©CopyrightJASSS

FrançoisRebaudo,VerónicaCrespo-Pérez,Jean-FrançoisSilvainandOlivierDangles(2011)

Agent-BasedModelingofHuman-InