnant
vegetationplaysanimportantrolefortherecoveryofmangroveforestafter

LEDGMENTSWCKNOA3.6.

83

estruction.drricaneuhtheTroecoveryconclude,pathtwhisaysastudyndsuggestssuccessionthatinmangrodisturbanceveinforests.tensitycDetailedanqinfluenceuan-
titativregenerationedataonproforestcesseswouldstructureprobvideeforeandstrongerafterevidencedisturbanceofthisandfollorelationship.wing
Hobationwever,regimetheeshouldxamplebofeCalabashconsideredCawyhenminangrotveserpretingshowedhorizonthattalthepzonationertur-
patternsofmangroveforests.

3.6Acknowledgments
ofTheBelizeaforuthorsfacilitwishyatondthankmoraltahessistance,InstituteasofwMellarineasSRachtudieselofBorgattitheUnivandersitAnney
ChamberlainforpreciousfieldworkhelpandHannoHildenbrandtforvaluable
comments.ThisworkwaspartlyfundedbyagrantfromtheNationalScience
Foundation(DEB-9981535)toI.C.Feller.

eferencesR3.7

Baldwin,A.,M.Egnotovich,M.Ford,andW.Platt.2001.Regenerationinfringemangrove
forestsdamagedbyHurricaneAndrew.PlantEcology157:149-162.
Ball,M.C.1980.PatternsofsecondarysuccessioninamangroveforestinsouthernFlorida.
226-235.44:Berlin)(OecologiaBardsley,K.1984.TheeffectsofCycloneKathyonmangrovevegetation.InK.N.Bardsley,
J.D.S.Davie,andC.D.Woodroffe(Eds.).CoastalandtidalwetlandsoftheAus-
tralianmonsoonregion,pp167-185.NorthAustraliaResearchUnit,ANUPress,Darwin,
Australia.Cahoon,D.R.,P.Hensel,J.Rybczyk,K.L.McKee,C.E.Proffitt,andB.C.PEREZ.
2003.MasstreemortalityleadstomangrovepeatcollapseatBayIslands,Hondurasafter
HurricaneMitch.JournalofEcology91:1093-1105.
ChapinIII,F.S.,andK.VanCleve.1989.Approachestostudyingnutrientuptake,use
andlossinplants.InR.W.Pearcy,J.R.Ehleringer,H.A.Mooney,andP.W.Rundel
(Eds).PlantPhysiologicalEcology,volumeFieldMethodsandInstrumentation,pp185-
207.ChapmanandHall,NewYork,USA.
Cintr´on,G.,andY.Schaeffer-Novelli.1984.Methodsforstudyingmangrovestructure.In
SnedakerC.J.andG.S.Snedaker(Eds).Themangroveecosystem:researchmethods,pp
91-113.UNESCOMonographsinOceanographicMethodology,Paris,France.
Davis,J.H.1940.TheecologyandgeologicroleofmangrovesinFlorida.Publicationsof
theCarnegieInstitute.Washington,D.C.,USA.
Duke,N.C.,andZ.S.Pinz´on.1992.AgeingRhizophoraseedlingsfromleafscarnodes:a
techniqueforstudyingrecruitmentandgrowthinmangroveforests.Biotropica24(2a):
173-186.

84

3CHAPTER

Feller,I.C.1995.EffectsofnutrientenrichmentongrowthandherbivoryofdwarfRhizophora
mangleL.(redmangrove).Biotropica28(1):13-22.
Feller,I.C.,D.F.Whigham,J.P.O’Neill,andK.L.McKee.1999.Effectsofnutrient
enrichmentonwithin-standcyclinginamangroveforest.Ecology80(7):2193-2205.
Feller,I.C.,K.L.McKee,D.F.Whigham,andJ.P.O’Neill.2002.Nitrogenvs.phosphorus
limitationacrossanecotonalgradientinamangroveforest.Biogeochemistry62:145-175.
Feller,I.C.,D.F.Whigham,K.L.McKee,andC.E.Lovelock.2003.Nitrogenlimitation
ofgrowthandnutrientdynamicsinadisturbedmangroveforest,IndianRiverLagoon,
405-414.134(3):OecologiaFlorida.Garcia,E.andK.Holtermann1998.CalabashCaye,TurneffeIslandsAtoll,Belize.CARI-
COMP-Caribbeancoralreef,seagrassandmangrovesites.Coastalregionandsmall
islandpapers3.B.Kjerfve.UNESCO,Paris,France.
Hill,A.V.1973.Diversityandevenness:aunifyingnotationanditsconsequences.Journal
237-24961:EcologyofImbert,D.2002.Impactdesouraganssurlastructureetladynamiqueforestiresdansles
mangrovesdesAntilles.BoisetForˆetsdesTropiques273(3):69-78.
Imbert,D.,A.Rousseau,andP.Labb´e.1998.Ouragansetdiversit´ebiologiquesdansles
forˆetstropicales.L’exempledelaGuadeloupe.ActaOecologica19(3):251-262.
Jim´enez,J.A.,andK.Sauter.1991.StructureandDynamicsofMangroveForestsAlonga
FloodingGradient.Estuaries14(1):49-56.
Krauss,K.W.,T.W.Doyle,R.R.Twilley,T.J.SmithIII,K.R.T.Whelan,andJ.K.
Sullivan.2005.WoodyDebrisintheMangroveForestsofSouthFlorida.Biotropica
-15.937(1):Lugo,A.E.1997.Old-GrowthMangroveForestsintheUnitedStates.ConservationBiology
11-2011:Macnae,W.1968.Ageneralaccountofthefaunaandfloraofmangroveswampsandforests
intheIndo-West-Pacificregion.AdvancesinMarineBiology6:73-270.
McKee,K.L.1993.Soilphysicochemicalpatternsandmangrovespeciesdistribution:recip-
rocaleffects?JournalofEcology81:477-487.
McKee,K.L.1995a.MangrovespeciesdistributionandpropagulepredationinBelize:An
exceptiontothedominance-predationhypothesis.Biotropica27(3):334-345.
McKee,K.L.1995b.SeedlingrecruitmentpatternsinaBelizeanmangroveforest:effectsof
establishmentabilityandphysico-chemicalfactors.Oecologia101:448-460.
Rabinovitz,D.1978.Dispersalpropertiesofmangrovepropagules.Biotropica10:47-57.
Roth,L.C.1992.HurricanesandMangroveRegeneration:EffectsofHurricaneJoan,Octo-
ber1988,ontheVegetationofIsladelVenado,Bluefields,Nicaragua.Biotropica24(3):
375-384.Roth,L.C.1997.Implicationsofperiodichurricanedisturbanceforthesustainablemanage-
mentofcaribbeanmangroves.InB.Kjerve,L.D.d.Lacerda,andE.H.S.Diop(Eds).
MangroveecosystemstudiesinLatinAmericaandAfrica.UNESCO&ISME.
Sherman,R.E.,andT.J.FAHEY.2001.HurricaneImpactsonaMangroveForestinthe
DominicanRepublic:DamagePatternsandEarlyRecovery.Biotropica33(3):393-408.
SmithIII,T.J.1987.Seedpredationinrelationtotreedominanceanddistributionin
mangroveforests.Ecology68:266-273.
SmithIII,T.J.1992.ForestStructure.InA.I.Robertson,andD.M.Alongi(Eds).Tropical
MangroveEcosystems,volume41.AmericanGeophysicalUnion,Washington,DC,USA.
SmithIII,T.J.,andN.C.Duke.1987.Physicaldeterminantsofinterestuaryvariationin
mangrovespeciesrichnessaroundthetropicalcoastlineofAustralia.JournalofBiogeog-
9-19.14:yraph

3.7.REFERENCES85

SmithIII,T.J.,M.B.Robblee,H.R.Wanless,andT.W.Doyle.1994.Mangroves,
Hurricanes,andLightningStrikes.Bioscience44:256-262.
Stoddart,D.R.1963.EffectsofHurricaneHattieontheBritishHondurasreefsandcays,
Oct.30-31,1961.AtollResearchBulletin95.
Thom,B.G.1967.Mangroveecologyanddeltaicgeomorphology:Tobasco,Mexico.Journal
301-343.55:EcologyofTomlinson,P.B.1986.Thebotanyofmangroves.CambridgeUniversityPress,Cambridge,
England.Vermeer,D.E.1963.EffectsofhurricaneHattie,1961,onthecaysofBritishHonduras.
ZeitschriftfrGeomorphologie7:332-354.

1961,

on

the

syac

fo

ritishB

Honduras.

86

CHAPTER3

Chapter

4

delingMo

rricaneuh

mangroev

the

ffecte

of

isturbancesd

forest

87

no

yrsitediv

88

4CHAPTER

Modelingtheeffectofhurricane
disturbancesonmangroveforest
yrsitediv

Piou,Cyril12;Berger,Uta1;HannoHildenbrandt13;&
Feller,IlkaC.4
ArticlesubmittedtoJournalofvegetationscienceinFebruary2006

bstractA4.1Questions:Whatarethefactorsinfluencingtreespeciesdiversityofman-
groves,anexampleofspecies-poorsystems?Whataretherespectiveim-
portanceandinteractionsofthesefactors?Istheintermediatedisturbance
hypothesisapplicabletomangroves?
Methods:WeusedthespatiallyexplicitindividualbasedmodelKiWito
investigatetheeffectsonspeciesdiversityofperturbationfrequencyandin-
attensity,individualdifferenlevtel.abioticThecsimonditions,ulatedsandystemincterspeonsideredcifictcomphethreeetitionCsimaribbulatedean
mangrovespecies:Rhizophoramangle,AvicenniagerminansandLaguncu-
tics.lariaracFirstlyemosa,e,ffectsaopplyingnspespciesecies-spdominanceecificogrofdwthifferenandtambioticortalitcyconditionsharacteris-rep-
resentedasnutrientavailabilityandpore-watersalinityweretestedwithtwo
competitionscenarios.Secondly,theeffectofperturbationfrequencyand
intensitywereinvestigatedwithselectedabioticconditions.
Results:Abioticconditionsinfluencedspeciesdominanceandinextreme
casesexcludedsomespecies.Abioticandcompetitionsettingscontrolledthe
successiondynamicsandtheresponseofspeciesdominancetoperturbation
regimes.Aresponseconsistentwiththeintermediatedisturbancehypoth-
esiswasobservedonlywithaconfigurationofplantinteractioninwhich
onespeciesbehavedasapioneersothatsuccessionoccurredbycompetitive
21CenCorrespteroforndingTaropicaluthor:MarineEcyril.piou@zmcology,Ft-bremen.deahrenheitstrasse6,23859Bremen,Germany
and3Evpresenotlutionaryaddress:Studies,h.hildenUnivbersityrandt@rug.nl,ofGroningen,TheoreticalBiologicalBiologyCen,tre,CentreKerklaanfor30,Ecological9751
NetherlandsheTHaren,NN4SmithsonianEnvironmentalResearchCenter,POBox28,Edgewater,MD21037,USA

ODUCTIONINTR4.2.

89

exclusion.Conclusions:Wesuggestthatthesuccessionaldynamicinteractingwith
theintensityandtimingofperturbationswilldeterminewhethermangrove
treediversitywillfollowanintermediatedisturbancehypothesispatternor
not.Formangroves,thissuccessionaldynamicissite-specificdependingon
abioticconditionsandspeciesconfigurations.

Keywords:individual-basedmodeling,KiWimodel,intermedi-
atedisturbancehypothesis,speciesdominance,perturbationregime,
systemsoroecies-psp

dominanceAbbreviations:heterogeneitFOy;N=RNAField=RofelativNeighebnorhoutrienodt;aIvSDaHilabilit=y;indexpsu=ofspeprac-cies
ticalsalinityunits;IDH=Intermediatedisturbancehypothesis;dbh=diam-
theighbreastateter

4.2Introduction
Forseveraldecades,plantecologistshavetriedtounderstandthepro-
cessesimplicatedinspeciesdiversityvariation(e.g.Chustetal.2006see
reviewsbyLoreauetal.2001,Barot&Gignoux2004,Vellend&Geber
2005).Amongtheseprocesses,perturbationshavebeenconsideredofhigh
importanceandledtoanon-goingdebateontheintermediatedisturbance
hypothesis,whichstatesthatspeciesrichnessismaximizedatintermediate
levelsofdisturbances(Connell1978;seereviewsbyMackey&Currie2001,
Sheil&Burslem2003,Sheaetal.2004).Thesituationofmangrovesalong
tropicalcoastlinesfavorspotentialdamagebymajordestructioneventssuch
ashurricanesortropicalstorms(Imbertetal.1998).SmithandDuke(1987)
addressedthequestionofdisturbanceeffectsonmangrovetreediversityin
NorthernAustralia.Theyshowedthattreespeciesrichnessdecreasedwith
increasinghurricanefrequency.However,veryfewstudieshaveanalyzed
changesinmangrovespeciescompositioninrelationtoperturbationregime
(Baldwinetal.2001,Piouetal.2006),andnoneevaluatedtheimplicated
processesbehindtheseeffects.Astraightforwardexplanationforthislack
ofconsiderationisthelownumberoftreespeciesonmangrovesystems.For
example,intheCaribbeanregion,whichisahotspotofhurricaneimpacts,
onlythreetofourtruemangrovespeciesarefound.Thus,studiesontree
speciesdiversityaremostlyseenassuperfluousinthissystem.
However,consideringspeciesdiversityasanexpressionofspeciesrich-
nessandevenness(Kempton1979),systemswithonlythreespeciescould

90

4CHAPTER

varyalsoinspeciesdiversity.Piouetal.(2006)usedanadaptationofthe
Simpson’sReciprocicalindexofspeciesdiversity(Simpson1949,Hill1973)
todeterminethatthedestructionintensityatdifferentmangrovesitesinBe-
lizehadaneffectontheheterogeneityofspeciesdominance.Althoughthe
patternsinBelizedifferedfromothersituations(e.g.Baldwinetal.2001),it
indicatedthattheeffectsoflargedestructiononspeciesdiversityalsoexist
forspecies-poormangrovesystems.
Itisasimportantforspecies-poorsystemsasfortheotherstounder-
standwhichfactorsdrivespeciesdiversityandtoassesstheroleofexternal
perturbationsonthesefactors.Theoverallobjectiveofthepresentstudyis
toevaluatetherespectiveimportanceandinteractionsoffactorsinfluencing
speciesdiversityofspecies-poorsystems.Wehypothesizethatthetypeof
speciesdominancesuccessiondependingontheconfigurationofinterspecific
competitionandabioticconditionswoulddeterminethesystemtypeofre-
sponsetoperturbations,suchashurricanes.Inthismanner,weevaluateif
theintermediatedisturbancehypothesisisapplicabletomangroveforestsand
ifageneralforecastofdiversitychangesformangrovessubjectedtofrequent
disturbancescouldbegenerated.Bymeansofsimulationexperimentswith
anindividual-basedmodel,weinvestigatedtheeffectsonspeciesdiversityof
perturbationfrequency,perturbationintensity,differentabioticconditions,
andinterspecificcompetition.

dsethoM4.3

4.3.1KiWimodelgeneralsettings
Theexperimentswerecarriedoutwiththespatiallyexplicitmangrove
modelKiWi(Berger&Hildenbrandt2000&2003),developedasdynamicli-
brarysoftwarewritteninC++andusinganinterfaceincMicrosoftcVisual
Basic(DLLandexamplesavailablebydemandtoauthors).TheKiWimodel
describesresourcecompetitiononthelevelofindividualsandsimulated
growthofmangrovestandscomposedofthethreemainCaribbeanspecies
(RgapmhizophorodelaFOmangleRMAN,Avic(Chenennia&Twilleygerminans1998)andpLrovidedagunculariathegroracwthemosaform).ulas,The
pnourtantrientttoandnsotetalinithatyteheffectsKiWimmoultipliersdelisandnotraespgapectivmoedelsparameters.inceitdItiescribsim-es
treesindividuallyandisspatiallyexplicit.WeusedBergerandHildenbrandt
(2000)ulatedintinnovationer-individualofthecompFieldeOftitionNeighforsbpaceorhooanddr(FON)esources.approacWeah,wssumedhichtshatim-
theFONdescribedtheareawhereatreeinfluenceditsneighborsandwas

METHODS4.3.

91

influencedbythembysharinglimitingresourcessuchaslightornutrient.
TheFONwasdefinedasacircularintensityfieldthatdecreasedfromthe
center(stemposition)downtotheboundary.Itspecifiedtheintensityof
competitionexertedbyatreeatanypositionwithinitsneighborhood.
Thegrowthofeachindividualtreewascalculatedwiththefollowing
formula(Berger&Hildenbrandt2000):
ddbhG×dbh×(1−dbhdbh××HH)
dt=274+3×b2×dbh−4max×b3×maxdbh2×fs(SALT)×fn(RNA)×fc(FA)
(4.1)where:dbhwasthestemdiameteratbreastheight(cm);Hwasthetree
height(cm);dbhmaxandHmaxweremaximumvaluesofdiameterandheight
foragiventreespecies(Table4.1);G,b2andb3werespecies-specificgrowth
constants(Table4.1)andthe3functionsfweregrowthmultipliers.The
functionfs(SALT)wasthegrowthmultiplierconsideringtheeffectofthe
porewatersalinityongrowth(Chen&Twilley1998):
1fs(SALT)=1+exp(d×(S0.5−S))(4.2)
where:SwasthesalinityattreepositionandS0.5anddwerespeciesspecific
constants(Table4.1).Thefunctionfn(RNA)wasthegrowthmultiplier
consideringtheeffectoftherelativenutrientavailability(RNA)ongrowth
998):1Twilley&(Chenfn(RNA)=c1+c2×RNA+c3×RNA2(4.3)
where:c1,c2andc3werespeciesspecificconstants(Table4.1).Thefunc-
tionfc(FA)wasthegrowthmultiplierconsideringtheFONeffectongrowth
(Berger&Hildenb⎧randt2000):⎫
1⎬⎨k=nfc(FA)=max⎩0;1−ϕ×(AOFONn(x,y)dO)⎭(4.4)
where:ϕwasanarbitrarymaximumvalueofeffectofcompetitionsimulating
resourcesharingcapacity,AwastheFONareaofthefocustreek,nwere
theneighborsofk,OwastheoverlapareaoftheFONareasbelongingto
thefocusandneighbortreen,andtheFONnfunctionwasreturningthe
intensityofcompetitionoftheneighbornateachpointofO.TheFON
functionwasc⎧alculatedas:⎫
⎨⎪⎪1for0≤r<CW/2⎬⎪⎪
FON(r)=⎪exp−|logR(−Frbminh)|×(r−rbh)forrbh≤r≤R⎪
⎩⎪0forr>R⎭⎪
(4.5)

92

4CHAPTER

fromwhere:therbshtemwapstheositionradiusofnof,anthedFsmintemwaatsbthereasthminimeighumtofinn,tensitrwyasofatheFdistanceON
(0.1,Berger&Hildenbrandt2000)attheFONradius(R).ThisFONradius
(R)dependedonthesizeofthetree:
R=a×rbhb(4.6)
tion”where:andaandappebwndixereA,scalingpage107).parametersThev(cf.alueof“settingbindeterminedterspeicificnverselycompteti-he
competitionintensityofindividuals(Berger&Hildenbrandt2003).
ofAnChenovanderallavTwilleyailabilit(y1998)ofarsecruitsRNtotw=as18sconsideredaplings.100mfrom−s2im.yr−1ulation(Chendata&
theTwilleynumb1er998).fromHoewacevhser,pethecies(annRNuali)nwuasmberpropofortionallyrecruitsvsetariedarccordingandomlytoandthe
occurrenceofmaturetrees(height>5m)ofeachspecies:
RNi=int(rnd1×pi×RNtot+rnd2×RNtot)(4.7)
where:uniformrrnd1andomwansaumberuniformbetwreenandom0.1anndum0.3;berandbetpwieenthep0.5ropaondrtion1.5;ofrndmature2a
oftreesvaofriationspeciesoftiheoverrandomthetnotalumnbuermibnertheoffirstmaturetermtreesoftheinbtherackplot.et(rnThed1r)wangeas
chosentodescribeanaturalfluctuationintheavailabilityofrecruitsper
(sprndecies.2)proThevidedrangeanoofvaccasionalriationoreappftehearancerandomofannumbalreadyerinethexcludedsecondspetermcies.
Theserecruitswereinstalledrandomlyonthesimulationarea,butwere
removinstallationedifthex,y)FOwaNsinthigherensittyhan(sumtheofspFOecies-spN(x,yecific)ofallthresholdtrees(atFAthep).ointThisof
maxthresholdwassettoFAmax=0.5forR.mangle(Berger&Hildenbrandt2000)
ainndastolerancesumeofdassFeedlingsAmaxof=0.0L.rforactheemosatwoandotherA.speciesgerminanstosim(Ballulate1980,thesMcKeehade
gro1993).wth-rateMortalitdepyoendenftasindividualdescribtreesedbynotBergerduetoandexternalHildenbperandtrturbations(2000).was

4.3.2Settingsofinterspecificcompetitionparameters
Thegrowthparameters(dbh,H,G,bandb,Eq.4.1,Table4.1)
andeffectsofsalinityandnutrienmaxtavamaxilability2(fs3andfn,Eq4.2&4.3)
createdspecies-specificdifferencesingrowthresponseatthestandlevel.For
additionalvariationininterspecificcompetition,weconsideredtwowaysof
simeredanulatingequalspatialeffectcompofeneightitionbatoringthecompindividualetitionlfevorel.treesTheoffirsttheonesamecsonsid-ize

METHODS4.3.

350016248.04

0.172

93

300024371.58

0.447

Table4.1:Growthandspatialcompetitionspecies-specificparametersusedintheKiWi
model.Sources:(1)ChenandTwilley1998,(2)seeappendixA.
ParameterDescription(Equation,units)A.germinansL.racemosa
dbhmaxMaximumdiameteratbreastheight14080
cm)4.1,(Eq.HmaxMaximumheight(Eq.4.1,cm)35003000
GGrowthconstant(Eq.4.1)162243
b2Constantinheighttodbhrelation-48.0471.58
4.1)(Eq.shipb3Constantinheighttodbhrelation-0.1720.447
4.1)(Eq.shipdSalinityeffectconstant(Eq.4.2)-0.18-0.20
S0.5Salinityeffectconstant72.065.0
psu)4.2,(Eq.c1RNAeffectconstant(Eq.4.3)-0.50-1.00
c2RNAeffectconstant(Eq.4.3)2.884.42
c3RNAeffectconstant(Eq.4.3)-1.66-2.50
aFONradiusscalingparameterfor13.717.0
heterospecificcompetitionparame-
4.7)(Eq.terizationbFONradiusscalingparameterfor0.720.95
heterospecificcompetitionparame-
4.7)(Eq.terization

0.18-72.0

0.50-.8821.66-13.7

0.72

-0.2065.0

-1.00.424-2.5017.0

0.95

mangleR.100

400026777.26

0.396

0.25-58.0

.000.3310.72-18.0

0.83

(1)

(1)(1)(1)

(1)

(1)1)(

(1)1)((1)2)(

(2)

94

4CHAPTER

forthethreespecies.Thus,theyhadthesameresourcesharingtolerance
(ϕ=2.000,Berger&Hildenbrandt2000)andidenticalaandbparameters
(11.0,0.64,respectively,cf.appendixA,Fig.4.6).Sincetheinterspecific
competitioninthisparameterizationwasonlythroughtherelativegrowth
rateofeachspecies,itishereafterreferredtoasspecieshomogeneousspa-
tialcompetition.Thesecondparameterizationconsideredthateachspecies
hadspatiallyspecificcompetitionstrength.Particularly,L.racemosa,which
wasdescribedasheliophilic(Wadsworth1959,Ball1980,Roth1992)was
settohavealowersharingtolerance(ϕ=2.222,assumingthatthemaxi-
mumFAwas10%lowerthantheotherspecies,i.e.maximumFA=0.45).
Additionally,species-specificaandbparameters(Table4.1)wereusedto
describethecanopyandrootsystemdifferencesforthethreespecies.These
parametersweretuned(AppendixA,Fig4.6)toreproducefielddataof
monospecificstandsoftreesizevs.densityrelationshipsfromBelizeanoff-
shoremangroves,andtosetL.racemosaaslesscompetitivethanthetwo
otherspecies.ThislowercompetitioncapacityofL.racemosawasuntil
diameteratbreastheight(dbh)<80cm;whiletheaandbvaluesalsode-
terminedthatA.germinanswasmorecompetitivethanR.mangleuntil
dbh>20cm.Thissecondparameterizationishereafterreferredtoasspecies
etition.comppatialsheterogeneous

4.3.3Effectsofabioticconditions
Ourfirstexercisewassettoanalyzetheeffectofabioticconditionson
speciesdiversitywithoutanyperturbations.Wealsoinvestigatedtheeffect
ofinterspecificcompetitiononspeciesdominancesuccessioninthisexercise.
Fivesalinities(0,20,40,50and60psu)andfourrelativenutrientavailabili-
ties(RNA)(100%,80%,60%and40%)wereconsidered.Tenreplicatesofall
possiblesalinity/RNAscenariosonthetwocompetitionparameterizations
weresimulatedona6000m2plotsandduring1000years.
Thenumberoftreesandbasalareaperspecieswereusedtocalculate
relativeabundanceanddominanceforeachtimestepandtransformedinto
importancevalues(IV)accordingtoCintr´onandNovelli(1984):
j=1Densjj=1BAj
IVi=100q×Densi+100q×BAi(4.8)
where:IVi,BAiandDensiweretheimportancevalues,basalareaand
densityoftreesofthespeciesiandqwasthenumberofspecies.Asameasure
ofspeciesdiversity,weusedtheindexofspeciesdominanceheterogeneity
(ISDH)fromPiouetal.(2006).Itwasadaptedfromthereciprocicalindex

METHODS4.3.

95

ofSimpson(Hill1973)andcomputedasfollows:
qqISDH=i=1qIVi×(i=1IVi−1)(4.9)
i=1(IVi×(IVi−1))
andThiswindexouldbegivindicatedenvaluerelativofe0spifneciesotreesdominancecouldigronwouratallthree-spbecauseeciesosfhystemarsh
1sabioticpeciessettings.presentIfontreesthecouldplot)grotow,3t(hetheISD3Hspwoeciesuldrtakeepresenvatlueingfromeach1(33%only
ofimportanceontheplot).Itwasnotmathematicallyindependentfrom
speciesrichness;therefore,wedecidednottousetheterm“evenness”to
avoidconfusionwithitscalculationsincommunitystudies(Smith&Wilson
index1996).couldHowever,indicateithroughfdifferenthetvatriationhree-spofeciesrelativesconfigurationspeciesofdominanceourstystemhis
wesalinitrey/relativRNeAlyriceffecthoronnotspieciesntdivermersitofys,ptheeciesmedian,diversit1sty.aAnds3rdqindicatorsuartilesof
ofISDHforeachscenariooverthelast400yrofsimulationswerecalculated.

4.3.4Effectsofperturbationregimes
Thesecondexercisewassettoanalyzetheeffectsofperturbationregimes
onspeciesdiversity.Massivekillingevents,whichsimulatedmortalityin-
ducedbyatropicalstormorhurricane,wereappliedatdifferentmortality
rates(intensity)andfrequencies.Becausethereisinconsistencyintheliter-
atureonthewayauthorsdescribedstormresistancecapacityaccordingto
speciesortreesize(e.g.,Vermeer1963,Stoddart1963,Bardsley1984,Roth
1992,Smithetal.1994,Roth1997,Imbertetal.1998,Sherman&Fahey
2001,Baldwinetal.2001,Imbert2002),wecouldnotconsideredthemortal-
ityeventsrelatedtosizeorspeciesinoursimulations.Theappliedintensities
wereprobabilitiesof30%,50%,70%,90%and99%ofmortalityforeachtree
attheeventtimes.Theperturbationfrequencies(1/100yr,1/80yr,1/60yr,
1/40yr,1/20yrand1/10yr)determinedtheexactnumberofyearsbetween
twoevents.
Toachieveastabilizedsystemintermofnumberoftrees,weexcluded
thefirst400simulationyears.Perturbationswereappliedonlyonthefollow-
ing400yrsothatthetotalsimulatedtimewas800yr.Theroleofabiotic
conditionsonsystemresponsetoperturbationwasconsideredbyselecting
scenariosfromtheresultsofthepreviousexercise.Benign(salinity0psu
and100%RNA)andmedium(salinity50psuand80%RNA)conditions
wereanalyzedbutextremeoneswerenotconsideredbecausetheyresulted
inasystemoverwhelmedbyonespecies.Tenreplicatesweresimulatedfor

96

4CHAPTER

eachabioticscenario(benignormedium),consideringeachcompetitionpa-
rameterization(homogeneousorheterogeneousspatialcompetition)andall
mortalityrate/perturbationfrequencyscenarios.Similartothepreviousex-
ercise,themedianofISDHwascalculatedoverthelast400yrforallcases.To
analyzethesignificanceofperturbationintensitywithselectedperturbation
frequency,Kruskal-Wallisnon-parametricanalysisofvariance(ANOVA)by
rankswereappliedonthelastISDHvaluesofeachsimulation.Toanalyzethe
effectofperturbationfrequencywithselectedperturbationintensity,identi-
calnon-parametricANOVA’sweredoneconsideringalltheISDHvaluesof
thesimulatedperturbationtime.Mann-WhitneyUtestswereusedtoas-
sesssignificantdifferencesofextremesandintermediateISDHvaluesinorder
tovalidatedisturbanceeffectpatternssuchasU-shaped,linearincreaseor
decrease,irregularorbell-shaped.

4.4esultsR

4.4.1Firstexercise:effectsofabioticconditions
Extremelylowrelativenutrientavailabilities(40%RNA)andextremely
highsalinities(60psu)decreasedsignificantlytheindexofspeciesdomi-
nanceheterogeneity(ISDH)forbothspatialcompetitionparameterizations
(Fig.4.1).Theseextremeabioticconditionscausedspeciesexclusionthrough
theparameterizationofR.mangleandA.germinansgrowthcharacteristics
tobenon-adaptedtohighsalinitiesandlownutrientavailabilitiesrespec-
tively.Attheworstcondition(salinity60psuand40%RNA),nospecies
grewatall,resultinginISDH=0.Consideringtherestoftheabioticsce-
narios,highestISDHvaluesinbothspatialcompetitionparameterizations
werefoundatintermediatelevelsofsalinityandRNA.ThemedianISDH
valuesoverthelast400yrwererelativelysimilarbetweenthetwospatial
competitionparameterizations.However,ISDHvaluesandspeciesimpor-
tancevariedmoreimportantlyduringthefirst400yrforallabioticscenarios.
Foramediumcaseofabioticscenario(salinity50psuand80%RNA),vari-
ationsofspeciesimportancevaluesshowedacyclingofspeciesdominance
(Fig.4.2).Thespeciesheterogeneousspatialcompetitionparameterization
createdaquicksuccessionfromL.racemosatoA.germinans(Fig.4.2b)
duringthefirst50yrofsimulations.Withhomogeneousspatialcompetition,
thedominanceofL.racemosavariedbutstayedalwayshigherthanthetwo
otherspecies(Fig.4.2a).Identically,forbenignabioticscenarios,thespecies
heterogeneousspatialcompetitioncreatedspeciessuccession,whiletheho-
mogeneousspatialcompetitionshowedimportancevaluesvariationwithout

STRESUL4.4.

shiftofspeciesdominating.

97

4.4.2Secondexercise:effectsofperturbationregimes
cenFortratedtheonlyanalysisontheofmediumphenomenaabioticexplainingscenario.therMespassivonseepmortalitattern,ywaeclteredon-
the4.3a)tempdidoralnotdmoynamicdifytofheISDHgeneral(Fig.trend4.3).ofThevalowriationpeofsrturbationpeciesrimpegimeortance(Fig.
valuesandISDHcomparedtonon-disturbeddynamics(Fig.4.2b).Withan
intermediateperturbationregime(morefrequentandstrongerdisturbances,
Fig.4.3bcomparedto4.3a)L.racemosagainedinimportancealthoughstill
lessimportantthanthetwootherspecies.Thisreducedthedifferenceinrel-
ativeimportanceofthethreespeciesandthusledtoanoverallhigherISDH
pethanrturbationwiththerloegimewpe(Fig.rturbation4.3c)rswitcegime.hedTthehemostsystemfrequenquictklyandfromdA.estructivger-e
eachminanstodisturbanceL.rachademosaaneffectdominance.ofkeepingAtL.thisracleveemosalofaspthemerturbationostimpregime,ortant
atspbecieseoginningnthe(firstplot.10yrs)Thisofsimcorrespoulations,ndstoastheifoL.rariginalcemosaswuccessionasthesituationpioneer

Figurediamond=100%,4.1:ISDtHvariangle=80%,riationssaccordingquare=60%,tosalinitcyaross=40%)ndrelativcenuonditionstrientfaorvtheailabilittwoy(compRNAe-:
titionparameterizations.Pointsaremedianvaluesofreplicatesimulations,errorbars
representfirstandthirdquartiles.

98

CHAPTER4Figure4.2:Dynamicalvariationsofthetwocompetitionparameterizationswithselected
abioticscenarios(medium=Salinity50psuandRNA80%)inspeciesrelativeimportance
andISDH(Blackline=medianISDH,darkgrey=medianimportancevalues(IV)of
Avicenniagerminans,grey=medianIVofLagunculariaracemosa,lightgrey=median
IVofRhizophoramangle,dashlines=respectivefirstandthirdquartiles)

speciesofthesystem.However,thischangeofdominancedidnotmodify
significantlytheISDHvaluescomparedtoloworabsentperturbationsbe-
causetheratiosofspeciesimportancevalueswereconserved.Inthiscase,
thehighfrequenciesstabilizedtheseratiosandISDHvaluesovertime.
Variationsinperturbationregimesalwayshadaneffectonthespecies
dominanceheterogeneityofthesimulatedstands(Fig.4.4).However,the
overallpatternsofsimulationresultsdependedonthedifferentcompetition
parameterization.Thespecieshomogeneousspatialcompetitionparameter-
ization(Fig.4.4a)showedlowerISDHvaluesatintermediateperturbation
regimesthanatlowerandhigherperturbationfrequenciesandintensities.
ThisU-shapedcurvepatternwasclearlyobservablefortheinfluenceoffre-

4.4.TRESULS99

Figure4.3:DynamicalvariationsinspeciesrelativeimportanceandISDHforthehet-
erospecificcompetitionparameterizationandmediumcaseofabioticscenario(salinity
talit50psu,y;b:80%fRNrequency=A),andp1/60yr,erturbationintensitry=egimes(a:70%mortalitfy;requency=c:frequency=1/100yr,intensit1/10yr,y=intensit30%mor-y=
99%mortality).(Blackline=medianISDH,darkgrey=medianimportancevalues(IV)
ofAvicenniagerminans,grey=medianIVofLagunculariaracemosa,lightgrey=median
IVofRhizophoramangle,dashlines=respectivefirstandthirdquartile)

100

CHAPTER4Figure4.4:MedianISDHvariationsaccordingtoperturbationfrequencyandintensity
forthetwocompetitionparameterizations(aandb)withmediumabioticscenario(Salinity
50psuand80%RNA).Dashedlinesrepresentselectedpatternillustrationforfigure4.5.

quencyregimewithaselectedperturbationintensity(Fig.4.5a),although
thevaluesshowedhighvariationamongsimulations(1stand3rdquartile
variations).Thespeciesheterogeneousspatialcompetitionparameterization
resultedinanoverallincreaseinISDHvalueswithincreasingdisturbance
regimesuntilnon-extremeintensityandfrequency,followedthenbyasmall
decrease(Fig.4.4b).Thus,thistrendledtoanoverallbell-shapedpat-

4.4.TRESULS101

Figure4.5:MedianISDHvariationsfollowingperturbationfrequencyforthetwocom-
peabiotictitionscenario(parameterizationsSalinity50(aandandRNb)Awith80)(N=30selectedformortaliteachpyoiinntt,bensitoyxesr(70%)epresenandtfirstmediumand
thirdquartiles,errorbarsrepresentminimumandmaximum).

tern,whichwasalsomorevisiblefortheinfluenceoffrequencyregimewith
selectedperturbationintensity(Fig.4.5b).
Figure4.5showstwoexamplesofpossibleISDHvariationpatternfor
mediumabioticconditions.Thesetypesofpatternwereanalyzedforbenign
andmediumabioticconditionsandforbothspatialcompetitionscenarios.
Overall,wefoundacleardifferenceofpatternsbetweenthetwospatialcom-
petitionparameterizations.Thehomogeneousspatialcompetitionparame-
terizationledtosomecasesofU-shapedpatternswhiletheheterogeneous
spatialcompetitiononthecontraryshowedbell-shapedpatterns.Notall
perturbationregimesledtotheseU-orbell-shapedpatterns:someledto

102

4CHAPTER

linearincreasingordecreasingpatterns,ornon-significantorirregularpat-
terns.Thesetrendswererespectedwiththetwoselectedabioticconditions
(seeAppendixB,page110fordetailedresults).

iscussionD4.5

thepThisrocessesstudywhicillustratedhcouldthatevexplainenforvaspriationsecies-poinorspseciesystems,divtheersityaredynamicsdivaersend
andinterconnected.Theinterplayofabioticconditionsandinterspecific
thecomppetitionerturbationprorducesegime,asaetofsystempotentwillialvfollowegetationadparticularynamics.traDepjectoryendingofthison
set,andthuseventuallyshowornottheexpectedintermediatedisturbance
hypothesispattern.
speciesOurosfsimpeulationscies-spinecifictegratetheparameterizationactualknoofgrowledgewth,onaCaribbdaptationseantomangroabioticve
conditions,settlementandspatialcompetitivestrength.Theresultsofthe
firstexerciseillustratethatabioticconditionsinfluencethedominancedistri-
butionofthesespecies,uptoeventuallyexcludingoneormorespecies.On
theabilitcyonfavtrary,orableinttoermediateallthreespconditionseciesofleadpotorewahigherterscoaliniteyaxistence.ndnuThetrientavsettingail-
ofspecies-specificgrowthparametersofourmodelisthusabletore-create
thethatdivwereersitnotyofcsponsideredeciesintdominancehisstudyo,bservsucehdaisnttheidalrCaribbegime,ean.tempeOtherrature,fsactorsoil
haphveysico-csimilarheemicalffectsproponspertiesecies(e.g.,richnessredoxandpotendtialominanceorisulfidenmconangrotenvets),systemscould
(Ball1980,McKee1993).
Theresultsofthefirstexercisealsoshowthatchangesinthecharacter-
isticsofspecies-specificspatialcompetitiondonotmodifysignificantlythe
cohvangeerallmintheeasureofsettingsspfeciesordivspatialersitcy.ompHoewevtitioner,atadrasticallygivenaaltersbioticthectondition,emporala
variationsofrelativespeciesdominance.Ourparameterizationofhomoge-
neousdominatingspatialalltcomphetimeetitionblecauseeadsotofiatscfasteryclinggrowdynamicthrate.butThewithhypL.orathesiscbemosae-
buthindnotthisinaspatiallyparameterizationexplicitiswthatay.spForeciesexample,differintreestheirofrtheesourcesameusesizewcapacitouldy
havethesamespatialextentofresourceusedisregardingtheirspecies.In
contrast,theheterogeneousspatialcompetitionparameterizationisderived
fromspatiallythehypdistributedothesisthatresourcesindividualsthanofindividualsL.racofemosaotherareslpesseciescomp(Weadswtitiveorthfor
1959,Ball1980,Roth1992).Thereductionofresource-sharingtolerance

DISCUSSION4.5.

103

fortheL.racemosatreesincreasedtheeffectsofneighborsontheirgrowth
rates.Additionally,species-specificchangesintheFONradiusinfluenced
speciesinteractionsbyconferringlowercompetitivestrengthtoL.racemosa
individualsthanequal-sizedA.germinansorR.mangletrees.Thus,after
thefirstyearsoffastgrowthofL.racemosatreesthisheterogeneousspa-
tialcompetitionparameterizationproducedashiftindominance.Thus,this
successionresultedfromtheswitchintheimportanceoftwoforces:a)the
primarygrowthrateofL.racemosawhichisknowntobefasterthanforthe
otherspeciesunderlowsalinityconditions,highnutrientandlightavailabil-
ity(McKee1995,Shermanetal.1998,Lovelock&Feller2003),andb)the
lowstrengthofspatialinterspecificcompetitionofL.racemosa(ashypothe-
sizedbyBergeretal.2006).Thesecharacteristicsaretypicalofpioneer-like
speciesinanyplantsystem.Inmangroveforests,suchsuccessionswerede-
scribedinsomesecondaryrecoveryareas(Ball1980,Bergeretal.2006),
whichsuggeststhatoursecondspatialcompetitionparameterizationissup-
portedbysomefieldobservations.Thesedifferencesinthedynamicsbetween
thetwoparameterizationsbecomeespeciallyimportantwhenconsideringthe
erturbations.pfoeffectsThesimulationswithperturbationsillustratedthatspeciesdominanceof
oursystemdependedonthefrequencyofthedestructioneventsandtheirin-
tensities.However,wehaveseenthatthepatternofresponsechangedmainly
dependingonthecompetitionparameterizationandtherebythesuccessional
dynamic.Perturbationscreatedgapsthatwouldtakethesametrajectoryas
thesystem’sdynamicsobservedwithoutperturbations.Foreachgaprecov-
ery,theseedlingsavailabilitydependedonthedominantspeciesintherestof
thestand.Inthecaseofhomogeneousspatialcompetitionparameterization,
ifthesystemwasperturbedeachtimewhenthemajorityofgapswerein
thecyclingphaseofhighestdominanceofL.racemosa,thedominanceof
thisspecieswouldincreasemoreandmore,asinaresonancephenomenon.
Thissituationwascreatedatintermediateperturbationsregimes,leading
tothelowestISDHvalues.Withextremedisturbanceregime,thesystem
wouldachievethecyclingphasesearlierand,thus,wouldreturntoamore
evenspeciesdistribution.ThisscenarioledtohigherISDHvalues,andover-
allcreatedtheobservedU-shapedpatterns.Withtheheterogeneousspatial
competitionparameterization,perturbationscausedthesystemtoreturnre-
iterativelytoconditionsseenduringtheinitialsuccessionphases.SinceL.
racemosawasthemostpioneer-likeofthethreespecies,itobtainedhigher
importancewithstrongerandmorefrequentperturbations,whichcreated
amorehomogeneousspeciesdominance.Eventually,withextremepertur-
bationregimes,L.racemosadominatedcompletely,reducingtheindexof
speciesdominanceheterogeneity.Inmangroveforests,itisthereforepossible

104

CHAPTER4toobservethebell-shapedpatterntypicallydescribedbytheintermediate
disturbancehypothesis(IDH)(Connell1978)ifwehaveabioticconfigu-
rationwhereL.racemosaispioneerandsuccessionhappensduringstand
recoveryorestablishment.However,inadditiontobell-shapedorU-shaped
patterns,ourresultsalsorevealedmanycasesoflinearincreasesordecreases
duetoperturbationregimesnotfittingexactlytheresonanceoftherecovery
dynamics.ThisdiversityofresponsestoperturbationfitstheobservationsofMackey
andCurrie(2001)andthepredictionoftheIDHaxiomsdetailedbySheiland
Burslem(2003).Specifically,tohaveanIDHpatternyouneed:a)adomi-
nancesuccessionalsequencewhennoperturbationsoccur,b)successiondue
tocompetitiveexclusionoffastestgrowingtrees,andc)perturbationsbring
thesystembacktoearliersuccessionalstages.Theresultsofourindividual-
basedmodelsimulatingcompetitionatindividual-levelconfirmtheseaxioms.
Thehomogeneouscompetitionparameterizationofourstudydidnotcreate
successionandthereforedidnotexhibitapatternpredictedbytheIDH.
However,thisdynamicispossibleinnature(e.g.inunderstoryspeciessys-
temsasinBeckage&Stout2000)andinmangroveecosystemsparticularly.
Onlyfewstudieshaveobservedarealspeciessuccessioninmangroveforests
(e.g.Ball1980,Bergeretal.2006).Lugo(1980)concludedthatzona-
tionwasasteadystateresultofabioticconditionsandrefutedDavis’(1940)
hypothesisthatzonationwastheresultofsuccessionandlandbuildingpro-
cesses.SinceLugo’spaper,successioninmangroveshasbeencautiously
attributedtochangesinabioticconditionsbecauseofexternalfactors,but
rarelytospecies-inducedmodificationsofabioticconditions(e.g.Bertrand
1999).BecausetheIDHpatternistheexpressionofthedynamicsofspecies
succession,itcanbeusedtocomparespeciessuccessionatdifferentdistur-
bancelevels,orconversely,tocomparetherecoverydynamicsofsitesthat
exhibitdifferentsuccessiondynamics.Bothaspectshaveneverbeenconsid-
eredinmangroveecology.Suchstudiescouldsupportoursimulationresults
thatinsomecasessuccessioncouldbeduetoplant-plantinteractionsand
notalwaysexclusivelytoabioticconditionschanges.
Finally,ourstudyattheindividual-leveldemonstratesthatevenifabiotic
conditionsstronglyinfluencespeciescompositioninmangroveforests,spatial
plant-plantinteractionsalsoplayanimportantrole.Weshowedthatthesuc-
cessionaldynamicisdependentonthecapacitiesofindividualsofdifferent
speciestocompetespatiallyforresources,andthatthesedynamicdetermine
thewayspeciesdiversitywillincreaseordecreaseincaseofperturbations.
Thus,wedemonstratethatvariationsofmangrovespeciesdiversitydueto
perturbationregimewilldependonaseriesofinteractingfactors:succession
configuration,actualdynamicphases,plantspatialinteractionsandabiotic

LEDGEMENTSWCKNOA4.6.

105

settings.Additionally,fieldstudiesshowthatchangesofabioticsettings
afterperturbations(e.g.,Cahoonetal.2003),recruitmentpatterns(e.g.,
Baldwinetal.2001,Clarke2004,Piouetal.2006)andalsodifferencesof
resistanceofspeciestotheconsideredperturbations(Baldwinetal.2001,
Imbert2002)couldinfluencespeciescompositionofmangroves.Hence,fore-
castingageneraltrendofevolutionofspeciesdiversityofmangroveforests
onlyconsideringtheperturbationregimeseemsrisky.Itcouldbepossible
onlyinasite-specificcase,knowingforthissitenotonlytheabioticcondi-
tions,butalsothetypeofspeciesinteractionsandsuccessionphenomenon
cur.cocouldthat

4.6Acknowledgements
TheauthorsareverygratefultoVolkerGrimm,MarthaLilianaFontalvo-
Herazo,ElizavetaPachepskyandananonymousreviewerforvaluablecom-
mentsonanearlierversionofthismanuscript.Thisstudywasfinancedin
theframeoftheMADAMproject,acooperationbetweentheZMT,Bre-
men,GermanyandtheUfPaandMPEG,bothBel´em,Brazil,financed
bytheGermanMinistryofEducation,Science,ResearchandTechnology
(BMBF)[MADAM-MangroveDynamicsandManagement(Projectnumber:
03F0154A)],andtheConselhoNacionaldePesquisaeTecnologia(CNPq).
ThisisMADAMcontributionnumber#.

eferencesR4.7

Baldwin,A.,Egnotovich,M.,Ford,M.&Platt,W.2001.Regenerationinfringemangrove
Ball,forestsM.C.d1980.amagedPabytternsHourricanefsecondaryAndrew.PsuccessionlantiEcol.na157,mangrov149-162.eforestinsouthernFlorida.
226-235.44,OecologiaN.,BardsleyD,avKie,.J.1984.D.S.,TheWeooffectsdroffe,ofCC.Dyclone.(Eds.)KathyConoastsmandangrotveidalvweegetation.tlandsofIn:theBAardsleyustralian,K.
Barot,monsoS.o&nGregion.ignoux,J.North2004.AustraliaMechanismsResearchUpromotingnit,pANUlantcoPress,existence:pp.167-185.canalltheproposed
processesbereconciled?Oikos106,185-192.
Beckpineage,savBa.&nna:AStout,testI.oJ.fthe2000.inEffectstermediateofrepedisturbanceatedhburningypoothesis.nspeJ.ciesVericg.hSci.ness11:inaF113-122.lorida
Berger,forestU.&dynamics:Hildenspacing,brandt,Hageing.2000.andAneighnbewourhoapproacodchomptoestitionpatiallyofmangroexplicitvemotrees.dellingEcol.of
287-302.132,del.MoBerger,andtUhe.&Hbiomass-densitildenbrandt,ytraH.jectories2003.ofThethestrengthcohort.ofPclantompeEcol.tition167,among89-96.individualtrees

106

4CHAPTER

Berger,U.,Adams,M.&Hildenbrandt,H.2006.Secondarysuccessionofneotropicalman-
groves:causesandconsequencesofgrowthreductioninpioneerspecies.Perspectivesin
PlantEcology,EvolutionandSystematics.7,243-252
Bertrand,F.1999.MangrovedynamicsintheRiviresduSudarea,WestAfrica:anecogeo-
graphicapproach.Hydrobiologia413,115-126.
Cahoon,D.R.,Hensel,P.,Rybczyk,J.,McKee,K.,Proffitt,C.E.&Perez,B.C.2003.Mass
treemortalityleadstomangrovepeatcollapseatBayIslands,HondurasafterHurricane
Mitch.J.Ecol.91,1093-1105.
Chen,R.&Twilley,R.R.1998.Agapdynamicmodelofmangroveforestdevelopment
alonggradientsofsoilsalinityandnutrientresources.J.Ecol.86,37-51.
Chust,G.,Chave,J.,Condit,R.,Aguilar,S.,Lao,S.&P´erez,R.2006.Determinantsand
spatialmodelingoftree-diversityinatropicalforestlandscapeinPanama.J.Veg.Sci.
83-92.17:Cintr´on,G.&Schaeffer-Novelli,Y.1984.Methodsforstudyingmangrovestructure.In:
Snedaker,S.C.a.J.G.S.(Eds.).Themangroveecosystem:researchmethods.UNESCO
MonographsinOceanographicMethodologypp.91-113(251).
Clarke,P.J.2004.Effectsofexperimentalcanopygapsonmangroverecruitment:lackof
habitatpartitioningmayexplainstanddominance.J.Ecol.92,203-213.
Connell,J.H.1978.Diversityintropicalrainforestsandcoralreefs.Science199,1302-1310.
Davis,J.H.1940.TheecologyandgeologicroleofmangrovesinFlorida.Publicationsof
theCarnegieInstitute.Washington,D.C.,USA
Hill,M.O.1973.Diversityandevenness:aunifyingnotationanditsconsequences.Ecology
427-432.54,Imbert,D.2002.Impactdesouraganssurlastructureetladynamiqueforesti`eresdansles
mangrovesdesAntilles.BoisetForˆetsdesTropiques273,69-78.
Imbert,D.,Rousseau,A.&Labb´e,P.1998.Ouragansetdiversit´ebiologiquesdanslesforˆets
tropicales.L’exempledelaGuadeloupe.ActaOecol.19,251-262.
Kempton,R.A.1979.Thestructureofspeciesabundanceandmeasurementofdiversity.
307-321.35,BiometricsLoreau,M.,Naeem,S.,Inchausti,P.,Bengtsson,J.,Grime,J.P.,Hector,A.,Hooper,D.U.,
Huston,M.A.,Raffaelli,D.,Schimd,B.,Tilman,D.&Wardle,D.A.2001.Biodiversity
andEcosystemFunctioning:CurrentKnowledgeandFutureChallenges.Science294,
804-808.Lovelock,C.E.&Feller,I.C.2003.Photosyntheticperformancesandresourceutilizationof
twomangrovespeciescoexistinginahypersalinescrubforest.Ecophysiology134,455-462.
Lugo,A.E.1980.Mangroveecosystems:successionalorsteadystate?Biotropica12,65-72.
Mackey,R.L.&Currie,D.J.2001.TheDiversity-DisturbanceRelationship:Isitgenerally
strongandpeaked?Ecology82,3479-3492.
McKee,K.L.1993.Soilphysicochemicalpatternsandmangrovespeciesdistribution:recip-
rocaleffects?J.Ecol.81,477-487.
McKee,K.L.1995.Interspecificvariationingrowth,biomasspartitioning,anddefensive
characteristicsofneotropicalmangroveseedlings:Responsetolightandnutrientavailabil-
ity.Am.J.Bot.82,299-307.
Piou,C.,Feller,I.C.,Berger,U.&Chi,F.2006.ZonationPatternsofBelizeanOffshore
MangroveForests41YearsafteraCatastrophicHurricane.Biotropica38,365374.
Roth,L.C.1992.HurricanesandMangroveRegeneration:EffectsofHurricaneJoan,Oc-
tober1988,ontheVegetationofIsladelVenado,Bluefields,Nicaragua.Biotropica24,
375-384.

APPENDICES4.8.

107

Roth,L.C.1997.Implicationsofperiodichurricanedisturbanceforthesustainableman-
agementofcaribbeanmangroves.In:Kjerve,B.,Lacerda,L.D.d.,Diop,E.H.S.,(Eds.)
MangroveecosystemstudiesinLatinAmericaandAfrica.UNESCO&ISME.
Shea,K.,Roxburgh,S.H.&Rauschert,E.S.J.2004.Movingfrompatterntoprocess:
coexistencemechanismsunderintermediatedisturbanceregimes.EcologyLetters7,491-
508.Sheil,D.&Burslem,D.F.R.P.2003.Disturbinghypothesesintropicalforests.Trendsin
EcologyandEvolution18,18-26.
Sherman,R.E.&Fahey,T.J.2001.HurricaneImpactsonaMangroveForestinthe
DominicanRepublic:DamagePatternsandEarlyRecovery.Biotropica33,393-408.
Sherman,R.E.,Fahey,T.J.&Howarth,R.W.1998.Soil-plantinteractionsinaneotropical
Simpson,mangrovE.eH.forest:1949.ironpMeasuremenhosphorustoafnddivsulfurersity.Naturedynamics.163,O668.ecologia115,553-563.
Smith,B.&Wilson,J.1996.Aconsumer’sguidetoevennessindices.Oikos76,70-82.
SmithIII,T.J.&Duke,N.C.1987.Physicaldeterminantsofinterestuaryvariationin
mangrovespeciesrichnessaroundthetropicalcoastlineofAustralia.J.Biogeogr.14,
9-19.SmithIII,T.J.,Robblee,M.B.,Wanless,H.R.&Doyle,T.W.1994.Mangroves,Hurri-
canes,andLightningStrikes.Bioscience44,256-262.
Stoddart,D.R.1963.EffectsofHurricaneHattieontheBritishHondurasreefsandcays,
Oct.30-31,1961.AtollResearchBulletin95.
Vellend,M.&Geber,M.A.2005.Connectionsbetweenspeciesdiversityandgeneticdiver-
sity.Ecol.Lett.8,767-781.
Vermeer,D.E.1963.EffectsofhurricaneHattie,1961,onthecaysofBritishHonduras.Z.
332-354.,7Geomorphol.Wadsworth,F.H.1959.GrowthandregenerationofwhitemangroveinPuertoRico.
CaribbeanForester20,59-71.

endicesppA4.8AendixppA4.8.1IntheKiWimodel,theFONradiusRofatreedependsonitssize:
R=a×rbhb(4.10)
where:aandbarescalingparameters.Theparameterizationofaandb
canbeeffectuatedfromthedbh-densitytrajectoriesofaself-thinningphe-
nomenon.

Demonstration:Inequation4.10,therbhishalfthedbh,so4.10canbewritten:
R=a×21b×dbhb

(4.11)

108

4CHAPTER

veTheryFweONll(BergerapproacahndhasbHildeneenbseenrandtasr2003).eproducingDuringthetheself-thinningself-thinningtrainjectoryKiWi
model,becauseofthemortalityfunction,thetotalFONareaofallindividuals
grocanwbthecoftheonsideredremnanast.cTonstanhistscorrespincetondshetodeadaconstanindividualstmaximarerumeplacedresourceby
use.LetassumethisconstanttotalareabeFONtot.Wecouldsimplifyits
as:calculation

FONtot=N×FONind(4.12)
whereFONindisthemeanareaoftheFONareaoftheindividualsdefined
as:

1FONind=π×R2=π×a2×2b×dbh2b(4.13)
2whereRanddbharerespectivemeanvaluesassumingtheyrepresenttheen-
tirecommunity.Assumingthatduringself-thinningwehavetherelationship
ofthedbh-densitytrajectory:

orlog(NN)==eαxp+(αβ)+×logdbh(βdbh)(4.14)

InterchangingEquation4.13in4.12andcomparingto4.15weget:
b2N=exp(α)+dbhβ=FONtot=FONtot×(2)×dbh−2b(4.15)
FONindπ×a2
b2Sinceexp(α)andFONtot×(π2×a2)arenotdependentsondbh,wecanlink
theβparameterdirectlytotheFONbparameter:

(4.16)

β=−2b(4.16)
Identicallywecanderivethevalueofa:
a=22b×FONtot(4.17)
)αexp(π×WedeterminedwiththeKiWimodelthatFONtotisconstant∼215%and
notdependingonanorb.Theserelationshipsareconfirmedbysimulation
experimentswithmonospecificstands(Fig.4.6).

APPENDICES4.8.

109

Parameterizationofspecies-specificvalues
DatafrommonospecificstandsofBelizeanmangroves(I.C.Feller,F.Chi
andamongC.Pdbhiouanddunpublished)ensity.Tathisgadifferenveustdtheensitαyandwereβusedparameterstocreateandtregressionsherefore
allowsustocalculate(withequations4.16and4.17)theparametersaandb
fordata,RthehizophorlinearamangleregressionsandaAndvicenniaresultsofgerminansmonosp.ecificFiguresim4.6shoulationwsthewithoutfield
recruitmentwiththecorrespondingFONaandb.

Figure4.6:Fielddbh-density(cmandstem/ha)dataonnaturallogarithmicscale
withmonospcorrespecificostandndingofRlinearhrizophoregressionam(angleplain(blaclines)k)aandndAvsimicuennialationresultsgerminans(dashed(grey)lines)withoutof
t.recruitmen

ForLagunculariaracemosa,notenoughmonospecificfielddatawereavail-
able,soweestimatedthatthisspecieswaslesscompetitiveinBelizeinterm
ofspatiallydistributedresourcesuchaslight.Thiswasthenconsideredin
theaandbparametergivingabiggerbvalue(0.95)andsmallera(17.0)
valuethanforR.mangle.

110

4CHAPTER

Parameterizationofspecies-identicalvalues
Tousethesameapproachforthetuningoftheaandbparameterinthefirst
parameterization(specieshomogeneousspatialcompetition),dataofdensity
andmeandiameterfrommixedstandsofthethreespecieswereconsidered.
WeusedthedatafromplotsoftheCARICOMPprogram(CARICOMP2002,
htgiontocreatethetp://www.ccdc.org.jm/mangroregressionandvecalculatedata.hthetml)poverarameterstheenatireandCbaribbeanconsideringre-
allthreespecies(Fig.4.7).

Figurelogarithmic4.7:scalewCARICOMPithcorrespdbhonding-densitylinear(cmarndegressionstem/ha)(plaindataline).ofmixedforestsonnatural

BendixppA4.8.2Theanalysisofvariationsinspeciesdiversity(ISDH)ofthesystemdepending
ontheperturbationregimeshoweddifferenttypeofpatternsforthedifferent
parameterizations(Fig.4.8).Thehomogeneousspatialcompetitionparam-
eterizationwithbenignabioticconditionsledto4U-shapedpatternsoutof
11analyses.Theheterogeneousspatialcompetitionparameterizationwith

4.8.APPENDICES111

bboethnignacases,bioticthecrestonditionsoftheledatonalyses4besholl-shapwededirregular,patternsoutoincreasingf11aornalyses.decreas-In
wingeremorepatternofoftenISDUH-shapvaedriations.orbell-shapWithmed,ediumbutwithabioticancidentonditionsicaltrend:theptheatternsho-
mogeneousspatialcompetitionparameterizationledto6U-shapedpatterns
andtheheterogeneousspatialcompetitionledto7bell-shapedpatternsout
of11analysesinbothcases.

112

CHAPTER4Figure4.8:PatternsofsystemresponseinmedianISDHvariationsaccordingtofre-
quencyeffectwithselectedintensityofdisturbance(a)oraccordingtointensityeffect
withselectedfrequencyofdisturbance(b).WhiteboxesindicateU-shapedpatternofre-
sponse,greyboxesindicatelinearincrease/decreaseorirregularpatternofresponse,black
boxesindicatebell-shapedpatternofresponse.+,-and=showrespectivelysignificant
increase,decreaseornodifferencesofISDHvaluesfromstarttoendofpattern.

Chapter

5

rtanceoImp

on

a

of

evmangro

ulationims

abiotic

zonation

xpe

tsradieng

patterns:

terimen

113

114

5CHAPTER

Importanceofabioticgradientson
mangrovezonationpatterns:a
simulationexperiment

Piou,Cyril12;Berger,Uta1;&Feller,IlkaC.3
Articleinpreparation

A5.1bstract

Specieszonationpatternsareamongthemoststudiedfeaturesofman-
groveecology.Manyhypothesesofforestdynamicprocessesareproposedto
proexplaincesseshtheseappenpatterns.maketHohatweevexpr,theerimenttsimeareandsdifficultpatialtoscaleestablishatwhictohvterifyhese
thesehypothesesinthefield.Individual-basedmodelstryingtoreproduce
jectivzonationeofthispatternsstudycouldwasthelpoevinatheluateathessessmenimptoortanceftheseofthheypoeffecttheses.ofThedifferenob-t
abioticgradientsonspecieszonationin4mangrovesitesaroundCalabash
Cay,Belize.WeusedthespatiallyexplicitindividualbasedmodelKiWito
simulatethegrowthofCaribbeanmangrovetrees.Wetestedifthepatterns
ofbasalareaofeachspecieswerebetterreproducedwithorwithoutthe
influenceof:asalinityand/ornutrientgradientinfluencingthegrowthof
individuals,andatidalgradientlimitingtheestablishmentofrecruitsalong
evthesaluateites.theThecpapacityattern-orienofeachtedmscenarioodelingtoreproinformationducethecriterionpatterns.wasTherappliedesultsto
showedanapparentroleoftidaleffectonthetwoeasternsitesofCalabash.
Thesalinityornutrientgradientswerenecessarytoreproducethezonation
ofthewesternsites.Theseresultsalsoimpliedtheimportanceofseedlings
availabilityandpasthistoryintherecoveryofmangrovezonationpatterns.
Furthermodelingstudiesshouldassessadditionalprocessesatvariousspatial
andtemporalscalestoanalyzetherelativeimportanceofalltheproposed
hypothesesexplainingthemangrovespecieszonationpatterns.
Keywords:Mangrovezonationhypotheses,individual-based
modeling,pattern-orientedmodeling,informationcriterion
21CenterforTropicalMarineEcology,Fahrenheitstrasse6,23859Bremen,Germany
3CorrespSmithsonianondingEnauthor:vironmentalcyril.piou@zmResearchtCenter,-bremen.dePOBox28,Edgewater,MD21037,USA

ODUCTIONINTR5.2.

5.2Introduction

115

Mangroveforestsaredistributedalongtropicalandsub-tropicalcoastlines
andestuaries.Althoughtheseecosystemsareconstitutedbyalownum-
behighrofdivtreeersitspyofeciesstructures.comparedtSevoeoraltherctropicallassificationsforests,ofthesemangrovestructuresspresenexistta
andenvironmentalsettingsareoftenbelievedtodrivethem(e.g.Tomlinson
1989,Smith1992,Saenger2002).Amongthesestructuralpatterns,horizon-
talandzhyponationothesesa(crossreviewtheinbytertidalSmitha1rea992haasndbeenSaengersub2ject002).toaSuchplethorapatternsofworkdis-
tinguishdominancebetw(speeneciesstructuralzonation),chbotharacteristicsdescrib(edasstructuralbandsoftenzonation)paarallelndsptotecieshe
shore.Thestructurallydefinedzonesdifferintreedensity,canopyheightor
treesition.Tdiametershehypowhilethesesthesppropeciesosedtodefinedzinfluenceonesthahevespeciesdifferenztsponationeciespcompatternso-
aresofar:H1)plantsuccessionassociatedtolandbuilding(Davis1940,
Bertrand1999),H2)geomorphologicalfactors(Thom1967),H3)differential
dispersalofpropagulesduetotidalgradients(Rabinovitz1978)orpreda-
totionphgradienysico-cths(emicalSmith1gradien987),ts(H4)Macnaespecies-sp1968),ecificH5)phspatialysiologicalinterspaecificdaptationscom-
pe1980,titionClarkate2individual004),H6)treepelevelrturbationwithroregimewithout(Piouhetabitatal.partitioning2006(Chapter(Ball3),
Imaietal.2006).Landbuildingwithplantsuccessionandgeomorphological
thefactorszaonationreinptertatternwinedin(Saengertheir2002)effectandonarethetypicallyinstallationactingoratmolargedificationspatio-of
temporalscales.Smith(1992)arguedafterLugo(1980)thatland-buildingis
notareattdirectlyheoriginofinfluencingzonationtheprimarypatterns,andsuccessionthattheandgzonation.eomorphologicalSpatialfinactorster-
spspecificecies-spcompecificcetitionharacteristicsimpliesintatteractionheindividualamonglevelindividuals.influenceMantyhesediffereninter-t
actions:growthcapacitiesaccordingtoabiotic/bioticconditions,seedling
shadeorotherstresstolerance,seedproductionandestablishment.Theef-
hyfectpoofthesesspatialinconcerningterspecifictheeffectcompofetitionbioticonazndonationabioticisgtradienhereforets,asrelatedwelltaso
thecapacityofthespeciestocopewithperturbationsatsmallscale.All
thesehypothesesofinfluencingfactorsaresummarizedinfigure5.1depend-
ofingboonx)andtheirtsheirpatio-tempinitiatororalormoscaleofdifying/sustaininginfluence(verticalroles(pohorizonsitiontalandpoextensitiont

116

CHAPTER5Figure5.1:Schemeofrepartitionofthehypothesesoffactorsaffectingmangrovespecies
zonationpatternsaccordingtotheircapacitytobeattheoriginofzonationpatternsor
toinfluenceonthem(horizontally),accordingtothescaleoftheirimpact(vertically)and
accordingtotheirinteractions(proximityoftheboxes).Inparenthesisarethehypothesis
numberreferredtointext.Thestarshowsthefocusofthisstudyassumingspatial
interspecificcompetition.

andextentofbox).Additionally,thestrengthofconnectionsbetweenthese
factorsisindicatedbytheproximityofboxes.
Untilnowthestudyofspecieszonationpatternsandrelatedhypothe-
seswaslimitedtostaticdescriptionsorshort-termtemporalanalyses(e.g.
Bertrand1999,McKee1995b,Piouetal.2006(Chapter3))atthecommu-
nitylevel,ortoexperimentsonindividualtreeperformancebymodification
ofenvironmentalconditions(e.g.McKee1995a,b,c)attheindividuallevel
togeneralizeatthecommunitylevel.Theactualprocessesactingatthe
individuallevelandproposedtoexplainthepatternsatsystemlevelshould
betestedbuttemporalandspatialscaleproblemsobviouslylimitsuchex-
perimentsonthefield.Theadvantageofindividual-basedmodelingusinga

5.2.ODUCTIONINTR

117

pattern-orientedapproachisthecapacitytosimulatedifferentassumptions
aboutindividualspecies-dependentcharacteristicsinordertoassesstheir
reliability.Inreproducingthepatternsobservedinnatureandparticularly
emergentproperties(Brecklingetal.2005)suchaszonationpattern,the
pattern-orientedapproachgivesthepossibilitytomakeinferenceonpro-
cessesmorelikelytooccur(e.g.Wiegandetal.2003,Grimmetal.2005).
Individualbasedmodelinginmangroveecologystartedwithagapmodel
byChenandTwilley(1998).Theirmodel(FORMAN)reproducedbasal
areavaluesandwasusedaspredictiontoolofspeciesdominancechanges
ofFloridianmangroves(ChenandTwilley1998)andforpredictionofre-
generationmanagementoftheCi´enagaGrandedeSantaMarta(Twilleyet
al.1999).TheFORMANmodelincorporatedinterspecificcompetitionwith
species-specificgrowthconstants.Thespatialcompetitionwasassumedto
happenonlyforthelightresource.Itwasevaluatedthroughrelationships
amongleaf-areaindexandsizeofthetrees,assumingamaximumleaf-area
pergaps.BergerandHildenbrandt(2000)proposedtosimulatethecompe-
titionforspatiallydistributedresourcesattheindividuallevelwiththeField
OfNeighborhoodapproach(FON),intheso-calledKiWimodel.TheFON
approachdoesnotspecifythetypesofresourcescompetedfor.Instead,it
assumesthattheeffectsofcompetitionforspatiallydistributedresourcescan
besynthesizedalltogetherintoonevariable.TheKiWimodelproduceda
setoftheoretical(BergerandHildenbrandt2000,2003,Bergeretal.2002,
2004,Baueretal.2002,2004,Chapter4)andapattern-orientedstudy
(Bergeretal.2006).Nevertheless,theapplicationofthesemodelswasso
farnotfocusingonzonationpatterns.Thespecieszonationpatternisone
ofthemoststudiedaspectsofmangroveecology.Thus,itshoulddefinitely
betestedwithsimulationshavingdiverseparameterizationcorrespondingto
differenthypothesestoanalyzethereliabilityandtheimportanceofeachof
them.Theobjectiveofthisstudyistoevaluatetheimportanceoftheeffectof
differentabioticgradientsandtheirinterconnectabilityontheexplainingof
specieszonationinaspecificmangrovesite.Wefocusonthezonationpat-
ternsdocumentedinPiouetal.(2006,Chapter3)forCalabashCay,Belize.
Thespecieszonationpatternwasofparticularinterestforthissitesinceit
wastheresultofregenerationonthelast41yrafterHattie,acatastrophic
hurricanethatdestroyedmostofthemangrovesinOctober1961.Thefact
thatMcKee(1995a)demonstratedthatcrabpredationdoesnotplayany
roleinBelizeanspecieszonationpatternallowedustodiscardapriorithis
aspect,whichwouldaskformuchmorecomplexmodelstobetested.Thus,
consideringtheCalabashsiteswecouldtestifdifferentialdispersalofpropag-
ules,aninfluenceofanutrientorsalinitygradientonindividualgrowth,or

118

5CHAPTER

acombinationoftheeffectsoftheseabioticgradientscouldreproducewell
thecreationofthemangrovezonationpatternsafterHattie.

dsethoM5.35.3.1TheKiWimodel
brandtWeused2000),thetossimpatiallyulateexplicit41yrofrmangroveegenerationmodelofKtiWihefour(Bergersitesand(AtoHilden-D)
describedbyPiouetal.(2006,Chapter3)aroundCalabashCay,Belize(See
mapofsitesinfigure3.1).ThegrowthfunctionusedinKiWi(Chenand
Twilley1998,BergerandHildenbrandt2000)wasalreadyparameterizedfor
thethreemainCaribbeanspecies:Rhizophoramangle,Avicenniagerminans
sivandelyLwhenagunculariagoingrafromcemosathe.sSitehorelineAtohad4thehinzonespterland,arallelandtotahelengthshoreofs100mucces-
perpendiculartotheshore.SiteBhad4zonesandalengthof190m.The
first3zones(outof6)ofsiteCdescribedinPiouetal.(2006,Chapter3)
weredwarfareaswithtrees<3m.Thus,treesdidnothaveaproperdiame-
teratTherefore,breastwehsimeight,ulatedwhicfhoristheessenpresentialtforonlythethegrolwastth3zonesfunctionofsusediteCin,wKiWi.hich
hadthenalengthof60m.ThesiteDhad3zonesandalengthof35m.The
3sppatternseciestoinbeeachreprozone.ducedThuws,ereinthetotalv12aluesBAofbweasalretobarease(reproBA)oducedfeainchositesfthAe
andB,while9BAinsitesCandD.Thesimulationareashadtherespective
lengthforeachsiteandalwaysawidthof50m.
TheindividualtreesintheKiWimodelweremanagedwithfourmain
wproastcesses:hebasisorecruitmenfmanty,gdroecisionwth,onmortalittheytahreendspatialothercproompecessestition.(seeTbheeFloOw).N
Thus,westartbyexplainingthecompetitionprocessesandfollowwiththe
cesses.proremaining

Competitionforspatialresource
W(BergereadescribndedHildeninbrandtter-individual2000),ssimpatialulatingcomptheetitionareauwsingheretheaFtreeONinfluencedapproach
itsneighborsandwasinfluencedbythemintheirresourceuse.Weassumed
ballespatiallyphenomenologisticallydistributedinresourcestegrated(lighint,thisnutrienapproacts,gh.roundWewaassumedter,etcane...)xpo-to
bnenytialapplyingdecreaseaninofrtensityesourcefielduseontgoingopofawtheayfrominfluencedthesarea.temTh(trunk)us,thepFositionON

METHODS5.3.

119

specifiedthestrengthofcompetitionexertedbyatreeatanypositionwithin
itsneighborhood:
⎫⎧⎨⎪⎪1for0≤r<rbh⎬⎪⎪
FON(r)=⎪exp−|logR(−Frbminh)|×(r−rbh)forrbh≤r≤R⎪
⎩⎪0forr>R⎭⎪
(5.1)whererbhwastheradiusofthestematbreastheightandFminwasthe
minimumintensity(0.1)oftheFONattheFONradius(R).TheFON
radiusRofatreedependedonitssize:
R=a×rbhb(5.2)
whereaandbwerescalingparameters.Theparameterizationofaandb
waspossibletoeffectuatewiththerelationshipamongmeantreediameter
atbreastheight(dbh)andtreedensityduringaself-thinningphase(cfAp-
pendixAofChapter4,page107,forthedescriptionofthesefitsandthe
explanationoftheselectedvalues).Weusedforthisstudythespecies-specific
aandbvaluescomingfromdataofBelizeanmonospecificmangrovestands
(Chapter4).Thissettingassuredthatifaspecieswouldcolonizeanempty
areawithouttheothertwospecies,thepatternsofexponentialrelationship
amongdbhanddensity,occuringnormallyinself-thinningsituation,and
documentedfrommonospecificstandsofBelize,wouldbereproduced(cf
AppendixAofChapter4,page107).

tRecruitmena)Numberofinvadingsaplings
simulationRecruitsandwereateachestablishedtimeostep.ntheThesesimulationrecruitsareawereatctheonsideredbeginningasaoflreadythe
growconditionsnupwasindividualstestedofasadbhvarying=2cm.TheparameternumbberecauseofintvheaderrangeNoinvfnatumbestartingrof
initialrecruits(i.e.theonesassumedtorecolonizetheareaonthefirstyear
ofrecovery)werenotknownprecisely.Wetested4values:100,500,1000
and5000saplings/ha.Thethreespecieshadequalproportionsofsaplings
recruits.firstthesewithinThenumberofnewrecruitspertimestepwascalculatedforeachspecies
asthesumofthepotentiallyproducedrecruitsofeachtree(Ns).This
fruitsrelationshipandflowwaesraprodaptedductionfromforRempiricalhizophoraregressionsppandbetnwon-eenRtreehizophorsizeaandspp

120

5CHAPTER

(Komiyama1988inSaenger2002).Wetransformedtheexponentialstruc-
tureoftheoriginalregressionformulatoapolynomialstructureforfaciliting
computing.Weassumedanecessaryweightof30gofflower/fruitsproduc-
tiontoobtainonepotentiallysurvivingR.mangleseedlingandof10gto
obtainonepotentiallysurvivingseedlingofA.germinansandL.racemosa
(Fig.5.2).Thustheproductionofeachtreewascalculatedas:
Ns=α×dbh3+β×dbh2+δ×dbh+(5.3)
whereα,β,δandwerespecies-specificparameters(Table5.1).Thepa-
rameterizationwasidenticalforA.germinansandL.racemosaandassumed
thattreesofthesespeciesproducedhighernumberofrecruitsthanR.mangle
treesforidenticalsize.

Figure5.2:Annualproductionofpotentialrecruitsofasingletreeaccordingtoitsdiam-
eteratbreastheight(dbh)(blackline:AvicenniagerminansandLagunculariaracemosa,
greyline:Rhizophoramangle)accordingtoequation5.3andparametersusedintable5.1.

b)Influenceoftidalsorting
Thetidalsortingofpropaguleshasbeenoftenproposedasanexplana-
tionofspecieszonationpattern(e.g.Rabinovitz1978,Jim´enezandSauter
1991).recruits.WeThetestedfirstcthreease,casasesanofullhyinfluencepothesis,oftwidesasocntheonsideringestablishmennotinfluenceofnoewf
tidesontheestablishmentofrecruits(referredtoasTideO).Theinvading
saplingswerethereforerandomlydistributed.Thesecondcase(referredtoas

METHODS5.3.

121

TideThresh)assumedthatthesaplingsofthedifferentspeciescouldsettle
anywhereuntilaspecies-specificmaximumtidalrange.Itassumedthatthe
influenceofthetideandwaveactionwouldexcludesomespeciesofthelower
intertidalonly(Fig.5.3a).Tosimulatethat,wecalculatedaprobability
tosettle(Ps)ataspecificpointdependingonthemaximumtidallevelat
thispoint(MTL,incm)andthespeciesofaconsideredsaplingwiththe
ula:formwingfollo1Ps=1+exp−0.5×(td1−MTL)(5.4)
wheretd1wasaspecies-specificconstant(table5.1,estimatedfromthehigh-
estmaximumtidallevelwherethespecieswasfoundinCalabashCayminus
5cm).Thethirdcaseassumedalsoaneffectofthemaximumtidallevel
butonbothsidesofthespeciesdistribution(referredtoasTidePar).This
simulatedaneffectofwaveandtideactiononthelowerintertidalbutalso
thatspecieswithbigseedlings(suchasR.mangle)wouldlesslikelyarrive
tohighgrounds(Fig.5.3b).Wecalculatedtheprobabilitytosettlewiththe
ula:formwingfolloPs=−0.5+td2×MTL−0.5×MTL2(5.5)
td3wheretd2andtd3wherespeciesspecificconstants(table5.1,td2wasesti-
matedfromhalfofthehighestmaximumtidallevelwherethespecieswas
foundinCalabashCay,td3wasstandardizedsothattheprobabilitygoupto
1.0).Inbothoftheselattercases(TideThreshandTidePar),newindivid-
ualswereproposedtoestablishatrandomlychosenpoints.Eachindividual
hadalreadyanassignedspeciesaccordingtotheproportionsdescribedabove
(page119).Theprobabilitytosettleatthispointwascalculatedwithspecies-
specificparameters(onEq.5.4or5.5)andtestedagainstauniformrandom
numberbetween0and1.IftherandomnumberwashigherthanthePs,
therecruitwassentrandomlysomewhereelseuntilfindingasuitableplace.
Doingso,theproportionofrecruitsfromdifferentspecieswasnotreduced
bytheproportionofsuitablehabitat.Themaximumtidallevel(MTL)for
eachpointofasitewasavailableinthemodelfromsite-specificbitmaps
representingthegradientofMTLmeasuredbyPiouetal.(2006,Chapter
3)inthe4sitesofCalabashCay.Thefirstinvaderswereestablishedatthe
beginningofthesimulationsaccordingtotheversionofthesetidaleffects,
whiletheyearlynewonesweresettledalsodependingonthestrengthofthe
competitionatthepointwherethetidalsortingleadthem(seebelow).
c)Influenceofcompetitionintensityofalreadyestablishedtrees
trecruitmenon

5CHAPTER122Aftertheinfluenceoftidalsortingontheendingpositionofarecruit,the
modelcalculatedtestedforifeacthhenewsaplingyearlycouldrecruitactuallytheshaumveofgrothewFnuONpaintttensithisyplace.FofWthee
alreadyestablishedtreesatitsstemposition(xrecruit,yrecruit):
nF(xrecruit,yrecruit)=FON(Disti)(5.6)
=1iwherenwasthenumberofneighboringtreesinfluencingat(xrecruit,yrecruit)
andDistiwasthedistanceof(xrecruit,yrecruit)totheneighborstemposi-
(tion.MaxT,hetablesum5.1).FwTashisthenchandlingomparedprevtenotedasrpeecruitscies-spfromecificbecomingthresholdavtalueree
Fofdbh=2cmiftheFvaluewasaboveMaxF.AlthoughtheFONapproach
assumeallspatialresources,thesevaluesofMaxFrepresentedacapacity
oftherecruitstodealwithshadow.Thesethresholdssimulatedtheshade
intoleranceofseedlingsofL.racemosaandA.germinans(Ball1980,McKee
1993).thwGroThegrowthofeachindividualtreewascalculatedwiththefollowingfor-
mula(BergerandHildenbrandt,2000):
ddbhG×dbh×(1−dbhmaxdbh××HHmax)
dt=274+3×b2×dbh−4×b3×dbh2×fs(SALT)×fn(RNA)×fc(FA)

Figure5.3:Sub-modelsofprobabilitytosettledependingonthespeciesandthe
maximumtidalrange.a)sub-modelofthresholdtypeoftideinfluenceonsettling
(TideThresh).b)sub-modelofparabolictypeoftideinfluenceonsettling(TidePar).

METHODS5.3.

123

wheredbhwasthestemdiameteratbreastheight(cm);Hwasthetree
height(cm);dbhmaxandHmaxweremaximumvaluesofdiameterandheight
foragiventreespecies(Table5.1);G,b2andb3werespecies-specificgrowth
constants(Table5.1).Themultipliersfs(SALT),fn(RNA)andfc(FA)
wererespectivelysimulatingthenegativeeffectofporewatersalinity,relative
nutrientavailabilityandspatialcompetitionongrowth.Theyreturnedvalues
between0and1dependingrespectivelyonthelocalsalinity,thelocalnutrient
availabilityandsumofFieldOfNeighborhood(FON).Theparameterizations
ofthesemultiplierswerealsospecies-specific.Thesalinitymultiplierwas
takenfromChenandTwilley(1998):
1fs(SALT)=1+exp(d×(S0.5−S))(5.8)
wheredandS0.5werespecies-specificparameters(Table5.1)andSwas
thelocalsalinity.ThelocalsalinitywasgiveninKiWibyabitmapmap
reproducingthemaximumvaluesmeasuredperzonealongtheintertidalby
Piouetal.(2006,Chapter3).Totesttheeffectofthissalinitygradientonthe
specieszonationanothersetofsimulationsweredonewithahomogeneous
benignsalinityacrossallthezonesofallsitesS=45psu.Thesalinity
gradientparameterizationwasreferredtoasSalinityGradwhiletheother
wasreferredtoasHomogeneousSal.
TherelativenutrientavailabilitymultiplierwasalsocomputedafterChen
1998):(Twilleyandfn(RNA)=c1+c2×RNA+c3×RNA2(5.9)
wherec1,c2andc3werespecies-specificparameters(Table5.1)andRNA
wasthelocalrelativenutrientavailabilityalsogivenbyanunderlyingbitmap.
TherelativenutrientavailabilitywasindicatedbyChenandTwilley(1998)
asanindicatorofrelativephosphorousavailability,whichtheybelievedto
bethemostlimitingnutrientintheirsites.Inourfocussites,phosphorous
andnitrogenmightbelimitingfactorsofgrowth(Piouetal.2006,Chapter
3).However,iftheyhadanylimitingeffectsithadtobestrongeronthe
shorelinesthaninsidesincePiouetal.(2006,Chapter3)observeddecrease
ofnutrientuseefficiencyfromtheshoretothehinterland,indicatinganin-
verseavailabilitypattern.Wetestedconsequentlytwosettingsofnutrient
availabilitytoanalyzeifagradienthadaneffectonthespecieszonation:a
homogeneousRNA=60%(hereafterreferredtoasHomogeneousNut)and
agradientofRNAfrom50%ontheshoreto70%inland(hereafterreferred

(5.7)

124

5CHAPTER

toasNutrientGrad).Thehomogeneousvaluewasselectedtorepresentthe
overallnutrientslimitationthatoccuronoffshoremangroveislandsonolig-
otrophicwaterssuchasontheCalabashCay.Thegradientsvalueswere
selectedtostillallowallspeciestogrowonallareas(RNA>40%,seeChap-
ter4,seeFig.4.1),andsimulatingapproximatelyarangeofvariationof
nutrientavailabilitythattheresorptionefficiencyandnutrientuseefficiency
measuredonthosesitesindicated(Chapter3,seeFig.3.3and3.4).
Thecompetitionmultiplierreducingthegrowthrateofasingletreewas
computedasproposedbyBergerandHildenbrandt(2000)asdependingon
thesumofallneighborsFONeffect:
⎨⎧1⎬⎫
fc(FA)=max⎩0;1−2×(An=kOFONn(x,y)dO)⎭(5.10)
wherenaretheneighborsofthefocustreek,AwastheFONareaofkandO
wastheoverlapareabetweentheFONareaofkandeachn.Asmentioned
earlierthespecies-specificparameterizationoftheFONradiuscalculation
(R,Eq.5.2)gavedifferentspatialcompetitionstrengthtothethreespecies.
Fortwotheoreticalindividualsofidenticaldbhandcloseenoughtohave
overlapoftheirFONareas,theonehavingthesmallerRfeltthemostthe
competitioneffect(Bergeretal.2002).ThusinoursettingofRcalcula-
tion,thecompetitionstrengthformostsizesofdbhofourfocus41yrswas
followingtheorderdescribedbyBall(1980):R.mangle>A.germinans>
L.racemosa.

yMortalitTheKiWimodelsimulatedmortalityasaconsequenceofgrowthrepression
duringacertaintimeperiod.Themeandbhincreaseoverthelast5yrs
wascomputedperindividualandcomparedtoaspecies-specificthreshold
(CritΔdbh,table5.1).IfthismeandbhincreasewasbelowtheCritΔdbh
thetreewassettodieandremovedfromthesimulationarea.Thismethodof
mortalitycoupledwiththeFONapproachhasbeenseentoreproduceseveral
patternsofbiomass-densitytrajectoriesandsizedistributionsoflivingdead
trees(Bergeretal.2002)andallowamoremechanisticmortalityprocess
thanwithrandomremoval.

5.3.2Simulationsandanalysis
Wesimulated20timeseachsiteswithallthepossiblecombinationofthe
sub-models(Table5.2,leadingto48possibleparameterizations).Foreach

METHODS5.3.

125

Table5.1:Species-specificparametersusedintheKiWimodel.Sources:(1)Chenand
Twilley1998,(2)Chapter4,(3)EstimationsfromPiouetal.2006(Chapter3)data,(4)
Estimations.ParameterDescription(EquationandunitsA.germinansL.racemosaR.mangle
applicable)if

baFFOONNrradiusadiussscalingcalingparameterparameter((Eq.Eq.55.2).2)
αConstantfordbhtosaplingrelationship
5.3)(Eq.βConstantfordbhtosaplingrelationship
5.3)(Eq.δConstantfordbhtosaplingrelationship
5.3)(Eq.Constantfordbhtosaplingrelationship
5.3)(Eq.td1ofConstanTideThreshtintidalesub-moffectdel(functionEq.5.4)
td2ofConstanTidePtainrabstidalub-moeffectdel(Eq.function5.5)
td3Constantintidaleffectfunction
MaxFofMaximTidePumaFrabONsinub-motensitdely(Eq.5.5)
tstablishmenefordbhmaxMaximumdiameteratbreastheight
cm)5.7,(Eq.GHmaxGroMaximwthumhconstaneightt((Eq.Eq.55.7).7,cm)
b2Constantinheighttodbhrelationship
5.7)(Eq.b3Constantinheighttodbhrelationship
5.7)(Eq.dSalinityeffectconstant(Eq.5.8)
cS10.5RNASaliniteyffecteffectcconstanonstantt(Eq.(Eq.5.9)5.8,psu)
c2RNAeffectconstant(Eq.5.9)
cCr3itΔdbhMeanRNAedbhffectincreaseconstant(Eq.threshold5.9)(cm.yr−1)

13.7.7200.00040.0489-0.20260.020.0012.500.0077625.00140350016248.040.1720.18-2.07-0.502.88-1.66.230

17.0.9500.00040.04890.2026.0015.0010.000.004950.080300024371.580.447-0.2065.01.00-4.422.50-.200

parameterizationreplicatewerecordedthefinalposition,dbh,andspeciesof
allthetreespresentattheendofthesimulations(41yrs).Wethenapplied
thesamesamplingtechniqueasinPiouetal.(2006,Chapter3)tobe
abletocomparerealdatawithsimulationdataofidenticalprecisions.This
samplingwasusingapointcenterquartermethod(PCQM)(Cintr´onand
Schaeffer-Novelli1984)with21randompointsacrosseachzonefromwhich

18.0.8300.00060.0302-0.16410.240155.0030.000.044950.5100400026777.260.3960.25-58.00.001.33-0.72.200

2)(2)((3)(3)(3)(3)(3)(3)(3)(4)(1)(1)(1)(1)(1)(1)1)((1)(1)1)(4)(

126

5CHAPTER

Tapattern)blea5.2:ndSub-moparameterdelsvaried(withincourorrespanalysisondingtohyparrivoethesistotheof48effectpoossiblenspcases.ecieszonation
SimulatedaspectsCasesSub-modelsorvariablesTestedhypothesisinfluen-
onationzeciesspcingFirstrecruitment4Densityofinvaders:100,500,
1000and5000saplings/haTidalsortingofrecruits
Tidalsorting3TideO/TideThresh/TidePardependingonelevation
tertidalinhetalongdaptationsaeciesSpSalinity2HomogeneousSal/SalinityGradtogradientsof
ysalinitdaptationsaeciesSpNutrientavailability2HomogeneousNut/NutrientGradntoutriengradientavtsofailability

thedistanceofthe4closesttreesinrespective4quadratsaroundthepoint
wtheerebasalnotedareaas(wellBA)aspterheirspspecieseciesperzandonedbhwas.Oevutofaluated.theseWerepemeasuremenatedthets,
randomPCQMsampling10timesperreplicatesimulationresults.Thisled
usto200observationsofBAofthe3speciesperzonesofeachsitestobe
comparedtothefielddata.Thepatternsoffocustobereproducedwere
thereforeeachfieldvalueofbasalarea(BA)perspeciesperzone(notshown
inPiouetal.2006,Chapter3,butpresentedinfigure5.4).
approacWehthenpresenappliedtedtinheChapterpattern-orien2totedestimatemodelingthelikelihoinformationodofascriterionim(ulationPOMIC)
parameterizationtoreproduceeachBAvaluesofthe3speciesinallthe
zonesofagivensite.Foreachspeciesineachzonethe200BAsimulation
resultsestimator(v(RectorDevBAs)elopmenweretfiCorerstTeamtransformed2006)ofwithbaandGwidthaussian(kbw)ernelcdalculatedensity
as:

bw=∼max(BAs)−min(BAs)(5.11)
10respwhereectivmaxely.(TBAhes)andresultingmin(BAdensitiess)w(erevtectorheDsmaxim)wueremtandhenminimscalediumntoofpBArob-s
abilitiesofobservationofBAvalues(Ps):
DsPs=max(H)(5.12)

METHODS5.3.

127

wheremax(H)wasthemaximumprobabilityvalueobtainedinahistogram
ofprobabilitydrawnwithBAsandclasswidthsbw.ThesePsvalueswere
always512values(standardoftheRGaussiankerneldensityestimator)
correspondingtoavectorBAPof512BAvaluesofrangeBAPrange=[min-
imumBAreturningaDs>0(BAminD),maximumBAreturningaDs>0
(BAmaxD)]andofconstantincrement(BAPstep):
BAPstep=BAmaxD−BAminD(5.13)
511Toestimatethelikelihoodofasimulationresulttohavereproducedafield
observationL(BAfield|parameterization)wethenusedthePsvalueofthe
correspondingBAPvaluetheclosesttothefieldBA(BAfield):
L(BAfield|parameterization)=Ps[k]ifBAfield∈BAPrange(5.14)
"!therwiseo0wherekwasthepositioninBAPwhereBAP[k]wastheclosesttoBAfield.
WethenappliedthefollowingformulatocalculatethePOMICsofasites
foreachparameterization(Chapter2):
3Z1POMICs=3×Zlog(L(BAfield|parameterization))(5.15)
zone=1sp=1
whereZwasthenumberofzonesintherespectivesitesandspwascor-
respondingtooneofthethreespecies.Thiscriterionwasdevelopedasa
goodnessoffitindicatorforpattern-orientedstudiesdonewithindividual-
basedmodels.ThesmallerthevalueofPOMIC,thebetterthepatternwas
reproduced.IftheL(BAfield|parameterization)ofonlyonespeciesinone
zonewas0,thePOMICwouldbecomeinfinite.Thiswouldmeanalackof
representationoftheparameterizationtoreproducethefocusbasalareaofa
speciesinonezoneofthissite.Tobeabletocompareparameterizationseven
inthecasethatallofthemledtoonespeciesnotreproducedinonezone,
weusedanadaptationoftheL(BAfield|parameterization)andcountedhow
manytimestheBAfieldwasnotelementofBAPrange(findinthe“Number
ofunmatchedpatterns”variablepresentedintheresults):
L(BAfield|parameterization)=Ps[k]i10−f323BAfieldotherwise∈BAPrange(5.16)
"!Thisallowedustostillobservewhatthebestparameterizationswereforall
theotherspeciesandzonesofthissite.

128

5CHAPTER

SinglevaluesofPOMICdonotinformmuch,soforeachsitewecom-
putedthePOMICdifferencesforeachparameterizationi:
Δs,i=POMICs,i−POMICs,min(5.17)
wherethePOMICs,minwastheminimumPOMICsvalueamongallpa-
rameterizations.Thesedifferenceswereusedtocomputetheprobabilityof
aparameterizationtobethebestoneamongthesetofparameterizationsΛ
testedtorepresentagivensites(Chapter2):
Ws,i=Λexpexp(−(Δ−s,iΔ)s,λ)(5.18)
=1λofTheseourweighdiscussionstsofabevidenceouttheinfproavorcessesofeacthathmighthaparameterizationvehappienedweinreeacthehbsiteasis
ofscriptsCalabashdevelopCaedybforetwteheenRs1961oftwandare2c002.(vAllersion2.3,analyses2006).wereeffectuatedwith

esultsR5.4NoparameterizationtestedreproducedallthebasalareapatternsofsiteA
(Table5.3).Theseunmatchedpatternswereduetoatoohighpresenceof
A.germinansonallbutthefirstzoneofthesite(Fig5.4a).Thebestfitting
parameterizationandthesecondbesthadonlyoneunmatchedpattern,but
theweightofevidenceshowedthatthebestparameterizationwasmuchmore
likely(70%)tobecorrectthanthesecond(30%)oranyotherones(Table
5.3).Fromthesetwobestparameterizations,theresultsshowedthatto
reproducethebestthespeciesbasalarea,themodelneededtoincludea
tidalsortingprocessaccordingtothesupposedresistanceofpropagulesto
waveaction(TideThresh).
Theparameterizationstesteddidnotreproduceentirelythebasalarea
patternsofsiteB(Table5.4).Asetof9parameterizationswerefoundwith
onlyonepatternofbasalareanotreproduced:thebasalareaofL.racemosa
inthefirstzone,whichwasalways0.0m2/0.1hainoursimulationsbutcloseto
2.0m2/0.1hainthefield(Fig5.4b).Thissetof9parameterizationsincluded
thesalinitygradientinfluence(SalinityGrad,Table5.4).Theweightsof
evidenceweresharedamongthese9parameterizationswith6ofthemwith
Wi≥0.1.These6bestparameterizationsshowedthattoobtainagoodfit,
thenutrientgradientwasnotnecessary.Theyalsoshowedthatitwasbetter
tousethetidaleffectparameterizationTidePar,andthatthenumberof
initialrecruitsdidnotmatter.

STRESUL5.4.

129

Table5.3:Best12parameterizationsofsimulationsofsiteAleadingtothereproduction
ofthespecies-specificbasalareapatterns.(Rec=Firstrecruitment/ha,Num=Number
atterns)phedunmatcofRecTidalsortingNutrientavailabilitySalinityNumPOMICiΔiWi
100TideThreshHomogeneousNutHomogeneousSal163.5600.7
100TideThreshHomogeneousNutSalinityGrad164.430.870.3
100TideParHomogeneousNutSalinityGrad2122.2558.690
100TideParHomogeneousNutHomogeneousSal2122.4358.870
1000TideParHomogeneousNutSalinityGrad3181.92118.360
1000TideParHomogeneousNutHomogeneousSal3181.93118.370
5000TideParHomogeneousNutSalinityGrad3181.99118.430
100TideParNutrientGradSalinityGrad3182.03118.470
100TideParNutrientGradHomogeneousSal3182.05118.490
500TideParHomogeneousNutSalinityGrad3182.09118.530
500TideParHomogeneousNutHomogeneousSal3182.1118.540
1000TideParNutrientGradSalinityGrad3182.11118.550
Anyotherparameterizationcombination≥3>182.110

Table5.4:Best12parameterizationsofsimulationsofsiteBleadingtothereproduction
ofthespecies-specificbasalareapatterns.(Rec=Firstrecruitment/ha,Num=Number
atterns)phedunmatcofRecTidalsortingNutrientavailabilitySalinityNumPOMICiΔiWi
500TideParHomogeneousNutSalinityGrad161.8900.18
1000TideParHomogeneousNutSalinityGrad162.110.230.14
100TideParHomogeneousNutSalinityGrad162.160.270.14
5000TideParHomogeneousNutSalinityGrad162.270.380.12
500TideThreshHomogeneousNutSalinityGrad162.360.480.11
100TideOHomogeneousNutSalinityGrad162.480.60.1
1000TideThreshHomogeneousNutSalinityGrad162.560.670.09
1000TideOHomogeneousNutSalinityGrad162.971.090.06
1000TideParNutrientGradSalinityGrad163.111.230.05
5000TideThreshHomogeneousNutSalinityGrad2121.9360.050
100TideThreshHomogeneousNutSalinityGrad2122.0260.130
100TideParNutrientGradSalinityGrad2122.1360.250
Anyotherparameterizationcombination≥2>122.130

enoughSimtoulationsmatcohftsheiteCopatternsbtained(Ta11blecases5.5).ofThesecasesparameterizationssharedfivettingrywcloseell
weightsofevidence,meaningthatnonereallyoutstoodtheothers.Most(9
outof11)ofthesecasesusedthesub-modelofgradientofsalinity(SalinityGrad)
indicatinganimportanceofthiseffect.Theotheraspects(tidalsortingeffect,
nutrientgradientornumberofinitialrecruitsperhectare)didnotappearto
beimportantontheirowntohaveagoodfit.Thebestfittingsimulation

130

5CHAPTER

Table5.5:Best12parameterizationsofsimulationsofsiteCleadingtothereproduction
ofthespecies-specificbasalareapatterns.(Rec=Firstrecruitment/ha,Num=Number
atterns)phedunmatcofRecTidalsortingNutrientavailabilitySalinityNumPOMICiΔi
1000TideONutrientGradSalinityGrad02.710
1000TideOHomogeneousNutSalinityGrad02.720.01
100TideOHomogeneousNutSalinityGrad02.750.05
5000TideONutrientGradSalinityGrad02.860.15
100TideThreshHomogeneousNutSalinityGrad02.940.23
500TideOHomogeneousNutSalinityGrad02.960.25
100TideONutrientGradHomogeneousSal03.030.33
5000TideOHomogeneousNutSalinityGrad03.140.43
500TideThreshHomogeneousNutSalinityGrad03.250.55
5000TideThreshHomogeneousNutSalinityGrad03.30.59
500TideParHomogeneousNutHomogeneousSal03.921.21
100TideONutrientGradSalinityGrad182.3479.64
Anyotherparameterizationcombination≥1>82.34

hadalwaysanover-estimationofBAofL.racemosainthethirdzone,and
thepresenceofR.mangleinthesecondzonewasalsonotwellreproduced
5.4c).(FigThesiteDobtained6parameterizationsmatchingallthebasalareapat-
ternsgradien(Ttableeffect5.6).wereForanecessarygood.fiTt,heastidalalinitsygortingradieneffectteffectwasnotand/orimpanortanutrientont
itsamongown.zonesFigurewere5.4dwellshoreprowsthatducedthebypthebatternsestpofspeciesarameterizationdominanceofthisinsite.BA

models:FinallyTi,ndeOo,HplainomognullehyneousNpothesisutandpHomoarameterizationgeneousS(alusing)withonlyanynullnumbsub-er
ofrecruitsperhectareenteredwithinthefirstquarterofthebestparame-
sites.heacofterization

iscussionD5.5Thisstudyanalyzedsomepotentialprocessesofinfluenceofabioticgra-
dienoffshoretsatitsland.heoriginOursofimspulationeciesresultszonationshowpatternsthatoofve4rall,mtheangroCvesalabashitesofCaany
zonationpatternscouldhavetheiroriginsinabioticconditions:atidalgra-
dientinfluencingrecruitestablishmentand/orasalinitygradientinfluencing
lo(2006,calspCecieshaptergro3)wth.fortThishisspisecificconcordansite,tandwithwithwhatotherpropmosedangrovePiouetecologyal.

Wi0.12.120.120.110.100.1.090.080.0700.07.04000

DISCUSSION5.5.

131

Table5.6:Best12parameterizationsofsimulationsofsiteDleadingtothereproduction
ofthespecies-specificbasalareapatterns.(Rec=Firstrecruitment/ha,Num=Number
atterns)phedunmatcofRecTidalsortingNutrientavailabilitySalinityNumPOMICiΔi
100TideThreshNutrientGradHomogeneousSal02.830
100TideONutrientGradSalinityGrad02.860.03
100TideOHomogeneousNutSalinityGrad03.060.23
1000TideThreshNutrientGradSalinityGrad03.190.35
500TideONutrientGradSalinityGrad03.630.8
1000TideThreshHomogeneousNutSalinityGrad03.991.15
100TideParHomogeneousNutSalinityGrad182.4779.64
500TideThreshHomogeneousNutHomogeneousSal182.7879.95
100TideThreshNutrientGradSalinityGrad182.7979.96
500TideThreshNutrientGradSalinityGrad182.9480.1
100TideThreshHomogeneousNutSalinityGrad182.9580.11
100TideONutrientGradHomogeneousSal183.0980.26
Anyotherparameterizationcombination≥1>83.09

studies(e.g.McKee1995b).Additionally,ourstudydifferentiatedbetween
therelativeimportancesofthedifferentprocessesenteringintoplayforeach
site.ecificspWeobservedthatthesiteB,onthenorth-easternsideoftheisland,could
haveitspatternsofbasalareasapparentlydrivenbythecombinedeffectof
astrongsalinitygradientandtheinitialestablishmentofrecruitsfollowing
atidalsorting.Theselectedtidalsortingprocesswasalimitationonboth
sidesoftherangeofdispersionofthespecies,assumingacombinedactionof
waveactionlimitingthelowestrange,andseedtransportlimitingthehighest
range.Identically,atidalsortingprocesswaslikelytobethemainprocess
leadingtozonationforthesiteA.However,forthissitetheselectedtidal
sortingprocesswasalimitationonthelowerrangeofestablishmentonly,
assumedtobebecauseofwaveaction.These2siteswereontheNorth-
eastern(seaward)sideofCalabashCay.Ontheotherside,thesitesCand
Ddidnotneedtidalsortingtoreproducetheirpatternsofbasalareas.They
appearedtobeundertheeffectofagradientofsalinityornutrientavailability
onindividualgrowth.Thismightberelatedtothewesternpositionofthese
sitesCandD,wheretheyaremoreprotectedagainsthightidesdrivenby
thewindandthereforemaybelessinfluencedbytidalregimes.Additionally,
Piouetal.(2006,Chapter3)arguethattheprotectedsituationofthese
2sitesallowmoresurvivalonthissideoftheisland.Thiswasproposed
asinfluencingthehomogeneityofspeciesdominancewithinthezonesin
Piouetal.(2006,Chapter3),andasproducingaquitehighavailabilityof
seedlingonthissideoftheisland.TheL.racemosaandA.germinansseeds

Wi0.24.230.190.1700.11.0700000000

132

5CHAPTER

Figure5.4:Fieldobservedbasalareas(openmarks)andbestKiWisimulationresults
(filledmarks)perspecies(triangles=A.germinans,squares=L.racemosaandcircles=R.
mangle)andzonesofthefoursites(atod)ofCalabashCay.Errorbarsofsimulation
resultsrepresentthestandarddeviationof200values.Thebestsimulationswereselected
astheparameterizationsobtainingthesmallestPOMICvaluepersites(thefirstlineof
thetables5.3to5.6respectively).

couldprobablycomefromthebigtreesthatsurvivedHattiethemostinland,
whiletheR.mangleonescouldhavebeenproducedbythedwarftreesthat
survivedthehurricane(Piouetal.2006Chapter3).
ThelackofreproductionofsomebasalareapatternsofsiteAmightbe
alsolinkedtoseedavailabilityquestion.Piouetal.(2006,Chapter3)pro-
posedthatsuccessionmighthaveleadtothesehomogeneouszonesonthe
easternsideofCalabashCay.Onthepresentsimulationstudy,wedidrepro-
ducespeciesdominancesuccessionwiththespecies-specificparametersasin
Chapter4.Thus,therewasprobablyanotherprocesstoexplainwhynoA.
germinanswerefoundonthesiteAonthefield.Thesimulationsshowed
thatthisspeciescouldgrowthere,withorwithoutaneffectoftheabioticgra-
dients.Weshouldtestwithothersimulationsifchangingtheinitialspecies

5.5.DISCUSSION

133

ratioofseedavailabilitywouldreproducethepatternsofbasalareaforsite
A.However,anotherprocessnotsimulatedonourstudymightbethatthe
siteAtopographycouldhavechangedduringthelast41yrs.ThefactthatR.
mangletreesinthe3firstzonesofthissiteisoftenfoundinbunchofstems
spreadinginalldirectionsfromacenterpoint(C.PiouandI.CFeller,per-
sonalobservations)couldbeatreearchitecturecharacteristicthatindicates
aninitialestablishmentofsparseR.mangletreesformingsmall“islands”
ofcolonizationandsediment-trap.Actually,thistypeofislandstructureis
nowfoundonthefringezoneofsiteA.Bysedimentationandpeatproduc-
tionaroundtheseislandsoriginallyover-washed,thefirst3zonesofsiteA
mighthaveincreasedinelevationcomparedto1961.Thus,previouslower
elevationcouldhaveretainedA.germinansseedlingtoestablish.Obviously,
beforearguingfurtherinfavorofthisoftenrefutedland-buildinghypothesis
(Davis1940,orseeBertrand1999),oneshouldalsotestotherhypothesisof
processesthatleadtotheabsenceofA.germinansonthissite.
Thenon-reproductionofthepresenceofL.racemosaonthefirstzoneof
siteBisanotherproblematicpattern.Thetidaleffectobviouslydoesnotlet
thisspeciesestablishonthiszoneinKiWi(e.g.bestfirst5simulations).And
withnotidaleffectsimulated(for6thbestparameterizationintable5.4),the
modelleadstothepresenceofA.germinansonthisfirstzonewhileitwasnot
seenonthefielddata.Assumingthattidalsortingeffectwouldhaveoccurred
onsiteB,aprocessinchangeofelevationcouldbeareasonofpresenceof
L.racemosainthefirstzone.TheseL.racemosawereobservedwithcable
rootsthatshouldnormallybeburied,onthesurfaceofthesediment.Thus,
asandbankmighthavebeenleftthereafterHattie,whereindividualsfrom
thisspeciescouldestablish,andanerosionprocessfromwavesofminor
stormscouldhavethenremovedthissediment.Thus,historicconfiguration
probablyplayedanimportantroleinsiteAandBrecoveryandtheirspecies
zonationpatterns.Eventually,palynologicalworksonpalaeo-vegetation(e.g.
Behlingetal.2001)andanalysisofsedimentorigin(e.g.Marchandetal.
2003)couldenhancethehistoricknowledgeonthese2specificsitestoanswer
thequestionsofpresence/absenceofspecies.
Weassumedinourstudythatinterspecificcompetitionoccuratthelevel
oftheindividualtreesamongthethreeCaribbeanmangrovespecies.Wecon-
sideredforthatdifferentgrowthcapacitieswithspecies-specificparameters,
aswellasspecies-specificcapacitiesofspatialcompetitionforresourcesimu-
latedwiththeFONapproach.Theobjectivewastotesttheeffectsofabiotic
gradientsandtidalsortingassuminganunderlyingcompetition.Neverthe-
less,withthesimulationsusingnoeffectoftidalsortingandabioticgradients,
weindirectlytestedifcompetitionamongindividualscouldappeartobea
processexplainingalonethezonationpatterns.Weobservedthatitdidnot.

134

5CHAPTER

Wedidunderlyingnottcompestdirectlyetition(ifnothespaecies-spbioticgecificradientsadifferencesndtidalinsgroortingwthpassumingarameters,no
orinFONparameters)couldleadtothereproductionofthebasalareapat-
notterns.torHoespweectver,otherusingotherpatterns.FONWeusedsettingsasoprgroecies-spwthepcificFarametersONwsettingsouldtimplyhat
assuredthatifaspecieswouldcolonizeanemptyareawithouttheothertwo,
thestandspofatternsBelizeofrwouldelationshipbereproamongduceddbh(asandindCensithapteryobserv4-edAppinmendixonospA,eandcific
firstanalyzedbyBergerandHildenbrandt2003).Additionally,thespecies-
specificgrowthparametersalsoreproducepatternsofrelationshipamong
modbhdeland(hCheneightandimplemenTwilleyted1in998).theSfiorstmunderangroavedpattern-orienynamictedfindividual-basedramework,
the“no-interspecific-competition”scenariowouldanywaymisstoreproduce
theseassess2theimpeffectortantoflackpatterns.ofAhabitatrecommendationpartitioningforpropfoseduturebwyorkClarkceouldb(2004):eto
testingiftheestablishmentofsaplingsbyproximityandwithdifferentca-
pacitpatterns,yoforicopingfitnwitheedstoshadebewcomould,binedbywithitself,otherarrivproetcoresses.eproducezonation
Finally,thisstudyillustratedtheimportanceofabioticconditionsonthe
creationofspecieszonationpatternsinmangroves.Otherpattern-oriented
hysimpoulationthesesstudiesillustratedsuchinastFigurehe5presen.1.Etonevidencecouldcriteriaassessbasedfurtherontheinformationdifferent
theoreticapproachsuchasthePOMIC,couldhelpinrankingtheimpor-
thentanceleadofetoacahcprolearercessbepicturehindofthesethespheypcificotheses.importanceSimofulationeachdstudiesrivingwforce.ould
Thescalesofactionoftheseforcescouldalsobeassessedandiftheyare
tobeconsideredasdriving-ormaintaining-forcesforthemangrovespecies
patterns.zonation

5.6Acknowledgements
ManythankstoMarthaLilianaFontalvoHerazoandMarcTaylorforreading
andgivinginterestinginputsonthispaper.Thisstudywasfinancedunder
theDFGprojectBE1960/2-1(PUME).

eferencesR5.7

BallMC(1980)PatternsofsecondarysuccessioninamangroveforestinsouthernFlorida.
44:226-235Berlin)(Oecologia

REFERENCES5.7.

135

BauerS,BergerU,HildenbrandtH,GrimmV(2002)Cyclicdynamicsinsimulatedplant
populations.ProceedingsoftheRoyalSocietyofLondonB269:2443-2450
BauerS,WyszomirskiT,BergerU,HildenbrandtH,GrimmV(2004)Asymmetriccom-
petitionasanaturaloutcomeofneighbourinteractionsamongplants:resultsfromthe
field-of-neighbourhoodmodellingapproach.PlantEcology170:135-145
BehlingH,CohenMCL,LaraRJ(2001)StudiesonHolocenemangroveecosystemdynamics
oftheBraganaPeninsulainnorth-easternPar´a,Brazil.Palaeogeography,Palaeoclimatol-
ogy,Palaeoecology167:225-242
BergerU,HildenbrandtH(2000)Anewapproachtospatiallyexplicitmodellingofforest
dynamics:spacing,ageingandneighbourhoodcompetitionofmangrovetrees.Ecological
132:287-302dellingMoBergerU,HildenbrandtH(2003)Thestrengthofcompetitionamongindividualtreesand
thebiomass-densitytrajectoriesofthecohort.PlantEcology167:89-96
BergerU,HildenbrandtH,GrimmV(2002)Towardsastandardfortheindividualbased
modelingofplantsimulations:Self-ThinningandtheFieldofNeighborhoodapproach.
NaturalResourceModeling15:39-54
BergerU,HildenbrandtH,GrimmV(2004)Age-relateddeclineinforestproduction:mod-
ellingtheeffectsofgrowthlimitation,neighbourhoodcompetitionandself-thinning.Jour-
nalofEcology92:846-853
BergerU,AdamsM,GrimmV,HildenbrandtH(2006)Moldellingsecondarysuccessionof
neotropicalmangroves:Causesandconsequencesofgrowthreductioninpioneerspecies.
PerspectivesinPlantEcology,EvolutionandSystematics7:243-252
BertrandF(1999)MangrovedynamicsintheRivi`eresduSudarea,WestAfrica:anecogeo-
graphicapproach.Hydrobiologia413:115-126
BrecklingB,Mu¨llerF,ReuterH,H¨olkerF,Fr¨anzleO(2005)Emergentpropertiesinindividual-
basedecologicalmodels-introducingcasestudiesinanecosystemresearchcontext.Eco-
logicalModelling186:376-388
ChenR,TwilleyRR(1998)Agapdynamicmodelofmangroveforestdevelopmentalong
gradientsofsoilsalinityandnutrientresources.JournalofEcology86:37-51
ClarkePJ(2004)Effectsofexperimentalcanopygapsonmangroverecruitment:lackof
habitatpartitioningmayexplainstanddominance.JournalofEcology92:203-213
DavisJH(1940)TheecologyandgeologicroleofmangrovesinFloridaPublicationsofthe
CarnegieInstitute,Washington,D.C.,USA
GrimmV,RevillaE,BergerU,JeltschF,MooijWM,RailsbackSF,ThulkeH-H,Weiner
J,WiegandT,DeAngelisDL(2005)Pattern-orientedmodelingofagent-basedcomplex
systems:lessonsfromecology.Science310:987-991
ImaiN,TakyuM,NakamuraY,NakamuraT(2006)Gapformationandregenerationof
tropicalmangroveforestsinRamong,Thailand.PlantEcology186:37-46
Jim´enezJA,SauterK(1991)StructureandDynamicsofMangroveForestsAlongaFlooding
Gradient.Estuaries14:49-56
KomiyamaA,MoriyaH,PrawiroatmodjoS,TomaT,OginoK(1988)Primaryproductivity
ofmangroveforest.In:OginoK,ChiharaM(eds)Biologicalsystemofmangroves.A
reportofeastIndonesianmangroveexpedition1986.EhimeUniversity,Ehime,p97-117
LugoAE(1980)Mangroveecosystems:successionalorsteadystate?Biotropica12:65-72
MacnaeW(1968)Ageneralaccountofthefaunaandfloraofmangroveswampsandforests
intheIndo-West-Pacificregion.AdvancesinMarineBiology6:73-270
MarchandC,Lallier-Verg`esE,BaltzerF(2003)Thecompositionofsedimentaryorganic
matterinrelationtothedynamicfeaturesofamangrove-fringedcoastinFrenchGuiana.
Estuarine,CoastalandShelfScience56:119-130

136

CHAPTER5McKeeKL(1993)Soilphysicochemicalpatternsandmangrovespeciesdistribution:recipro-
caleffects?JournalofEcology81:477-487
McKeeKL(1995a)MangrovespeciesdistributionandpropagulepredationinBelize:An
exceptiontothedominance-predationhypothesis.Biotropica27:334-345
McKeeKL(1995b)SeedlingrecruitmentpatternsinaBelizeanmangroveforest:effectsof
establishmentabilityandphysico-chemicalfactors.Oecologia101:448-460
cMcKeehKaracteristicsL(1995c)ofnInterspeotropicalecificvmangroariationveinseedlings:growth,Rbespoiomassnsetolighpartitioning,tandnandutrientadefensivvail-e
ability.AmericanJournalofBotany82:299-307
PiouC,FellerIC,BergerU,ChiF(2006)ZonationPatternsofBelizeanOffshoreMangrove
Forests41YearsafteraCatastrophicHurricane.Biotropica38:365-374
RDevelopmentCoreTeam(2006)R:Alanguageandenvironmentforstatisticalcomputing.
RFoundationforstatisticalcomputing,Vienna,Austria,URLhttp://www.R-project.org
RabinoSaengervitzPD(2002)(1978)MangroDispveersalpecologyrop,esrtiesoilviculturefmangroandvecponservropagules.ation,KluwBiotropicaerAcademics10:47-57Pub-
lishers,Dordrecht,TheNetherlands
SmithIIITJ(1987)Seedpredationinrelationtotreedominanceanddistributioninman-
groveforests.Ecology68:266-273
SmithIIITJ(1992)ForestStructure.In:RobertsonAI,AlongiDM(eds)TropicalMangrove
ThomBGEcosystems,(1967)Vol41.MangroveAmericanecologyGeophandydsicaleltaicUnion,Wgeomorphology:ashington,TDC,obasco,USAMexico.Journal
55:301-343EcologyofTomlinsonPB(1986)Thebotanyofmangroves,CambridgeUniversityPress,Cambridge
TwilleyModeltRR,oSRivimeulatera-MonroTrayjectoriesVH,inChenRR,estorationBoteroL(Ecology1999).MarineAdaptingPanollutionEcologicalBulletinMangro37:404-ve
419WiegandT,JeltschF,HanskiI,GrimmV(2003)Usingpattern-orientedmodelingforre-
vealinghiddeninformation:akeyforreconcilingecologicaltheoryandapplication.Oikos
100:209-222

ni

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North

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137

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Chapter

Spatial

6

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139

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orth-BrazilN

140

6CHAPTERSpatialstructureofaleaf-removing
crabpopulationinamangrove
North-BrazilofPiou,CyrilAr12ticle;tBobeerger,submitteUtad1to;&FWetlandseller,IlkaC.3

bstractA6.1playsTheakeyecologicalroleinengineerBrazilianandmlangroeaf-removeevingcosystems.decapoWdecrab,analyzedUcidesthecsorpatialdatus
distributionofaspecificpopulationatdifferentscalestoobservehowindi-
vidualbehaviorcouldalterspatialdistributionatpopulationlevel.First,
wtheeRconductedhizophoraamanglespatialpoinproptropatternotsontheanalysisofmangrothevefloburroorwatentscalerancesoffandew
meters.Theburrowentrances,althoughaggregatedaroundtheproproots,
fectshowofedinartraspegularlyecificscomppacedetitionadistributionmong(the∼c25cm)rabs.sSecondlyignalizing,waeapnalyzedrobableatef-
largescale(>10m)theeffectsofsurfaceelevation,lightintensity,proproot
coverage,typeofneighboringtreespecies(R.mangle,Lagunculariarace-
numosamb,erAofvicburroenniawengerminanstrances.)aThisnddemonstratedpneumatophoresthedensitpreferenceyonofthethesizecarabsnd
toinstalltheirburrowsatintermediatesurfaceelevationandproprootcov-
erage,conductedandainnaR.nalysismangleofclustering-dominatedofathereas.crabsFinallyaround,stilltheatR.largemanglescale,trees.we
ThisconfirmedthepreferenceofaggregationaroundR.mangletreesinR.
mangle-dominatedforest,butnotinL.racemosa-dominatedforest.Food
ancompetitionexplanationleadingforetoxclusionthesofmallsmallerscalecrabsregularfrompatternspreferredwashyphabitatsothesizedseenaast
largescale.Thishabitatpreferenceandtheobservedtransferofinfluenceof
thefeedingbehaviorfromsmalltolargescalemightexplainthevariationof
U.cordatusimportanceinNeotropicalmangroves.
KeyWords:Ucidescordatus,populationstructure,multiple
scales,spatialstatistics,habitatpreference,intraspecificcompeti-
tion.

1CenterforTropicalMarineEcology,Fahrenheitstrasse6,23859Bremen,Germany
2Correspondingauthor:cyril.piou@zmt-bremen.de
3SmithsonianEnvironmentalResearchCenter,POBox28,Edgewater,MD21037,USA

ODUCTIONINTR6.2.

6.2Introduction

141

Burrowingorganismsareecosystemengineersparexcellence(Jonesetal.
1997).Inmangroveecosystems,burrowingdecapodcrabsmaybethesecond
mostimportantgroupofphysicalecosystemengineersafterthetreethem-
selv1997)es.sinceSptheyecificallym,odifyburrothewinghabitatscrabsfaorreotherallogenicmangrovengineerse-floor(Jonesinhabitanetatsl.
andforthetrees(e.g.,Warren&Underwood1986,Smithetal.1991).In
cothermdatusangroL.ve1763forests(Ocypofondidae)orthernplaBysrazil,akeytheroleburroinwingleafremocrabval,Ucidesnuctrienortdatuscy-
clingprocesses(Schoriesetal.2003,Nordhausetal.2006),andthetrophic
corstructuredatusisoftalsoheseeconomicallyecosystems(Wimpolffortanetatl.for2000,thisKocregionh&Wwhereolff2they002).areUcideshar-
vestedintensivelyforhumanconsumption(e.g.,Glaser&Diele2004,Dieleet
al.2005).Thus,besidesbeingecosystemengineers,U.cordatuspopulations
playacriticalroleinthesehighlyproductivemacrotidalmangroveforests.

ThedistributionofU.cordatusisthetropicalandsub-tropicalmangrove
coastsoftheeasternAmericasfromsouthernFloridatosouthernBrazil
(Bright&Hogue1972).Acloselyrelatedsubspecies,U.cordatusocciden-
talis(sometimesrefertoasU.occidentalis)isfoundonthePacificsideofthe
AmericasfromBajaCaliforniatonorthernPeru(Bright&Hogue1972).In
additiontoBrazil,keyecologicaland/oreconomicrolesforthesecrabswere
reportedonlyintheGuayasRiverEstuaryinsouthernEcuador(Twilleyet
al.1997)andintheDominicanRepublic(Geraldes&Calventi1983).This
scarcityofreportsisnotduetothelackofstudiesonNeotropicalmangrove
ecosystems,whichhaveincreasedexponentiallyinthepast30years.Many
studiesofNeotropicalmangrovesreportedthepresenceofU.cordatusin
otherareas,e.g.,Belize(Middleton&McKee2001,McKeon&Feller2004),
Jamaica(Warner1969),CostaRica(Delgadoetal.2001),Panama(Sousa
etal.2003),Colombia(Canteraetal.1999),FrenchGuyana(Artigasetal.
2003).However,thebiologyofthiscrabhasseldombeenstudiedoutside
Brazil,probablyduetoeitheralackofunderstandingofitsimportancein
mangroveforestsortheabsenceoflargeU.cordatuspopulationsasinBrazil-
ianforests.TheseobservationsleadNordhausetal.(2006)toaskwhatare
thefactorsmakingU.cordatuspopulationsmoreorlessimportantforlitter-
processingroleindifferentNeotropicalmangroves.Theydemonstratedthat
thelitter-processingroleofsesarmidcrabsintheIndo-Pacificmangrovesis
occupiedbyU.cordatusinnorthernBrazil(Nordhausetal.2006).These
findingrefutedthehypothesisthatleaflitterprocessingisdrivenbyherbivo-
rousdecapodsinIndo-Pacificmangrovesandbythedetritalpathwayinthe

142

6CHAPTER

Neotropics(McIvor&Smith1995).
Toavoidthesegeneralizationsandunderstandthefactorsthatdrivethese
differencesamongmangroveecosystems,weneedtoconsidertheproblemof
scale.Itisunlikelythatobservationsbasedonasmallpartofthedistribution
ofU.cordatusholdforentirebiogeographicbiome.Levin(1992)argued
thatscaleiscentraltointerpretingecologicalpatternsandthattoscale
ecologicalprocessesfromsmalltoahigherlevel,onemustunderstandhow
informationistransferred.Levinalsopointedoutthatpatternsobserved
andunderstoodatlargescalesaremoreoftendrivenbyexternalforcesthan
atfinescales,whicharegenerallyautonomouslygenerated.Thus,thereare
compoundedriskstoseparatebiogeographicpatternsfromfindingsderived
locally.First,itwouldimplyanexternalforcesignificantlydifferentinthe
twobiogeographicbiomes.Second,understandinglocalpatternsdoesnot
assurethatthesameforcesaredrivinglargerscalepatterns.
Forburrowingandleaf-removingcrabs,andparticularlyforU.cordatus,
biologicalknowledgeisrudimentary.Oneofthemainchallengesforecologists
istounderstandthetransferofinformationfrombiologicalcharacteristics
attheindividualleveltothepopulationlevelorhigher.Thisinformation
transferisunderstandablethroughthestudyofspatialpatternsatdifferent
scale(e.g.Schooley&Wiens2001,Rossi2003a).Spatialpatternshave
beenanalyzedextensivelyforvegetationstructure,landscapeecology,and
soilecologywithstatisticalmethodsdevelopedfor>50yr(e.g.Clark&
Evans1954,Diggleetal.1976,Ripley1977,Diggle&Gratton1984,Rossi
etal.1992).Throughcharacterizationsofregularorclumpedpatternsof
individualsatdifferentscalesandcomparisonwithothertypeofevents,one
canunderstandwhichprocessesofinteractionamongindividualsarestronger
andhowtheyinfluencethepatternsathigherlevels.Atypicalexampleisthe
regularitythatappearsduringthegrowthofeven-agedforeststandswhile
individualtreescompeteforlightand“self-thin”inclumpedpartsofthe
forest(e.g.Kenkel1988).Toourknowledge,thespatialdistributionsof
burrowingdecapodshavenotbeenanalyzed.Investigationsonthespatial
patternsofecosystemengineersareneededtoincreaseourunderstandingof
theirinfluenceonthedistributionsofotherspecies(e.g.Schooley&Wiens
2001).Butadditionally,theunderstandingofthefactorsinfluencingspatial
distributionofU.cordatusatdifferentscalescouldleadtotheidentification
ofpreferredhabitattypethatcouldlaterexplaintheabsenceoflargeU.
cordatuspopulationinsomemangrovesoftheNeotropicandtheirlocallack
ofimportanceinlitterprocessing.
ThepresentstudyexaminesfirstthespatialpatternsofburrowsofU.cor-
datusatsmallscale(<10m)inthemangroveecosystemsontheCaet´ePenin-
sula,Brazil.Thespecificobjectiveofthisfirstapproachwastoinvestigateif

METHODS6.3.

143

theinteractionamongcrabs,whichwereseenasterritorialandfoodlimited
(Nordhaus2004,Nordhausetal.2006),ledtocompetition-characteristicpat-
ternsofregularspatialdistributionasplantsdoundercompetitionforspace.
Second,weanalyzethespatialdistributionoftheseburrowsinrelationto
RhizophoramangleL.proproots,whichareassumedtoprovidecrabswith
refugeandburrowstability(Rademaker,unpublishedmanuscript).Third,
weanalyzethefactorsinfluencingthecrabdensityandsizeatlargescale
(>10m),focusingonlightavailability,elevationoftheground,rootzoneoc-
cupation,andneighboringtreespecieswhichwerethemainfactorshypoth-
esizedtoinfluenceU.cordatuspopulationdensities(Nordhausetal.2006).
Finally,alsoatlargescale,westudytheclusteringofcrabburrowsaround
R.mangletrees,whoseleavesarethefavoritefoodsourceforU.cordatusin
thisstudyarea(Nordhaus2004,Nordhausetal.2006).

dsethoM6.3

areatudyS6.3.1

ThestudyareasweretwomangrovesitesoftheCaet´ePeninsula,thefocus
areaofthelong-termresearchproject,MangroveDynamicsandManagement
(MADAM,Bergeretal.1999).Mangrovescovers140km2ofthispeninsula
thatislocatedjustnorthofBragan¸ca,200kmeastofBel´em,Par´a,Brazil
(forDieleemoretal.details2005,seeWoNordhauslffetal.et2al.000,2006).KochO&urWolfffirst2site,002,cKocalledhetRF,al.w2as005,a
R.mangle-dominatedforestwithsparseAvicenniagerminansL.individuals
etonal.the2n006).orthTofhethepsecondseninsulaite(∼(within10kmawtheasy),iteRcalledFdLF,escribwaedsdbyominatedNordhausby
wLasragunculariaegeneratingracafteremosathe(L.)Gconstructionraetn.f.owfaithroadfewR.acrossmangletheptrees.eninsulaThisduringsite
the1970s(ontheoppositesideoftheroadofsiteAFdescribedbyNordhaus
etal.2006).Weselectedthese2sitestocover2typesofvegetationfound
intheCaete´peninsulawhereUcidescordatusisfoundinrelativelyhigh
anddensities.localvaNoteriationsthatinothertdominanceypesofavlsoeogetationccur,arefrequenftoundlyinlinktheedptoeninsula,ground
ation.elev

144

CHAPTER6

6.3.2Noteonthesamplingofburrowsasproxyofcrab
pulationopPopulationestimationsfromburrownumbershavebeenusedwidelyfor
othermangrovecrabspecies(e.g.Macintosh1988,Warren1990,Skovetal.
2002,Salgado-Kent&McGuinness2006).Forthepurposesofthisstudy,we
estimatedthatburrowcountsandmeasurementsweremorepracticalthan
crabfishing.Inthestudyarea,crabcollectorscollectcrabsbyentering
theirbarearmintotheburrows.Thismethodleadsalwaystotheextensive
disturbanceofthemuddysubstrate.Othermethodsareusedinotherpart
ofBrazil,butthelocalpopulationisnotawareofthoseandwepreferrednot
tointroducethemasitcouldentailthesustainabilityofthefishery(Dieleet
al.2005).Totesttheassumptionthatburrowentrancewasrelatedtocrab
size,apreliminarysurveywasdoneduringneaptidesinthedryseasonof
2003atsiteRF.Diametersofburrowentrances(N=310)weremeasured
tothenearestcm.TheU.cordatuslivingontheseburrowswerefished,and
theircarapacewidthsweremeasuredtothenearestmm.Anon-parametric
regressionwasappliedtodetermineiftherewasasignificantrelationship
betweentheentrancesizeandthecarapacewidthofthecrabs.

6.3.3Spatialdistributionofburrowentrances
calessmallatInordertoanalyzethespatialdistributionofU.cordatusburrowsata
smallscale,weproducedmapsofoccupiedburrowsvisibleinthesubstrate
ofopennon-rootedareas.Fivemaps,1×3m,wereproducedoutofpho-
tographsofanidenticalareaatfivesuccessivedatesfromDecember2003to
January2004.Butbecausethenumberofpointswasrelativelylowforthe
statisticalanalysis(closeto20)anadditionalmapof3×5mwasdoneby
directmappingofanotheropenareaatthesameelevationinOctober2004.
Toobservetherelationofburrowpositionwiththepositionsofthesurround-
ingproproots(i.e.,aerialrootsofR.mangle),a2×1mmap(enoughin
thisplottohave>20burrowsand>20roots)wasproducedofaR.man-
gle-rootedareawhereallburrowandprop-rootpositionsweremarked.All
thesemapsweredoneinsiteRF,atlocationsofelevationsabovemeansea
level>200cm,andwithamediansizeofburrowentrances<5cm.These
mapsshowedtheX,Ypositionforeachburrowentranceandproproot(for
thesecondcase)withaprecisionof±5cm.
Spatialpointpatternwereanalyzedusingtheunivariate(distributionof
burrowsalone)orthebivariate(distributionofburrowsaccordingtoposition
ofroots)Ripley’sK-function(Ripley1977,1981)toassesstherandom,clus-

METHODS6.3.

145

ofteredevenortsr(1egularand2p:inatterntheofbivtheseariatepocase,sitions.rootpoConsideringsitionsandtwoburrowdifferenpttositions;ypes
intheunivariatecaseonlyburrowpositions),theK-functionwascalculated
ula:ormfthewith

An1n2
K1→2(r)=n1×n2ωi(r)δij(r)(6.1)
=1j=1iwhererwastheradiusofacirclewherethedensityofpointshadtobe
pointsconsidered;tobeAwasconsideredtheefnortiretypaereaofofevtenhet1plot;and2n,1randespnectiv2theely;nωum(rb)weraosf
afunctionofedgecorrectioncalculatedfromthedensityoftype2onthe
areareturningof1radiusiftrheaporoundintjthewaspaointti(distanceoftyp≤er1);ofapndointδ(ir)andwas0afotherwise.unction
Theunivariateadaptationofthisfunctionconsideredonlyonetypeofpoints
(type1=type2=burrowpositions,andalwaysj=i).Theprecisionof
therincrementwasconsideredasthefieldmeasurementprecision(5cm),
andthemaximumrwasconsideredhalfofthesmallersideoftheplots.
TheK-functionunderaPoissonprocessdistribution(orcompletespatial
randomness)shouldfollowπ.r2,andwasthereforelinearisedtoamoreeasily
readableL-function(DiscussionofBesagonRipley1977):
#L1→2(r)=K1→2(r)−r(6.2)
πForeachanalysis,aconfidenceenvelopeat95%forcompletespatialran-
domness(CSR)wascalculatedusingthe2.5%and97.5%quantilesofthe
L-functionof999MonteCarlorandomizationsimulations.IftheL-function
valuesoftheobservedareawerehigherthanthisconfidenceenvelopefora
specialradius(r)ofmeasurement,clusteringorattractionwasconsideredat
thescaleofthecorrespondingradius.However,iftheL-functionvalueswere
lowerthantheconfidenceenvelope,regularityorrepulsionwasconsideredat
thescaleofthecorrespondingradius.

6.3.4Habitatheterogeneityeffectoncrabpopulation
caleslargeatulationInordertstructureoanalyzeatsthecalespofotensevtialeraleffectsmeters,ofthreedifferentvtransectsariablesofon94cm,rab59pop-m
andously6,0mthesewetrehreelaidtransectsacrossdidmangronotvecovforesterarareasepresenintNoativveemsberample2004.ofallObthevi-
mangrovesofthepeninsula(213m2sampledagainst140km2ofmangroves

146

6CHAPTER

onthepeninsula),butwereselectednon-randomlytocoveranaswideas
possibleelevationrangeandtwotypeofforest:R.mangle-dominatedand
L.racemosa-dominated.ThefirsttwotransectsweredoneatsiteRFina
frequentlyinundatedarea.Thethirdtransectwaslaidinahigher,lessfre-
quentlyfloodedareaatsiteLF.Alongthesetransects,each1m2wastaken
asasamplingquadratwherethefollowingmeasurementsweredone:number
andsizeofoccupiedcrabburrowentrances;surfaceelevation,rootoccupa-
tion,speciesofneighboringtrees,andlightavailability.Measurementsof
crabburrowsweredoneduringlowtideatneaptidesothatwecouldseethe
maximumofburrows.Theburrowentrancediametersweremeasuredatthe
nearestcm.Allburrowswereopeneddownto30cminthemudtoconfirm
thatonlyoneburrowentrancewasconsideredpercrab.Theadditionalen-
trancesofasingleindividualwerethereforediscarded.Tocomparethethree
sitesrelativetomeansealevel,surfaceelevationwasmeasuredwithanop-
ticalleveltothenearestcm,takingasreferencefixtidalgauges.Twotypes
ofrootoccupationofthesurfaceofthe1m2wereconsidered:areaoccupied
byR.mangleproproots,andareaoccupiedbyothermangrovespecies(i.e.,
AvicenniagerminansandL.racemosa)aerialroots,orpneumatophores.For
R.mangle,wemeasuredthepercentageofthesurfaceareaoccupiedbyR.
mangleproproots.SinceA.germinansandL.racemosahavecableroots
thatrununderthesurfaceofthemudandthepneumatophorescomingup
thesurfaceweretoonumeroustobemeasured,itwasnotpossibletoquan-
tifytheactualareathatwouldinfluencewherethecrabsbuilttheirburrows.
Thus,aqualitativemeasurementwasattributedtoeachplotareaaccord-
ingtotheapproximateproportionofareaoccupiedbypneumatophores:0
-nopneumatophores,1-lessthan∼1%occupied,2-between1%and5%
occupied,3-morethan5%occupied.Weusedaqualitativemeasurement
todescribetheneighboringtreesspeciesinthesurrounding3mper1m2
quadrat:0-whennotreetrunkswerefound;1-whenA.germinanswas
foundordominated;2-whenL.racemosawasfoundordominated;and3
-whenR.manglewasfoundordominated.Lightavailabilitywasmeasured
withlightsensorsLI-190(LI-CORinc.).Photosyntheticallyactiveradiation
(PAR)wasestimatedaroundnoon,onnon-cloudydays,withthreeofthese
sensorsinthemiddleandontwobordersper1m2at75cmabovetheground.
ThemeanPARofthesesensorswasthencomparedtoasensoroutsidethe
canopymeasuringPARatthesametime.Theselightmeasurementswere
usedtocharacterizethecanopydensitydirectlyabovethequadrates,to-
getherwiththeshadowofbigrootsandtrunksofthesurroundingassumed
tobepreferredbyU.cordatus(Rademakerunpublishedmanuscript).
Thenon-parametricKruskal-Wallisanalysisofvariance(ANOVA)was
usedtoanalyzetheeffectofthetwoqualitativecategoricalvariables(neigh-

METHODS6.3.

147

boringspeciesoftree,andpneumatophoresimportance)andthetransecton
themedianburrowsizeandnumberofburrows.m−2.Ageneralregression
modelwasconstructedbyforwardstepwiseselectionofvariablesproposing
thethreecontinuousexplanatoryvariables(i.e.,percentageofR.mangle
rootscoverage,surfaceelevationabovemeansealevel,andpercentagePAR
ousreacvhingariancesthesofoilsmedianurface)burroandtwheirsizerespandectivnuembersquaresoftburrooews.mxplain−2.thecontigu-

6.3.5Spatialdistributionofburrowentrances
caleslargeatToanalyzethepatternsofspatialdistributionofU.cordatusatlargescale
(tensofmeters),weusedthemethodofspatialpatternanalysisalongtran-
thesectsdadaptedistributionsbyOof’Driscollseabirds.(1998)ThisfromanalysistheKconsidered-functionoftransectsRipleytoofabinsnalyzeof
measurementwhereeachpointwithinabinwasconsideredofdistanceB/2
(Bproacbehingworktheedsizeonlyofifthethesbin)izetoofttheheobintherwpasoinntsotwithinsmallertthishanbin.theThiswidthap-of
thetransect.Weconsideredthethreetransectsdescribedintheprevious
2sectionmeasuredinseparatelythese,binswhereweereach1assumedmwnaseighabbinorsofinthereading.rangeAllofthe0.5m.burroWwse
conductedanunivariateanalysistoestimatetheclusteringoftheseburrows
ovmateeriflargeapotendistancestial(upclusteringtohofalftthesehelengthburrowsofwtheasduetotransects).thepAlso,resencetoofesti-R.
mangletrees,eachtrunkofthisspecieswithinthe1m2wasalsoconsidered
forabivariateanalysis.TheK-functionwascalculatedwithincrementsofr
=1mwiththesimplifiedformulaforonedimension:
1n1n2
K1→2(r)=n1×n2i=1ωi(r)j=1δij(r)(6.3)
Foburrorthewsunivmeasuredariatealonganalysis,thenen1tirewaseqtransectualton(with2andalweaysqualjto=i).theInnumthebecraseof
ofthethebburroivws.ariateForbanalysis,othtcases,hetyptoe1evwasaluatethetheR.smangleignificancetrees,ofandthetcypelustering2was
atdifferentscales,999Monte-Carlorandomizationsoftheburrowpositions
Kˆalong(r)otfheK(r)transectswerewceregalculated.enerated.TheFfromunctiontheseL999(r)swimasulations,calculatedthefmoreansthe
datasetsandthe5thmaximumvaluesofthe999simulationsas:
L1→2(r)=K1→2(r)−Kˆ1→2(r)(6.4)

148

6CHAPTER

IftheL(r)ofthedatasetwashigherthantheL(r)ofthe5thmaximum
values,clusteringorattractioncouldbeconsideredattherscalewitha
5%.9foconfidenceAlllicensespatialR-softawanalysesre(vwereersionc2.2).onductedOwtherithastatisticallgorithmsanalysespreparedwerewithdtheoneGwNU-ith
STATISTICAcStatsoft(version6.0).
esultsR6.46.4.1Burrowsasproxyofcrabpopulation
Thesizeofthe310capturedU.cordatuswassignificantlycorrelatedto
theirburrowentrances(Fig.6.1),whichindicatedthatthisvariablecould
beusedasaproxyofcrabsize.

Figure6.1:Relationshipbetweensizesof310burrowentrancesandsizesofUcides
cordmangroatusvesofcapturedtheinCaete´them.PSeninsulaamples(graylmadeineratepresenneaptttideheinregressionOctober-Noline,veSpmberearman2003Ron=
0.74,SpearmanRanktestp<0.01).

6.4.2Spatialdistributionofburrowentrances
calessmallatNon-rootedareaspresentedaregularspatialdistributionofburrowen-
trances,withspacingaround25cm(Fig.6.2).Thelargerareagaveamore
significantregularpattern(Fig.6.2g)thanmostofthesmallerareas(Fig.

6.4.TRESULS149

Figure6.2:Spatialpointpatternanalysisofburrowentrancesonnon-rootedareas.a)
areaplottedthe27thofOctober2004,b)tof)areasplottedfrompicturestakenbetween
December2003andJanuary2004ofanidenticalarea,g)UnivariateL-functionresult
ofa),h)UnivariateL-functionresultofb)tof).Forg)andh)dashedlinesrepresent
95%confidenceenvelopeforcompletespatialrandomness(CSR)using999MonteCarlo
randomizations.

6.2h),but2smallplots(Fig.6.2candd)gavealsoasignificantregular
patternaround20-25cmofradius.Thesetemporalvariationsinregularity
ofthepatternmightbeduetotemporaldifferencesofburrowusedepending

150

CHAPTER6onsitionthewtasidalarlsooegimebservandedcarabroundactivittheys.ameArscaleegularforptatternheroofotedburroareawssurvdispoey-
(Fig6.3b).However,whentheattractionoftherootsfortheburrowswas
Thus,considered,U.coracdatuslearpreferenclusteringtiallyappecreatedaredattheirscaleburroof1w0etnot15rancescm(closedFig.6to.3c).R.
mangleproproots.Thecrabsinthissituationstillkeptaregulardistance
other.heacfrom

Figure6.3:Spatialpointpatternanalysisofburrowentrancesandproprootpositionon
aRhizophoramanglerootedarea.a)areaplottedthe8thofNovember2004,b)Univariate
L-functionresultforburrowpositionsc)BivariateL-functionresultforburrowinteraction
withrootposition.Forb)andc)dashedlinesrepresent95%confidenceenvelopefor
completespatialrandomness(CSR)using999MonteCarlorandomizations.

STRESUL6.4.

151

Table6.1:Meanoccupiedburrownumbersandsizesof2burrowentrancepertransects.(*
notethatthemediannumberofburrowsandsizepermwereusedinthenon-parametric
statisticalanalysis,notthemeans)
TransectNumberofm2Mean*numberofMean*sizeof
analysedoccupied2burrowsburrowentrances
perm(±SD)(cm±SD)
1946.44±3.216.02±1.89
2594.68±2.204.93±1.89
3606.93±2.844.23±1.58
All2136.09±2.995.21±1.96
6.4.3Habitatheterogeneityeffectoncrabpopulation
Wefoundsignificantdifferencesinburrowsizesandnumbersamongthe
threetransects(Table6.1,Kruskal-WallisANOVAs:H(2,213)=56.291,
p<0.0001;H(2,213)=20.698,p<0.001,respectively).Thethirdtran-
secthadsmallerburrowsandthesecondonehadfewerofthem.Theef-
fectofspeciesofneighboringtreeswasalsosignificantonsizeandnumber
withgenerallymoreandbiggerburrowsclosetoR.mangletrees(Fig.6.4,
Kruskal-WallisANOVAs(H(3,213)=35.562,p<0.0001;H(3,213)=26.267,
p<0.0001,respectively).Thesizeandthenumbersofcrabburrowswere

neighFigureboring6.4:treeNumspeberciesin(crosses)the3mandamroundedian(0:sizeno(botrees,xes)1:ofA.burrowsgerminansdependingdominated,onthe2:
L.racemosadominated,3:R.mangledominated).Errorbarsrepresentfirstandthird
quartiles.

152

6CHAPTER

notlargerwithAvicenniagerminansandL.racemosatreesintheneighbor-
hoodthanwithout(Fig.6.4).Thiswasconfirmedbynegativerelationships
betweenburrowsizeandnumberagainstthequalitativevariableofpneu-
matophoresoccupation(Fig.6.5).Thequadratswiththehighestvaluesof
thisvariableweretheoneswithlowestnumbersandsmallestcrabburrows.

itativFigureed6.5:escriptionNumbofer(crosses)pneumatophoresandmedianocsizecupations(boixnes)theofbsquareurrowsmeterdepeofndingmoneasuremenaqual-t
more(0:nopthan5%neumatophores,occupied).1:Errorlessbthanarsr∼1%epresenoctcupied,firstand2:tbethirdweenquartiles.1%and5%occupied,3:

Surfaceelevationwasseenasrelatedtoburrownumberandsize(Fig.
6.6).Onlyquadratsabove150cmofelevationhad>9burrows.m−2.The
quadratswithmedianburrowsize>7cmwereinelevationsbetween150and
200cmabovemeansealevel.Rhizophoramangleproprootsoccupationwas
alsocorrelatedtoburrowssincethequadratswithmedianburrowsize>7
cmor>9burrows.m−2werealwayswithR.mangleroots(Fig.6.6).The
PARpercentagereachingthegroundhadalessstraightforwardrelationship,
exceptthatquadratswithmedianburrowsize>7cmor>9burrows.m−2
wereinhighlylightenedpoints(PAR%>60%).Thestepwiseselectionof
thegeneralregressionmodelconfirmedthesetrends(GRM,table6.2).It

6.4.TRESULS153

excludedthepercentageofPARbutincludedelevationandR.mangleprop
rootscoverageasexplanatoryvariablesofmedianburrowsizeandnumber.
numSurfaceber.Belevothationewasxplanatorysignificanvatlyriableschadorrelatedtheirtosquareburrowrosoizetsbutalsonottincludedotheirin
theGRMwithnegativeparameters,implyinganoptimalsituationofsize
andnumberofburrowsatintermediateelevationandcoverageofR.mangle
ots.roprop

Figure6.6:Numberofburrowspersquaremeterdependingontheelevation,R.mangle
propsizesorofotthecoveburroragewsandmPeasuredARpeinrceneachtagesquarereachingmeterthearesrquareepresenmteteredwithmeasured.thesMymboedianls:
crosses<5cm,5cm<triangles<7cm,squares>7cm.

154

6CHAPTER

Table6.2:ResultsofGeneralRegressionModelwithbackwardstepwiseselectionamong
thethreecontinuousexplanatoryvariablesandtheirrespectivesquarestoexplainthe
contiguousvariationofnumberofburrowspersquaremetersandmediansizeofburrows.
LasttwocolumnsshowtherespectiveparametersestimatesintheGRM,boldedcases
showsignificantinfluenceatunivariatelevel.
FEffectErrorpParametervalueParametervaluefor
dfdfforburrowburrowmediansize
number(±SE)(±SE)
Intercept1.78122070.171-0.0347±2.545-2.194±1.16
Proproot%of28.95322070.0000.822±0.1470.347±0.067
occupation
(R%)Elevation(E)24.75822070.0000.036±0.030.094±0.013
%ofPARpooled0----
groundhingreacAR%)(PR%215.59322070.000-0.048±0.0119-0.021±0.005
E228.83722070.000-4.6e−5±8.6e−5-3.0e−4±3.9e−5
PAR%2pooled0----

6.4.4Spatialdistributionofburrowentrances
caleslargeat

ThethreetransectspresenteddifferenttrendsofaggregationofU.cordatus
burrows(Fig.6.7).Thefirsttransectshowedsignificantclusteringofburrows
atascalebetween2and15m,withthehighestsignificancearound10m
(Fig.mangle6.7b).treesTwithheburrohighestwsweresignificancealsosignificanaroundatly5amsggregatedcale(Fig.around6.7c).theTheR.
secondtransectpresentedonlyaverysmallsignificantclusteringatscaleof
a3-45mms(Fig.cale6around.7e).HothewevR.er,tmangleheburrotreeswsw(Figere6.7fstill).Trsignificanansecttlythree,aggregatedwhichwaast
inaL.racemosa-dominatedforest,stillhadsomeR.mangletreespresent
(Fig6.7g).But,theburrowswerenotclusteredatanyscale(Fig.6.7h),
oraroundtheR.mangletrees(Fig.6.7i)alongthistransect.Thus,the
presenceofR.mangleseemedtodriveanorganizationofU.cordatusat
largescaleinclustersaroundthetrees,butonlyinforestsdominatedbythis
ecies.sp

DISCUSSION6.5.

155

threeFiguret6ransects.7:(1:Spatiala-c;p2oin:td-f;3pattern:g-i;1analysisand2ofareburroinwaenR.trancesmangleaggregationdominatedaflongorests,the3
isperinsaL.quareracmeetersmosaalongdominatedthetfransectorest).(blackHistogramsbars),a,tdogetherandgwithshowthetheonumccurrenceberofocfrabsR.
burromanglews.treesGraphs(grayc,fabars).ndishoGraphswtbhe,ebivandahriateshoawtnalysisheounivfariateaggregationanalysisofbofurrowsclusteringaroundof
R.mangletrees.Forallgraphs,thesolidlinerepresenttheresultofthetransectdata
setandthedashedlinerepresentthe95%confidenceenvelopecalculatedfrom999Monte
andomizations.rCarlo

iscussionD6.5

WeanalyzedthespatialorganizationofU.cordatuspopulationontwo
mangrovesitesoftheCaet´ePeninsulaatdifferentspatialscalesandsome
potentialfactorsexplainingthedistributions.Atlargescale,U.cordatus
seemedtopreferclusteringaroundR.mangletrees.Thecrabspreferentially
builttheirburrowsinintermediaterootedareasandintermediateelevation
areas,where,ingeneral,thebigcrabsdominatedandprobablyexcluded
smallerindividualstosecondaryareas.AlthoughU.cordatusindividuals
aggregatedthemselvesintheserootedareasatalargescaleandclosetothe
rootsatasmallscale,ourobservationsindicatedthatarepulsionprocess
probablyduetointraspecificcompetitionforfoodorganizesthecrabsina

156

CHAPTER6

regularpatternatsmallscale.
Crabdensitiesestimatedinourstudyweremuchhigherthanreported
inpreviousworkdoneontheseareas.Thedifferencewasclearlyduetothe
samplingdesign.Twofactorsmighthaveplayedanimportantroleonthat.
Schoriesetal.(2003),Dieleetal.(2005),andNordhausetal.(2006)esti-
matedpopulationdensityduringspringebbtidesandbyfishingthecrabs.
Althoughtheysometimesconsideredunfishedcrabsintheirdensitycalcu-
lations,theyneverreacheddensityvaluesashighasours.Ourmethodof
samplingbycountingandopeningburrowscouldalsobecriticized,but,the
majordifferencewasactuallyduetocrabbehavioratthesamplingtimes
(i.e.,springvs.neaptide).Specifically,mostofthesmallcrabsclosetheir
burrowsbeforespringtides(K.Diele&C.Piou,personalobservations).The
closedburrowentrancesaregenerallyover-washedbythetideandtherefore
notvisibleatebbtide.Thus,evenwiththeburrowsnotfishedincluded
intheirdensitycalculations,thepreviousstudiesprobablymissedmanyof
thesmallcrabs.Thesecondfactormightbethefactthatwefocusedvol-
untarilyondenselypopulatedareas.Thepreviousstudiessampledmore
randomly,coveringthereforealsoareasofthepeninsulaofreallylowcrab
density(suchaschannelsordryland).Themeandensityofthesestudies
isthereforeprobablyanoverallbetterestimateforthepeninsulathanthe
onewecouldhavedrawnfromthe213m2coveredinourstudy.However,
withthesehighdensitiesfoundontheR.mangle-dominatedforestandre-
generatingL.racemosa-dominatedforest,thelitter-processingrolesofU.
cordatusdocumentedbySchoriesetal.(2003)andNordhausetal.(2006)
ishigherthanpreviouslyassumed.Identically,thefoodlimitationcalcu-
latedbyNordhaus(2004)mighthavemoreeffectthanexpectedinourR.
mangle-dominatedsite(alsoplaceofNordhauswork).
Becauseofthisfoodlimitation,competitionforfoodcanbeproposed
tobethemainfactordrivingthespatialdistributionofthecrabsatsmall
scale.Thetypicalleaf-harvestingbehaviorofU.cordatusisanindicatorof
thishighintraspecificcompetition.Forexample,whenaR.mangleleaffalls
onthemangroveforestfloor,U.cordatuswillmoveslowlytowardsitand
grabit.Thefirstcrabtogettheleafwillpullitquicklyintoitsburrowto
eatatsomelatertime(Nordhaus2004,C.Pioupersonalobservation).These
observationsindicatehowimportantitmightbeforthecrabstodistributein
arelativelyregularpatternonthemuddysurfacesothattheopportunities
forleavesareevenlydispersed.Nordhaus(2004)alsodemonstratedthatU.
cordatusfedonmangrovemudmorethan30%ofthetime,probablylooking
aftermicrophytobenthostocompensatethehighC:Nratioofmangroveleaves
asSteinkeetal.(1993)suggestedforasesarmidcrab.Ucidescordatusoften
digoutlargeamountsofanoxicmudfromtheirburrows.Thisbehaviormay

DISCUSSION6.5.

157

belinkedtothecareoftheburrowstructure,butmightalsobeassociated
withmudfeeding.Withtheasperitiescreatedinthesubstrate,thecrabsthus
increasedthetotalsurfaceareaofthemudsurroundingtheirburrowsand
providedmorespaceformicrophytobenthostodevelop.Thus,theregular
spatialdistributionoftheburrowscouldalsobetheresultofcompetitionfor
spaceformicrophytobenthos.Competitionforspacecanleadtomovement
ofchangeofburrowasproposedbyChapter7inamodelingstudy.And
anotherfactorthatmaybeinvolvedinthissmall-scale,regulardistribution
isthecapacityofU.cordatustomoveitsburrowentrance.Eachtimeacrab
closeditsburrow,itcouldmovethenextopeningofupto10cm(C.D’Lima,
C.Pioupersonalobservations).Whenentrancesofadjacentburrowsget
tooclose,acrabcanmoveitsentranceandtherebydecreasedirectspatial
etition.compWealsoobservedthissmall-scale,regulardistributioninrootedareas,but
thecrabspreferredtoinstalltheirburrowentrancesclosetotheproprootsof
R.mangletrees.Severalfactorsmightexplainthispattern.First,aburrow
closetoaproproothasmorestabilityandmightbeeasiertomaintainonvery
softmudsuchasthesedimentofthefrequentlyinundatedmangrovesofthe
Caete´Peninsula.Second,rootsalsoproduceashelteragainstpredatorssuch
asmangroveraccoon(Procyoncancrivorus),monkeys(e.g.Cebusapella)or
humanswhofishthecrabsbypullingthemoutoftheirburrows.Rootedareas
areobviouslyharderifnotimpossibletoaccessandfishthanunvegetated
areas.Finally,thebottomsofproproots,whicharecoveredinmudand
algae,aresometimesfedonbyU.cordatus(C.Pioupersonalobservation).
Thus,thismightbeanotherfeedingadvantageforthecrabstoinstalltheir
burrowsclosetoroots.
ThefeedinghabitsandspatialcompetitionofU.cordatuscanbetrans-
ferredtothelargerscaletoexplainsomepartofthehabitatpreferencede-
scribedbythetransectstudy.WefoundthatthereweremoreandlargerU.
cordatusassociatedwithintermediaterootedandelevatedareas.Ucidescor-
datusfeedingpreferenceforR.mangleleaves(Nordhaus,2004)mayexplain
whytheygenerallyinstalltheirburrowsclosetothisspecies.Thesefindings
areconcordantwiththeobservationsofDieleetal.(2005)andNordhaus
etal.(2006)whoproposethatthepreferenceforR.mangleproprootzone
offersprotectionagainstpredation.Theothertwomangrovespeciesdonot
providethisshelter,andgenerallygrowathigher(thushardersediment)or
lowerelevationthantheR.mangle.However,highR.manglerootdensities
closetothetrunkofthetreemightreducetheavailablespaceforsedimentto
settle.Toourknowledge,nostudieshaveevertriedtoquantifydifferencesof
leaflitteraccordingtothedistanceofthetrunk,butitseemslikelythatthe
leaveswillnotfalldirectlybeneaththetrunkwheretherootdensityisgener-

158

CHAPTER6

allythehighest.Forthesurfaceelevationpreference,wesawthatU.cordatus
favoredanintermediatesituation.Athighelevationswheretheyareflooded
lessfrequentlybythetide,theycannotrefreshtheirgillsasfrequently(C.
Pioupersonalobservation).Theyalsohavelessaccesstomicrophytoben-
thosproductionathighelevations.Atlowelevations,frequentinundations
reducethenumberofhoursavailableforharvestingfallingleaves.Thus,the
intermediateelevationsprovideoptimalconditionsforleaflitteravailability,
microphytobenthosproductionandphysiologicalpreferences.
However,wehaveseenthatU.cordatusalsooccursinhabitatsother
thanR.mangle-dominatedforests.Thesearegenerallysmallercrabs,in
concordancewithobservationsofDieleetal.(2005),andareprobablythe
resultofcompetitiveexclusionfromtheirpreferredhabitats.Ucidescordatus
isaveryslowgrowingcrab,reaching6cmcarapacewidthat>4yr(Diele
2000,Pinheiroetal.2005).Thedensityofsmallcomparedtobigindividuals
inthepreferredhabitatsdefinedaboveistoolowtoassumeagrowthwithin
thesameburrowfortheentirelifeofacrab.Movement,whichhastooccur,
wasalsodemonstratedinChapter7astheresultofintraspecificcompetition
atindividuallevel.Thepopulationrepartitionofsmallcrabsinadjacent
habitatsandbigcrabsinpreferredhabitatscouldconsequentlybetheresult
ofasymmetriccompetitionwhereafewbigcrabscanexcludeseveralsmall
crabsfromanarea.
WealsodemonstratedthatthecrabsaggregatedaroundR.mangletrees
atalargescaleinareasdominatedbythisspecies.Althoughweassumedit
wastheirpreferredhabitat,theydonotshowaclusteringaroundR.mangle
inaL.racemosa-dominatedforest.Therearetwopossiblereasonsforthis
pattern.First,thetwotransectsinourstudythatshowedclusteringaround
R.mangletreesalsohadrelativelylargerburrowentrancesandtherefore
biggercrabsthanintheL.racemosaforest.Thesesmallerandmorenumer-
ouscrabsmighthavebeenexcludedfrombeneaththeR.mangletreesinthe
L.racemosaforestandthustheclusteringisnotapparentinthistransect.
Second,theL.racemosaforestwasatahigherelevationthantheothertwo
transects.Thus,thesedimentwasharderevenbeneathR.mangletrees.Ad-
ditionally,theL.racemosaforestwasrelativelyyoungforestbecauseitwas
inastateofrecoveryfollowingperturbationbyaroadconstructionacross
thepeninsula(Bergeretal.1999).Thehardnessofthesedimentandthe
previousdisturbancetothesitemighthaveresultedinalowerfrequencyof
predationthaninthetallR.mangleforests.Theadvantagesofstability
ofthesedimentandshelteragainstpredationprovidedbyproximitytoR.
manglerootswerenotapparentinthissituation,andthecrabshadfewer
reasonstoprefertherootedareas.Thissuggeststhattheonlyotherreason
forthecrabstoprefertheR.manglerootedareasisthefeedingpreferenceof

DISCUSSION6.5.

159

U.cordatusforR.mangleleaves(Nordhaus2004).However,thispreference
wasnevertestedforcrabsfromL.racemosa-dominatedforests,andcould
thereforebedifferentforcrabsoftheseforests.

Differencesinorganizationpatternsatdifferentscaleistypicalofburrow-
ingorganismsandhasbeendemonstratedforkangaroosratsinNorthAmeri-
sacanvadnnaeserts(Rossi(Schoo2003a).ley&TheWiens2001)influencesoreofarththewhormabitatspeciesinheterogeneitanAyfricanondistri-grass
forbutionotherpearthatternswowrmsereianlsoaseenColomforbianthesepastureearthw(Decaorm¨spensecies&Rossi(Rossi2001).2003b)Inandour
case,wefoundthattheorganizationofU.cordatuspopulationatlargescale
isinresponsetohabitatheterogeneity.However,competitionforfood,which
occursattheindividuallevel,probablyalsoinfluencesthedistributionofU.
corhabitatdatustyatpeaslargeahighlyscale.TproheseductiveobservR.ationsmanglecanhelp-dominatedindfefiningorest,aatpintreferrederme-
diatequestionpropproosedotboyccupationNordhausetandal.s(urface2006)elevregardingationctheonditions.reasonsToofalacddresskoftheim-
portanceofU.cordatusinotherNeotropicalmangroves,ourstudyprovides
afitransferrstdoocfiumennfluencetationofftorhethedfeedingefinitionandooftherpreferredindividualhabitatbehavandiorsthefromobservsmalled
tolargescale.Onabiogeographicscale,thistransferofinformationob-
asviouslyinterspdoeescificnotcompdependetitiononlyandonlarvalindividualdispebrsalehavmighiortbalsoecauseplayfactorsimportansucth
roles.However,thequalityofthehabitatasafoodsourceforthisspeciesis
pstilloimppulationsortandt.evCelopwonsequenouldtly,notwebeexpmectangrothatvefplacesorestswwithherelargedominanceU.corofdatusA.
floogerminansding,ororotherL.rcacemosaonditions,lowsuchlitterasprodifferentduction,substrateinfrequentyptesorortocoompefrequentingt
leaf-eatinganimalsonthemangrovefloor.Finally,tosupportthishypothesis
ofpreferredhabitats,U.cordatuspopulationsshouldbeestimated,spatially
inveNeotropicalstigatedandmangrotheirves.rolesInintheparticular,litterptheseroincessingvestigationsanalyzedinshouldmanfoycusotheron
largecontiguousNeotropicalmangroveecosystemswithfinesiltysediment
andexphectighlyhighproimpductivortanceeofforestsU.dcorominateddatus.InbysucRhenhizophorvaironmensppt,s,withereiswimpewortanouldt
todeterminewhichofthetwoecosystemengineers,R.mangleorU.corda-
tus,patternsisfirstoftvoergetationecolonizeinzonationgapasareas,propandosedwforhethergrapsidU.corcrabsdatusinIndo-Pinfluencesacificthe
mangroves(Smith1987).

6CHAPTER

6CHAPTER1606.6Acknowledgements
WethankA.deMelo,S.Manuel,D.Ara´ujo,C.D’Lima,M.L.Fontalvo-
Herazo,J-PRossi,A.R.Araujo,I.Nordhaus,K.DieleandM.Protazio.
ThisstudywascarriedoutasapartoftheBrazilian-GermanCooperation
ProjectMADAMandwasfinancedbytheBrazilianNationalResearchCoun-
cil(CNPq)andtheGermanMinistryforEducationandResearch(BMBF)
underthecode03F0154A.ThisisMADAM-ContributionNo.#.

eferencesR6.7

ArtigasLF,VendevilleP,LeopoldM,GuiralD,TernonJ-F(2003)Marinebiodiversityin
FrenchGuiana:Estuarine,coastal,andshelfecosystemsundertheinfluenceofAmazonian
waters.Gayana(Concepc.)67:302-326
BergerAninU,tegratedGlaserM,approacKochhB,tomKrauseangroG,vedRubenynamicsL,Saainndt-PaulUmanagemen,Scht.oriesJD,ournalWolffofMCoastal(1999)
5:125-134tionaConservBrighofttheirDB,aHoguerthropoCdL(symb1972)iontAssandynopsisburroofwtheassoburrociates.wingConlandtributionscrabsofinthewScience,orldandNaturallist
AngelesLosuseum,MHistoryCanteraJR,ThomassinBA,ArnaudPM(1999)Faunalzonationandassemblagesinthe
PacificColombianmangroves.Hydrobiologia413:17-33
ClarkPJ(1954)Distancetonearestneighborasameasureofspatialrelationshipsinpopu-
35:445-453Ecologylations.Deca¨ensheterogeneitT,RyossiinaJ-P(tropical2001)pasture.Spatio-tempEcographoralsytructure24:671-682ofearthwormcommunityandsoil
DelgadomentPand,HphenselysicalPF,fJactorsim´enezinJA,mangroDavyeJW(2001)distributionalTheimppatternsortanceinaofpCostaropaguleRicanestablish-estuary.
71:157-178otBAquatDieleK,KochV,Saint-PaulU(2005)Populationstructure,catchcompositionandCPUE
oftheartisanallyharvestedmangrovecrabUcidescordatus(Ocypodidae)intheCaete´
estuary,NorthBrazil:Indicationsforoverfishing?AquatLivingResour18:169-178
DiggleofPdistanceJ,BesagmethoJ,dGs.leavesBiometricsTJ(1976)32:659-667Statisticalanalysisofspatialpointpatternsbymeans
DigglePJ,GrattonRJ(1984)MonteCarlomethodsofinferenceforimplicitstatistical
moGeraldesdels.JMGd,ournalCalvofenttheiIRBdoyal(1983)StatisticalEstudiosSocexpietey.SrimeneriestalesBpara(Methoelmandological)tenimiento46:193-227encau-
tiveriodelcangrejoUcidescordatus.CiencInteram23:41-53
GlasereconomicM,DieleandsKocial(2004)sustainabilitAsymmetricyofaoutcomes:mangrovecrabassessingfisherycen,tralUcidesaspectscoroftdatushe(Ocypbiological,odi-
dae),inNorthBrazil.EcologicalEconomics49:361-373
JonesphCysicalG,LaecosystemwtonJH,eSngineers.hachakEMcology(1997)Po78:1946-1957sitiveandnegativeeffectsoforganismsas
KenkhypeloNCthesis.E(1988)cologyPatternof69:1017-1024self-thinninginJackPine:Testingtherandommortality

REFERENCES6.7.

161

KochV,WolffM(2002)Energybudgetandecologicalroleofmangroveepibenthosinthe
Caete´estuary,NorthBrazil.MarEcolProgSer228:119-130
LevinSA(1992)Theproblemofpatternandscaleinecology.Ecology73:1943-1967
MacintoshDJ(1988)Theecologyandphysiologyofdecapodsofmangroveswamps.In:
FinchamAA,RainbowPS(eds)AspectsofDecapodCrustaceanBiology.Thezoological
societyofLondon,Oxford,England,p315-341
McIvorCC,SmithIIITJ(1995)DifferencesinthecrabfaunaofmangroveareasataSouth-
westFloridaandaNortheastAustralialocation:Implicationsforleaflitterprocessing.
18:591-597EstuariesMcKeonSC,FellerIC(2004)ThesupratidalfaunaofTwinCays,Belize.AtollResearch
526:22ppBulletinMiddletonBA,McKeeKL(2001)Degradationofmangrovetissuesandimplicationsforpeat
formationinBelizeanislandforests.JEcol89:818-828
NordausI(2004)Feedingecologyofthesemi-terrestrialcrabUcidescordatuscordatus(De-
capoda:Brachyura)inamangroveforestinnorthernBrazil.PhDThesis.ZMTcontri-
bution18,Bremen,Germany.
NordausI,WolffM,DieleK(2006)Litterprocessingandpopulationfoodintakeofthe
mangrovecrabUcidescordatusinahighintertidalforestinnorthernBrazil.EstCoast
67:239-250ciSShelfO’DriscollRL(1998)Descriptionofspatialpatterninseabirddistributionsalonglinetran-
sectsusingneighbourKstatistics.MarEcolProgSer165:81-94
RipleyBD(1977)ModellingSpatialPatterns.JournaloftheRoyalStatisticalSociety.Series
B(Methodological)39:172-212
RipleyBD(1981)Spatialstatistics.JohnWiley&SonsINC.,Hoboken,NewJersey,USA
RossiJ-P(2003a)Clustersinearthwormspatialdistribution.Pedobiologia47:490-496
RossiJ-P(2003b)Thespatiotemporalpatternofatropicalearthwormspeciesassemblage
anditsrelationshipwithsoilstructure.Pedobiologia47:497-503
RossiRE,MullaDJ,JournelAG,FranzEH(1992)Geostatisticaltoolsformodelingand
interpretingecologicalspatialdependence.EcolMonogr62:277-314
Salgado-KentCP,McGuinnessKA(2006)Acomparisonofmethodsforestimatingrelative
abundanceofgrapsidcrabs.WetlandsEcologyandManagement14:1-9
SchooleyRL,WiensJA(2001)DispersionofkangarooratmoundsatmultiplescalesinNew
Mexico,USA.LandscapeEcology16:267-277
SchoriesD,Barletta-BerganA,BarlettaM,KrummeU,MehlingU,RademakerV(2003)
Thekeystoneroleofleaf-removingcrabsinmangroveforestsofNorthBrazil.Wetlands
EcologyandManagement11:243-255
SkovMW,VanniniM,ShunulaJP,HartnollRG(2002)Quantifyingthedensityofmangrove
crabs:OcypodidaeandGrapsidae.MarBiol141:725-732
SmithIIITJ(1987)Seedpredationinrelationtotreedominanceanddistributioninman-
groveforests.Ecology68:266-273
SmithIIITJ,BotoKG,FrusherSD,GiddinsRL(1991)Keystonespeciesandmangrove
forestdynamics:theinfluenceofburrowingbycrabsonsoilnutrientstatusandforest
productivity.EstCoastShelfSci33:419-432
SousaWP,QuekSP,MitchellBJ(2003)RegenerationofRhizophoramangleinaCaribbean
mangroveforest:interactingeffectsofcanopydisturbanceandastem-boringbeetle.Oe-
137:436-445cologiaSteinkeTD,RajhA,HollandAJ(1993)Thefeedingbehaviouroftheredmangrovecrab
SesarmameinertiDeMan,1887(Crustacea:Decapoda:Grapsidae)anditseffectonthe
degradationofmangroveleaflitter.SAfrJMarSci13:151-160

162

CHAPTER6TwilleyRR,PozoM,GarciaVH,Rivera-ManoryVH,ZambranoR,BoderoA(1997)Litter
dynamicsinriverinemangroveforestsintheGuayasRiverestuary,Ecuador.Oecologia
111:109-122WarnerGF(1969)TheoccurenceanddistributionofcrabsinaJamaicanmangroveswamp.
JAnimEcol38:379-389
WarrenJH(1990)Theuseofburrowstoestimateabundancesofintertidalestuarinecrabs.
15:277-280colEJAustWarrenJH,UnderwoodAJ(1986)Effectsofburrowingcrabsonthetopographyofmangrove
swampsinNewSouthWales.JExpMarBiolEcol102:223-235
WolffM,KochV,IsaacV(2000)AtrophicflowmodeloftheCaet´emangroveestuary(North
Brazil)withconsiderationsforthesustainableuseofitsresources.EstCoastShelfSci
50:789-803

Chapter

7

latinguSim

of

a

cryptic

evangrom

phenomena

fishery

tsemenvom

rab:c

after

163

evrecory

malls

scale

164

7CHAPTER

Simulatingcrypticmovementsofa
mangrovecrab:recoveryphenomena
aftersmallscalefishery

CyrilPiou12;UtaBerger1;HannoHildenbrandt13;Volker
Grimm4;KarenDiele1andCoralieD’Lima1
AuthorPosting.Thisistheauthor’sversionofthework.Thedefinitiveversion
willbepublishedbyEcologicalmodelling.Articleacceptedthe1stofFebruary
2007.http://dx.doi.org/doi:10.1016/j.ecolmodel.2007.02.008

bstractA7.1Thesemi-terrestrialburrowingcrabUcidescordatusisanimportanteco-
logicalcomponentandeconomicresourceofBrazilianmangroveforests.The
crabpopulationoftheCaet´epeninsula(thelocationofourstudysites)has
beenexploitedforthelast40years.Recoveryoffishedareasbycrabsfrom
non-fishedareasundertherootsofthemangrovetreeRhizophoramangle
washypothesizedtobeanimportantbuffermechanismagainstrapidover-
fishing.However,catchperuniteffortdecreasedinrecentyears,suggesting
thatthesustainabilityofthecrabfisherymightbecomeendangered.Itis
crabs,thereforeevenimpthoughortantittoisbehardttertounderstandobservethedirectlym.ovFolloementwingbehathevaiourpproacofhtheseof
pattern-orientedmodelling,wedevelopedanindividual-basedmodeltoinfer
movementbehaviourfrompatternsindensityrecoverythatwereobserved
infieldexperiments.Twoalternativesubmodelssimulatingfactorscausing
movementwerecontrasted:withandwithoutlocalcompetitionamongcrabs.
Todescribelocalcompetition,thefield-of-neighbourhood(FON)approach
wasused,whichwasoriginallydesignedforsessileorganisms.Withoutcom-
1Zentrumf¨urMarineTropen¨okologie(ZMT),Fahrenheitstr.6,28359Bremen,Ger-
man2yCorrespondingauthor:Tel:+492380058,Fax:+492380050,E-mailaddress:
-bremen.detcyril.piou@zm3Universitpresenytofaddress:Groningen,TheoreticalBiologicalBiologyCen,tre,CentreKerklaanfor30,Ecological9751andNNEvHaren,olutionaryTheNether-Studies,
brandt@rug.nlh.hildenlands,4analyse,PeHelmholtz-Zenrmoserstr.trum15,f¨ur04318UmweLeipzig,ltforschungGerman-y.UFZ,Department¨OkologischeSystem-

ODUCTIONINTR7.2.

165

peobservtition,edlinearunrealisticallyrecoveryhighpatterns.movemenWithtfcomprequenciesetitionwereincluded,requiredbetotterfitfitsthe
tomovethemenrtecoveryfrequenciespatternswerewesreufficienobtained,t.Thisandloindicateswerandthatthlouscalmcoreompreealistictition
betweencrabsisthemainreasonforthemtomoveandchangetheirbur-
rows.OurworkshowsthattheFONapproachissuitabletodescribelocal
inganismsteractionsinnotconditionsonlyofamongcompsessileetitionfororganisms,resources.butTalsohesimamongulationmobileresultsor-
rapidillustrateovtheer-fishing.impTortanceheIBUoftmheodelnon-fishedpresentsroaoptedotenareastialforasfbuffersutureaanalysisgainst
ofthesebuffermechanismsandthusforabetterunderstandingofthecrab
fisheryanditsmanagement.
neighKeyborhoWoords:d,pUcidesattern-oriencorteddatusm,oideling,londividual-basedcalcompmeodtition,el,fimeldove-of
.tmen

7.2Introduction
Thesemi-terrestrialcrabUcidescordatuscordatus(Linnaeus1763)(here-
afterreferredtoasUcidescordatus)isanimportantecologicalcomponent
(Branco,1993;Blankensteynetal.,1997;Wolffetal.,2000;KochandWolff,
2002;Schoriesetal.,2003;Nordhausetal.,2006)andeconomicresource
ofBrazilianmangroveforests(Glaser,2003).Fisheriesonthiscrabhave
beenreportedfrommanyplacesofBrazil(e.g.Alcantara-Filho,1978;Nordi,
1994a,b;Alvesetal.,2005),andcatchescanreachveryhighvalues,up
to∼8.0g.m−2.yr−1intheCaete´peninsula,whereourstudywascarried
out(Diele,2000;A.-R.Araujo,unpublisheddata).TheCaete´peninsulais
coveredby140km2ofmangrovesandislocated200kmeast-north-eastof
Bel´em.Itwasthefocusareaofalong-terminterdisciplinaryresearchproject
onsustainablecoastalmanagement(MADAMproject;Bergeretal.,1999)
includingworkonthebiologyofU.cordatus(Diele,2000;Nordhaus,2004;
Dieleetal.,2005;DieleandSimith,2006;Nordhausetal.,2006).
Thelocalcrabpopulationhasbeenexploitedfor40years,buttodate,
crabcollectorsmainlyemploynon-destructive,artisanalcapturetechniques
byusingtheirbarearmorahookedsticktopullthecrabsoutoftheirbur-
rows(GlaserandDiele,2004).Mainlymaturelargemalesareharvested,and
crabcollectorsreportrecoveryoffishedareasinlessthantwoweeks(Diele
etal.,2005;C.Piou,personalobservation).Sofar,thetraditionalfishing
techniquesdonotseemtohaveaffectedthebiologicalsustainabilityofthe
Caete´crabpopulation(Dieleetal.,2005).However,6and8%decreasesin

166

CHAPTER7

catchperuniteffortoccurredin1999and2000,respectively(stablevalues
thereafter)(Dieleetal.,2005),suggestingthattheeconomicandsocialsus-
tainabilityofthecrabfisheryinthisareamightbecomeendangered(Glaser
2004).iele,DandTherecoveryofthefishedareasisnotyetfullyunderstoodandthefactors
influencingitattheindividuallevelarenotknown.Ucidescordatusgrows
veryslowlyandreachesmaturityafter∼2.5yearsandfishingsize(usually
>6.5cmcarapacewidth)onlyafter7years(Diele,2000).Thisshowsthatthe
specimensthatrestockfishedareasarenotrecentlysettledyoungrecruits,as
believedbycrabcollectors.Theadditionalfactthatlarge(i.e.old)andsmall
(i.e.young)crabsareusuallynotfoundinsamedensitiesinthemangrove
forest(e.g.Dieleetal.,2005)indirectlyindicatesmovement.Finally,oneim-
portantbuffermechanismleadingtorecoveryoffishedareasisbelievedtobe
themovementofcrabsfromnon-fishedareastofishedones.InRhizophora
mangleforests,themostimportantfishinggrounds,non-fishedareasare
patchesofdenseroots,whichareinaccessibletothefishermen(Dieleetal.,
2005).ForestsdominatedbyAvicenniagerminansandLagunculariarace-
mosaarelessfrequentlyfishedbecauserootcarpetsand/orsandysubstrate
hamperfishery.Bothtypes,non-fishedandlessfishedareas,mightfunction
asbuffersatdifferentspatialscales.However,inA.germinansforests,crab
densityandaveragesizeismuchlowerthaninR.mangledominatedforests
2000).(Diele,Sofar,onlyscarceinformationcouldbecollectedonindividualmove-
mentbehaviour.Crabsmovinglongdistancesandsearchingwheretoestab-
lishanewburrowwereonlyveryscarcelyseeninatotalofmanydozens
offulldayobservations.Nordhaus(2004)investigatedthebehaviourofU.
cordatusneartheirburrowsandfoundthatmostcrabsremainquasiimmo-
bileinornearbytheirburrowentrances.Shequantifiedtheirshort-distance
movementsaroundtheburrowsforforagingonmangroveleaflitter(during
0.3%ofthetimeandwithmaximumdistanceof∼1m),butcouldnotesti-
matehowoftencrabschangeburrowsandtowhatdistancenewburrowsare
builtorovertaken.Nevertheless,animportantconclusionmadebyNord-
hausetal.(2006)isthattheU.cordatuspopulationattheCaet´epeninsula
isfoodlimited.ThisbecomesobviousfromthefactthatU.cordatususu-
allycompletelydepletestheleaflitterfromthefloorofRhizophoramangle
forests.ThepurposeofthisstudywastounderstandthebehaviourofU.cordatus
crabsthatpromotestherecoveryoffishedareasonasmallscales(<1ha)
inRhizophoramangleforests.Wetriedtoquantifythisrecoverypattern
andthemovementofcrabsinthefield.Wedevelopedanindividual-based
modelofthecrabsandtheirbehaviourandfollowedtheideaofpattern-

XPERIMENTSEFIELD7.3.

167

orientedmodelling(Grimmetal.,1996;GrimmandBerger,2003;Wiegand
etal.,2003;Grimmetal.,2005)thatpatternsatthesystemlevelcontain
informationaboutprocessesattheindividuallevel.Wethusformulated
alternativesub-models,ortheories(GrimmandRailsback,2005),ofmove-
mentbehaviourandcheckedhowwelltheywereabletoreproducerecovery
patternsobservedatthepopulationlevel.
derstandOneofowhaturmainforcesthemquestionstogiveregardingupatheburromowvinementtheofcfirstrabsplacewastandotun-o
establishthemselvesinanewarea,e.g.afishedone.Wetestedwhether
compcouldbeetitiontheatmongriggercrabsforcforrabfomoodvasemendot.cumenInttheedfbyollowing,Nordhausweetdal.escrib(et2006)he
patternsobservedinthefield,theIndividual-Based-Ucides(IBU)modeland
itssubmodels,andfinallyshowtheassumptionsunderwhichIBUbestfits
theobservedrecoverypatterns.

7.3Fieldexperiments
dsethoM7.3.1Tostudytherecoveryoffishedareasonasmallscales(<1ha),fieldexper-
imentswereconductedinamangroveforestdominatedbytallRhizophora
mangletreesinthenorthern◦partofthe◦Caet´epeninsula,closetothetidal
channel,FuroGrande(050’15”Sand4638’30”W).Althoughnotaccord-
ingtothefishingmethodsappliedbylocalcrabcollectors,twoexperiments
ofcompleteexclusionofcrabsfromareasofhighdensityofcrabs(>4m−2)
withoutrootswereconductedinNovember-December2003and2004.The
proportionsofclosedburrowsversusopenburrowsaswellasoccupiedbur-
rowsversusnon-occupiedburrowswereestimatedbeforetheexperiments
started.Inthefirstyear,oneplotof12.25m2wasfishedentirelyandthe
mudflattenedtoremovethesignsoffisheryandburrowentrances(hereafter
referredtoasexperiment1).Inthesecondyear,6plotsofthesamesize
werefishedentirelybuttheburrowentrancesandtheholescreatedbythe
crabcollectorwereleftaccessibleforre-colonization(experiment2).The
numbersofactiveburrows,indicatingthenumberofreturningcrabs,were
determinedfor50daysinexperiment1andforonly15daysinexperiment
2becauseofasamplinghazard.Theratioofnumberofoccupiedburrows
afterfisherytotheoriginalnumberbeforefisherywastakenasanindicator
e-colonization.rforAdditionally,9plotsof3m2coveringamorediversetypeofhabitat(in
elevationandrootdensity)aswellasdatafromDiele(2000)anddatafrom

168

7CHAPTER

transectsampling(Piouetal.,unpublisheddata)wereusedtoestimatepro-
portionsofburrowoccupationandstatus(closedoropen)andtoestimate
meancrabdensityandrelatedsize.
ToenhancetheknowledgeonU.cordatusbehaviour,wealsoobserved
individualspecimensinthefield.Ucidescordatuscanspendseveraldays
initsburrowwithoutcomingoutandblocksitsentrancewithaplugof
mud.Wefollowedtheburrowstatusof>100crabsduring2to5weeks
toobtainestimationsonhowoftenburrowswereclosedandforhowlong.
In2003and2004severaltagging-observationexperimentswereperformed
(intotal98individualstagged)toevaluatethefrequencyofburrowchange
anddistancescoveredwhencrabschangetheirburrow.Taggingmethods
includedradio-tracking,paintorothervisualmarksfixedonthebackofthe
individuals.ofcarapace

esultsR7.3.2Fortheareasofthetworecoveryexperiments,meanburrowdensitybefore
fisherywas5.29±0.97burrow.m−2.Afterfishery,recoverywasfasterwhen
leavingholesonthegroundsurface(2004,experiment2)thanafterflattening
(2003,experiment1)(Fig.7.1).Comparingthefirstdayafterfisheryinthe
twoexperiments,recoverywashigherinexperiment2becauseexistingbur-
rowscouldimmediatelybecolonized.Wefoundlinearcorrelationsbetween
theproportionofoccupiedburrowsfoundontheplot(F)andthenumber
ofdaysafterfishery(t)forthetwoexperiments:
F(t)2003=0.0056+0.0189t
7.1)(andF(t)2004=0.2568+0.0287t
withR2of0.99and0.71respectively.Theseregressionformulasweretaken
asInthemgeneral,ainpinatternsforestsofdlinearominatedrecovebryyRtobehizophorreproaducedmangleby,mtheeaIncBUrabcmoardel.a-
pacesizewas6.05±0.9cmwithmeandensityof3.16crab.m−2.Thepropor-
tionofclosedburrowswasmeasuredasatleast60%,whiletheunoccupied
burrowproportionwasabout20%.Bothproportionsvariedinspaceand
dependedonthetidalcycle.
Noneofthemethodsoffollowingthecrabs’movementsinthefieldwas
entirelysuccessfulbecausecrabsweregenerallynotre-observedafterrelease.
Weobtainedroughestimatesofthefrequencyofmovementfrom>0to0.15
move/crab/dayandameanwalkingdistancebetween0.2and50m/day.
Furthermore,ourfieldobservationsshowedthatonaveragecrabsclosedtheir

THE7.4.MODELBUI

169

burrowsonceaweekandthattheburrowsremainedclosedforameanperiod
ofabout3days.

Figure7.1:Proportionofoccupiedburrowsthroughtimeafterthefishingexperiment,
flatteningthesurfacein2003(experiment1:crosses)andleavingtheholesin2004(ex-
periment2:circles)withrespectiveregressionlines.

7.4TheIBUmodel
Description7.4.1Theindividual-folloandwingamogentdel-baseddmoescriptiondelsfollo(GrimmwstheandODDRailsbacprotok,c2ol005;fordGrimmescribinget
al.,2006)andconsistsofsevenelements.Thefirstthreeelementsprovide
anmoodel’sverview,design,theandfourththerelemenemainingtthreeexplainselemengeneraltspcrovideonceptsdetails.underlyingthe

osePurpThemainpurposeoftheIBUmodelwastoreproducethepatternsof
recoveryofthecrabpopulationafterfisheryatsmallscales(<1ha).Itwas
testedwhetherlocalcompetitionamongneighbouringcrabsisareasonable
explanationforthecrabs’movement.

170

7CHAPTER

Structure,scalesandstatesvariables
Thesimulatedareacorrespondedtoahomogeneousmangrovemudflat
of15×15mwithasquarefishedareainthecenterof12.25m2.Thearea
hadperiodicboundaries(=Torus),sothatthenumberofcrabswasconstant
throughoutthesimulation.Thetemporalunitwasoneday.
Thestatevariablesofindividualcrabswere:identitynumber,position,
carapacewidth(CW),angleofdirectionofmovement,andidentitynumber
ofoccupiedburrow.Theburrowsstatevariableswere:identitynumber,
position,hostedcrabid(ifany),open/closestatusandtimewithoutacrab
(ifnotoccupied,tempty).

Processoverviewandscheduling
Duringeachtimestep,thefollowingsequenceofprocesseswassimu-
lated:updatingofparametersofthesubmodelsthatdescribetheinterac-
tionsamongthecrabs,checkingthestatusofallburrowswithremoving
thosethatwereemptyfortoolongtime(seesubmodels),andcheckingthe
statusofallcrabsinarandomorder.Duringthislastprocess,individual
crabscouldaccomplishoneofthefollowingactions:donothing;changethe
open/closestatusofitsburrow;orleaveitsburrow(ifitwasopen)andtake
overorcreateanewone.Themovementofacrabconsistedofdifferentsub-
processes:reasonformoving,walkingbehaviourandreasonforstopping,
whichdeterminedthreemodulesdescribedinthesubmodelssection.

conceptsDesignhaviourEmergence.ofthe-individualRecovceryrabsofand,enintirelyfishedparticular,areasfromtheiremergesintfromeractionsthevbiae-
localcompetition.
Interaction.-Forcrabsintheirburrows,twoassumptionsofcompe-
titioninteractionsinfluencingtheirreasonofmovementweretested:noap-
parentinteractions(Nullassumption);andcompetitionwithneighbouring
individualsforsharedresources(FieldOfNeighbourhoodorFONassump-
tion).Foodresources(mangroveleavesfallenfromthetrees)forwhichU.
cordatuscompete,areassumedascontinuouslyrenewedandhomogeneous
ondepethendsmonangrotheirvefloor.distanceHofweromver,thethecburroompweentitiontranceinatensitnd,yforprobablythese,onleatveshe
hosizeodof(FtheON)invaolvepproacdhtoindividuals.describTehus,compweetitionadapted(tBergerheFieldandOfHildenNeighbbrandt,our-
eac2000;h2crab003).represenTheFtingONitsaharvpproacestharea.assumesCrabsawecircularreintconsideredensitytofieldinteractaroundif

BUITHE7.4.MODEL

171

intheirtensitfiyeldsofotvheirerlappFOed.NDeffectistanceonaagndivensizeofcrab.theTnheeighsumbooursftdheFOeterminedNeffectsthe
wasassumedtoinfluencetheprobabilityofleavingaburrow.Therefore,
mothisvemenapproacth(Nordhausimplicitlyetal.,assumed2006).aneffectoffoodlimitationonthecrabs’
closing/opStocehasticitningitsy.-burroMostw,takingelemenovtserofaburroindividualw,andcrrabeason,behaviourdirection(sucorhtheas
ruledstoppingbyeofmompiricallyvementfordeterminedsomespubmorobabilitiesdels)a(ndTableburrow7.1).Sdisapptoceharanceasticitywweares
andusedtheforefactachothatfthesedetailedloprobabilities.werlevelThisinformationaccountedonforprocindividualessesvdeterminingariability
thesebehaviorsisnotavailable.
Observation.-Informationaboutcrabsandburrowscouldbeobtained
ateachtimestepwithagraphicaluserinterfaceincludingamapofburrows,
wacrabs,susedfieldsforofmodneighelbtestingorhoods,andandvisualmovdemenebuggingtpaths(Grimm,(Fig.7.2).2002).ThisinNumericalterface
outputswereusedforfurtheranalyses.

InitializationIBUsimulationswereinitializedbyfirstcreatingthenumberofcrabsgiven
bytheinputdensity(Dc)togetherwiththeirburrowsinrandomposition
inpiedtheaburrorea;wsatandrandomsecondlypbyositions.addingThetheoppropoen/closedrtions(PtatusropUofanlloc)theofburrounowsccu-
wpropasdortionetermined(PrropClandomlyosed).folloThesewinglastaptworobabilitpropyocrtionsorrespwereondinggivtoenexpasectedinput
fromfieldobservation.Carapacesizeofindividualcrabswasrandomlyat-
tributedaccordingtoanormaldistributionwithagivenmeansize(CWpop)
7.1andfsoralltandardthesedeviationparameters).(SDCWAfterpop)aforssigningthesimtheseulatedinitialpsopulationtates,sim(seeTulationsable
wecrabs’reruninforteractions.tendayTsiestsnoshorderwedtothatestablishtendaaystywepicalresufficiensituationtforctausedhis.bTyhen,the
fishingwassimulatedinthecentralfishingareabyremovingallcrabsand
alsoremovingornotremovingtheburrows,tosimulatethetwofieldexperi-
mentsrespectively(seedescriptionofexperiment1and2above,andmodel
w).loebanalysis

InputEnvironmentalconditionswereassumedtoremainconstantduringthe
simulationexperiment,sonoinputwasrequiredaftertheinitializationphase.

172

7CHAPTER

TableCompilation7.1:ofPadatarametersfromandDielei(nitialization2000)andvaaluesfdditionalorthemIBUeasuremenmodel.tsonpSources:opulation(1)
fromstructure;expe(2)rimenEtsonstimationifndividualromicrabndividualbehavbeiour.haviourofNordhaus(2004);(3)Estimation
ParameterDescriptionInitialAssumptionsSource
luesavnameDc/mCrab2)startingdensity(in3.16doesnotHomogeneousconsiderareahtabitathat(1)
yheterogeneitPropUnocpiedPropburroortionwsofatsunotartccu-22%Neaptidesituation(1)
PropClosedProportionofclosedbur-60%-(1)
startatwsroCWpoptheMeansimulatedcarapacecrabsizepop-of6Fmoreewsmallerfished-sizeonescrabsand(1)
cm)in(ulationSDCWpopthemStandardeancarapacedeviationsizeooff1-(1)
thesimulatedcrabpopu-
m)c(inlationaandbConstantsfortheinter-19and15cmForacrabofCW=1cm(2)
(Eq.action7.2)radiuscalculationRabointve=CW24.5cm,=9cmandall
=100cmRcrabsintPc1overProbabilitanocycupiedofburrotakingw0.0Impossible(3)
Pc2overProbabilitacylosedofempttakingy0.25Ptopossibleifpassjuston(3)

banda

P1cP2cP3cPosingclPopening

takingofyProbabilitoveranoccupiedburrow
overProbabilitacylosedofempttakingy
wburrooverProbabilitanyopenofempttakingy
wburroProbabilitythatacrab
closesitsburrowateach
steptimeyrobabilitpclosed,Onceofeacophtimeeningisteptsburrowat

0.00.25

1.00.140.33

Wouldalwayspreferto
stopiffindanopen
wburroyemptCloseitsburrow∼oncea
keweClosingperiodof∼3days

(2)3)((3)

(3)(3)3)(

7.4.THEBUIMODEL173

Figure7.2:SnapshootofIBUmodelinterfacewithexamplesofparticularfeaturesre-
(a:latedstingleotcherabfishingFONexparea,ebrimen:etandxampletheoffieldanofareaneighofinborhoteractionsod(FON)withintvisualizationeractionosubmofFdONel
areasofallcrabs)

elsdSubmo

Dispersalofcrabswasdescribedasacombinationofthreemodules:Rea-
sonformovement(RM),walkingbehaviourandreasonforstoppingmove-
ment.TheRMmodulehadtwosubmodelsbasedongeneralassumptions
ofinteractionsamongcrabs(NullandFON).Thetwoothermoduleshad
onesubmodeleach.Additionally,IBUhadasimplesubmodeldescribingthe
limitedlifetimeofunoccupiedburrows.

Reasonformovement
Randomreasonsubmodel(RMr):ThissubmodelfollowedtheNullas-
sumptionofnointeractionamongthecrabs,whichthereforehadaconstant

174

7CHAPTER

probabilityPmove(Table7.2)ofleavingtheirburrow(ifitwasopen)ateach
steps.timeCompetitionsubmodel(RMFON):ThissubmodeladaptedtheFieldOf
sessileNeighborhoorganismsodapproac(BergerhathatndwaHildensobriginallyrandt,2dev000,elop2ed003).forThetreesraadiusndofotherin-
teraction(Rint)wascalculatedforeachcrabatthestartofthesimulation
withthefollowingformula:
Rint=min{a×(CW/2)+b,Rmax}(7.2)
whereassumedatoandbeb1w00erecm.Rconstants(reflectedTablethe7.1),raadiusndofRmaxdailyamactionaximum(excludingradius
intburroobservwactionshange)(ofNordhaus,crabsa2004;ccordingC.toPiou,theirpesizersonalandwasobservationestimated).Thefinromtfiensiteldy
oftheFONatanypointwithdistancerfromagivencrabwasconsidered
as(BergerandHildenbrandt,2000):
⎫⎧⎨⎪⎪1for0≤r<CW/2⎬⎪⎪
0forr>Rint
FON(r)=⎩⎪⎪exp−R|lnint(F−minCW)/|2×r−2CWforCW/2≤r≤Rint⎭⎪⎪
(7.3)whereFminwastheminimumintensity(0.01)oftheFONatRint.Thesum
ofwasthethenFONdividedintensitbyyitsofotwhenFneighONbarea.orsoTvehertheresultingFONvaarealueoFfaisgiveusedncasraba
Ameasureofcompetitionintensity.Notethatthismeasuretakesintoaccount
wsizeasc(carapacealculatedawttidth)hebeandginningdistanceofaeacwhayftimeromtstepheforneigheacbhcouringrab.crabs.WhentFheA
crabswereindividuallychecked,FAwasusedtodeterminetheprobabilityof
leaving(Pmove)analreadyopenburrow:
FAPmove=Pbase×FA−max(7.4)
whereprobabilitFAy−omaxfmwoasvaement,constanandtPtowtransformasabasethecompprobabilitetitionyofinctensithangingyintoof
baseburrowateachtimestep(Table7.2).

Walkingbehavior
Thewalkingbehaviorwasdefinedasthetypeandorderofactionsacrab
wouldexecutewhenitleftitsburrowandlookedforanotheroneorcreated
anewone.Thisbehaviorwassetasarepetitionofthreeactionsdefining
amovementstep:1)movingashortdistance;2)checkingthesurrounding

MODELBUITHE7.4.

175

area;and3)decidingwhethertocontinueornot(describedinthenext
module).Thedirectionofmovementwasassumedtochangebetweeneach
movementstepandwasthereforecalculatedatthebeginningofeachstep.
Afirstrandomangle(α0)wasattributedtothecrabatthebeginningofits
movementandthenextones(αn)calculatedas:
αn=αn−1+Rnd(αdev)(7.5)
whereαdevwasthe“maximumdeviationangle”andRnd(αdev)anangle
randomlytakenfromtheinterval[−αdev,+αdev](Table7.2).Thedistance
ofamovementstepwasattributedrandomlybetween10and50cm.On
arrivingatitsnewpositionthecrabcheckedforalltheburrowsinaradius
ofperception,Rmove,definedas:
Rmove=CRmove×CW(7.6)
whereCRmovewasaconstant(Table7.2).Ifnoburrowwasfoundinthis
area,thecrabdecidedwhetheritshoulddoanothermovementstepornot
(seenextmodule).Ifburrowswerefound,thecrabtriedtotakethemover.
Thistakeoverwasimpossibleifaburrowwasoccupied,andfolloweddiffer-
entprobabilitiesofsuccessintheothercases(parametersPc1toPc3,Table
7.1).Thecrabkeptinmemorytheburrowsthatithadvisitedsincethe
beginningofthewalk.Ifanoccupiedburrowhadbeenpreviouslychecked,
theprobabilityofsuccessoftakingoverwassettozero.

Reasonforstoppingmovement
Thefirstreasonforstoppingwaswhetheritmanagedtotakeoveranother
burrow.Thecrabpositionwasthensettothisburrowposition.Ifnoburrows
weretakenoveratthisstep,thecrabcontinuedmovingwithprobability1-
Pstop(Table7.2),orelsecreatedanewburrowatitsactualposition.

Burrowlifetimesubmodel
Emptyburrowssoonerorlaterdisappearfrommangrovefloorbecause
oftidalwashandbio-perturbation.Tomodelthisinasimpleway,the
probabilityofdisappearance(Pdisap)oftheemptyburrows,wasdetermined
as:Pdisap=cdisap×tempty(7.7)
wherecdisapwasaconstantdefinedasthe“disappearingfactorofburrows”
(Table7.2)andtemptythenumberofdayssinceacrablastoccupiedthefocus
burrow.Thus,thelongeraburrowwaswithoutacrab,thehighertheproba-
bilityofitsdisappearing,untiltheburrowwoulddisappeardeterministically
afterthetimetempty=1/cdisap.

176

0.002,.001,00.0080.004,43,2,1,

7CHAPTER

0.004,.002,00.0081

Table7.2:Descriptionsandvaluesofparameterstestedwiththetwomodels,analyzing
theireffectonempiricalpatternreproduction.
ParameterDescriptionValuestestedwithValuestestedwith
nPameProbabilityofmovementt0.01,heN0.1,ullm0.2,ode0.3ltheFO-Nmodel
moveateachtimestep
PbaseBaseprobabilityof-0.1,0.2,0.3
movementateachtime
7.4)(Eq.stepPstopmoveProbabilitmentyatofseachtoppingmove-0.001,0.004,0.002,0.0080.002,0.004,0.008
steptmencRmoveConstancalculationtforoftcherabspradiuser-1,2,3,41
ofceptionmoveofmenbturro-stepswsat(Eq.end
7.6)αdevgleMaximbetuwmeendeaceviationhmovan-e-π/π,4,ππ//220,π/4
7.5)(Eq.steptmencdisapburroDisappws(earingEq.7.7)factorof00.15,.02,0.07,0.0050.02
FA−MAXMaximumFONneigh--0.1to1.9
bfeelorseffectwithoutaicrabncreasingcouldwithiof0.2ncrement
itsburropwrobabilit(Eq.y7.4)toleaveits

π/π,4,ππ//2,π20
0.07,0.15,0.005.02,0-

4/0.02with0.1itoncremen1.9t
0.2of

7.4.2Modelanalysis
Twodifferentmodelswereanalyzedtofindtheparameterizationthatbest
fitthepatternsobservedinthefieldexperiments.Thefirstmodelusedonly
theNullassumptionofinteractionbetweencrabs(RMr)(hereafterreferred
toasNullmodel).Fiveparametersthatwerehardtoestimatefromfield
knowledgewereconsideredtohaveapossibleinfluenceonthere-colonization
patterns(Table7.2).Fourvalueswereassignedforeachoftheseparameters
andallpossiblecombinationsofparametervaluesweretested.Foreachpa-
rameterset,twotypesofsimulationexperimentswereperformed,whichcor-
respondtothefieldexperiments1and2:removingofallburrowsandcrabs

BUITHE7.4.MODEL

177

ofa12.25m2area(experiment1),andremovingonlythecrabsofanidentical
areabutleavingtheburrows(experiment2).Thesimulationslasted50or15
daysrespectivelyaftertheinitialphaseofrandomization/organisationof10
days.Note,thatbothexperimentsmimicthefieldexperimentscarriedout
duringthisstudy.Theydonotimitatethetraditionalbehaviourofcrabcol-
lectors,whocatchonlybigmalesanddonotconcentrateonaquadratearea.
Thirtyreplicatesimulationsofeachtypeofexperimentwereperformed.To
checkthefittothetwolinearpatternsofre-colonizationobservedinthefield
(Fig.7.1),anerrorofdeviationfromeachpattern(ΔRec)wascalculated
withtheformulaofrootmeansquaredeviation(e.g.Jamiesonetal.,1998;
1998):al.,etWiegand2NΔRec=t=1obs(F(t)−Sim(t))(7.8)
NobswhereNobswasthenumberofdaysofobservations(50forthefirstexperiment
and15forthesecond),F(t)wastheregressiondescribingtheobservedlinear
recoveryofthepercentofoccupiedburrowsattimetafterfisheryandSim(t)
wasthecorrespondingsimulatedvalue.Atotalerrorestimation(ΔTot)was
s:acalculatedΔTot=ΔRec2exp1+ΔRec2exp2(7.9)
$whereΔRecexp1andΔRecexp2aretheerrorofdeviationforexperiment1
and2,respectively(fromEq.7.8).Additionally,theproportionofcrabs
thatmovedpertimestepandtheproportionofoccupiedburrowsontheen-
tireareawereregisteredandcomparedtofieldestimations.Tounderstand
therelativeeffectsofparametersandtheirinteractiononthetotalerror
(deviationbetweensimulatedandregresseddynamicsofre-colonization),a
generallinearmodel(GLM)wascomputedasalargedesignANOVA.Mul-
tiplecomparisonsamongmeansofgroupswerebasedonTukey’s“Honestly
SignificantlyDifferent”testsinordertodifferentiatehomogeneousgroupsof
parameterizationsthatcouldbeconsideredashavingidenticalfittothefield
patterns.ThesecondmodelincludedlocalcompetitionamongcrabsusingtheFON
approachinthereasonformovingsubmodel(RMFON)(hereafterreferredto
asFONmodel).Threebaseprobabilitiesofmovement(Pbase)andproba-
bilitiesofstoppingmovementweretested,respectively(Table7.2).Forthe
parameterFA−maxofcalibrationoftheFONintensity,tenvaluesweretested
(Table7.2).Withthese30possibilitiesforPbaseandFA−maxcombinations,
wecoveredalargerangeofPbase/FA−maxratiosasanindexoftransformation
ofFONintensity(FA)intoprobabilityofleaving(Eq.7.4,Pmove).Foreach

178

7CHAPTER

oftheparameterscRmove,αdevandcdisapavaluewaschosenbasedonthe
resultsfromNullmodel(Table7.2;asimilarapproachforparameterization
isusedbyMullonetal.,2003).Thirtyreplicatesofeachpossibleparam-
eter’sconfigurationwereperformedforbothfisheryexperiments,1and2.
Thedeviationsfromthefieldpatternswerecalculatedwiththesameestima-
tionsoferrordescribedabove(ΔRecexp1andΔRecexp2Eq.7.8,andΔTot
Eq.7.9).Tobeabletocomparethetwomodelversions(NullandFON),
theresultsoftheNullmodelwithidenticalparameterset(cRmove=1,αdev=
Pi/4,cdisap=0.02)wereconsidered.Themeanfrequencyofmovementof
crabsweremeasuredduringthesimulations.

esultsR7.5

7.5.1Nullmodel
Alltestedparameterssignificantlyinfluencedthetotalerrorofrecovery
pattern(GLMwithallparameters2asgroupingvariablesandallcrossin-
teractions,allp<0.05,AdjustedR=0.836).Smaller“maximumdeviation
angle”betweenmovementstepsreducedthetotalerror(Fig.7.3)bydecreas-
ingtheerratictypeofmovement.Likewise,asmallerradiusofthecrab’s
perceptionofburrowsalsodecreasedthetotalerror(Fig.7.3)byincreasing
thepprobabilitrobabilityofycofolonizingfinallythecreatingfishedanewarea.burroThew,andlongertthehereforelifetimeincreasingofemptthey
burrows(lowcdisap),thebetterthesimulationswereatfittingtherecovery
patterns.Thiswasparticularlytrueforexperiment2,whichcouldbetter
reproducethehighrecoveryproportionatthebeginningofrecolonization
ws.burrolong-lastingwithTheprobabilityofmovementwasseenasoneofthemostimportantpa-
rameterinfluencingtherecoverypatternswithhigherfrequencyofmovement
leadingtobetterfits(Fig.7.4).However,thetotalerrorofsimulationswith
Pmove=0.3werenotsignificantlylowerthanwithPmove=0.2becausewitha
too-highfrequencyofmovement,simulationsledtoaveryhighrecoveryrate
forexperiment1.Theprobabilityofstoppingmovementtogetherwiththe
maximumangleofdeviationdeterminedthedistancewalkedbycrabs.This
alteredtherecoverypatternfitincasesofextremelyshortorextremelylong
walks.Tooshortortoolongwalksledtonomovementcrossingthefishedar-
ofeasoexprehigherrimentp1,robabilitthereforeyofleadingfindingantosloemptweryrecoburrovewrys.Theomewhere81belseestinfittingcase
parameterizations(lowestΔTot)werenotfoundtobesignificantlydifferent
(TukeyHSDtest;Homogeneousgroups,BetweenMS=0.00343,df=29696).

7.5.TRESULS179

Figure7.3:Effectsofmaximumdeviationangleduringmovement(αdev),rangeofcrab’s
perceptionofburrows(cRmove)anddisappearingfactorofburrows(cdisap)ontherepro-
ductionoftherecoverypatterns(TotalErrorΔTot).Dataselectedforthisgraphhadall
identicalprobabilityofmovement(Pmove=0.1)andprobabilityofstopping(Pstop=0.004).
Eachpointcorrespondstoonesimulationresult.

Theyprobabilitwereyofmainlymovemenfollot,winginthetermediatepreviouslywalkingdescribedistance,dtrends:smallradiusincludingofbur-high
rowperceptionandlonglifetimeofemptyburrowsonthesurface.
However,theseparameterizationsrequiredprobabilitiesofmovementwhich
ledtohighmeasuredfrequenciesofmovementtoobtainthebestfits.These
frequenciesofmovementweremuchhigherthantheestimateof15%ofcrabs
perdayleavingtheirburrows.

180

7CHAPTER

Figure7.4:Effectsofprobabilityofmovement(Pmove)andprobabilitytostopmoving
(Pstop)onthereproductionoftherecoverypatterns(TotalErrorΔTot).Dataselectedfor
thisgraphhadallidenticalmaximumdeviationangle(αdev=pi/4),disappearingfactorof
burrows(cdisap=0.02)andrangeofcrab’sperceptionofburrows(cRmove=1).Eachpoint
correspondstoonesimulationresult.

delmoONF7.5.2terminedWithttheheuseovoferalltheeFrrorON(sΔToubmot)deland(RMtheFOmN),easuredtherfatiorequencyofPbaseof/FmoA−vemaxmende-t
ofratiocrabs(∼0.003duringtothe0s.007),imtheulationsmean(Fig.total7.5).errorAtshoinwedbtermediateestfitsPtobaset/FheA−fieldmax
movpatternemenotfrwithecovtheeryF(ONFig.mo7.5),del.Theindicatingprobabilitanyoptimalofsrtoppingangeofmovemenfrequencytalsoof
hadaneffectonthesetotalerrors,showingbetterfitswithhigherPvalues
(Fig.7.5).ButforthethreePstopvaluestested,similarpatternsofstopeffectof
thePbase/FA−maxratiosonthetotalerrorwereobserved(Fig.7.5).Among
theseassumingthatparameterizations,abetterpthevarameterizationarianceoftwotalouldberrorethewasonenotreproidentducingical,athend
onesfieldwithpatternsmallermorevoften,ariancetheofbtestotalerror.parameterizationswerebelievedtobethe
theFFigureONmo7.6delshoawsgainstthetheirmeanresptotalectiveevrroraofriance.eachAdditionallyparameterizationtheselectedusing

STRESUL7.5.

181

Figure7.5:Effectofthescalingparametertotransformcompetitionintensitytoad-
ditionalprobabilityofmovement(100×Pbase/FA−MAX,axis=log(x))onthemeantotal
cles:errorPofstopd=eviation0.002;fromUpwatherdfieldtriangles:patternPofstopreco=0very.004;withDownthewasrdecondttriangles:ypeofPmostopdels.=0C.008.ir-
Grayintensityofmarkersrepresentsthemeanfrequencyofmovementofcrabsduring
simulations.Eachpointrepresentthemeanof30replicates,variationsofmeanswerenot
presentedheretofacilitatereading(seeFig7.6and7.7).

correspondingparameterizationsofthemodelusingtheNullinteractionsub-
modelwerealsoplottedonFig.7.6.ForthisNullmodel,theparameter-
izationleadingtothelowestmeantotalerrorwasnotrealisticintermsof
measuredfrequencyofmovement(>0.20move/crab/day,parameterization
α1onFig.6b:Pmove=0.3,Pstop=0.004).Consideringamorerealisticfre-
quencyofmovement,themostrealisticparameterizationcouldbeselected
(β1onFig.7.6:Pmove=0.2,Pstop=0.004)forthisNullmodel.FortheFON
model,highfrequencyofmovementledtohighmeantotalerrorandhigh
varianceinthefitofthefieldpatterns.Someparameterizationsleadingto
verylowmeantotalerrorwerealsoobservedwithrelativelyhighvariance
(e.g.thesmallestmeantotalerrorgivenbyparameterizationα2onFig.7.6b:
Pbase=0.3,Pstop=0.008andFA−max=0.7).Wecouldselectthebestandmost

7CHAPTER182realisticparameterizationconsideringacompromisebetweenthegoodnessof
fit,thelowvarianceandthelowfrequencyofmovement(β2onFig.7.6b:
Pbase=0.3,Pstop=0.008andFA−max=0.9).

Figure7.6:Meantotalerroragainstvarianceoftotalerrorinthereproductionofthe
recoverypatternfortheparameterizationsofthesecondmodeltype(usingtheRMFON
submodel,circlesmarkers)andselectedparameterizationofmovementstepbehavior
(cRmove=1,αdev=Pi/4,cdisap=0.02)ofthefirstmodeltype(usingtheRMrsubmodel,
diamondsmarkers).Parameterizationsonthelowerleftcornerarethebestandmore
reliableparameterizations(zoomedinonpartb).Grayintensityofmarkersrepresentthe
meanfrequencyofmovementofcrabsduringsimulations(blackmarkersarenotrealistic
withafrequencyhigherthan0.20move/crab/day,i.e.>20%ofthepopulationmoveevery
day).Greeklettersreferstobestparameterizationsfollowingonlythemeantotalerror
(α1andα2ofrespectivemodeltypes)andselectedbestparameterizationsaccordingtoa
compromisebetweenthemeantotalerror,thevarianceandthefrequencyofmovement
(β1andβ2ofrespectivemodeltypes).
TheFONmodelingeneralneededlowermeanfrequencyofmovement
ofindividualcrabstoachievebetterrangeofgoodnessoffitthanthecor-
respondingNullmodels(Fig.7.6).Thiswasalsotrueforthetwoselected
mostrealisticparameterizationsoftherespectivetwotypesofmodels(β2
with0.065moves/crab/dayhadlowermeantotalerrorthanβ1with0.137
moves/crab/day).Thesetwoselectedmostrealisticparameterizationswere
distinctintheirfittothefieldpatternsmainlybecauseβ2reproducedbetter

7.6.DISCUSSION

183

thelinearrecolonizationinexperiment1andhadafasterrecoveryinexper-
iment2thanwithβ1(Fig.7.7).Thereasonformovementaccordingtothe
intensityofcompetition(RMFON)allowedthereforetohavebetterfitsand
morerealisticfrequencyofmovementthanassumingonlyarandomreason
forthecrabstochangeburrows(RMr).

iscussionD7.6lectorsOvterall,hatfiourshedfieldeareasxpareerimenrecotsvecredwonfirmedithintthewowstatemeneeks.HtoofwevU.er,coinrodatusurfieldcol-
experiments,weachievedamaximumrecoveryrateofabout80%duringthis
timeframe,whichalsoconfirmstheresultsofDiele(2000).Severalfactors
andexplainthetheresultssmallofourdiscrepancyexperimenbetts:weencrabthecollectorsstatemenctoollectftheonlycrablargemcollectorsales
more,whilecwerabcremoveollectorsdcdrabsonofotallconcensizestrateduringonaoursmallfieldareaexpaswerimenetdid,s.Fbutuwrther-alk
largearoundburroinwtheafndorestthuscatcnevhingereantcrabirelyhdereaepletingndalltherelwargeithoutmalesaprobinglongevtheirery
path.Finally,theirperceptionofrecoveryisnotquantitativeandwhatthey
callfullrecoverymightnotbe100%.
Nevertheless,thelinearrecoveryphenomenaareimportantpopulation-
levfromelponeatternsburroswincetoatheynotherdemonstratedespitetthehatfactU.cothatrdatuswefoundindeedratherregularlylittlemeovvi-es
modenceveomenftthisbehafromviourdirectrbesultedehaviniouralahighobservuncertainationstinyofthefidataeld.Thisregardingcrypticthe
mofrequencyvingpeorfdcayrabs’wasmcovonsideredement.asTheanmeaximxtremeumvalueestimatebeofcause15%itwofouldtheimplycrabs
thatcrabschangetheirburrowsevery∼7daysonanaverage.Suchahigh
thatturn-oU.vercoorfdatusburrospwsendsdoes>not90%soeemfitstimecompatibleinsidewithortheinactivfieldeoontbservopaoftionits
004).2(Nordhaus,wsburrofasterThewhenfieldeholesxpareerimenlefttsonthefurtherrevsedimenetaledafterthattheafishedpassageareaoftherecovcrabersmcollec-uch
tor.holethanUcidestocordigdatusanenobtirelyviouslynewporefersne.toThisestablishobserviatselftioninanaindicateslreadythatcreatedbur-
rowsarepreciousresources,energy-expensivetobuildandconserve.Thus,
statheyqinguestionwhereasittowaswhicbheforefactorarose.forcedaAccordingcrabttoochangeNordhausitsetburroal.w(2006),insteadtheof
boCaete´uringcrabcprabs.Bopulationasedisonfoothedlimited,informationindicatingonindividualcompbetitionehaaviourmongandneigh-on

184

CHAPTER7Figure7.7:Recoverypatternsofthemostrealisticandbestfittingparameterizationsfor
Pthebasetwo=0.2,typPeofstopmo=0.004,dels:ac)Rusing=1,theαndevo-in=Pi/4,teractioncdisaps=ubmo0d.02);el(b)RMursing)(patheramFetONerizatsubmoiondβel1:
emovofinteraction(RMFON)(parameterizationβ2:Pbase=0.3,Pstop=0.008,FA−MAX=0.9)
exp(Soliderimenblactk,awndithrgreyemolines:vingtmheeanoburrofpwsropoorrtionleavoingfrtecoheveryburroawftersrespfishingectivfromely;30blacsimkaundlationsgrey
dashedlines:correspondingconfidenceinterval;interruptedboldlightgreylines:field
patternsofrecovery,c.f.Fig7.1).

asrecovmosterysuitablepatterntoontesttheplotwhetherlevcel,rabsimmovulationementexpetriggeredrimentsbywloerecalccomponsideredeti-
tioncouldexplainthelinearrecoverypatternsobservedinthefield.
Bydefinition,localorneighbourcompetitionoccursamongindividuals

7.6.DISCUSSION

185

thatinteractwitheachother.Thus,weconsideredanindividual-based,spa-
tiallyexplicitmodelasanadequatetool.Existingindividual-basedmodels
implyingcompetitionamongmovinganimalseitherexplicitlydescribere-
sourcesuse(e.g.CuddingtonandYozdis,2000;RailsbackandHarvey,2002)
orindirectlyrepresentcompetitionbyassumingmovementtobedensity-
dependent(e.g.Taylor,1981;Mogilneretal.,2003).Bothoftheseap-
proacheshavetheirprosandcons:thedirectapproachismechanistic,but
requiresdetailedknowledgeonbehaviourandresourcedynamics.Theindi-
rectapproachdoesnotrepresentfeedingbehaviourbutthedirectinteractions
amongindividuals(byproximity,fightorterritoriality).Ittransformsdis-
tancesofindividualsintoforcesanddirectionofmovementoftheindividuals
fortheanalysisofanimalaggregations(e.g.Mogilneretal.,2003).Thus,this
secondtypeofapproachassumesinterferencecompetition(animalsinteract
directly)andnotexploitationcompetition(competitionthroughtheuseof
identicalresourceswithoutdirectinteractions,definitionsfollowingKeddy,
1998).Weneededbothinourcase.
Forthesereasons,wechoseanapproachthatisinbetweenthedirect
andindirectapproachestomodellingmovement:interactionsamongcrabs
aremodelledexplicitlybutwithoutdirectlyreferringtofeeding,resources
oragonisticinteractions.Thiskindofmodellingoflocalinteractionshasa
longtraditioninplantecology(Cz´ar´an,1998)butthereisnoreasonwhyit
shouldnotbeusedforanimalecologyaswell.Toourknowledge,thereis
onlyonepreviousattempttomodelinteractionsamonganimalsandamong
animalsandplantsinasimilarway:theGECKOmodel(Booth,1997)which
isappliedinmicrobialecology(Kreftetal.,1999;2001)andforarthropod
foodwebs(Schmitz,2001).InGECKO,individualsareassumedtohave
acircularzone-of-influenceandzoneoverlapsareconsideredasinteraction.
Individualsarerepresentedbyspheresratherthanthemoredome-shaped
field-of-neighbourhood,andthedetailsofhowinteractionsareimplemented
aredifferent.Moreover,themodeofinteractionofGECKOhasneverbeen
analysedbyitselforcontrastedtoothermodes,includingaNullmodelof
nointeractionatall.Incontrast,thepropertiesoftheFONapproachhave
beenanalysedingreatdetail(Baueretal.,2002;2004;Bergeretal.,2002;
2004;BergerandHildenbrandt,2003).
Nevertheless,theapplicationsofGECKOconfirmourconclusionfrom
usingtheFONapproachformodellinglocalinteractionsamonganimals:the
approachisconceptuallysimpleandconstitutesagoodcompromisebetween
too-detailedandtoo-highlyaggregatedapproaches.Bergeretal.(2002)
arguethattheFONapproach,orsimilarapproaches,couldbedeveloped
intoastandardwayofrepresentinglocalinteractionsamongplants.Herewe
wouldliketoconcludethatFONandsimilarapproaches,whicharebased

186

CHAPTER7

onthenotionofazoneofinfluence,couldandshouldalsobedeveloped
intoastandardapproachforrepresentinginteractionsamonganimals.Such
standardbuildingblocksareneededfordevelopingindividual-basedmodels
ofcommunitiesandecosystems(GrimmandRailsback,2005).
Weshowthat,atleastifresourcesaredistributedandreplenishedhomo-
geneously,theFONapproachiswellsuitedfordescribingthecompetition
intensitythateachcrabexertsonthisresource.SinceNordhaus(2004)ob-
servedthatU.cordatusgenerallystaysclosetoitsburrowandhasahigher
chanceofobtainingleavesthatlandonthegroundclosetoitsburrowen-
trance,weconsideredthatthehighestcompetitionintensityacrabexertsis
atitsburrowposition,andthisintensityshoulddecreasewithincreasingdis-
tancefromtheburrow.TheFONapproachwithanexponentiallydecreasing
fieldwasthenbelievedtosimulatethecompetitioninteractionamongindi-
vidualcrabswell.Acomparisonwithotherapproachescomingfromplant
interactionmodelssuchasFixedRadiusNeighbourhoodandZoneOfInflu-
ence(ZOI)(e.g.Cz´ar´an,1998,chapter6.3,p218)couldinformaboutthe
specifictypeofintra-specificcompetitionbutthiscouldnotbedonewithin
thescopeofthisstudy.
Wealsodidnotaddressdifferencesbetweenrootedandnon-rootedareas.
Asmentionedabove,crabcollectorscannotfishunderneathdenseR.mangle
roots.Theseareasare,therefore,consideredasbuffersagainstrapidover-
fishingastheyarelikelytopromotetherecoveryoffishedareas.However,
wedonotyethaveanyinformationuponhowthecrabs’behaviourdiffers
amonghabitattypes.Thus,inthemodelweassumedtheareasurrounding
thefishedplottobehomogeneous.Sinceourexperimentsproduceddifferent
crabdensities,i.e.withinandoutsidethefishedarea,weindirectlytestedthe
relativeimportanceofneighbourcompetitiondependingonhabitatquality
butnottheimpactofhabitatheterogeneity.
TheNullversionoftheIBUmodelwasusedasana-prioritestoftheim-
portanceandrangeofmovementparameters.Comparingsimulationresults
withfielddata,amediumrateofburrowdisappearanceandanintermediary
“maximumdeviationangle”wereselectedasthemostreliableparameters.
Incombinationwithanindividual’sprobabilitytostopandtheradiusofa
crab’sburrowperception,theseparameterswerelinkedtothedistancecov-
eredbythecrabsandtheprobabilitythatacrabsettlesinsideafishedarea.
Notsurprisingly,theprobabilityofcrabmovementwasthemostimportant
parameteraffectingtherecoveryoffishedareasforthatmodelversion.High-
estmovementfrequenciesfittedthelinearrecoverypatternsobservedinthe
fieldbest.Thesefrequenciesexceeded,however,themaximumvalueob-
servedinthefield.TheNullmodelversionthusrevealedthatnon-triggered
movementcannotexplaintheobservedlinearrecoveryinthefieldbecause

DISCUSSION7.6.

187

itrequiresunrealisticallyhighmovementfrequencies.
InthesecondversionoftheIBUmodel,thefrequencyofmovementis
linkedtothecompetitionamongcrabs,andexpressedbytheoverlapoftheir
Field-of-Neighbourhoods(FONs).Thisdescriptionassumesanimpactof
foodcompetition,suggestedbyNordhausetal.(2006)onthefrequencyof
burrowchangeofU.cordatusinthestudyarea.Itresultedinasignificant
decreaseofthemovementfrequencynecessarytoreproducethelinearre-
coverypattern.Crabsunderhighcompetitioninthenon-fishedareasmove
morefrequentlythanspecimensunderlowcompetition,suchasthoseal-
readyre-establishedinthefishedarea.Theseresultsimplythatmovement
istriggeredbycompetitionforresources,andisthereforedensity-dependent.
Perturbationofburrowentrancesmightalsotriggercrabmovements(C.
Piou,personalobservations).Thisfactorshouldbeinvestigatedsystemati-
callyinthefield.However,suchperturbationsarelikelytoberandomevents
andarethusindirectlyconsideredbyourNullmodel.
Density-dependentmovementisacharacteristicbehaviourthathasim-
plicationsforthemanagementofU.cordatusasaresourceforhumanpop-
ulations.InareasofR.mangledominatedforeststhatareeasytoaccess,
largemalesarefrequentlyfished.Thecrabshiddenundertherootsarenot
accessibletothecrabcollectorsandprobablyreplacethefishedonesbe-
causeofhigherdensity(Piouetal.unpublisheddata)andthereforehigher
competitionundertherootsthanontheaccessibleareas.Additionally,we
observedwiththedifferentparameterizationsoftheIBUmodelthatU.cor-
datusshallnotwalktoolongdistancesforthelinearrecoverypatterntobe
reproduced.Thus,comparingthelocalnon-fishedareasofhighrootdensity
tothepeninsulalevelless-fishedareas,theformerareprobablymoreim-
portantasalocalbuffersystemfortherecoveryofartisanallyfishedareas.
Thisarguesinfavourofkeepingthetraditionalcatchingmethodsandnot
harvestingtheselocalbuffersbymoreadvancedtechniquesasobservedin
otherplacesofBrazil(Personalcommunications).Thepeninsulalevelless-
fishedareassuchasAvicenniagerminansdominatedforests,oreventually
theless-visitedR.mangleforests,mightnotactasbufferwithinanidentical
timeframebecausetheyarefurtheraway.However,aslongasintraspecific
competitionofU.cordatusishighintheseareas,theycouldfunctionaslarge
scalebuffersystemrefillingthelocalscalebuffers.Theimpactoffishingtech-
niquesallowingcrabcollectorstofishintheseareasshouldbeanalyzedto
concludeontheirpossibleneedofregulation.However,thecapacityofboth
thelocalandthepeninsulalevelbuffersystemswoulddependultimatelyon
recruitmentasunderahierarchicalsystem.Therelativeimportanceofthese
buffersystemsversustherecruitmentprocessesisstilltobeinvestigated.
InthecaseoftheCaet´epeninsulawhichwasnotintensivelyexploited

188

7CHAPTER

unpacittilytbheecauseendooffthhearve80’ssting(Dielewithinetaalll.,m2005),angrovoevaerallreaschmighangetofexplainbuffertheca-6
andbuffer8%dsystemsropinhcypatchothesizedperunitaboveeffortiscinorrect,theltatehis9wo0’s.uldIfthenthesuggesthierarchythatof
thecompetition-inducedlocalrecoveryratethatweobservetodaycouldhave
beenmuchfasterseveraldecadesagowhenfisherywaslessintensive.This
coincideswithcrabcollectors’statements(SenhorManuelandDomingosde
beArajo,donepemursonalchcfasterommunicseveralationsdecadestoC.ago.Piou)Fthaturtherfisherystudyoflcouldargeinmalesvcestigateould
theseaspectsatmultiplescales.OurIBUmodelcouldbeusedinthefuture
toquantifythebuffercapacityatlocalscaleandtoexplorehowitisindi-
rectlyrelatedtorecruitment.Larger-scaleanalysismighttheninformhow
theandtbufferherebyhelpsystemsaestablishndthetheoverallsustainablerecruitmenyieldtthataffectcantheberatetakenoffrecoromvtehery
system.

7.7Acknowledgements

WewishtothankAldodeMelo,SenhorManuelandDomingosdeAra´ujo
fortheirprecioushelpandsupportduringthefieldwork,MarthaLiliana
FontalvoHerazoandtwoanonymousreviewersforvaluablecommentson
earlierversionofthismanuscript,andAnaRosaAraujo,IngaNordhausand
CandyFellerforfruitfuldiscussionsonmangrovecrabecology.Amanda
Stern-PirlotverifiedtheEnglishlanguage.Thisstudywascarriedoutas
apartoftheBrazilian-GermanCooperationProjectMADAMandwasfi-
nancedbytheBrazilianNationalResearchCouncil(CNPq)andtheGerman
MinistryforEducationandResearch(BMBF)underthecode03F0154A.
ThisisMADAM-ContributionNo.110.

eferencesR7.8

Alcanu¸c´a,tUciara-Filho,descoPrd.atd.,usco1978.rdatuConstribu¸(Linnaeus,c˜aoao1763)estudoda(Crustacea,biologiaDeecapoecologiada,doBracchyura),aranguejo-no
manguezaldoRioCear´a(Brasil).Arquivosdeciˆenciasdomar18:1-41.
Alves,gatherersR.R.ofN.,theNcishida,rab’A.K.,caranguejo-u¸andHc´a’ernandez,(UcidesM.cIo.rM.,datus,2005.DecapEnoda,vironmenBractalhypura)erceptionaffectingof
theircollectionattitudes.JournalofEthnobiologyandEthnomedicine1.
Bauer,plantS.,pBerger,opulations.U.,PHroildenceedingsbrandt,ofH.,theaRndoyalSoGrimm,V.,cietyof2002.LondonCyclicBd269:ynamics2443-2450.insimulated

REFERENCES7.8.

189

Bauer,S.,Wyszomirski,T.,Berger,U.,Hildenbrandt,H.,andGrimm,V.,2004.Asymmetric
competitionasanaturaloutcomeofneighbourinteractionsamongplants:resultsfrom
thefield-of-neighbourhoodmodellingapproach.PlantEcology170:135-145.
Berger,U.,Glaser,M.,Koch,B.,Krause,G.,Ruben,L.,Saint-Paul,U.,Schories,D.,and
Wolff,M.1999.Anintegratedapproachtomangrovedynamicsandmanagement.Journal
ofCoastalConservation5:125-134.
Berger,U.,andHildenbrandt,H.,2000.Anewapproachtospatiallyexplicitmodelling
offorestdynamics:spacing,ageingandneighbourhoodcompetitionofmangrovetrees.
elling:287-302.doMEcologicalBerger,U.,Hildenbrandt,H.,andGrimm,V.,2002.Towardsastandardfortheindivid-
ualbasedmodelingofplantsimulations:Self-ThinningandtheFieldofNeighborhood
approach.NaturalResourceModeling15.
Berger,U.,andHildenbrandt,H.,2003.Thestrengthofcompetitionamongindividualtrees
andthebiomass-densitytrajectoriesofthecohort.PlantEcology167:89-96.
Berger,U.,Hildenbrandt,H.,andGrimm,V.,2004.Age-relateddeclineinforestproduc-
tivity:modellingtheeffecrtsofgrowthlimitation,neighbourhoodcompetitionandself-
thinning.JournalofEcology92:846-853.
Blankensteyn,A.,CunhaFilho,D.,andSantarosaFreire,A.,1997.Distribui¸c˜aoesto-
quespesqueiroseconte´udoprot´eicodocaranguejodomangueUcidescordatus(L.1763)
(Brachyura:Ocypodidae)nosmanguezaisdaba´ıadaslaranjeiraseadjacˆencias,Paran´a,
Brasil.Arquivosdebiologiaetecnologia40:331-349.
Booth,G.,1997.Gecko:Acontinuous2-Dworldforecologicalmodeling.ArtificialLife
:147-163.3JournalBranco,J.O.,1993.Aspectosbioecol´ogicosdocaranguejoUcidescordatus(Linnaeus,1763)
(Crustacea,Decapoda)domanguezaldoItacorubi,SantaCatarina,Brazil.Arquivosde
36:133-148.tecnologiaebiologiaCz´ar´an,T.,1998.Spatiotemporalmodelsofpopulationandcommunitydynamics.Chapman
pp.284London,Hall,&Cuddington,K.M.,andYodzis,P.,2000.Diffusion-limitedpredator-preydynamicsineu-
clideanenvironments:anallometricindividual-basedmodel.TheoreticalPopulationBi-
58:259-278.ologyDiele,K.,2000.LifehistoryandpopulationstructureoftheexploitedmangrovecrabUcides
cordatuscordatus(L.)(Decapoda:Brachyura)intheCaet´eestuary,NorthBrazil.Ph.D.
Thesis,ZMTContribution9,Bremen,Germany.
Diele,K.,Koch,V.,andSaint-Paul,U.,2005.Populationstructure,catchcomposition
andCPUEoftheartisanallyharvestedmangrovecrabUcidescordatus(Ocypodidae)in
theCaete´estuary,NorthBrazil:Indicationsforoverfishing?AquaticLivingResources
18:169-178.Diele,K.,andSimith,D.,2006.SalinitytoleranceofnorthernBrazilianmangrovecrab
larvae,Ucidescordatus(Ocypodidae):Necessityforlarvalexport?EstuarineCoastaland
600-608.68:cienceSShelfGlaser,M.,2003.Interrelationsbetweenmangroveecosystem,localeconomyandsocial
sustainabilityinCaete´Estuary,NorthBrazil.WetlandsEcologyandManagement11:265-
272.Glaser,M.,andDiele,K.,2004.Asymmetricoutcomes:assessingcentralaspectsofthe
biological,economicandsocialsustainabilityofamangrovecrabfishery,Ucidescordatus
(Ocypodidae),inNorthBrazil.EcologicalEconomics49:361-373.
Grimm,V.,2002.Visualdebugging:awayofanalyzing,understandingandcommunicating
bottom-upsimulationmodelsinecology.Naturalresourcemodeling15:23-38.

190

7CHAPTER

Grimm,V.,andBerger,U.,2003.Seeingthewoodforthetrees,andviceversa:pattern-
orientedecologicalmodelling.Pages411-428In:L.SeurontandP.G.Strutton,editors.
HandbookofScalingMethodsinAquaticEcology:Measurement,Analysis,Simulation.
CRCPress,BocaRaton.
Grimm,V.,andRailsback,S.F.2005.Individual-basedmodelingandecology.Princetown
UniversityPress,Princeton,N.J.,480pp.
Grimm,V.,Frank,K.,Jeltsch,F.,Brandl,R.,Uchmanski,J.,andWissel,C.,1996.Pattern-
orientedmodellinginpopulationecology.TheScienceoftheTotalEnvironment183:151-
166.Grimm,V.,Revilla,E.,Berger,U.,Jeltsch,F.,Mooij,W.M.,Railsback,S.F.,Thulke,
H.-H.,Weiner,J.,Wiegand,T.,andDeAngelis,D.L.,2005.Pattern-orientedmodelingof
agent-basedcomplexsystems:lessonsfromecology.Science310:987-991.
Grimm,V.,Berger,U.,Bastiansen,F.,Eliassen,S.,Ginot,V.,Giske,J.,Goss-Custard,J.,
Grand,T.,Heinz,S.K.,Huse,G.,Huth,A.,Jepsen,J.U.,Jorgensen,C.,Mooij,W.
M.,Mueller,B.,Pe’er,G.,Piou,C.,Railsback,S.F.,Robbins,A.M.,Robbins,M.M.,
Rossmanith,E.,R¨uger,N.,Strand,E.,Souissi,S.,Stillman,R.A.,Vabo,R.,Visser,
U.,andDeAngelis,D.L.,2006.Astandardprotocolfordescribingindividual-basedand
agent-basedmodels.EcologicalModelling198:115-126.
Jamieson,P.D.,Porter,J.R.,Goudriaan,J.,Ritchie,J.T.,vanKeulen,H.,andStol,W.,
1998.AcomparisonofthemodelsAFRCWHEAT2,CERES-Wheat,Sirius,SUCROS2and
SWHEATwithmeasurementsfromwheatgroanunderdrought.FieldCropsResearch
55:23-44.Keddy,P.A.,1989.Competition.Chapman&Hall,London,202pp.
Koch,V.,andWolff,M.,2002.Energybudgetandecologicalroleofmangroveepibenthos
intheCaete´estuary,NorthBrazil.MarineEcologyProgressSeries228:119-130.
Kreft,J.-U.,Booth,G.,andWimpenny,J.W.T.,1999.Applicationsofindividual-based
modellinginmicrobialecology.In:C.R.Bell,M.Brylinsky,P.andJohnson-Green,editors.
MicrobialBiosystems:NewFrontiers(Proceedingsofthe8thinternationalsymposiumon
microbialecology).AtlanticCanadaSocietyforMicrobialEcology,Halifax.
Kreft,J.-U.,Picioreanu,C.,Wimpenny,J.W.T.,andvanLoosdrecht,M.C.M.,2001.
Individual-basedmodelingofbiofilms.Microbiology147:2897-2912.
Mogilner,A.,Edelstein-Keshet,L.,Bent,L.andSpiros,A.,2003.Mutualinteractions,po-
tentials,andindividualdistanceinasocialaggregation.JournalofMathematicalBiology
47:353-389.MullonC.,Fr´eon,P.,Parada,C.,vanderLingen,C.,andHuggett,J.,2003.Fromparticles
toindividuals:modellingtheearlystagesofanchovyintheSouthernBenguela.Fisheries
12:396-406.yOceanographNordhaus,I.2004.Feedingecologyofthesemi-terrestrialcrabUcidescordatuscordatus
(Decapoda:Brachyura)inamangroveforestinnorthernBrazil.Ph.D.Thesis,ZMT
contribution18,Bremen,Germany.
Nordhaus,I.,Wolff,M.,andDiele,K.2006.Litterprocessingandpopulationfoodintakeof
themangrovecrabUcidescordatusinahighintertidalforestinnorthernBrazil.Estuarine,
CoastalandShelfScience67:239-250.
Nordi,N.,1994a.Acapturadocaranguejo-u¸c´a(Ucidescordatus)duranteoeventorepro-
dutivodaesp´ecie:Opontodevistadoscaranguejeiros.RevistaNordestinadeBiologia
9:41-47.Nordi,N.,1994b.Aprodu¸c˜aodoscatadoresdecaranguejo-u¸c´a(Ucidescordatus)naregi˜ao
dev´arzeanova,Para´ıba,Brasil.RevistaNordestinadeBiologia9:71-77.

7.8.REFERENCES191

Railsback,S.F.,andHarvey,B.C.,2002Analysisofhabitat-selectionrulesusinganindividual-
basedmodel.Ecology83:1817-1830.
Scusehmitz,ofeO.J.,mpirical2001.insighFrtsominintheoryterestingdetailsconstruction.toOikdynamicalos94.relevance:towardmoreeffective
ScV.hories,2003.D.,ThekBarletta-Bergan,eystoneroleAof.,lBarletta,eaf-remoMving.,crabsKrumme,inmU.,angroveMehling,forestsU.,oafndNorthRademakBrazil.er,
WetlandsEcologyandManagement11:243-255.
Taylor,R.A.J.1981Thebehavioralbasisofredistribution.I.theΔ-modelconcept.Journal
50:573-586.EcologyAnimaloftionWiegand,fortT.,heNabrovwes,nJb.,ear(Stephan,UrsusT.,arcatosnd)Fienthernandez,A.,Cordillera1998.CanAssessingtabrica,theSpain.riskofEcologicalextinc-
68:539-570.MonographsforWiegand,revT.,ealingJheltsciddenh,F.,iHanski,nformation:I.,aandkeyfGrimm,orV.,reconciling2003.eUsingcologicalptheoryattern-orienandtedmoapplication.deling
100:209-222.soOikWolff,(NorthM.,KoBrazil)ch,V.,withandIsaac,considerationsV.,2000.forAttherophicflosustainablewmoduelseofoftheitsCraet´eesources.mangroEveestuarine,stuary
CoastalandShelfScience50:789-803.

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CHAPTER7

Chapter

eTsting

8

ecificrasptni

phenomenological

delsmo

at

ducerepro

patterns

titioneompc

leindividual-lev

ot

pelpulation-levo

of

a

evangrom

193

crab

194

8CHAPTER

Tecompstingietitionntraspmoecificdelsatphenomenologicalindividual-level
toreproofaducempangroveopulation-levcrabelpatterns

1iouPCyrilArticleinpreparation

bstractA8.1Intraspecificcompetitionamongindividualsofthesemi-terrestrialcrab
Ucidescordatuswasdemonstratedtohappeninanorth-Brazilianmangrove
forest.Previousstudiesalsohypothesisedthatcompetitionwasthemain
factordrivingpopulationspatialorganizationandindividualmovementsof
changeofburrows.However,thelinkbetweenindividualbehaviourand
comppresentsetitiontudywwasassotoafarssessnotendifferentirelyttypesanalyzed.ofbehaTheviormainrepresenobtedjectivbeyofdiffer-the
entindividual-basedmodelsfortheircapacityinreproducingpopulationlevel
patterns.TheIndividual-BasedUcidescordatus(IBU)modelwasadapted
tousedifferentphenomenologicalcompetitionmodelscorrespondingtosym-
metricorasymmetriccompetitionbehavioranddifferentsizeofharvesting
area.Thepattern-orientedmodelinginformationcriterionandmeansquared
deviationwereusedtoassessthegoodnessoffitofthesemodelstopatterns
ofrecoveryafterfisheryandspatialorganizationonasmallscale(<10m).
Therorganizationesultscbutonfirmedweretlessheroleofcategoricalcompforetitionthearsecoavmainerypfactoratterns.drivingTheovespatialrall
bestfitswereobtainedwithmodelsimplyingahigherimportanceforclose-by
relatedresourcestotthanhesizefurtheroftheawacyrabsones.couldFurtherinformsotudyntonherolefrequencyofofasymmetricmovemencom-ts
petitionamongindividualsofdifferentsizeshypothesizedtohappenwiththe
bestfittingmodelofthepresentstudy.
KeyWords:Ucidescordatus,phenomenologicalindividual-based
model,pattern-orientedmodeling,intraspecificcompetition,asym-
man1y.ZenTtrumf¨urel:+492380058,MarineFaTropen¨x:+492380050,okologie(E-mailZMT),Faddress:arhenheitstr.cyril.piou@zm6,28359t-bremen.deBremen,Ger-

ODUCTIONINTR8.2.

etitioncompmetric/symmetric

8.2Introduction

195

Thesemi-terrestrialcrabUcidescordatuscordatus(L.1763)(hereafterre-
ferredtoasUcidescordatus)isanimportantecologicalcomponent(Branco
Sc1993,horiesBetlankal.2ensteyn003,eNtal.ordhaus1997,etWal.olff2006)etal.and2000,economicKocharesourcendWooflffBrazil-2002,
ian(Bergermeangrotavl.ef1999),orests(U.Glasercordatus2003).wasInthethefsubramejectofofthedifferenMtADsAMtudyproonjectits
2006,biologyC(Dielehapter7)2000,andNpordhausopulation2004,structureNordhaus(Dieleetal.2000,2006,DieleDieleetandal.2Simith.005,
umenChapterted6).withThethewfeedingorkofbNehavordhausiorofU.(2004)corwhodatusswhoaswepdthatarticularlythewellpreferreddoc-
foodofdemonstratedthiscrabfromareltheseeavesffeedingallingstudiesfromtRhathizophorU.coardatusmanglewastrees.foodShelimitedalso
cificandthucompsinetitiontraspwecificascompdemonstratedetitionatomongexplainindividualscrabmovmighetmenotsccur.ofcInhangetraspoe-f
burrowsexplainingtherecoveryoffishedareas(Chapter7)andproposedas
amainfactororganizingspatiallythecrabpopulation(Diele2000,Chapter
6).U.cTorhedatusobserv,asamtionsanyoofNtherordhausBrachyuran(2004)oncrabs,haindividualvebterritorialehaviorbsehahovweiorsdtandhat
particularlyinrelationtotheuseandprotectionoftheirburrows.These
observationshypothesizedthatbothinterferencecompetition(animalsinter-
actthroughdirectlythetouseoobtainfthearresourceesource)andwithoutexploitationdirectincompteraction,etition(compdefinitionsetitionfol-
lodescribwingedKeddythatb1989)oththecouldfightshappandenedharvamongestingareuindividuals.suallyoNccurringordhauswithin(2004)a
smallareaaroundtheirburrows.However,theactualknowledgecannottell
wtheouldevdistanceenutuallyntilleadwhicahctrabhetosensegoaofwaythesefromtwaomechighlyhanismsdemandedofacomprea.etition
shipTheamongworkgofastroinNtordhausestinalcon(2004)tentalsoandsizeofdemonstratedthecrab,ashonon-linearwingatendencyrelation-
forbiggersmallcrabs.crabsShetonobserveed,edpropalsotortionallyhatthetobiggertheircwrabseight,moreassimilatesloresourceswerttheirhan
lofoodosingthansomeasmallervailablecrabs.foodTbheseecausefindingsofthewouldpresencesuggestoftotherhattcherabsimpacthaveofa
non-proportionallyhigherimpactonstarvationofsmallcrabsthanonbigger
ones.asymmetricIntheccompompeetitiontitionsforfituation.oodconMoreotext,ver,thiscouldNordhausbein(2004)terpretedbehavasioralan

196

8CHAPTER

observationsshowedthatinfightssituation,thelargerindividualswinmost
ofthetime.Thus,asymmetriccompetitionisoccurringininterferencecom-
petitionamongindividualsaswell.Competitioncanalwaysshowdifferent
degreeofsymmetry/asymmetry(SchwinningandWeiner1998),butfunda-
mentallyasymmetriccompetitionwouldmeanadisproportionateadvantage
forlargerindividuals(relativetotheirsize)oversmallerones.Asymmetric
competitioninplantpopulationsmightsometimesbeareasonforawider
sizedistributionthanexpected(SchwinningandWeiner1998).Chapter6
proposedthatthespatialorganizationofU.cordatusatthepeninsulalevel,
findinglargeindividualsinmostfavorablehabitatsandsmallonesinsec-
ondaryhabitats,couldbearesultofasymmetriccompetition.
Ucidescordatuspopulationsarethereforeshowinginterferenceandex-
ploitationintraspecificcompetitionwithpossibletendencyforasymmetry.
However,thereisnoinformationsofarontherelativeimplicationsofall
thesedifferentaspectsofintraspecificcompetitioninthedecisionofcrabsto
changeburrows.Identically,thespecificaspectsofcompetitionthatcould
leadtotheregularspatialorganizationofindividualsatsmallscale(<10m)
seeninChapter6arenotknown.Particularly,understandingtheroleof
asymmetriccompetitionattheindividuallevelcouldhelpinexplainingthe
patternsofpopulationorganizationatthepeninsulalevelasproposedin
Chapter6.Thus,aseriesofquestionsarestilltobeinvestigatedonthese
aspects.Thepresentstudywillfocusonthefollowingtwo:-doesthesup-
posedasymmetriccompetitionoccurringamongindividualsplaysagamein
therecoveryofthecrabpopulationafterfisheryandthespatialorganization
?-anddoestheterritorialbehaviorandtheindirectcompetitionforfood
showatrendofspatialimportancesuchthatfoodand/orterritory(alto-
getherfromnow-onconsideredas“resources”)closertotheburrowaremore
importantthanfurtheraway?
Chapter7proposedtoanalyzethetypeofinteractionsamongindividuals
withdifferentindividual-basedcompetitionmodels.Secondaryobservations
ofindividual-basedmodelsdevelopedinapattern-orientedmodelingframe-
workcanleadtofindingsasinterestingastheexplanationoftheoriginalfocus
patterns(Wiegandetal.2003,Grimmetal.2005).Theavailableindividual-
basedmodelsimulatingU.cordatusindividuals(IBU)wasdevelopedwith
apattern-orientedmodelingapproachandtestedtoreproducepatternsat
populationlevel.IBUsimulatescompetitionwithaphenomenologicalap-
proach,i.e.notallthestepsofresourceusearesimulatedmechanistically.
Thisapproachwasthefieldofneighborhood(FON)developedbyBergerand
Hildenbrandt(2000)whichisaparticularlygoodexampleofphenomenolog-
icalmodelsimplifyingcompetitionamongindividualsbutstillreproducing
manyprocessesandassociatedpatterns(e.g.BergerandHildenbrandt2003,

ODUCTIONINTR8.2.

197

Bergeretal.2002,2004,2006,Baueretal.2002,2004).InIBU,themath-
ematicalstructureofFONassumesthatforacrabtodecidetochangeof
burrow,theresourcesfurtherawayarelessimportantthantheonecloseto
theactualburrow.Also,accordingtoBaueretal.(2004),theFONapproach
simulatesasymmetriccompetition.Thusthisapproachhadalreadyassump-
tionsaboutthetwofocusquestionsofthepresentstudy.Otherindividual-
basedapproachmighthoweverbeconsideredtotesttheseassumptions.For
example,anotheroneknowntosimulateasymmetriccompetition(Weineret
al.2001)isthezoneofinfluenceapproach(ZOI).Thefixedradiusneigh-
borhood(FRN)approachisasimplerphenomenologicalwayofdescribing
competitionamongindividuals(PacalaandSilander1985).Thisapproach
considersthecompetitionintensity(i.e.thepressureofalltheneighborson
thecommonresourceofanindividual,Keddy1989)tobedirectlylinkedto
thedensityofneighboringindividualsonaharvestorresourceusearea,and
therebydoesnotgivemoreweighttoclose-byresources.Thedifferencesof
mathematicalstructureandpossiblederivedassumptionofbehavioralrep-
resentationofthesethreetypesofindividual-basedapproachessimulating
competition(FRN,ZOIandFON)givealreadyapanelofpossibilitiesin
termofcompetitionsymmetryandproximityofresources.Changingthe
sizeoftheradiusofinteractionwhichisthebaseofthesethreemodelswould
alsoallowassessingfurtherthequestionofimportanceoftheproximityof
resources.

Thepresentstudyconsiderconsequentlythesethreedifferentphenomeno-
logicalwaysofsimulatingcompetitionattheindividuallevelwithdifferent
sizeofradiusofinteraction.Themainpurposesweretoinvestigate:(1)if
thebehaviorofU.cordatusshoweddifferentresourceimportancedepending
onthedistancetotheburrow,and(2)ifthecrabuseofresourcesledto
anasymmetriccompetitioncondition.Toinferonthesequestions,Iana-
lyzedunderwhichassumptionsofIBUthreepopulation-levelpatternswere
reproduced.Inadditiontothetworecoverypatternsafterlocalfishery,as
analyzedinChapter7,Itriedheretoreproducealsothespatialorganiza-
tionatsmallscale(<10m)documentedinChapter6.Thereby,Iaimedin
verifyingtheassumptionsofChapter6thatcompetitionamongindividuals
isaprobablefactorleadingtospatialorganizationoftheirburrowsbecause
oftheirmovement.

198

dsethoM8.3

8CHAPTER

8.3.1TheIBUmodel
TheIBUmodelwasdevelopedtosimulateindividualU.cordatusbehavior
atsmallscale,primarilytounderstandthephenomenonleadingtorecovery
offishedareas(Chapter7).TheIBUmodelisaself-standingobject-oriented
programdevelopedinC++(Stroustrup,1997)andwasextensivelydescribed
inChapter7usingtheODD(Overview,Designconcepts,Details)protocol
(Grimmetal.2006).Inthepresentchapter,Iindicatejustthechanges
operatedtotheoriginalversion.
Thesub-modelsofreasonforcrabmovementwerethefocusofthepresent
study.Iconsidered3sub-modelsofcompetitionattheindividuallevel(2
morethaninChapter7)assumingthatcompetitionisthefactortriggering
thecrabstochangeburrowandonenullsub-modeldescribingthechangeof
burrowasarandomevent(describedalsoinChapter7).Eachsub-model
determinedtheprobabilitythatacrabhastomoveawayfromitsburrow
tofindorcreateanewburrowinanotherlocation.Thiscouldbecalled
thecompetitioneffect.Tousephenomenologicalapproachesthoroughly,the
simplifiedphenomenaneedtobeclearlydefinedaswellasthelimitsandas-
sumptions.Thus,toadaptthethreedifferentphenomenologicalapproaches
totheIBUmodel,theyshouldhandlecompetitioninacomparableway.I
assumethatallthreesub-modelsshouldleadtotheestimationofacompe-
titionintensityfeltbyeachindividual.Idefineforthispurposetheterm
competitionintensityasaphenomenologicalevaluationofthepressureof
competingorganismsontheresourceswantedbyafocusorganism.This
competitionintensityshouldbethentransformedintoacompetitioneffectin
identicalway.The3sub-modelsofcompetitionwerebasedonestimatingthe
competitionintensityfeltbyafocuscrabinaninteractionarea.Theyused
anidenticalcalculationoftheinteractionarea,definedasacircularzoneof
interactionaroundtheburrowofacrab.Theradiusofinteraction(Rint)was
calculatedforeachcrabatthestartingofthesimulationwiththefollowing
ula:formRint=min{a×(CW/2)+b,Rmax}(8.1)
whereCWwasthecrabcarapacesize(incm),aandbwereconstants(values
ofa=5,10or19,cf.below,valuesofb=15),andRmaxamaximumradius
assumedtobe100cm(Nordhaus2004).Thesurfaceoftheareaofinteraction
Aintwastherefore:
Aint=π×Rint2(8.2)
InthefirstIBUversion(Chapter7),Rintreflectedtheradiusofdailyaction

8.3.METHODS

199

(excludingburrowchange).Thesizeofthedailyactionradiuswasassumed
tobdecisionerelatedtochtoangecrabsburroize.woHonlywevoner,ascomphorteretitionzone,mighi.e.tbteheimpinfluencingortancecrabof
burroresourceswiftahewaycloserfromtheresourcescrabarenmighottnotsharedbelwitheadingothertocrabs.decisionThus,toIcthestedange
3movvealuesmenotftwheascorrespparameterondingatotoanalyzetheeinfttirehehinarveteractionstingaarearealoreadingnot.toInocrabw
describethe4sub-modelsofreasonofmovementtestedinthisexercise.

Sub-modelsofreasonformovement
tionRofandominreteraction:asonsubmocrabsddelo(notRMmor)v:eTbhisecausesub-moofsdelpatialfollowcompedaetitionnullforfoassump-od.
itwCrabsasohpaden)atthereforeeachatimeconstansteps.tprobabilityPmoveofleavingtheirburrow(if
Densityrelatedcompetitionsub-model(RMDENS):Thissub-modelwas
1985),inspiredexceptaftertthehatifixnthisradiusapproacneighhborhotheordadiusapproacofinht(PeractionacalawaasndnotSilanderfixed
butareasizewasdepceountndenedtat(cf.eacEq.h8time.1).stepThen(Num).berNofcwarabssusedwithintotheindetermineteractionthe
competitioneffect,i.e.theprobabilityofleaving(Pmove)analreadyopen
burrow,accordingtothefollowingformula:
Pmove=CN×N(8.3)
AintwhereCNwasascalingconstanttoobtainawantedmeanfrequencyof
bmoelovew,menandtofseetheTpableopulation8.1forv(furtheralues).Iexplanationsassumedinw“iththisparameterization”equationpthatart
thecindividualompwetitionasrelatedintensitytothe(i.e.tdensitheyofpressurecomponetingthecneighommonbor(rN/Aesource)int).onSincean
ofthethecnompeighbetitionors,thisintensitysub-mowasdelnotcoulddependencorresptoonndthetoaatctualerritorialneedbofehaviorresourcesof
individualsincompetingeitherdirectlyorindirectlytoassuretheirresource
needs.wasaHomodaptedgeneafteroustheintensityzonecofompinfluenceetitionmosub-models(delZOI,(RMasZOI)describ:Tedhisinsub-moCz´ar´delan
1998,sourceinpp219,use.Idid231-239).notsThehareZmecOIhofananisticallyindividualwithrrulesepresenthetstheresourcespatialamongre-
crabs1991).wIithaovessumedrlappingthattheZOI,pasropoitisrtiondoneofovinerlapmostofiZOIntmoeractiondels(areae.g.withBonana
neighboringcrabwasameasureofcompetitionintensity.Thus,withthis

200

8CHAPTER

approachthestrengthofcompetitionofacrab(i.e.thecapacitytoincrease
thecompetitionintensityonothercrabs)wasconstantatanypointwith
distancerofthiscrab.Theoverlapareasofalltheneighboringcrabswere
summed(Ov)anddividedbytheinteractionareaofthefocuscrab(Aint)
toevaluateitsprobabilityofmovement:
Pmove=CZ×Ov(8.4)
AintwhereCZwasascalingconstanttoobtainawantedmeanfrequencyof
movementofthepopulation(furtherexplanationsin“parameterization”part
below,andseeTable8.1forvalues).Thishandlingofcompetitioncouldbe
seenassimulatinganidenticalprobabilityofharvestingleavesorinteracting
directlywiththeneighborsontheentireinteractionareaofthecrab.In
termofbehavioralinterpretation,thecrabscouldbeconsideredasgiving
thesameimportancetoallresourcesontheinteractionarea.
Decreasingintensitycompetitionsubmodel(RMFON):Thissub-model
wasadaptedaftertheFieldOfNeighborhood(BergerandHildenbrandt2000,
2003)andwastheoriginalcompetitionmodelinChapter7.Thestrengthof
competitionofanindividualinitszoneofinteractionwasconsideredatany
pointwithdistancerfromagivencrabasfollowingthefunctionFON(r)
describedas:⎧⎫
⎨⎪⎪1for0≤r<CW/2⎬⎪⎪
FON(r)=⎪⎪exp−R|lnint(−FCWmin)/|2×r−2CWforCW/2≤r≤Rint⎪⎪
⎩0forr>Rint⎭
(8.5)whereFminwasanarbitraryminimumcompetitionstrength(0.01)atRint.
ThisFONfunctioncouldbedescribedasthedecreasingpressurethatan
individualcreateonthefoodresourcesgoingawayfromitsburrowposition.
Thus,Iconsideredthecompetitionintensityaffectingafocuscrabasthesum
ofintegralsoftheFONintensityoftheneighborsovertheoverlapsoftheir
interactionarea(definedasFA,seeChapter4,5or7formoreprecisions)
dividedbytheareaofinteraction(Aint)representingtheneededresources.
Thiscompetitionintensity(FA/Aint)wasthentransformedintocompetition
effectasfortheothersub-models:
Pmove=CF×FA(8.6)
AintwhereCFwasascalingconstanttoobtainawantedmeanfrequencyofmove-
mentofthepopulation(furtherexplanationsin“parameterization”partbe-
low,andseeTable8.1forvalues).Thecorrespondinghypothesisofbehavior

METHODS8.3.

201

Table8.1:ParametervaluesofconstantsCinequations8.3(RM),8.4(RM)
and8.6(RMFON)forthedifferentvaluesofconstantaincalculationDEoNfSRint(Eq.ZO8.2)I
a=5CRMDE=755.98NSCRM=0.224ZOICRMFO=1.864N
FZNaa=19=10CCNN=376.06=439.19CCZZ=0.025=0.066CCFF=0.279=0.687

ofcrabswouldbethattheycompetethroughinterferenceorexploitation
activitygivingmoreimportancetotheclosestresourcesthantheonefurther
awayontheinteractionarea.

Parameterizationofthesub-models

Eachofthesesub-modelsweretestedwiththreeconstantsainthera-
diusofinteractioncalculation(Eq.8.1),correspondingtotestingdifferent
importanceofproximityareasaroundtheindividualsinfluencingdecisionof
movement.Tobeabletocomparetheeffectofthesecombinations(fromnow
on,called“models”)onthefocuspatternsatpopulationlevel,butlimiting
thenumberofotherindependentfactorsinfluencingthesepatterns,Icon-
sideredthateachmodelparameterizationshouldleadtoanarbitrarymean
valueoffrequencyofmovementofcrabs(f,calculatedasthetotalnumber
ofmovementsdonebyallcrabsduringaperiodoftimedivided−2bythistime
periodandnumberofcrabs)foragivendensity(individuals.m),meansize
ofthecrabsandsizeofradiusofinteraction(dependingonparametera).
Thus,foreachofthemodelsusingcompetitionsub-models(nottheRMr),
preliminarysimulationswererunwithfixedcrabdensityandmeancrabsize
(Table8.2,columna)tofindthecorrespondingscalingconstantC(inequa-
tions8.3,8.4or8.6)obtainingameanfrequencyofmovementofthecrabsof
f=0.07movement.crab−1.day−1.Idecidedtotakethisarbitraryvalueoff
=0.07movement.crab−1.day−1becauseitisapproximatelytheoneleadingto
thebestreproductionofthefieldpatternsofrecoveryinChapter7.Table8.1
givestheCvalueswiththecorrespondingradiuscalculationandcompetition
sub-model.Forthenullmodel(usingRMr)Pmovewassetto−0.11too−1btain
ameanfrequencyofmovementofcrabsof0.07movement.crab.daybe-
causeoftheproportionofcrabsstayinginaclosedburroweachday(cf
AppendixA,page218forcalculation).

202

8CHAPTER

Table8.2:ParametersenteringinthefourtypesofsimulationsofIBUforeachofthe28
models:2simulationswithcolumnafortherecoverypatternreproduction,1simulation
withcolumnbforthereproductionofthespatialdistributionpattern,and1simulation
withcolumncfortheanalysisoffrequencyofmovementcorrelatedwithsize.Theuseof
individualparametersofprobabilityofaction(Px)isdescribedinChapter7.
ParameterDescriptiona)b)c)
(Xmax,Ymax)Sizeofthesimulationarea(inm)(15,15)(7,5)(7,5)
MaxtimeTimelengthofsimulation(days)(10+)50or15100100
DcCrabstartingdensity(in/m2)3.166.23.16
PropUnocProportionofunoccupiedbur-22%22%22%
startatwsroPropClosedProportionofclosedburrowsat60%60%60%
startCWpopMeancarapacesizeofthesimu-6.556.5
latedcrabpopulation(incm)
SDCWpopStandarddeviationofthemean2.5*1.02.5
carapacesizeofthesimulated
crabpopulation(incm)
Pc1Probabilityoftakingoveranoc-0.00.00.0
wburrocupiedPc2Probabilityoftakingovera0.050.050.05
closedemptyburrow
Pc3Probabilityoftakingoveran1.01.01.0
openemptyburrow
PclosingProbabilitythatacrabclosesits0.140.140.14
burrowateachtimestep
PopeningOnceclosed,probabilityofopen-0.330.330.33
ingitsburrowateachtimestep

*TheSDCWpopwasincolumna)theonlydifferentparametertoChapter7tosimulateapopulation
sizestdifferenmorewith

METHODS8.3.

203

ulationsimS8.3.2patternselpulation-levoPEachofthe9competitionmodels(3sub-model×3sizesofradiusof
interactions)andthemodelusingthenullsub-model(altogetherhereafter
referredtoasthe10models)weretestedtoreproducethreefieldpatternsat
populationlevel(Table8.3).3simulationswith30replicateseachwererun
toevaluatethereproductionofthesethreefieldpatterns.Theyconsisted
of:thedatapointsofproportionofrecoverednumberofburrowstakenfrom
thetwoexperimentsofrecoveryofentirelyfishedareas(withorwithout
removingburrows)describedinChapter7(Fig.7.1,page169,thedata
pointsbutnottheregressionlines);andthespatialdistributionpattern
evatsmallaluatedscalewith(∼the25cm)L-RipleydescribfedunctioninatChapter6individual-lev(Fig.6.2g,elshopagewing149,butregularitonlyy
onthescaleofrbetween0to50cm).Thetwofirstsimulationswererunwith
thedescribpediarametersnCphapterresen7:ted10instepsTableafter8.2the(columninitializationa),andoftwithheasimschulations,edulingtheas
crabsofacenterareaof12.35m2wereremoved.Therecoverywasevaluated
during50and15days(correspondingtothe2experimentsrespectively)
astheproportionofcrabsre-installedinthefishedareacomparedtothe
originaldensitybeforeremoval.Thethirdsimulationwasrunwithdifferent
parameters(Table8.2columnb)tosimulatethistimeasmallareawith
localdensityandcrabsizecorrespondingtothesmallscalemapof3×5m
whicdescribhneodcinrabsCwhapterere6.removTheseed.simThesulationspatialwererdistributionunfor1o00fthetimecrabstepspoduringsitions
wereevaluated2afterthese100dayswithanL-Ripleyfunctiononacenter
areaof15masdescribedinChapter6(Eq.6.1and6.2,page145).

ymmetrysetitionCompThedifferencesofwayofmeasuringcompetitionintensityamongthethree
sub-models(equations8.3,8.4and8.6)wereassumedtodevelopdifferentde-
greeofsize-symmetrycompetition.FortheRMDENSsub-model,thedensity
aroundthefocuscrabwasthemeasurementofcompetitionintensity.Thus,
thecompetitioneffectshouldbesize-independent.Thissize-independent
effectcouldbeexpressedassimulatingaproportionalshareofresources
dependingontheirneeds.Consequently,IexpectedthatthisRMDENSsub-
modelsimulatedsymmetriccompetition.Fortheothertwosub-models,pre-
viousstudiesgavetheseassumptions.Weineretal.(2001)considereda
ZOImodelsimulatingresourcepartitioningwitharuleofequalshareamong
overlappingindividuals.However,theystipulatedthataninherentchar-

204

8CHAPTER

(TSiamble)c8.3:onsideredinDescriptiontheoanalysisffieldofpgoodatternsness(ofObfits)ofathenddcorrespifferentomondingdelss(imNobsulation=nuvmbalueser
ofpointstoreproduce).
PatternsNobsObsSim
menRecotv1ery(expREC1)*eri-18Vsitayluesrecoofvepropred(ortionatofdifferenden-ttionSimuoflationdensitvyarluesecovoferedpropor-
shery)fiaftertimemenRecotv2e(ryexpREC2)*eri-30Vsitayluesrecoofvepropred(ortionatofdifferenden-ttionSimuoflationdensitvayrluesecovoferedpropor-
timeafterfishery,andfrom
plots)tdifferentionSpatial(SPdAT)istribu-10L(r)3x5mmapRipleyofChapterfunction6forofL(r)lationRipleyresultsafterfunction100daofyssimfuor-
r=[5,50]cmr=[5,50]cm

*Notethattherecoverypatternsinthisstudyaretheoriginalpointsofrecoveryproportionandnotthe
linearregressionasinChapter7.

acteristicofZOImodelsisthatapartialsize-asymmetryoccurswithsuch
configuration,becausethelargerof2competingindividualshasalwaysa
lowerpercentageofitsareaundersharethanthesmallestindividual.Thus
IexpectedtheRMZOIsub-modeltocreatepartialasymmetriccompetition.
Baueretal.(2004)arguedthattheFONapproachshouldcreateasymmet-
riccompetitionconditions.Thereby,IexpectedtheRMFONsub-modelto
etition.compasymmetricalsocreateTotesttheseassumptions,asimulationforeachofthe10models(with
theadditionalparametersdescribedintable8.2columnc)wasruntorecord
thefinalnumberofmovementthateachcrabhaddoneduring100timesteps.
Ichoseheretosimulateanidenticalcrabpopulationthanintherecovery
experiment,butwithoutremovalofindividuals(hencetheadditionalsimu-
lations).Usingthecompetitionsub-models,theprobabilityofmovementis
directlydependentontheeffectofcompetition.Thiscompetitioneffectwas
theexpressionofacompetitionintensityfeltbytheindividuals.Iftheeffect
ofcompetitionishigherforsmallindividualsthanbigones,thefrequencyof
movementoftheformershouldbehigherthanforthelatter.Itwouldalso
meanthattheresourcesweresimulatedasnotproportionallysharedsince
thecompetitioneffectsweresetasindependentontheresourceneed(sup-
posedbythedivisionbyAintinequations8.3,8.4and8.6).Thus,foreach
model,Ianalyzedifasignificantcorrelationbetweenthenumberofmove-

METHODS8.3.

205

mentsdonebyeachcrabandtheirsizesexistedandwithwhatsign(positive
ornegative).Forverifyingthesignificanceofthecorrelation,asimplelin-
earregressionanalysiswithanalysisofvarianceontheparametersofthe
regressionmodelwaseffectuated.Icouldestimateoutofthesecorrelations
ifamodelledtomoremovementsofsmallorbigcrabs,oriftherewasno
significanttrendamongsizes.Iinterpretedasignificantnegativecorrelation
asasignofasymmetriccompetitioninfavorofbigcrabs.Ontheotherhand,
asignificantpositivecorrelationwasseenasasignofasymmetriccompeti-
tioninfavorofsmallcrabs.Alackofsignificancewasseenasasymmetric
ituation.setitioncomp

8.3.3Analysisofgoodnessoffittothepatterns
Fortheassessmentofreproductionofthethreepatternsforeachofthe
10differenmotdelsthanIuinsedCtwohapter7)approacandhtes:heaPamttern-Orienean-squaretedMdeviationodelingmethodInformation(abit
twoCriterioncriteria(POofMgoIoC)dnessaofpproacfit,hadescribfirstedincalculationChapterev2.aluatedForhoeacwhweoflleactheseh
patternwasreproduced,andasecondevaluatedthetotalgoodnessoffitof
themodeltothe3patternstogetherassumingthateachpatternhadthe
ortance.impsameThemeansquare-deviation(MSD)wascalculatedforeachpatternas:
MSD=130Nobs(Obs−Sim2)2(8.7)
30×Nobsr=1t=1
whereObswasthefieldobservations,Simwasthecorrespondingsimulation
resultsofthereplicaterandNobswasthenumberoffieldobservations(Table
8.3).Atotaldeviationerror(TotMSDi)wascalculatedas:
TotMSDi=13MSDj,i(8.8)
3j=1minMSDj
wawherestheiwaminimstheummovadelluecofMSonsidered,Dforjtheindicatedpatternjtheofpallatternour10andtestedmin(moMSDdels.j)
foreacThehpPOattern.MICForeaccalculationhofthewas10amlsooduels,sedttheosimindicateulationthegoresultsodnessoftheof30fit
replicateswerecombinedperobservationsforthecorrespondingObs(the
tthobservationofthefieldpattern)inavectorof30valuesVSimtoftrange
Simestimatorrange.(TRhisDvevectorelopmenwastfirstCoretTeamransformed2006)owithfbaandGwaussianidthd(bwensit)yakepprornelxi-
matelyequaltoatenthofthedifferencebetweenthebiggerandsmaller

206

8CHAPTER

valuesofVsimt.Theresultingdensities(vectorDs)werethenscaledinto
probabilitiesofobservation(Ps).ThiswasdonebydividingDsbythemax-
imumprobabilityvalueestimatedfromthefrequenciesofobservationsinthe
vectorVsimtdividedinclassesofwidthsbw.ThePsvalueswerealways512
values(standardoftheRGaussiankerneldensityestimator)corresponding
toavectorPSimof512hypotheticalSimvaluesofrangePSimrange=[min-
imumvaluereturningaDs>0,maximumvaluereturningaDs>0]andof
constantincrement(maximum-minimum/511).Thelikelihoodofamodel
tohavereproducedafieldobservationL(Obst|model)wasthendetermined
as:"!L(Obst|model)=Ps[k]if−Ob314st∈PSimrange(8.9)
1.09×10otherwise
wherekwasthepositioninvectorsPsorPSimwherePSim[k]wasthe
closesttoObst.The1.09e-314valuewasanarbitraryvalueclosetozerogiven
tothelikelihoodwhenthesimulationrange(Simrange)wasnotcloseenough
tothefieldobservation(Obst)tohaveaPs>0.Itwassettoavoidgetting
infinitevaluesofPOMIC(becauseofthelogarithmfunctioninPOMIC,
seebelow).Thenumberoftimethisoccurredwashoweverkeptinavariable
(Nun)tocountthenumberoftimetheconsideredmodelhaditssimulation
resultsnotcoveringthefieldobservations.Thegoodnessoffitindicatorfor
eachmodeliwasthencalculatedas:
Nobs1POMICi=−Nobslog(Li(Obst|model))(8.10)
=1tThePOMICapproachwasalsousedtoinformaboutthetotalgoodness
offitofeachofthe10modelstothethreepatternsconsideredtogether.
AccordingtoChapter2,thistotalgoodnessoffitwascalculatedasthemean
POMICofthethreepatterns:
31TotPOMICi=3POMICi,j(8.11)
=1jwhereiwastheconsideredmodelandjindicatedoneofthethreepatterns.
TheadvantageofthisapproachcomparedtoTotMSDwasthatthetotal
goodnessoffitforonemodelwasindependentofthegoodnessoffitofother
models.Additionally,theTotPOMICcriterionkeptatrackofthenumberof
timethesimulationresultsdidnotrangesuchthatthecorrespondingob-
servationvaluefellwithinorclosetothem.NotethatallPOMICvalues
(orTotPOMIC)shouldbeconsideredintermoftheirdifferencestothesmall-
estone.Ingeneral,itcanbeassumedthatwhenthisdifferenceis<1,the

STRESUL8.4.

207

correspondingmodelisatashighevidenceasthebestmodel(Chapter2).
Forthefinalgoodnessoffitindicator,thedifferencesofTotPOMIC(Δi)were
calculated:Δi=TotPOMICi−TotPOMICmin(8.12)
wheretheTotPOMICminwastheminimumTotPOMICvalueamongall10
models.Thesedifferenceswereusedtocomputetheprobabilityofamodel
tobethebestoneamongthesetof10(Chapter2):
Wi=10exp(−Δi)(8.13)
r=1exp(−Δr)
AllanalyseswereeffectuatedwithscriptsdevelopedfortheRsoftwarecversion
2.3(RDevelopmentCoreTeam2006).

esultsR8.4Meanfrequenciesofmovementofcrabsweremeasuredas∼0.07movement.crab−1.day−1
formostmodels(Table8.4,columnFreq).OnlytheRMZOIsub-modelof
competitionwithsmallradiusofinteraction(parametera=5)resultedin
frequencyofmovement>0.075movement.crab−1.day−1.
Thecorrelationsamongcrabsizeandnumberofmovementforsimula-
withtionsuthesingdifferenthetRMvDEaluesNSofthesub-modelparametershoweadaforthedifferentradiustrendofinofteractioncorrelationscal-
culation(Table8.4,columnSign).Withsmallandintermediateradiusof
interaction,thecorrelationsshowedpositivesigns,indicatingasignificant
highernumberofmovementsofbigcrabsthansmallones.Withlargeradius
ofinteraction(a=19)thecorrelationledtonon-significantdifferenceofnum-
berofmovement.Simulationsusingthetwoothersub-modelsofcompetition
obtainedalwaysthesamepatternsofcorrelationsacrossthedifferentradius
ofinteractions.TheRMZOIsub-modelledalwaystosignificantlyhigher
numberofmovementofsmallcrabsthanbigones.Withthesub-modelus-
ingtheFONapproach,thecorrelationsledtonon-significantdifferencesof
nledumablsoertofoamonvemenon-significantamongtsizes.differenceTheofnnullummoberdelofumosingvethementRMramongsub-mosizes.del
ThefirstpatternofrecoverywasbestreproducedwiththeRMZOIsub-
modelaccordingtobothindicators(table8.4columnsREC1),althoughnot
withidenticalradiusofinteraction.Allmodelshadsimulationresultsinclud-
ingallfieldobservationpointsintheirrange(table8.4,columnNun=0in
REC1).MostPOMICvalues(9outof10)showeddifferencestothesmall-
estPOMIC<1.Thisindicatedthattheevidenceofreproductionofthis

208

8CHAPTER

Table8.4:Resultsofeachmodelinfrequencyofmovementofcrabs(Freq),signof
correlationcrabsizevs.frequencyofmovement(Sign)andindicatorsofgoodnessoffitfor
eachpattern(REC1,REC2orSPAT).a=ValuesofainRintcalculation,MSD=mean
squaredeviation(Eq.8.7),POMIC=Patternorientedmodelinginformationcriterion
(Eq.8.10),Nun=Numberofnon-reproducedobservationsbythesimulations.Thebest
resultsofMSDorPOMICforeachconsideredpatternsareindicatedinbold.Inthe
POMICcolumns,modelshavinglessevidencethanthebestoneareingrey(POMIC
differences>1).†indicatesthemodelselectedtoshowonFig.8.1thereproductionof
therecoverypatterns(REC1andREC2),‡indicatesthemodelselectedtoshowonFig.
8.2thereproductionofthespatialdistributionpattern(SPAT).
Sub-REC1REC2SPAT
amodelFreqSignMSDPOMICNunMSDPOMICNunMSDPOMICNun
RMDENS0.073+1.2242.28900.98226.5991285.6972.6100
5RMZOI0.086-0.8921.07100.70849.9712178.7251.9180
RMFON0.067=0.5391.53400.79949.9652107.6051.9090
10RMRMZODEIN†S0.0700.069-+0.6420.43911.236.625000.9220.85026.04450.27912222.452168.0932.2411.79700
RMFON‡0.068=0.4811.35400.78150.2472111.9151.6530
RMDENS0.070=0.5501.36800.90650.7802274.3452.5930
19RMZOI0.069-0.5271.30300.82526.0551324.49674.6721
RMFON0.069=0.4821.41200.82926.4551209.1642.7070
RMr0.068=0.8211.76200.85626.2001490.8183.9220

patternwasthesameforallthese9models.Thesecondpatternofrecovery
wasalsobestreproducedwiththeRMZOIsub-modelaccordingtobothin-
dicators(table8.4columnsREC2).Fivemodelshadequivalentevidenceof
goodnessoffitthanthebestoneaccordingtothePOMICdifferences.The
POMICvaluesalsoindicatedthattheNullsub-modelofinteraction(RMr)
wasbetterinreproducingthispatternthanmanyofthemodelsusingcom-
petitionsub-models.Thefieldobservationswerenotreproducedentirely
withanymodel(table8.4,columnNun>0inREC2),withatleastone
fieldobservationalwaysnotreproduced.Thepatternofspatialdistribution
atsmallscalewasbestreproducedbytheRMFONsub-modelaccordingto
bothindicators(table8.4columnsSPAT),althoughnotwithidenticalradius
ofinteraction.Asetof3models,includingtheoneusingtheRMrsub-model,
hadlessevidenceofreproducingthepatternthanthebestmodelaccording
tothePOMICvalues(difference>1).Thefigures8.1and8.2showthebest
modelsthatreproducerespectivelytherecoverypatterns(REC1andREC2)
(RMZOIwitha=10,seeTable8.4)andthespatialdistributionatsmallscale
(SPAT)(RMFONwitha=10,seeTable8.4).
TheTotMSDindicatoroftotalgoodnessoffitofthethreepatternsto-
getherindicatedthatoverall,thebestassumptionofinteractiontousewas
theRMFONsub-model(Table8.5)withintermediate(a=10)radiusofinter-

DISCUSSION8.5.

209

Figure8.1:Reproductionoftherecoveryafterfisheryofthemostrealisticmodelfor
thispattern(RMZOIwitha=10,selectedinTable8.4)(Solidblackandgreylines:mean
ofproportionofrecoveryafterfishingfrom30simulationsexperiment,withremovingthe
burrowsorleavingtheburrowsrespectively;blackandgreydashedlines:corresponding
maximumsandminimums;blackandgreytriangles:respectivefieldpatternsofrecovery
7.1).Figc.f.REC2),(REC1,

action.indicatingAasetpootenf4tialmodelsequivhadalentedifferencesvidenceofofbToeingtPOtheMICbesttomtheodbelesttofitall<of1,
them.Theweightsofevidenceoutlinedthatthebestmodel,theRMZOIwith
intermediatesizeofinteractionarea,hadaprobabilitytobethebestmodel
<0.90.ThemodelusingtheRMrsub-modelreceivedthelowerweightofev-
idenceofthissetofmodelsthatobtainedrangeofsimulationresultscovering
allbutonefieldobservation(inpatternREC2).

iscussionD8.5ThisstudyusedtheIndividual-basedUcidescordatusmodel(IBU)totest
differentmodelsofindividual-levelcompetitioninreproducing3patternsob-
servedatpopulationlevel.Theresultsillustratedthatamodelsimulating
theeffectofcompetitionamongneighborsasinitiatingforceofmovement
reproducebetterallpopulation-levelpatternsthananullmodelconsidering
randomreasonofmovement.Theresultsarealsoshowingatrendofhigher
importanceofresourcesclosetotheburrowsintriggeringindividualmove-
ment.Theinfluenceandimportanceofasymmetriccompetitionishowever

210

8CHAPTER

Figure8.2:Reproductionofthespatialdistributionpatternatsmallscalewiththe
mostrealisticmodelforthispattern(RMFONwitha=10,selectedinTable8.4)(Solid
blackline:L-Ripleyfunctionofthefieldobservations;blackdashedlines:95%confidence
envelopeforcompletespatialrandomness(CSR)using999MonteCarlorandomizations
(c.f.Fig6.2g);solidgreyline:meanL-Ripleyfunctionfrom30simulationsexperiment;
greydashedlines:correspondingmaximumsandminimums).

estimate.toharder

8.5.1Modelstructureandsymmetryofcompetition
TheChapter7arguedthatthefrequencyofmovementofindividualswas
oneofthemostimportantfactorstoreproducetherecoverypatternsofU.
cordatuspopulationsobservedonmangroveforestofNorth-Brazil.Inthe
presentstudy,eachmodelversionwasconfiguredto−repro1duce−1anoverall
identicalfrequencyofmovement(0.07movement.crab.day).Particu-
larly,themodelsusingacompetitionsub-modelwereparameterizedfrom
preliminarysimulationstoassurethattheoverallcompetitionintensitywould
bweantedotransformedverallmintoeanfrequencyprobabilitiesofofmomvoevmenement.tOofnlytheindividualssub-modelleadingusingtothethe
zoneofinfluenceapproachwithsmallradiusofinteractionledtofrequen-
asciesofbiologicallymovementaacceptablebittooinhigh,Chapterbut7(still<0.14withinmoavermenanget.crabthat−1wa.dasyd−1).efinedIt
seenmightashaavemongtheinfluencedbestrtheeproresultsducingofthegoorecodnessveryofpfitatterns.sincetHohiswevmoer,delitwdidas

DISCUSSION8.5.

211

Table8.5:Resultsofeachmodelinoverallindicatorsofgoodnessoffit:TotMSD=
totalmeansquaredeviation(Eq.8.8),TotPOMIC=totalpatternorientedmodeling
informationcriterion(Eq.8.11).Theordersshowthe“best”(1,inbold)tothe“worse”
(10)fittingmodelaccordingtotherespectivecriterion(TotMSDorTotPOMIC).The
weightsofevidencearecalculatedfromTotPOMICvalues(Eq.8.13)andcanbeseen
asprobabilitytobethebestmodel(a=valuesofainRintcalculation,greyvaluesof
TotPOMICindicatedifferencestothebestmodel>1).
aSub-modelsTotMSDTotPOMICOrderTotMSDOrderTotPOMICWeightofevidence
RMDENS2.31510.499930.193
5RMZOI1.59217.653650.000
RMFON1.13617.802270.000
RMDENS1.42917.901480.000
10RMZOI1.4709.840510.373
RMFON1.09517.751160.000
RMDENS1.71118.247790.000
19RMZOI1.81034.0108100.000
RMFON1.41910.191320.263
RMr2.57310.6281040.170

notleadtooverallbetterevidencetoreproducethethreepatternstogether.
Thissmallerrorinparameterizationshouldthereforebekeptinmindforthe
inferenceontheroleofasymmetryanddistanceofresources.
Thechangeofsymmetriccompetitiontypewiththesimplestcompeti-
tionsub-model(RMDENS)canbeexplainedfromthemodels’structures.
Thelargeradiusesproducedasymmetriccompetitionsituationasexpected
forthissub-model.Thetwootherradiusesshowedasymmetriccompetition
infavorofsmallindividuals.Withparameterizationoflargeradiusesofin-
teraction,thecompetitioneffectthatanindividualfeelsisdependingless
onthelocalvariationofdensitythanwithintermediateandsmallradiuses.
Thesmallandintermediateradiusesofinteractionparameterizationleadto
highervariabilityinestimatingthedensity.Thisistransformedtohigher
variabilityincompetitionintensityestimationandtherebyhighervariabil-
ityofprobabilityofmovementforeachcrabthanwiththelargeradiusof
interaction.Additionally,consideringanidenticaldensityaroundasmallin-
dividual,thisdensitymightbeunder-estimatedtobe0withsmallradiuses
ofinteraction.Inthiscase,theprobabilityofmovementbecomesthenequal
to0.Byincreasingtheoverallvariabilityofprobabilityofmovementbutcut-
tingitsdistributiononitslowerend,thesesmallerradiusesofinteractions
arecreatingadistributionofnumberofmovementdependingonthenumber
oftimeseachindividualhadanestimationofdensityonitsinteractionarea
equalto0.Thus,thesmallertheradiusofinteraction,themorethecompe-
titionbecomesasymmetricinfavorofsmallcrabs.Thischaracteristicofthe
density-basedcompetitionmodels(usingRMDENS)shouldleadtopreferan

212

8CHAPTER

interactionradiuscorrespondingtothefieldobservationsthanwithsmaller
ones.Thiswouldinsurethesymmetryofcompetitiontobedependenton
thecompetitionsub-modelandnotthesizeoftheradiusofinteraction.

andFtortherebheytwotheoatherssumedcomptypetitioneofscompub-moedels,titionthesymmetrytrendsofwasncorrelationotdifferensign,t
ingamongthetZheOIthreesub-mordelsadiusesledoftionttheeractionexpectedpartialparameterizations.asymmetricThecmompodeelstitionus-
thanwherebbigysmallcrabs.Wcrabseinerareetamorel.(2001)influencedconsideredbyidenaticalZOIcmoompdeletitionsimulatingintensityre-
andsourceapparentpartitioning.lythisTZOIheircZOImharacteristicodelfcouldorcednottrhemeprotocducepompareerfectpartialsymmetrysize-
asymmetry(accordingtoSchwinningandWeiner1998)tototalasymmetry
thewhereptresenhetbigstudy,individualIdidtnotakescallonsiderresourcesmecinhanisticoverlaprsesourceituation.Inpartitioningthecasewithof
anyoftransformationthesub-motocdels,ompbutetitionaeffect.Aphenomenologicalssumingcthatomptheetitioncorrelationintensityamongand
msizeyandstudynshoumbwesrtofhatmaovementisphenomenologicalagoodaindicatorpproachofleadscomptoetitionidentsicalymmetryresults,
thanthemoremechanisticoneofWeineretal.(2001).

ThetypesofcompetitionassumedwiththeFONsub-modelsledtoap-
parentcompetitionsymmetrywithalltheradiusofinteraction.Thisgoes
againsttheexpectationsofBaueretal.(2004)whousedameasureofcom-
pcomeetitionfromintensitythefactastinhattthehepmoresendeltofBstudy.auerHetowal.ever,usedanaedifferenxplanationtformmighulat
toestimatethecompetitioneffectthantheoneusedhere(here:competi-
tioneffect=constanttransformingfactor×competitionintensity).They
compcalculatedetitionthiscintensityompasetitionintheeffeKctiWibymotakingdel(theBergermaximandumHildenamongbrandt0and2000).1-
sityThiswomauldyleadnottoaincreasethresholdthecsompituationetitionwhereeffect(seeincreasealsoincAppompendixetitionB,inten-page
219couldforbefurtherconfirmedargumenwithtaations).nalyticalAtmleast,athematicalthesedevdifferenceselopmenotfa(notpproaceasilyhes
solvresultsable)woithftIheBUtwwooulddifferenbetthenways.thatAntheinimpterestingossibilityfindingtohavecomingperfectfromsym-my
metry(SchwinningandWeiner1998)underaZOIapproach(asseenabove)
oncouldplanbetpgivoenbpulations.ytheFONapproachforfurtherstudiesonsymmetryeffect

DISCUSSION8.5.

213

8.5.2Differencesinmethodsanalyzingthereproduc-
tionofpopulation-levelpatterns
Theresultsofpatternofrecoveryreproductionsbythedifferentmodelver-
sionswererelativelycomplementarytotheobservationsofChapter7.The
measureofgoodnessoffitwiththemeansquaredeviation(MSD)confirmed
thatthemodelversionwiththesub-modelofrandomreasonformovement
hadaworsefitthanthemodelusingtheoriginalFONapproachasinChap-
ter7.However,theresultsofthepattern-orientedmodelinginformation
criterion(POMIC)approachdemonstratedthattheevidenceofthecom-
petitionmodelswasnothigherthanforthenullmodelastobereproducing
theprocessesleadingtotherecoverypatterns.Althoughspeakingofsignifi-
cancewithinformationcriteriaisnotrecommended(seee.g.Burnhamand
Anderson2002),theseresultscouldbeinterpretedinsimplerwordsasalack
ofsignificantdifferenceamongthenullandthecompetitionmodelsforthe
reproductionofthese2firstpatterns.However,thisdoesnotcontradictthe
findingsofChapter7thatcompetitionwouldbethetriggerofcrabmove-
mentleadingtorecoveryoffishedareas.This,mainlybecausetheChapter7
analysisfocusesontryingtoreproducethelinearaspectoftherecoveryand
notonlythedatapointsasIdidhere.
TheMSDresultsshowedthatthenullmodelwasnotreproducingthe
spatialpatternatsmallscaleaswellasalltheothermodels.ThePOMIC
approachgivesadditionalinsightsintermofevidenceofthemodelstofit
thespecificspatialpattern.Itsresultsshowthatitispossiblethatthenull
modelofreasonofmovementreproduceallpointsofobservation.However,
thegoodnessoffitofthismodelissuchthatthePOMICdifferencesdemon-
strateamuchlowerevidenceofbeingagoodmodelreproducingtheprocess
underneaththespatialpatternthanthebestcompetitionmodelsusingthe
FONapproach.Thus,thePOMIChelpinbeingsecuredthatthecompeti-
tionmodelshouldbepreferredintermofgoodnessoffit.
Consideringthethreepatternstogetherandofequalimportance,the
MSDandPOMICindicatedifferentbestsub-modelstousetosimulate
crabinteractions.Thesedifferencescomemainlyfromthesensitivitythat
POMICgivestotheoverallrangeofsimulationresultsthatshouldcoveras
muchaspossiblethefieldobservationspoints.POMICisalsodependent,
astheMSD,onthedistanceofthesimulationresultstotheobservation
points(throughthelikelihoodfunctionthatreturnslowervalues(leading
tohigherPOMIC)asthesimulationsresultsarefurtherawayfromthe
fieldobservations).ButtheadditionalcharacteristicofPOMICmakesfor
examplethatthebestmodelaccordingtoMSDisfoundatthe6thposition
withPOMICandwithaweightofevidenceof0astobeagoodmodel

214

CHAPTER8

reproducingthepatterns.POMICalsoinformsthatoverallthenullmodel
ishavinga17%probabilityofbeingagoodmodelreproducingthethree
patternstogethergiventhesetofmodeltestedinthepresentstudy.Thisis
muchhigherthanmanyothermodelversions,butlessthanhalftheevidence
ofthebestmodelwithZOI.

8.5.3Competitionatindividuallevelandinferringon
iorvehabindividualAlthoughthePOMICapproachshowedthatoveralltheintraspecificcom-
petitionamongindividualsisnotnecessarilythephenomenonleadingtothe
originobserveofdrtheecosverypatialpatterns,patternothisfostudyrganization.confirmtBothhehgoypoodnessthesisoftfithatitisindicators,atthe
MSwithDmoanddelsPOsimMICulating,showcompedaetition,betterandrpeproarticularlyductionofthetheonespatialimplyingpatternthe
degreeditionallyof,aimplltheortancemodoelsfrthatesourceshadevidenceaccordingtotortheireproducedistancesthis(FpatternON).wAd-ere
consideringsmallorintermediateradiusofinteraction.Thustoreproduce
thispattern,theclose-byresources(foodand/orterritory)wereseenmuch
moreconfirmedimptortanhetexpethanctationfurtherofConeshapterfor6tthehatcrabtheretoisdecideprobablytomoavre.Tepulsionhese
proregularcessoamongrganizationcrabsobservthroughedcatompsemalltitionscale.forsThesepacecandfoonclusionsodthatcanleadbetoctom-he
paredtotheeffectofcompetitionamonggrowingtreesleadingtoaregular
spatialorganization(e.g.Kenkel1988).
bestfittingConsideringmodelsallpofatternseachtcompogether,etitionthesrub-moadiusdelsofintypesteraction(DENS,usedbZOIyother
FON)helpedininferringonthepresenceornotofaspatialpreferenceofU.
cordatusinresources.Thesimplestmodel(DENS)measuringcompetition
theintensityclosestasresourcesdirectlyflinkoredactorabdensittodysecidehoweifditamushouldchmohigherveorimpnot.ortanceTheof
secondsimplestmodel(ZOI)reproducedbetterthefieldpatternswithan
inclosertermediarytotheradiusburrowoftinhantteraction,heoriginallyimplyingbeanlieveimpdradiusortanceooffhthearvest.resourcesThe
bestFONmodelusedthelargestinteractionradius.Thisconfirmedthe
previousobservationofhigherimportanceofresourcesclosetotheburrow.
awThisayFONresourcesmodelmighcantanotlsobbeecintompeerpretedtedforasawithnewathypoerritorialthesisbtehahatvior,furtherbut
vbeetterrifiedtwithhroughmecindirecthanisticmodelsexploitationsimculatingompeclearlytition.tThiserritorialwooruldhaveexploitationtobe

DISCUSSION8.5.

215

behaviors.Allmodelsindicatethatthemostimportantresourcesarethe
onesclosetotheburrow,andthattoohighcompetitionintensityonthese
resourcesmightleadacrabtotakethedecisionofchangingburrow.Thesizes
pofozonessibilitiesofaharvndestinageneralssumedU.incoCrdatushapterw7oauldreusesthereforemallertheareas.extremelargest
Finally,theresultsofthebestfittingmodelofthisstudy(RMZOIwith
intermediaryradius)alsoargueinfavorofthehypothesisthatbigcrabshave
moreinfluenceinexcludingsmallindividualsthantheirequivalentshareof
theresource.ThiswouldexplainmoreeasilytheobservationsofDiele(2000)
andChapter6illustratingthatsmallcrabsareexcludedfrombesthabitats
towardperipheralhabitatbyfewbigcrabs.However,thistrendonlyarrives
consideringallthepatternstogether.Whenconsideredindividually,noindi-
andcationlargeletbradiuselieveDENS)preferencomptiallyetitionthatishasymmetricappening(ZOI)amongorsymmetricindividuals.(FOTN,he
movementsthatleadtotherecoverypatternmighthaveatendencytobe
moreduetoasymmetriccompetition,althoughthedifferencesofevidence
donotletconcludesurelyaboutit.Identically,themovementsthatlead
totheregularspatialorganizationatsmallscaleareonlyalittlebitmore
likelytobecausedbyasymmetriccompetitionthanbyanasymmetriccom-
petition.Furtherfieldworkdocumentingtherelationshipamongfrequency
ofmovementofcrabsandtheirsizecoulddeterminewhetherasymmetric
orsymmetriccompetitionoccurswiththehelpofthepresentfindings.At
least,thesecouldgivenewpatternstobefitbythemodels,andthushelp
ininferringontheotheraspectsofintraspecificcompetitioninU.cordatus
pulations.op

Toconclude,thisstudytouchedseveralaspectsonanalyzingcompetition
modelswithapattern-orientedmodelingapproach.First,itillustratedthe
capacityofPOMICtohelpinasituationofstronginferenceonmodels
fittingseveralpatterns.ItconfirmedtheobservationofChapter7,withone
patternmore(thespatialpattern)thatcompetitionforresourcemightbeat
theoriginofcrabdecisiontochangeburrow.Itillustratedtheimportance
ofthewayofdescribingthetransformationofcompetitionintensityinto
competitioneffectinindividual-basedphenomenologicalcompetitionmodels
toproducedifferenttypeofcompetitionsymmetry.Andfinally,thisanalysis
ofcompetitionsymmetryshowedalsotheneedofnewfieldworktoinvestigate
thetrendoffrequencyofmovementsamongcrabsizeclasses.

216

8CHAPTER

8.6Acknowledgements
Ihavetothankalltheco-authorsofthefirstIBUmodelpaper(Chapter
7)KarenfortDheiriele,helpCoralieondeveD’Lima,lopingHandannoaHildennalyzingbrandttheIandBUVmoolkedel:rGUtarimm.Berger,This
evmanenutuallyscriptisincorpaporatereliminarysomeofvethesersioncofo-waorkfutureersascpublicationo-authorstdhatepwendingillthenon
theirinputs.ThisstudywasfinancedundertheDFGprojectBE1960/2-1
(PUME).

eferencesR8.7

Bauer,plantS.,pBerger,opulations.U.,-HProildenceedingsbrandt,ofHt.heandRoyalGrimm,SocietV.yof2002.LondonCyclicB269:dynamics2443-2450.insimulated
Bauer,S.,Wyszomirski,T.,Berger,U.,Hildenbrandt,H.andGrimm,V.2004.Asymmetric
competitionasanaturaloutcomeofneighbourinteractionsamongplants:resultsfrom
thefield-of-neighbourhoodmodellingapproach.-PlantEcology170:135-145.
Berger,U.,Adams,M.,Grimm,V.andHildenbrandt,H.2006.Moldellingsecondarysuc-
cessionofneotropicalmangroves:Causesandconsequencesofgrowthreductioninpioneer
species.-PerspectivesinPlantEcology,EvolutionandSystematics7:243-252.
Berger,Wolff,U.,M.Glaser,1999.MAn.,Koinch,tegratedB.,Krause,approacGh.,toRubmen,angroL.,veSdaint-Pynamicsaul,aU.,ndSchories,managemenD.t.and-
JournalofCoastalConservation5:125-134.
Berger,forestU.adynamics:ndHildenspacing,brandt,Hageing.2000.andAneighnewbourhoapproacodhtcomposetitionpatiallyofmexplicitangromovetdellingrees.o-f
EcologicalModelling:287-302.
Berger,andtheU.andbiomass-densitHildenbrandt,ytraH.jectories2003.ofThethestrengthcohort.o-fcPlanompteEtitioncologyamong167:i89-96.ndividualtrees
Berger,ualbUased.,moHildendelingbrandt,ofplanH.tasndimGrimm,ulations:V.S2002.elf-ThinningTowardsandathestandardFieldofforNteighheborhoindivid-od
approach.-NaturalResourceModeling15.
Berger,modellingU.,theHildeneffectsbrandt,ofgH.roawthndGrimm,limitation,V.2004.neighbourhoAge-relatedodcompedeclinetitioninfandorestsproelf-thinning.duction:
-JournalofEcology92:846-853.
Blankensteyn,A.,CunhaFilho,D.andSantarosaFreire,A.1997.Distribui¸c˜aoestoques
pesqueiroseconte´udoprot´eicodocaranguejodomangueUcidescordatus(L.1763)(Brachyura:
Ocypodidae)nosmanguezaisdaba´ıadaslaranjeiraseadjacˆencias,Paran´a,Brasil.-Ar-
quivosdebiologiaetecnologia40:331-349.
Bonan,indicationG.B.of1991.neighbDensitourhoyodecffectsompeontition.the-sizeAnnalsstructureofBotanofaynn68:ualplan341-347.tpopulations:an
Branco,(Crustacea,J.O.D1993.ecapoAspda)edoctosbioemanguezalcol´ogicosdoIdoctacorubi,aranguejoSantaUcidesCatarina,corBdatusrazil.-A(Linnaeus,rquivos1763)de
133-148.36:tecnologiaebiologiaCz´ar´an,T.1998.Spatiotemporalmodelsofpopulationandcommunitydynamics.Chapman
284pp.London.-Hall&

REFERENCES8.7.

217

Diele,K.2000.LifehistoryandpopulationstructureoftheexploitedmangrovecrabUcides
cordatuscordatus(L.)(Decapoda:Brachyura)intheCaet´eestuary,NorthBrazil.PhD
thesis-UniversityofBremen.103pp.
Diele,K.,Koch,V.andSaint-Paul,U.2005.Populationstructure,catchcompositionand
CPUEoftheartisanallyharvestedmangrovecrabUcidescordatus(Ocypodidae)inthe
Caete´estuary,NorthBrazil:Indicationsforoverfishing?-AquaticLivingResources18:
169-178.Diele,K.andSimith,D.2006.SalinitytoleranceofnorthernBrazilianmangrovecrablarvae,
Ucidescordatus(Ocypodidae):Necessityforlarvalexport?-Estuarine,CoastalandShelf
600-608.68:ScienceGlaser,M.2003.Interrelationsbetweenmangroveecosystem,localeconomyandsocial
sustainabilityinCaete´Estuary,NorthBrazil.-WetlandsEcologyandManagement11:
265-272.Grimm,V.,Berger,U.,Bastiansen,F.,Eliassen,S.,Ginot,V.,Giske,J.,Goss-Custard,
J.,Grand,T.,Heinz,S.,Huse,G.,Huth,A.,Jepsen,J.U.,Jorgensen,C.,Mooij,W.
M.,Mueller,B.,Pe’er,G.,Piou,C.,Railsback,S.F.,Robbins,A.M.,Robbins,M.M.,
Rossmanith,E.,R¨uger,N.,Strand,E.,Souissi,S.,Stillman,R.A.,Vabo,R.,Visser,
U.andDeAngelis,D.L.2006.Astandardprotocolfordescribingindividual-basedand
agent-basedmodels.-EcologicalModelling198:115-126.
Grimm,V.,Frank,K.,Jeltsch,F.,Brandl,R.,Uchmanski,J.andWissel,C.1996.Pattern-
orientedmodellinginpopulationecology.-TheScienceoftheTotalEnvironment183:
151-166.Keddy,P.A.1989.Competition.Chapman&Hall-London.202pp.
Kenkel,N.C.1988.Patternofself-thinninginJackPine:Testingtherandommortality
hypothesis.-Ecology69:1017-1024.
Koch,V.andWolff,M.2002.Energybudgetandecologicalroleofmangroveepibenthosin
theCaete´estuary,NorthBrazil.-MarineEcologyProgressSeries228:119-130.
Mehling,U.2001.AspectsiftreeprimaryproductioninanequatorialforestinBrazil.PhD
thesis-UniversityofBremen.155pp.
Nordhaus,I.2004.Feedingecologyofthesemi-terrestrialcrabUcidescordatuscordatus
(Decapoda:Brachyura)inamangroveforestinnorthernBrazil.PhDthesis-University
203pp.Bremen.ofNordhaus,I.,Wolff,M.andDiele,K.2006.Litterprocessingandpopulationfoodintake
ofthemangrovecrabUcidescordatusinahighintertidalforestinnorthernBrazil.-
Estuarine,CoastalandShelfScience67:239-250.
Pacala,S.W.andSilander,J.A.J.1985.Neighborhoodmodelsofplantpopulationdynam-
ics.1Single-speciesmodelsofannuals.-TheAmericanNaturalist125:385-411.
RDevelopmentCoreTeam.2006.R:Alanguageandenvironmentforstatisticalcomputing.
RFoundationforstatisticalcomputing.URLhttp://www.R-project.org.
Reynolds,J.H.andFord,D.E.2005.Improvingcompetitionrepresentationintheoretical
modelsofself-thinning:acriticalreview.-JournalofEcology93:362-372.
Schories,D.,Barletta-Bergan,A.,Barletta,M.,Krumme,U.,Mehling,U.andRademaker,
V.2003.Thekeystoneroleofleaf-removingcrabsinmangroveforestsofNorthBrazil.-
WetlandsEcologyandManagement11:243-255.
Schwinning,S.andWeiner,J.1998.Mechanismsdeterminingthedegreeofsizeasymmetry
incompetitionamongplants.-Oecologia113:447-455.
Stroustrup,B.1997.TheC++programminglanguage.Addison-Wesley-Boston.1020pp.
Weiner,J.,Stoll,P.,Muller-Landau,H.andJasentuliyana,A.2001.Theeffectsofdensity,

218

8CHAPTER

spatialpattern,andcompetitivesymmetryonsizevariationinsimulatedplantpopula-
tions.-TheAmericanNaturalist158:438-450.
forWiegand,revT.,ealingJheltsciddenh,Fi.,nformation:Hanski,I.aandkeyGforrimm,V.reconciling2003.eUsingcologicalptheoryattern-orienandtedmoapplication.deling
-Oikos100:209-222.
Wolff,M.,Koch,V.andIsaac,V.2000.AtrophicflowmodeloftheCaet´emangroveestuary
(NorthBrazil)withconsiderationsforthesustainableuseofitsresources.-Estuarine,
CoastalandShelfScience50:789-803.

endicesppA8.88.8.1AppendixA.HowtoparameterizethePmovevalue
toobtainameanfrequencyofmovementof0.07
movement.crab−1.day−1forthenullsub-modelRMr.
Ieacwhanttosub-moobtaindelsa(f=precise0.07mmeanovfemenrequencyt.crabof−1mo.davey−men1).tofTheallntheullcrabssub-mowithdel
(RMr)isthesimplestonetoparameterizeforthatsinceitdependsonly
onfrequencythepropofomortionvemenoftop(inenmoburrovemenwstand.crabt−he1.day−1parameter)isthePmoveresults.Tofheanameanp-
proximatelyconstantproportionofmovingindividualateachday(x,thus
Iwantx=7%).Ateachtimestep,onlythecrabswithanopenburrowwill
potentiallymove,sowehaveoverall:
x=Pmove×Pop(8.14)
wowhereuldbPoepthisisthepropproportionoofrtionopofenopeburronwsburrotows.findIjwhatustneedshouldtobeePstimate.Awhatfter
emovthesevoeralriginaltimesteps,settings,whenPoptheispdepropeondenrtiontofonoptheenburroindividualwsisbnotehavdepiors,endingi.e.tonhe
itsopprobabilitenedyofburroawcrab(Pcltoosingop,entableitsc8.2).losedThisburrowshould(Pbopeningeat,tfirst:able8.2)orclose
NwsburroenOpPop=(OpenBurrows+Closedburrows)=NO+ONC(8.15)
ConsideringateachtimestepthatOpenburrows(NO)aretheonesalready
opennotchanging+theonesgoingtoopenfromtheClosedburrows(NC),
:avehuyoNOatt1=NOatt0×(1−Pclosing)+NCatt0×Popening(8.16)
Sothatafterenoughtimestepsastablesituationcanbeexpressedas:
NO≈NO(1−Pclosing)+NC×Popening(8.17)

APPENDICES8.8.

219

(8.18)

(8.19)

Whichcanbere-wrote:
1≈(1−Pclosing)+(NC/NO)×Popening(8.18)
:OrPclosing/Popening≈NC/NO(8.19)
Sochanging8.15intermofNC/NO,Ihave:
1/Pop=(NO/NO)+(NC/NO)=1+Pclosing/Popening(8.20)
Whichgivesthen:
Pop=Popening/(Popening+Pclosing)(8.21)
So,IcancalculatedirectlywhatshouldbePmoveforaspecificx(andthereby
):f

(8.20)

Pmove=x×(Popening+Pclosing)(8.22)
PopeningSincewewantx=0.07,andwesetPopeningandPclosingintable8.2,we
obtainPmovetobeapproximately0.1.

8.8.2AppendixB.Whytheasymmetriccompetition
demonstratedbyBaueretal(2004)mightnot
becomingfromtheFONapproachatindividual
l?elevwithBaueranetindexal.c(hecfromkforcompWyszomirski)etitionaandsymmetryindividualat2levlevelels:apossumingpulationthatlevtheel
asymmetrywouldbevisibleineither:
1.Theun-scaledtracjectoryompofetitionthecompintensityetition(F=FintensityA×AZOI(theirwherevariableAZOIFisA)athenzdonean
ofinfluencearea)duringthegrowthoftwointeractingindividuals.
2.ThedifferenceGR−(ΔRD)basalinrelativegrowthrates(S)givenbyD=|S1−S2|
withS=GR=1−CwhereGRisthegrowthratewithout
cisompthegetitionrowthefferctate(depwithendingcomponetitionRbasal,effe=ctthesandizeoCftishethetrece),ompΔRetitionbasal
effectonthegrowthrateGRtoobtainΔRbasal.

8CHAPTER220TheproblemthatIencounteredcomesfromtheindividuallevelevaluation
ofasymmetryandexplainstheasymmetryobservedatpopulationlevelwith
index.theLet’sseefirsttheargumentationofthesecondindicatorofasymmetry:
thedifferenceinrelativegrowthratesD.TheauthorsassumedthatDshould
beequalto0ifthetwoplantswereinsymmetriccompetitionsituation.
Accordingtothedefinitiontheauthorsgiveonthefirstsentence:
“Asymmetriccompetitionamongindividualsisdefinedascompe-
titioninwhichlargerindividualshaveadisproportionateadvan-
tage(relativetotheirsize,e.g.mass)oversmallerindividuals.”
inasymmetriccompetitionsituationbetweentwoindividualsofdifferent
size,thecompetitioneffectofthefirstindividualontheother(C2)shouldbe
proportionaltoitssize(Size1):
C2=Constant×Size1(8.23)
Andthereby,asymmetrycouldbeassumedtooccurinanysituationwhere:
C2=Constant×Size1(8.24)
Thus,asymmetryshouldbeevaluatedasadifferenceofcompetitioninfluence
ongrowthinrelationtothesizes.However,theDparameterdoesnotinclude
the“relationtothesizes”aspect.
etakewIf(8.25)C=1S−is:DthenD=|(1−C1)−(1−C2)|(8.26)
orD=|C2−C1|(8.27)
WithC=1−2FA(8.28)
wehave:

C=1S−

D=|(1−C1)−(1−C2)|

D=|C2−C1|

C=1−2FA

D=2×|FA1−FA2|

(8.25)

(8.26)

(8.27)

(8.28)

(8.29)

APPENDICES8.8.

221

Thus,Dismeasuringthedifferenceofcompetitioneffect(Eq.8.27),butit
doesnotcheckthisinrelationtothesizes.OrDmeasurethedifferencein
FONintegrations(differentforthe2individualsbecauseofdifferentsizesand
differentlyawayfromthestem)dividedbytheZOIareas(differentforthe2
individualsbecauseofdifferentsizes)(Eq.8.29).The2integrationsofFON
overtheoverlapareasaredifferent(i.e.unscaledcompetitionintensitiesare
different),butthescalingdonewiththedivisionofthisFONintegrationby
theZOIareaisnotobviouslyleadingFAtogiveinformationoncompetition
intensityrelativetothesize(itmightbethatthe(factordependingonsize)/(
factordependingonsize)divisionannulthisrequiredinformation).Andthus,
Disnotobviouslygivinginformationoncompetitioneffectrelativetothe
sizesofthe2individuals.
Inbiologicalterms,IcannotinterprettheintegrationofFONentirely
andthuscannotconcludeontheproductionornotofanasymmetriccompe-
titionsituationwiththeparametersgivenbyBaueretal.Onlyinthecase
thattheirIminparameteris1(comingbacktoanoriginalZOImodel)the
FONintegrationwouldbeequals,andthenthedivisionbytheZOIareato
obtainFAissurelygivingsizeun-proportionalcompetitioneffect,asargued
byWeineretal.(2001).Butfinally,ameasureofasymmetryofcompetition
shouldnotbedonewiththecompetitioneffectmeasureitself.Therelative
growthratecouldbeatoolofcomparisonsamongindividualsandanalysisof
competitiontype,butrelativetothesize,notcalculatedrelativetothecom-
petition.(e.g.ThomasandWeiner1989,Includingcompetitiveasymmetry
inmeasuresoflocalinterferenceinplantpopulations,Oecologia80:349-355.
Theycalculatedtherelativegrowthrate(RGR)asRGR=(Sizeatt2-Size
att1)/Sizeatt2).
Thefirstargumentofobservationofasymmetryatindividuallevelwas
ashiftinthetrajectoryinsize,FAorF.Althoughbasedonassumptions
notcompletelyexplained,ashiftintrajectoriescouldbeassumedasasign
ofasymmetry.Letassumethisistrue,butletalsoseewheretheshifts
observedbytheauthorsarecomingfrom.Inalltheirgraphs(figure5and
6oftheirpaper),thisshiftoccurwhentheFAofthesmallerindividual
reach0.5,asmentionedintheresultpartofthepaper.Thisthreshold
valueisnotbecauseofaparticularityoftheintensityfieldintheFON,but
fromtheuseandcalculationofthe“competitionfactor”Cmeasuringthe
competitioneffect,whichissetto0whenFAreach0.5.Theauthorsset
thisvaluebecauseofthewayCiscalculated:C=1−2×FAsothatif
FA>0.5theCwouldnotbecomenegative.Butthisvalueof2multiplying
theFAtotransformcompetitionintensityintocompetitioneffect(whatI
calledthesharingcapacityinChapter4)hasnobiologicalmeaningonthis
article,neitherapreciseparameterization.Itcouldtakeanyvalueina

222

8CHAPTER

theoreticalstudy.Particularly,inastudyofanalysisoftheFONreproduction
ofasymmetryamong2individualsitshouldhavebeensetto1,sothatthe
realeffectofConthetrajectorieswouldhavebeendirectlyseen(andnotthe
effectofathreshold).InsuchcasetheFAofthe2individualswouldnever
reach1andCwouldalwaysbe>1.Thethresholdnotbeingmet,there
wouldhavebeennoshiftintrajectory.ThiswasobtainedbyBaueretal.
withthelowIminsimulationbecausethe2individualsneverobtainedaFA
reaching0.5.Baueretal.usedthenthefirstcriterion(relativegrowthrate)
toarguethatasymmetriccompetitionwasneverthelessvisibleinthiscase
oflowImin.Ibelieveitisnotasecureindicatorofasymmetry(cf.above),
soIwouldconcludethattheasymmetriccompetitionoccurringamongthe
2plantsbecauseoftheFONwasnotprovedinthispaper.
Ibelievehoweverthatthegeneralapproachofthesimulation,usinga
factorofcompetitioneffectongrowthasC=max(0,1-Competitionintensity)
leadtoasymmetryingeneralatthepopulationlevel.Theconnectionbetween
thewayofdeterminingthecompetitionintensityforeachindividualina
populationofn>2individualsandthecalculationofthecompetitioneffectis
thekeytoasymmetry.Withtheabovecompetitioneffectcalculation,ifthe
competitionintensityvaluecanget>1foranindividual,thenbecauseofthe
competitionfactorCcalculation,soonerorlatterindividualswillreachC=0
andstopgrowing.Therepressedindividualscreatethenacleardifference
ingrowthrateswiththeonesstillgrowing(becausenotyetatC=0),which
shouldbethebiggerones(asseenintheirindividualexercise).Theoverall
situationpresentfinallysomeplantsmuchbiggerthantheirneighborsthat
stoppedgrowingmuchearlierbecauseoftheirspatialconstellation,whichcan
beseenasasymmetrywiththeindexusedinBaueretal.Theymeasured
competitionintensitywiththe2×FAevaluatedinaspatiallyexplicitway,
andcouldgeteasilyvalues>1.Thus,asymmetryappearedatpopulation
level.Thisresultisveryinterestingandstillvaluable,buttomyopinion,
becauseofthedescriptionatindividuallevel,Ibelieveitisnotbecauseof
theFONapproachitself,butbecauseoftheCcalculationchosengiventhe
wayofestimatingcompetitionintensity.
IfBaueretal.meantbythe“FONapproach”theentirewayofsimulating
competitionfromtheindividualdescriptionwithaFONaroundthecentral
position,tothewayofassumingcompetitioneffectongrowthwiththeC
calculation,thentheproblemisonlyofsemantics.Inthiscase,Iunderstand
whyforthem,thenyesthe“FONapproach”iscreatingasymmetriccompe-
tition.Idonotconsiderthe“FONapproach”asallthatbecauseIuseda
differentwayoftransformingtheFONintegrationintoacompetitioneffect
intheIBUmodel,andevenchangingthe“sharingtolerance”inmyKiWi
studies(Chapter4).Wouldtheoriginalauthorsofthe“FONapproach”call

8.8.the

APPENDICESseu

of

the

ONF

in

IBU

omethings

tdifferen

hant

a

ON“F

approac”?h

223

224

CHAPTER8

Chapter

General

9

Discussion

Conclusions

225

and

226

GENERALDISCUSSION&CONCLUSIONS

9.1Organizationofthischapter

Ineachthispartlasttochtheapter,fieldIosfhouldmangrocomeveebackcologytoandthestpheecificrespadvectivaencestopics:givenb(1)y
mangroveforestdynamicsand(2)Ucidescordatusbiology.Ishallcover
thesetopicsinthetwofirstsections,focusingalsoonansweringthespecific
objectivesofeachpartgiveninthegeneralintroduction(pages18and20
respectively).Idiscussinathirdsectionthecontributionsofthethesistothe
spsectionecificIfieldsdiscussofalsoindividual-basedthepaattern-orienndtedpattern-orienmodelingtedmodinformationeling.Inthiscriterionsame
(PO(pageM1IC6).)tIonathenswerlastthesectionmethoIdpresenologicaltgobeneraljectivegivenconclusionsintheintanalyzingroductionthe
possibleparallelsbetweenthetwofocussystemsandtheirrespectivelevels
ofcompetition.Thisshouldallowanevaluationofthethesis’contributionsto
thegeneralobjective(givenpage15).InthisfourthsectionIfinishproposing
anideaoftheoreticalframeworkforcomplexrepresentationofindividual-
teractions.inbased

9.2DiscussiononPartI.Interspecificcom-
petitioninCaribbeanmangroveforests

9.2.1Generalcontributionstomangroveforestecol-
ogyThefieldworkandmodelingofmangroveforeststructureanddynamics
increasedtheknowledgeonfactorspotentiallyinfluencingspecieszonation
patternsbyproposinganewfactor:theperturbationregime.Although
alwaysconsideredasafactorinfluencingforeststructure(e.g.Smithand
Duke1987),theperturbationregimewasneverlinkedtospecificeffectson
zonationpatternsuntil2006withthepublicationofChapter3andinparallel
theworkofImaietal.(2006),whichproposesaverysimilaraspect.Chapter
4illustratesthatmangrovestanddiversitycouldbedirectlyinfluencedby
perturbationregimes.Whenconsideringthatazoneinnaturecouldbea
standsimulatedinthisstudy,thisconfirmsthefindingsonspecieszonation:
theheterogeneityofthezonesofasitecanbedependentonitsperturbation
regime.Chapter5proposestoorganizethehypothesesinfluencingspecies
zonationdependingonthescaleofactionandthecapacityofeachfactor
tocreateorinfluencethepatterns(particularlywithFig.5.1).Chapter5
re-demonstratedtheimportanceofabioticgradientsontheinstallationof
specieszonationpatternsinCalabashCayashypothesizedbythestatistical

9.2.DISCUSSIONONPARTI

227

analysesofChapter3.Thiswasconcordantwiththehypothesisofspecies
adaptationtoabioticgradientsproposedbyMacnae(1968)andRabinowitz
(1978)andanalyzedatdifferentscalesbyotherauthors(e.g.McKee1995,
Felleretal.2002).
Chapter4alsoimprovedmangroveforestecologyknowledgeontheques-
tionofapplicationoftheintermediatedisturbancehypothesis(Connell1978).
Thiswas,tomyknowledge,nevershownbeforeformangroveforests.Chap-
ter4concludesontheimportanceofthelocalconfigurationofspeciesinter-
actionthatitselfdependsonabioticconditionsanddynamicalphase(tem-
poralsequenceofasuccessionphenomenon)toevaluatewhatcouldbecome
theeffectofaperturbation.ThefindingsofChapter4alsoproposeacloser
looktowardsuccessionofmangroveforeststhroughtheobservationofspecies
diversitypatternsrelatedtopastperturbationregimes.

9.2.2Aboutinterspecificcompetition
Zonationofspeciesalongtheintertidalcanbeseenasacapacityofthespecies
topartitionthehabitatandtherebyresources:eachspeciesshouldbedomi-
natingtheareaswheretheyhavetheirmostfavorableconditions.Thework
ontheabioticsettingsinfluencingzonation(Chapter5),showedthatfactors
abilitinfluencingyintheonlysimgroulationwthandsettings)nothadestablishmenhigherimpt(salinitortanceyonatndhenuappetrientaranceavail-of
zonationpatternsofsiteswithrelativelymixspeciesdominance(highindex
ofspeciesdominanceheterogeneity).Thefactorsinfluencingestablishment
(tidalsortingorseedavailability)werecomplementarytothesefirstfactors
oncouldthebseitesseenwithasasclearlyetofdfactorsefinedzlinkones.edtoThefresourceactorspartitioninginfluencingonlythroughgrowtheth
differentgrowthstrategiesofthespeciesingivenenvironments.Thesec-
ondfactors(i.e.influencingestablishment)couldbeseenasfactorsrelated
tothecapacitiesofthespeciestopartitiontheirresourcesthroughdifferent
reproductionandestablishmentstrategies.Interspecificcompetitionmight
havebeenattheoriginofevolutionandadaptationofallthesestrategies
(growth,reproductionandestablishment)leadingtohabitatpartitioning,
butthiswouldrequiredemonstration,andissofarpurelyspeculative.The
influenceofinterspecificcompetitioninthisdifferentiationofrealizednicheof
thethreeCaribbeanspeciesisparticularlyspeculativeconsideringthatthey
arenotamonophylogeneticgroup,withprobabledifferentoriginofspecia-
tions(Saenger2002).Theactualspatialinterspecificcompetitionthatwe
simulatedthroughtheuseoftheFONapproachwithspecies-specificsettings
wasnotseenasenoughtoreproducethezonationpatternsofCalabashCay.
Therefore,spatialinterspecificcompetitiondoesnotappeartobeamajor

228

GENERALDISCUSSION&CONCLUSIONS

factorforthespatialorganizationofthesethreeCaribbeanspeciesinzones
acrosstheintertidal.
Thesuccessionofspeciesdominancewasindirectlystudiedwiththecre-
ationofdifferentscenarioswithdifferentFONsettings(Chapter4).Both
afastsuccession(lessthan50yr)andslowvariationofoveralldominance
(over500yr)wereobserveddependingontheseFONsettings.TheFON
settingbasedonidenticalspatialcompetitionstrengthofthethreespecies
didnotshowsuccession,butfollowedtheoriginalsenescencephasesseenin
thefirstmangroveIBMsimulator(ChenandTwilley1998).Thepossibility
ofsenescencephasesinCaribbeanmangroveforestsishighlyquestionable
becauseofpermanentperturbationsoftheseecosystemswithstormsofdif-
ferentsizes(seealsoGeneralintroduction,section1.3.2,page12).Theother
FONsetting,basedonspecies-specificstrengths,producesthefastsuccession
pattern.Wesawthatthissuccessionpatternhasanimportantinfluenceon
producinganintermediatedisturbancehypothesispattern.Butadditionally,
theresultingfastsuccessioniscorroboratedwithfieldobservationsofBall
(1980)inFloridaandBergeretal.(2006)withthesamegroupofspecies
inBrazil.Species-specificspatialcompetitionstrengthmightthereforebe
likelytohappenintheCaribbeanmangrovetreecommunity.Wedidnot
testdirectlyifotherfactorscouldinfluencethereproductionofsuccession.
However,thechangeofdynamicswiththechangeofcompetitionsetting
mightleadtobelievethatinterspecificcompetitionisamajorfactorforthe
successionintreespeciesdominanceinCaribbeanmangroves.

okutloO9.2.3Overall,thethreestudiesshowedtheimportanceofspecies-specificcharac-
orderteristicstoctoreatecopzewonationithphoyrosical-ctherhtypemicalesofenhabitatvironment(inpartitioning.abroadThewosense)rkonin
therecoveryinfluencewasofpprofoundlyerturbationdeprendenegimest(onChapterthe3individualsand4)sholeftwedafterthataspdistur-ecies
bance.Severalworkalreadyanalyzedthedifferentresponsesofmangrove
treestodestructionbystrongwindsdependingontheirspeciesorsizes(e.g.
Vermeer1963,Stoddart1963,Bardsley1984,Roth1992,Smithetal.1994,
Roth1997,Imbertetal.1998,ShermanandFahey2001,Baldwinetal.
tion2001,Imexercisesbert2be002).causeIofdidtheirnotlackincorpoforateconsistencytheseotbservhroughoutationstohentheCaribbsimean.ula-
bHoewevincorper,ofolloratediwingnsimtherulationsecoveryandofwaospuldecificprobablysite,tleadhesetoobservotheraintionstcerestingould
findingsonquestionsofspeciesdominancedependingonthestrengthofthe
rturbation.ep

9.3.DISCUSSIONONPARTII

229

Theunderstandingthreeofstudiesforestalsostructure.illustratetheTheseimpworksortanceareofftheorestcontinudynamicsationoofndty-he
namicalassessmentofforeststructurewiththeoreticalmodels(e.g.Jim´enez
etal.1985,Duke2001,Fromardetal.1998,2004)orsimulationmodels
(FORMAN,ChenandTwilley1998,KiWi,BergerandHildenbrandt2000).
Simulationsstudiesshouldbeperformedinthesedirectionstounderstand
pefurtherrturbationsontheonspinfluenceeciesozfaonationbioticpsettings,atterns.bioticGenerallyint,oeractionsthersimandulationexternalex-
coulderciseswhelpithinmansworeneringumeroustheimppatternsortancetoofreaceprohpduce,roposedandfmactorsulti-scaleonthemodinstal-els,
lationandchangesofspeciesandstructuralzonationpatternsinmangrove
forests.Ultimately,consideringthespecieszonationpatterns,thesefurther
simulationstudiescouldhelpinansweringthegeneralhypothesisobserved
indrivingothersipnteciesertidalspatialareas:intdistributionerspecificacrosscomptheetitioninitertidalsan(impe.g.ortanfortreviewfactoroinn
evidenceofcompetitioninshapingrockyshoresbenthiccommunities,see
p253-255).2001enNybakk

9.3DiscussiononPartII.Intraspecificcom-
petitioninNorthBrazilianUcidescor-
pulationsopdatus

9.3.1Generalcontributionstointraspecificcompeti-
tionamongUcidescordatus
ThefieldworkonUcidescordatus(Chapter6)documentedthespatialdis-
hypotributionthesisoftthathistspheseeciespatternsinaNoforthdistributionBrazilianamreangroinfluencedve,andbypropcomposedetitionthe
forscaler(>esource10m).atCsmallhapterscale6(s<how10m)edawhileclearpmorereferencedrivenbofyU.habitatcortdatusypeatindivid-large
ualstobeclosetoRhizophoramanglerootsandmoregenerallyunderR.
hausmangle(2004)trees.thatTheseR.manglefindingsleacvesonfirmedaretheindirectlypreferredftheooodofbservU.acotionsrodatusfN.Tord-he
smallscalefindingsonceintegratedintheIBUmodelconfirmedthehypoth-
foresistthehatintorganizationraspecificoftcomphepoetitionpulationatonaindividualsmalllevscaleelisan(Chapterimportan8).tfactor
Chapter8alsoshowedthatrandomreasonformovementofcrabsmight
leadtrasptoecificrecovecompryofharvetition-basedestedreasonareaswforithmeovqualement.evidenceThisthancouldwbeithsaeennin-as

230

GENERALDISCUSSION&CONCLUSIONS

contradictingfindingsofChapter7atfirst,butseveralfactorsshouldbe
takenintoconsideration.ThepatternsusedonChapter7focusedonthe
reproductionoftherecoveryofharvestedareawithalinearrecovery,while
Chapter8usedtherawdatapointsaspattern.Boththelinearandtheraw
datapatternsareinterestingtoreproduce,thefirstforprobableunderlying
processesleadingtothisobservation,andthesecondforthehigherrelia-
bilityonthepointsofobservations(sincethefirstisastatisticalmodelof
thesecond).Chapter8focusedonthesecondaspectusingthePOMIC
approach.Chapter7wasfocusingonfrequencyofmovementquestions.It
showedthatforthelinearpatterntobereproduced,therandommovement
modelneededanunrealisticallyhighfrequencyofmovement.Thiswasre-
ducedwhenusingthecompetitionmodelandlinearitywasthenmoreeasily
reproduced.Chapter8complementedonthisaspectshowingthatevenif
notconsideringthelinearity,themodelusingrandomreasonformovement
stillhavealowergoodnessoffitthanmodelsusingcompetitionasreason
formovement.TheuseofthePOMICallowedthentoidentifythatthese
twotypesofmodelshadsimilarevidence,anassessmentnotentirelypossible
withmean-squaredeviationorroot-mean-squaredeviationmeasurementsas
inChapter7.Butgenerally,Chapter8complementsthefindingsofChapter
7thatspatialcompetitionistriggeringthemovementsofindividualcrabs.

9.3.2Discussingfurtherimplicationsofintraspecific
competitiononUcidescordatuspopulation
Thefindingsonmovementsofcrabsbeingdependentonintraspecificcom-
petitionandthusondensitywerediscussedinChapter7intermofnecessity
toprotectthebufferareasthatconstitutenon-fishedareasunderR.mangle
roots.Particularly,consideringthatthespatialdistributionpatternatsmall
scalewasseenastheresultsofcompetitionamongindividuals,movements
ofU.cordatuswereverifiedtobedensity-driven.Chapter7proposestobe
particularlycautiousonthetechniquesofharvestthatcrabcollectorsmight
usetocatchU.cordatusundertheR.mangleroots.Theroleastemporally
slowerbufferofsecondaryareas,suchasforestsoftheCaet´epeninsuladom-
inatedbyothertreespecies,werealsodiscussedonChapter7.Theresults
ofChapter7andtheknowledgeacquiredonChapter6(andDiele2000)
showingthatU.cordatusindividualsaresmallerandmorenumerousingen-
eralontheseareas,couldproposeamultiple-scalebuffersystem(temporally
andspatially).Inthissystem,smallindividualswouldgrowonperipheral
habitatsand,whilegrowing,movetowardpreferredhabitats,namelyunder
R.mangletrees.Sincetheareasaroundthesetreesarebeingharvestedby

9.3.DISCUSSIONONPARTII

231

humans,thegrowingcrabswouldbasicallybecomingcloserandcloserto
thefishinggroundofcrabcollectorsuntilfinallybecaught.
riccompChapteretition8couldamongnotindividualsconcludeofdefinitivdifferenelytosnizestheforimptheirortancedecisionofatosymmet-leave
anarea.Thus,Icannotverifythehypothesisoflargescalepopulationorga-
Ifnizationtheadrivsymmetricenbyacompesymmetrictitioniisntverasprifiedecificwithcompfutureetitionwfork,oritthebcouldesthhaveabitats.im-
plicationsfortheideasofmultiple-scalebuffer.Thefirstimplicationwould
betheexplanationgivenaboveofspatialorganizationbyout-competition
andthereforeexclusionofsmallcrabsfromthepreferredhabitatsofU.cor-
datusonR.mangleforests.SomeworksofDiele(personalcommunications,
manuscriptsinpreparations)wouldargueinfavoroftheestablishmentof
verysmallindividuals(justafterlastmetamorphosis)closetolargeindivid-
uals.Thesesmallindividualscouldapparentlygrowtheirfirstyearascrabs
incoexistencewithlargerindividualsduetofeedingdifferences(Diele,per-
sonalcommunications).Asymmetriccompetitionwouldstartoccurringonce
thesmallcrabsbegintofeedonR.mangleleaves.Thesesmallindividuals
wouldthenbeexcludedtowardworsehabitats.Onceintheselessfavorable
assumehabitats,thatasthethesecrabsindividualsgrow,twheohuldypocomethesisbacofkmstepbultiple-scaleysteptowbufferardbesystemtter
habitat.explainingHothiswevmoer,veamentsymmetricback.cInomptheewotitionrsewhouldabitatsthardlyhebcrabseangrohypwingothesisbig-
gerwouldhavenoreasontoleavethesehabitats,sincetheywouldcollect
easilyalltheavailablefoodagainstthesmallerindividuals.Thehabitatand
foodqualityshouldhavethenaroleonmovementsofgrowingcrabsbackto
thepreferredhabitat.Theroleofcompetitionmightthenbelessimportant
onthisaspectoflargescalebuffersystems.

okutloO9.3.3Finally,othermodelingstudiesincludinghabitatqualitycouldhelponthe
analysisofthedifferentscalebuffersystemsandonthepresenceandim-
portanceofasymmetriccompetitionamongcrabs.TheIBUmodelscaleof
integration(theindividual)mightbecomeaproblemforlargespatialscale
analysesbecauseofcomputationlimitationindealingwithahighnumberof
individuals.However,upscalingmethodsexists(e.g.Jeltsch1997)usingthe
resultsofsmallscalemodelsintomodelsworkingathigherscale.Suchan
approachmightbenecessarytoanalyzethemultiple-scalequestions.Ulti-
mately,theIBUandKiWimodelcouldbeusedinparalleltosimulatetheef-
fectoftreepositiononcrabspatialdistributionandtoanalyzemultiple-scale
buffersystems.Theseparallelmodelsshouldthensimulategrowthratesand

232

GENERALDISCUSSION&CONCLUSIONS

competitionstrengthofindividualcrabsdependingonthespatialleaf-litter
variationfollowingtreegrowthandpositions.Itcouldeventuallyintegratea
componentofsoilqualityvariationfortreesdependingonaerationbycrab
burrows.Aninterestingpattern-orientedmodelingworkwouldbetoanalyze
ifthepresenceofsmallcrabscouldexplainpatternsoftreere-growthand
eventualreforestationseenindegradedareaoftheCaet´epeninsula.

9.4Discussiononecologicalmodeling

9.4.1Onindividual-basedmodeling
Thepartonmangroveforestdynamics(Chapters4and5)usedanalreadyes-
tablishedandrecognizedspatially-explicitindividual-basedmodel:theKiWi
amonewdel(Bergerspatially-explicitandHildenbrandtindividual-based2000).Tmheodel:secondthepartIBUmpresenodeltedand(Chapterused7
andindividual8).tAlthoughreesofthedifferensptecificspeciesquestionsfocusingoffooncuswtheirereintdifferenerspt,ecificonescompimulatingetition
andtheothersimulatingmovingcrabsandtheirintraspecificcompetition,
theseoreticaltwowoprksarts(toe.g.okpartBergerinandaproHildencessbrandtalreadys2003,tartedBwergerithetmaanl.yo2002,ther2the-004,
2006,Baueretal.2002,2004):thegeneralizationoftheFieldOfNeighbor-
hoodapproachinanalyzingspatiallyexplicitcompetitionsituations.
Chapter4particularlyinnovatedonapplyingtheFONapproachand
anIBMtosituationsofperturbationregimestoanalyzethepossibilityof
occurrenceoftheintermediatedisturbancehypothesis(IDH,Connell1978).
isThisofhighsettingimpofmoortancedelinginaanalysisnalyzingwapseinnovrturbationatingbregimeecausesinfluencepatialocompnspetitionecies
fordivaersity,nalyzingbutwtheasItoDHmoycknocurrence.wledgenevSpatialerintproegratedcessesataretheseenasindividualmorelaevndel
moreimportantintheexplanationofdiversitypatterns(e.g.Tilman1994,
PacSpatialhepskycompetal.etition2001)attheandspeindividualciescolevelexistencewas(seenBarotasandinfluencingGignouxsp2ecies004).
relativeabundancedistribution(Pachepskyetal.2001),inaccordancewith
theresultsofChapter4ontheimportanceofspeciescapacitiesofspatial
competition.Chapter4particularlyconfirmedtheaxiomsofdependenceof
thereproductionoftheIDHpatterndetailedbySheilandBurslem(2003):
onsuccessionoccurrence,onsuccessionduetocompetitiveexclusion,andon
pgoeodrturbationsexampleofhbringingypothesisthesaystemssessmentotewarlierithasnuccessionalindividual-basedstages.(andThismisorea
generallyprocess-based)simulationmodel.

9.4.DISCUSSIONONECOLOGICALMODELING

233

Chapter7and8presentingtheIBUmodelinnovatedalsoontwoaspects
ofindividual-basedmodeling.Thefirstonewastoincorporatethespatial
competitionaspectsofananimalduringfeedingphasesandtheinterference
competitionproducedbydirectinteractionwithneighborswithinaphe-
nomenologicalcompetitionmodel.AssaidonChapter7,thiswaspreviously
doneonlywiththeGECKOmodel(Booth,1997),althoughnotmentioned
assuch.Theintegrationoftwodifferenttypesofcompetition,generallyan-
alyzedseparatelyinotheranimalIBMs,madetheIBUmodeltoreproduce
threepatternsofexpressionofcompetition.Thesecondinnovativeaspect
wastocompareseveralindividual-basedapproachofcompetitiononChapter
8.Thesecomparisonsbroughtunderstandingintoasymmetriccompetition
realizationwithindividual-basedapproaches.Theyparticularlyproposedthe
FONasasolutiontosimulaterealsymmetriccompetition,hardlyrealizable
withotherapproaches.Infutureworks,thesedifferentapproachescouldbe
furtherinvestigatedintermofbehavioralinterpretations,andcomparedto
moremechanisticapproachesofsimulatingresourceuseandcompetition.
ThefactthattheFONapproachsimulatesphenomenologicallythecom-
petitionamongindividualswasseenasadrawbackbyarecentreviewon
representationofcompetitionforthestudyofself-thinning(Reynoldsand
Ford2005).Thiscriticisbasedontheneedforself-thinningstudiestoun-
derstandtheprocessofresourcesharingamongindividualsleadingtothe
specificbiomass-densitytrajectories.Atthislevel,consideringtreesgrowing
inastandwithoutreproduction,itistruethattheFONdoesnotsimulate
mechanisticallytheresourceuse.However,theuseoftheFONapproachin
theKiWimodelallowsincludinganidenticalwayofestimatingspatialcom-
petitioneffectatallphasesofthelife-cycleofanindividual:itincludescom-
petitionduringestablishment,growthandultimatelydeterminethedeathof
theindividuals(throughgrowthrepression).InChapter4and5thecompeti-
tioneffectongrowthalsoinfluencedindirectlythereproductioncapacitiesof
individuals.Thus,consideringthelife-cycleofanindividualasthetemporal
basisofacommunitystudy(asinChapters4and5),theKiWimodelusing
theFONapproachismechanisticallysimulatingprocessesthatcaninfluence
tructure.syunitcommTheusesoftheFONandotherso-called“phenomenologicalapproaches”
withtheIBUmodelalsodemonstratesthatdependingonthefocusofthe
ecologicalquestion,thephenomenologicalaspectofamodelisrelative.The
focusofIBUsofarwasnottoreproducethefeedinganddirectinteractions
ofcrabs,buttolookatthepotentialgeneraleffectofspatialcompetition
ondecisionformovement.Theneedofincludingbothinterferenceandex-
ploitationcompetitionledtoachoiceofphenomenologicalrepresentationof
competition.However,theoverallbehaviorofthecrabasopening/closing

234

GENERALDISCUSSION&CONCLUSIONS

itsburrow,decidingtomove,checkingpotentialburrowsforinstallationand
installingweremechanistic.Theanalysisoftheeffectofthisoverallbe-
havioronpopulationstructuremightalsobedonephenomenologicallywith
diffusion-processequationsfortheanalysisoftemporalpatterns.However,
thiswouldneverallowunderstandingtheprocessbehindtheregularspatial
organizationatsmallscale.

Asproposedabove(section9.3.3page231),IBMstostudymangroveecol-
ogycouldbeenhancedbymultiplescaleapproacheseventuallyintegrating
IBUtoKiWi.Althoughtheywerebothdevelopedinanobject-orientedlan-
guage(C++),thiswouldbetechnicallycumbersomebecauseoftheKiWi
sourcecodesincorporatingmanyspecializedalgorithmstomakeitusable
withaVisualBasicuserinterface.However,parallelrunsofthetwomodels
couldbeasolutionwithoutputsofoneasinputsoftheother.Thisrealiza-
tionwouldbecomeawiderinnovationintoindividualbasedmodelingand
thedevelopmentofecosystemsrepresentationswithindividualprimarypro-
ducersandindividualprimaryconsumersinfluencingeachotherandwithin
eachlevel,competingamongthem.

9.4.2Onpattern-orientedmodeling
Thepattern-orientedmodelingapproach(POM,Grimmetal.1996,Wie-
gandetal.2003,GrimmandBerger2003,Grimmetal.2005)wasapplied
todeveloptheindividual-basedmodelIBU.Wefollowedthe4stepsofthe
protocol(seeGeneralIntroduction,section1.1,page5).1)Thebiologi-
calknowledgeaccumulatedoncrabbehaviorduringtheMADAMproject
(specificallyNordhaus2004andDiele2000)wasintegratedonthisIBM.2)
Theparametersofindividualbehaviorwereselectedfirstaccordingtoesti-
matesfrompopulationleveldataorbehavioralestimations.Theprocesses
simulatedwereselectedtofocusonthereproductionoftherecoverypat-
tern,whilestillincludingrealisticindividualbehavior.Obviously,themodel
complexitypresentedinChapter7istheresultofseveraltrialsanderrorsof
development,selectingornotprocessesandparametervaluestoarrivetoa
goodcompromisebetweenmodelcomplexityandpayoffinpatternreproduc-
tion(whatGrimmetal.(2005)presentastheMedawarzoneofamodel).3)
Themodelresultsweresystematicallytestedagainstthepatternsofrecovery
andspatialdistributionpattern.Assecondaryoutcome(4),theasymmetric
competitionanddistanceofimportanceofresourceswereanalyzed.Thisled
tothepropositionofnewfieldworkinordertodocumentapatternthat
couldhelpinferringonasymmetriccompetitioninafuturePOMcycle.

9.4.DISCUSSIONONECOLOGICALMODELING

235

ThesametypeofPOMcycleiswhatmadetheKiWimoreandmore
BergerreliableaandsIBMHildentobstudyrandtthe2000dtoynamicsBergerofNetal.eotropical2006andmangrovChapterseforests4a(ndfrom5).
Further,thePOMapproachallowedparameterizinganotherspeciesofman-
grovetreefromtheIndo-WestPacific(Rhizophoraapiculata)fortheKiWi
model(Fontalvo-Herazo,inpreparation).Thisshouldgiveprecise-enough
tionsdescriptionfortheofmforestanagemendtynamicsoftsomeouseIWPthemmoangrodelvtoes.Asassesssecondarysylviculturaloutcome,ques-
ptheoKssibleiWispmoeciesdelintdominancehepresenvttariationshesispofrotheducedsystemsuccessiondepeandndingdooncpumenertur-ted
bationregimes.ThiswasproposedinChapter4asabasisfornewfield
samplingtodocumentspeciessuccession.Chapter5wasthefirstPOMpro-
cedureappliedtoKiWiusingaquantifyingindicator(POMIC)toanalyze
systematicallythequalityofreproductionofthepatternsbythemodelre-
sults.

9.4.3OntheuseofPOMIC
ThePOMICdevelopmentwaspresentedonChapter2witharelatively
simpleexampleofapplication.Thenumberofprocessesandparametersin-
volvedinthisexamplearenotcorrespondingtothelevelofcomplexitythat
traditionalIBMsmightpresent.However,Chapter5applicationofPOMIC
showeditsuseformorecomplexsimulationmodel.AndChapter8appli-
cationofPOMICinparalleltothemeansquaredeviationdemonstrated
thecapacityoftheinformationcriteriontoinferonmulti-patternsituation
selectingmodelsamongasetofpossiblenon-nestedones.
Inthistwoapplications,thecomplexityofthemodelswasnotconsidered
asacriterionofselection.Thiswasnotinfocusbecausetheorientationof
eachstudywastoinferonpossibleprocesses(whatisdescribedas“strong
inference”inChapter2)andnotonlytoparameterizeabestmodeltoselect
foradditionaluse.Intheeventualityofwillingtoapplyan“Ockham’sRazor”
principleasdescribedinChapter2fortheultimateselectionofamodel
withinasetofmodelsofidenticalevidence,wewouldneedtodescribeand
argueaboutthecomplexityofeachproposedmodel.Inthecaseofthe
KiWistudy,thiswouldhavebeenrelativelyeasyfollowingthenumberof
nullsub-model(TideO,HomogeneousNutandHomogeneousSal)ineach
modelresult,assumingthatanullsub-modelislesscomplexthantheothers.
Identically,intheIBUstudytherandomsub-modelofreasonformovement
couldbeconsideredastheleastcomplex.Therankingofcomplexityofthe
other3sub-modelswouldfollowtheirrespectivemathematicalcomplexity.
Itcanbenotedthatthisultimateselectionsteptakenas“thebestmodel”

236

GENERALDISCUSSION&CONCLUSIONS

tomakeinferencewouldhavechangedabitthespecificinterpretationofthe
2studies,butnotthegeneralmessages.
moLaterdelingPOstepsMIaCndstrongapplicationsinferenceshouldprofoccusedure.onuAssingittatisticalbothfortexaminationheinverseof
thec“individual-basedapacitiesofPOmoMIdelers”Cwcouldommalsounity.helpAnditinbparticularlyecoming,adacceptedeepertocom-the
parisoncriterionbuetwsingeenthisdeviancescriterionmethoadsnd(asmethoindsoWiegandfmodetelal.2selection004aw,b)ithmshouldultiplebe
done.

9.5Integratingtheecologicallessons
fromPartsI&II
conclusionsGeneral9.5.1Theunderstandingofthefactorsdrivingspatialdistributionofspeciesofhigh
importancewithinanecosystemishighlyvaluablefortheunderstandingof
spatialdistributionanddynamicsofotherspecies.Particularly,thetwo
componentsofthepresentthesis(mangrovetreesandburrowingcrabs)can
beseenasengineeringtheshapeofmanyspatiallydistributedresourcesin
mangroveecosystems.Thecanopy,thetrunk,theroots,theshading,the
leaf-litterorthepropagulesoftreesareresourcesformanyotherorganisms
inmangroveecosystems.Theholesinthesediment,theexcavatedmud,
thefeces,ortheburrowingcrabsthemselvesarealsoresourcesforother
organisms.UcidescordatusinNorth-Brazilianmangrovesisaverygood
exampleofthese.Theplacestofindthesetwokeygroupsandtheprocesses
drivingthedistributionsarethereforeinterestingfortheunderstandingon
otherspeciesspatialdistributionsanddynamicsofNeotropicalmangrove
ecosystems.

Usingidenticalindividual-basedmodelingapproaches,thetwopartsofthe
presentthesisillustratesomeinterestingparallelsanddifferencesofprocesses
influencingthespatialandtemporaldistributionofthesetwogroups.The
spatialpatternsseeninthefieldwerereproducedaspropertiesemergingfrom
theindividuals’intrinsiccharacteristics.However,theroleofspatialcompeti-
tioninexplainingthesepatternswasdifferent.Theinterspecificcompetition
forspacewasapparentlynotsoimportantinexplainingspecieszonation
patternofCaribbeanmangrovetrees.Ontheotherhand,theintraspecific
competitionforspaceamongU.cordatuswasapparentlydrivingsmallscale
regularspacingoftheirburrows.Thetwospatialpatternsoffocuswereof

9.5.INTEGRATINGTHEECOLOGICALLESSONS

237

differendistribution)tnaturebut(onethelloevoelskingofatcspompeeciestitioninvdistribution,estigatedtheweotherreatcorrespindividualonding
tothesepatterns(interspecific/intraspecific).
Competitionamongindividualtreesisbelievedtobeattheoriginof
(e.g.regularKenksepacingl1988).afterInsthiself-thinninghypothesis,phasestheoffdeathorestsofandindividualwasdotreescumentthated
donotsupportthestrongcompetitionpressureoftheirneighborswouldbe
attheoriginofaregularspatialdistributionoftheremainingtrees.The
out-competitionofindividualsissimilartotheprocessprobablyhappening
amongcrabsandleadingtotheobservedspatialpatternatsmallscale.As
bsuceh,tcomparedheproctoesstheofmproovcessemenoftofdeaththeseofcrabssessilebecauseindividualsofcompunderetitionhighccouldom-
paevoidtitionorpressure.increaseinMtobileeraction,iorganismsnpusearticularmpainlytheredation,movreproementaductionssortrategycom-to
petition.Sessileorganismsunderhighcompetitionsituationdonothave
theseterestingabilitiesintheasndensehavofenoobservingotheroptiondifferentthanstotrategiesdie.oTfohisrganismscomparison(goaiswain-y,
orcompetetodeath)underanintraspecificcompetitionsituationleadingto
identicalspatialpatterns.
tionThethatscoulduccessionbepinatternsterestingafornalyzedtheontsecondhefirstone.partThearefirstalsopgartsivinghowedinforma-that
Itspatialcouldcbeompetitionconsideredmighthattbetheatctherabsoofriginofdifferenstuccessionsizesofhavspeeciesdifferentsdominance.patial
competitionstrengthastheindividualtreesofdifferentspecies.Thereby,
thesuccessiondrivenbycompetitioncouldbeinvestigatedalsoforcrabpop-
ulationdynamics.Particularly,iftheasymmetriccompetitionhypothesized
amongcrabsofdifferentsizesreallyoccurs,therecoveryofemptiedarea
couldbedonefirstbysmallindividualslaterreplacedbylargeones.This,
bmoevingcausethemoresmalloftencarabsndwotherebuld,yinccaseomeofbackfiasymmetricrsttoacneompemptiedtition,abrea.etheTheseone
sizefurtherdifferencesfieldexpeduringrimentthes.rAndtheecolonizationoverallprocessdominanceshouldpberedosize-classescumentedcouldwith
parallel.inanalyzedeb

Ingeneral,furtherstudiesshouldgodeeperonevaluatingtheroleofspatial
competitionininfluencingdynamicsandspatialdistributioninmangrove
ecosystems.Forexample,afieldstudydocumentingtheindividual-level
spatialdistributionoftreeswithintheecotonesofspeciesdominanceofa
zonationpatterncouldgiveinterestingpatternsofaggregationorregularity
ofindividualsofdifferentspecies.Coupledwithapattern-orientedmodeling

238

GENERALDISCUSSION&CONCLUSIONS

approachitwouldbepossibletoevaluatehowtoreproducethesepatterns
andtherebyincreasethereliabilityofestimatingtheroleofinterspecific
spatialcompetitionintheshapingofzonationpatterns.Anotherexample
couldbetolookathowtoreproducethelargescaledistributionofU.cordatus
showingasortofzonationofcrabsizesalongelevationgradientsofthe
intertidal(asdocumentedinChapter6).Thisspatialdistributionwasseenas
apparentlydrivenbyabioticconditions.Buttheadditionalroleofinter-and
intra-specificcompetitiononthisdistributionwasnotentirelyinvestigated.
Finally,interactionsbetweenthetwogroupsarealsotobeinvestigated.
Assaidabove(section9.3.3page231,andsection9.4.1page234),multi-level
modelswouldhelpfortheseanalyses.Individual-levelinformationoneffectof
burrowingactivitiestothephysiologyofmangrovetreeswouldbenecessary.
Lotsofworksarethereforestillremainingonthesetwoareas(modelingand
fieldwork).Andultimately,thiscouldhelptoanswerthequestionsproposed
inChapter6andpartiallyabove(section9.3.3page231),astoknowwhich
ofthetwoecosystemengineers,thetreesortheburrowingcrabs,isfirstto
recolonizeingapareas,andwhetherspecificallyU.cordatusinfluencesthe
patternsofvegetationzonationinBrazilasproposedforgrapsidcrabsin
Indo-Pacificmangroves(Smith1987).

9.5.2Concludingoninter-andintra-specific
etitionscomp

Asseenabove,theeffectsofinter-andintra-specificcompetitiononcom-
munityorpopulationstructurescanbeparalleledwhenconsideringpatterns
ofrespectiveinterests.Thegeneraltheoriesdevelopedfromquestionsofco-
existenceatecosystemlevelcanbeusedatthesimplercommunitylevel(e.g.
themetricIDHcompinetitionChapteron4)oresuccessionvenpthatopulationmightolevcelcur(we.g.ithdifferenimplicationtsoizedfacrabssym-
howduringcompareecotitionvery).worksRevanderselywhatandpmatternsoreimpareortandrivtenly,btyhetheintunderstandingeractionsaoft
thehigherpintopulationegrationlevelevle(le.g.understandings.self-thinning,rAnegularexamplespacing)inthecpanresenbetusefulthesisfisor
thespecies-specificparameterizationoftheFONapproachwithself-thinning
patternsofmonospecificstands.Thisinformationonhowindividualsinter-
actatintraspecificlevelistransferedtotheinterspecificlevel.
Theunderstandinguseofofdifferenindividual-basedtlevelsofmoindelingtegration.canhelpThisaislotobintviouslyhenotgatheringnewtofo
IBMs,andphenomenologicaleithertdotegrees,hetpresenhetimpthesis.ortantproButIcessesBMsshappimulate,eningwforithadifferencommont

9.5.INTEGRATINGTHEECOLOGICALLESSONS

239

unitofallecologicalintegrationlevels:theindividual.IBMsarethereby
lookingattheprocessesemergingoneachlevelofintegrationabovetheindi-
vidual.Doingso,therolesofinter-andintra-specificcompetitionaremuch
easiertoanalyze.Eventually,IBMscouldbeusedtolookattheoriginal
questionthatcreatedtheseparationamonginterandintra-specificcompe-
tition:howmuchisdrivenbyeachtypeinstablestatecondition(inKeddy
2001).However,IBMs,andparticularlyspatially-explicitones,areusedin
otherdirectionstounderstandtheroleofcompetitionintheprocessesthat
shapecommunities.Forexample,Kerretal.(2002)analyzedthecoexistence
of3differentbacteriatypesdependingonthestartingdensityofeach.They
usedlaboratoryworkandanIBMforsimulatingthemechanicalprocessesof
competitiontounderstandhowandwhencoexistencecanoccur.Identically,
manyspatiallyexplicitIBMssimulatingtheoreticalspeciesweredeveloped
withlattice-basedevaluationofindividuals’interactionstoestimatetherel-
ativeimportanceofinterspecificcompetitionandotherfactorsinexplaining
speciesdiversity(e.g.Pachepskyetal.2001,Chaveetal.2002).Amaincon-
tributionoftheFONapproachinanalyzingspeciesdiversitypatternsisthat
thestrengthofcompetitionofindividualsisfollowingnotonlythespecies’
characteristicsbutalsoandprimarilythoseoftheindividual(i.e.sizeand
growthrateinfluencedbyabioticconditionattheindividual’slocation).

Toconcludeontheseaspects,themorerealisticrepresentationsofspatial
competitiongivenbytheFONorotherindividual-basedphenomenological
approachesusedinthepresentthesisshouldbecomeveryusefultostudyin-
terspecificcompetitioninthefuture.Futureworkanalyzingtheroleofspa-
tialcompetitionwouldparticularlybenefitfromtheintegrationofknowledge
fromdifferenttypesofcompetitionoccuringinacommunity(inter-/intra-
specific,butalsoexploitation/interferenceandasymmetric/symmetric).For
exampleitwouldbeveryinterestingtoapplytheseapproachestoother
zonationpatternsofintertidalareasrenownedasinfluencedbyinterand
intra-specificcompetition:Rockyshoresand,particularly,musselbedsthat
showevidenceofself-thinning(Gui˜nezandCastilla1999),intermediate-
disturbancehypothesisexamples(Lenzetal.2004),andspecieszonation
frominterspecificcompetition(Nybakken2001).

9.5.3Propositionofaprobabilisticapproach
Thislastsub-sectionisanideaIhavenottestedyet.Itcameoutofthecon-
siderationsforrepresentingspatialcompetitionattheindividual-levelana-
lyzedinthepresentthesis,andmoreparticularlywithChapter8.Thereby,I
proposetotheinterestedreader,tolookatspeculativeaspectsofwhatcould

240

GENERALDISCUSSION&CONCLUSIONS

bingecomeseveraltcomplexypesofintindividual-basederactionamongmodelingindividuals.ofnaturalcommunitiessimulat-

Whenaninteractionamongtwoindividualsoccursthroughtheneedofa
commonlimitedresource,thisinteractioncanbecalledcompetition.How-
ever,interactionsmightalsobepositive,andmediatedamongindividuals
beGeneralcauseionftroaduction,commonrsectionesource1.2,orpbageecause5,andoneTisableresource1.1).oftheother(c.f.
hoodWhen(FRN,PacalaphenomenologicalandSilanderapproac1985)hessoruchtheafiseldtheofnfixedeighboradiusrhoodneigh(FbOor-N,
BergerandHildenbrandt2000)areusedtosimulatecompetition,theseap-
proacdistributedhesfocusoresourcesntheoreffectsoultimatelyfinteractionsneedingaspacemongasrindividualsesource.usingspatially
TheFONmathematicalstructure,andtheequivalentZOIandFRN
ovmoerdeltheofCindividual’shapter8,inarecteractionalculatingarea(onlyinatheirsumrespofectivneighebFAoring,inOvandteractionsN).
Thishasbeensofarconsideredascompetition,andisthentransformedinto
compindividualsetitionisintensitmediatedyintallhroughmodaels.sHopatiallywever,ifdistributedtheintresourceeractionandamongleadingtwo
topoematicallysitiveintoeffectsapforositivtehem,effectthefinorttheeractionindividual.sumcouldThisbewouldtransformedthensimmath-ulate
onesfacilitation.houldgetEvaenpotuallysitiv,eifteffectheinbuttersptheecificotherwosituationuldinotscbeconsideredhangedwbyherebthey
interaction,themathematicalsumofinteractioncouldbetransformedinto
apositiveeffectforthefirstandnotconsideredforthesecond.Thiswould
posimtentulateialofthesecommensalism.phenomenologicalConsideringmodthese,elstoonesimcouldulateseeallakindsfirstofimpinortanterac-t
tionwithinacommunity.
Themathematicalsumofinteractiondescribedabove,andspecificallyfor
thetion.FInONotherapproacwohrd,,ccouldonsideringalsobeafoviewcusedasaindividual,sumoftheintprobabilitensityyofofithentfierac-eld
ofabilitneighytboiorhontoderactwacrossithaitsinneightberactionorateacareahspcouldecificbepinointoterpretedftheasinitsteractionprob-
thisareapropwhileosition.tryingThetosgetum(orofprotheseduce)aprobabilitiesresource.ofintThefieractiongureov9.1ertheillustratesover-
inlapateractionreawithareaa(Aneighb)orw(ouldFA,astillsinbeaptraditionalrobabilitFyON)ofintdividederactionbythewithtotalthe
intor:bneigh

FAPinteraction=A
int

9.5.INTEGRATINGTHEECOLOGICALLESSONS

241

ThisPinteractionwouldbethenthemeanprobabilityofinteraction(overthe
area)withtheneighbor.Inanindividual-basedmodelassumingtheseas-
pects,thisprobabilityofinteractionwouldbepertimestep.Ifallthe
Pinteractionwithalltheneighborshavinganoverlapwiththefocusindivid-
ual’sinteractionareaaresummed,thissumwouldbecomequickly>1and
wouldnotmakesenseintermofprobabilitieswhencrowdedsituationare
simulated.However,thissumcouldbeconsideredastotalinteractioninten-
sitywhichwouldthenbetransmittedtoapositiveornegativeeffecttoone
oftheindividual’sstrategy.Notethatinpractice,thisisexactlywhatthe
FONapproachisdoinginChapter8.

FOFigureNisc9.1:onsideringChangeacofrabinofcterpretationarapacewofidththeCW,fieldasoifnnCeighhapterborho8od.Thenotingofthe
However,thisdifferenceofinterpretationoftheFONmakesthingsmore
inactforteresting.oneFirst,resource.theinThisteractionwouldwmeanouldbethatinthetermaofpproachprobabilitwoyuldtobeintcomeer-
muchmoremechanistic,andonecouldthenimaginehavingmultipleFONs
fornomenologicaldifferentrmoesourcesdelsu(propsedionsedCbyhapterUta8couldBerger).alsobeSecondlyin,tterpretedheotherintphe-erm
ofprobabilitiesofinteraction(Fig.9.2).Andthisinterpretationwouldgive
thepossibilitytousedifferentshapesofinteractionprobabilityfordifferent
speciesaccordingtotheirspatialresourceuseorcreationefficiency.Other
shapescouldbethoughtof,aslongasthemathematicalintegrationofthe
9.3).sumoFforpexample,robabilitiesforofitrees,ntthiseractionshapmakeoefsptherobabilitmodelyosftillinteractionrunnablefor(e.g.gettingFig.
(1theatlightstem,cpouldosition)followtotgheetlightraditionaltcloseFtoONtheshapstemewiththanagoinghigherapway.robabilitThisy

242

GENERALDISCUSSION&CONCLUSIONS

interpretationcouldevenhelpfortheparameterizationoftheapproachsince
physiologicalcharacteristicsofindividualswouldbeconsidered.Thetradi-
tionalZOIapproachtransformedintothephenomenologicalonepresentedin
Chapter8,couldberepresentingtheinteractionprobabilityofaterritorial
animalprotectingitsspatial“property”withaprobabilityofinteractionof
1overtheentirearea.

basedFigures9patial.2:moDifferendels:ttheFRNprobabilisticandinZOItusederpretationinCofhapterother8phenomenologicalindividual-

Speculatingfurther,withmultipleFONsofdifferentshapesfordifferent
resourcesandfordifferentspecies,onecouldimaginerepresentingahigh
rangeofpossiblesystemswithanIBM.Forexample,themangrovetree
lighcommt,tunitempyeoffratureocusandinPnartutrienIcts.ouldThehavecanopthreeyrshapesofesource-basedeachspinecieswteractions:ould
determinethetypeofradiuscalculationandprobabilityofinteractionto
catchthelight.Therootsystemwouldbehardertoparameterizebutcould
befollowtheapnotherrobabilitFOyNofsfhape.acilitatingAndthetestablishmenempetofrature-basedseedlingsinlimitedteractionbcyloouldw
.3).9(Fig.eraturestempOnecouldthinkofthisgeneralapproachasasolutiontolookatmany
questionsofcoexistenceorspeciation.Itwouldbeveryusefultoevalu-
atecommtheunitimpy,andortancetoherebfydifferenhowtspperocies’cessesstrategiesinfluencingarefavindividualored.Instheuccesscaseinofa
mangroveecosystems,thisapproachcouldbeveryusefulfortheconstruc-
tionofmulti-levelmodelsasproposedabove,orfurtherstudiesonspecific
amspecunities.tsofdHoynwaevmeicr,sothisfUcidesapproaccohrwdatusouldphaovepulationonesortrongdramangrowvbacek:tforestheneedcom-

9.5.TINGINTEGRAHETECOLOGICALLESSONS243

ofsimulatingresourcechangescreatedbytheindividuals,whichcanbecome
verycomplexwhenresourcesarenotconstantlyrenewedorspatiallyhomo-
geneous.Finally,thePOMICandother“Ockham’sRazor”principlesmight
avoidtousethesecomplexmodelsforpredictionpurposeaslongaswedo
nothavemorepatternsdocumentedonsystemsoffocus.

Figure9.3:Apropositionofprobabilisticindividual-basedspatialrepresentationof
tree-treeinteractions:lightandnutrientsarecompetedfor,temperature-basedcouldbea
positiveresource-basedinteraction

244

9.6eferencesR

GENERALDISCUSSION&CONCLUSIONS

Baldwin,A.,Egnotovich,M.,Ford,M.,andPlatt,W.2001.Regenerationinfringemangrove
forestsdamagedbyHurricaneAndrew.PlantEcology157:149-162.
Ball,M.C.1980.PatternsofsecondarysuccessioninamangroveforestinsouthernFlorida.
44:226-235.Berlin)(OecologiaBardsley,K.1984.TheeffectsofCycloneKathyonmangrovevegetation.Pages167-185In:
K.N.Bardsley,J.D.S.Davie,andC.D.Woodroffe,editors.Coastsandtidalwetlands
oftheAustralianmonsoonregion.NorthAustraliaResearchUnit,ANUPress.
Barot,S.,andGignoux,J.2004.Mechanismspromotingplantcoexistence:canallthe
proposedprocessesbereconciled?Oikos106:185-192.
Bauer,S.,Berger,U.,Hildenbrandt,H.,andGrimm,V.2002.Cyclicdynamicsinsimulated
plantpopulations.ProceedingsoftheRoyalSocietyofLondonB269:2443-2450.
Bauer,S.,Wyszomirski,T.,Berger,U.,Hildenbrandt,H.,andGrimm,V.2004.Asymmetric
competitionasanaturaloutcomeofneighbourinteractionsamongplants:resultsfrom
thefield-of-neighbourhoodmodellingapproach.PlantEcology170:135-145.
Berger,U.,andHildenbrandt,H.2000.Anewapproachtospatiallyexplicitmodelling
offorestdynamics:spacing,ageingandneighbourhoodcompetitionofmangrovetrees.
EcologicalModelling132:287-302.
Berger,U.,andHildenbrandt,H.2003.Thestrengthofcompetitionamongindividualtrees
andthebiomass-densitytrajectoriesofthecohort.PlantEcology167:89-96.
Berger,U.,Hildenbrandt,H.,andGrimm,V.2002.Towardsastandardfortheindivid-
ualbasedmodelingofplantsimulations:Self-ThinningandtheFieldofNeighborhood
approach.NaturalResourceModeling15:39-54.
Berger,U.,Hildenbrandt,H.,andGrimm,V.2004.Age-relateddeclineinforestproduction:
modellingtheeffectsofgrowthlimitation,neighbourhoodcompetitionandself-thinning.
JournalofEcology92:846-853.
Berger,U.,Adams,M.,Grimm,V.,andHildenbrandt,H.2006.Moldellingsecondarysuc-
cessionofneotropicalmangroves:Causesandconsequencesofgrowthreductioninpioneer
species.PerspectivesinPlantEcology,EvolutionandSystematics7:243-252.
Booth,G.1997.Gecko:Acontinuous2-Dworldforecologicalmodeling.ArtificialLife
:147-163.3JournalChave,J.,Muller-Landau,H.C.,andLevin,S.A.2002.Comparingclassicalcommunity
models:theoreticalconsequencesforpatternsofdiversity.TheAmericanNaturalist159:1-
23.Chen,R.,andTwilley,R.R.1998.Agapdynamicmodelofmangroveforestdevelopment
alonggradientsofsoilsalinityandnutrientresources.JournalofEcology86:37-51.
Connell,J.H.1978.Diversityintropicalrainforestsandcoralreefs.Science199:1302-1310.
Diele,K.2000.LifehistoryandpopulationstructureoftheexploitedmangrovecrabUcides
cordatuscordatus(L.)(Decapoda:Brachyura)intheCaet´eestuary,NorthBrazil.PhD
Thesis,ZMTContribution9,Bremen,Germany.
Duke,N.C.2001.Gapcreationandregenerativeprocessedrivingdiversityandstructureof
mangroveecosystems.WetlandsEcologyandManagement9:257-269.
Feller,I.C.,McKee,K.L.,Whigham,D.F.,andO’Neill,J.P.2002.Nitrogenvs.phosphorus
limitationacrossanecotonalgradientinamangroveforest.Biogeochemistry62:145-175.
Fromard,F.,Vega,C.,andProisy,C.2004.Halfacenturyofdynamiccoastalchange
affectingmangroveshorelinesofFrenchGuiana.Acasestudybasedonremotesensing
dataanalysesandfieldsurveys.MarineGeology208:265-280.

REFERENCES9.6.

245

Fromard,F.,Puig,H.,Mougin,E.,Marty,G.,Betoulle,J.L.,andCadamuro,L.1998.
Structure,above-groundbiomassanddynamicsofmangroveecosystems:newdatafrom
FrenchGuyana.Oecologia115:39-53.
Grimm,V.,andBerger,U.2003.Seeingthewoodforthetrees,andviceversa:pattern-
orientedecologicalmodelling.Pages411-428In:L.SeurontandP.G.Strutton,editors.
HandbookofScalingMethodsinAquaticEcology:Measurement,Analysis,Simulation.
CRCPress,BocaRaton.
Grimm,V.,Frank,K.,Jeltsch,F.,Brandl,R.,Uchmanski,J.,andWissel,C.1996.Pattern-
orientedmodellinginpopulationecology.TheScienceoftheTotalEnvironment183:151-
166.Grimm,V.,Revilla,E.,Berger,U.,Jeltsch,F.,Mooij,W.M.,Railsback,S.F.,Thulke,
H.-H.,Weiner,J.,Wiegand,T.,andDeAngelis,D.L.2005.Pattern-orientedmodelingof
agent-basedcomplexsystems:lessonsfromecology.Science310:987-991.
Gui˜nez,R.,andCastilla,J.C.1999.Atridimensionalself-thinningmodelformultilayered
intertidalmussels.TheAmericanNaturalist154:341-357.
Imai,N.,Takyu,M.,Nakamura,Y.,andNakamura,T.2006.Gapformationandregenera-
tionoftropicalmangroveforestsinRamong,Thailand.PlantEcology186:37-46.
Imbert,D.2002.Impactdesouraganssurlastructureetladynamiqueforesti`eresdansles
mangrovesdesAntilles.BoisetForˆetsdesTropiques273:69-78.
Imbert,D.,Rousseau,A.,andLabb´e,P.1998.Ouragansetdiversit´ebiologiquesdansles
forˆetstropicales.L’exempledelaGuadeloupe.ActaOecologica19:251-262.
Jeltsch,F.,M¨uller,T.,Grimm,V.,Wissel,C.,andBrandl,R.1997.Patternformation
triggeredbyrareevents:lessonsfromthespreadofrabies.ProceedingsoftheRoyal
SocietyofLondonB264:495-503.
Jim´enez,J.A.,Lugo,A.E.,andCintr´on,G.1985.TreemortalityinMangroveforests.
17:177-185.BiotropicaKeddy,P.A.2001.Competition(2ndedition).KluwerAcademicsPublishers,Dordrecht,
202pp.etherlands,NTheKenkel,N.C.1988.Patternofself-thinninginJackPine:Testingtherandommortality
hypothesis.Ecology69:1017-1024.
Kerr,B.,Riley,M.A.,Feldman,M.W.,andBohannan,B.J.M.2002.Localdispersors
promotesbiodiversityinareal-lifegameofrock-paper-scissors.Nature418:171-174.
Lenz,M.,Molis,M.,andWahl,M.2004.Testingtheintermediatedisturbancehypothesis:
responseoffoulingcommunitiestovariouslevelsofemersionintensity.MarineEcology
278:53-65.eriesSProgressMacnae,W.1968.Ageneralaccountofthefaunaandfloraofmangroveswampsandforests
intheIndo-West-Pacificregion.AdvancesinMarineBiology6:73-270.
McKee,K.L.1995b.SeedlingrecruitmentpatternsinaBelizeanmangroveforest:effectsof
establishmentabilityandphysico-chemicalfactors.Oecologia101:448-460.
Nordhaus,I.2004.Feedingecologyofthesemi-terrestrialcrabUcidescordatuscordatus
(Decapoda:Brachyura)inamangroveforestinnorthernBrazil.PhDThesis,ZMTcon-
tribution18,Bremen,Germany.
Nybakken,J.W.2001.Marinebiology:anecologicalapproach-5thedition.Benjamin
Cummings,SanFrancisco,CA,USA,516pp.
Pacala,S.W.,andSilander,J.A.J.1985.Neighborhoodmodelsofplantpopulationdy-
namics.1Single-speciesmodelsofannuals.TheAmericanNaturalist125:385-411.
Pachepsky,E.,Crawford,J.W.,Bown,J.L.,andSquire,G.2001.Towardsageneraltheory
ofbiodiversity.Nature410:923-926.
Rabinovitz,D.1978.Dispersalpropertiesofmangrovepropagules.Biotropica10:47-57.

246

GENERALISCUSSIOND&ONCLUSIONSCReynolds,J.H.,andFord,D.E.2005.Improvingcompetitionrepresentationintheoretical
modelsofself-thinning:acriticalreview.JournalofEcology93:362-372.
Roth,berL.1988,C.on1992.theVHurricanesegetationoandfIMsladangroelVveeRnado,Begeneration:luefields,NEffectsicaragua.ofHurricaneBiotropicaJoan,O24:375-cto-
384.Roth,L.C.1997.Implicationsofperiodichurricanedisturbanceforthesustainableman-
agementofcaribbeanmangroves.In:B.Kjerve,L.D.d.Lacerda,andE.H.S.Diop,
editors.MangroveecosystemstudiesinLatinAmericaandAfrica.UNESCO&ISME.
Saenger,lishers,P.D2002.ordrecht,Mangro360pp.veecology,silvicultureandconservation.KluwerAcademicsPub-
Sheil,inD.,EcologyandandBurslem,EvoD.lutionF.R.P18:18-26..2003.Disturbinghypothesesintropicalforests.TRENDS
Sherman,DominicanR.RE.,aepublic:ndFahey,DamageT.J.Pa2001.tternsandHurricaneEarlyRecoImpactsvery.onaBiotropicaMangroveF33:393-408.orestinthe
SmithmangroIII,veT.spJ.,eciesandricDukhnesse,aN.C.roundt1987.hePhtropicalysicalcoastlinedeterminanofAtsofustralia.interJestuaryournalvofariationBiogeog-in
14:9-19.yraphSmithIII,T.J.,Robblee,M.B.,Wanless,H.R.,andDoyle,T.W.1994.Mangroves,
Stoddart,Hurricanes,D.R.and1963.LightEffectsningofStrikes.HurricaneBioscienceHattieon44:256-262.theBritishHondurasreefsandcays,
Tilman,Oct.D.30-31,1994.1961.AComptollRetitionesearcahndBbioulletindiversit95.yinspatiallystructuredhabitats.Ecology
75:2-16.Vermeer,D.E.1963.EffectsofhurricaneHattie,1961,onthecaysofBritishHonduras.
ZeitschriftfrGeomorphologie7:332-354.
Wiegand,T.,Jeltsch,F.,Hanski,I.,andGrimm,V.2003.Usingpattern-orientedmodeling
forrevealinghiddeninformation:akeyforreconcilingecologicaltheoryandapplication.
100:209-222.soOikpoWiegand,pulationT.,Rmoevilla,dels.EB.,ioanddiveKrsitynauer,andF.Conserv2004a.ationDealingw13:53-78.ithuncertaintyinspatiallyexplicit
Wiegand,(UrsusT.,arctos)Kinnauer,totheF.,easternKaczenskyAlps:,P.a,sandpatiallyNaves,explicitJ.2004b.poEpulationxpansionmodel.ofbroBiowdnivbersitearsy
13:79-114.ationonservCand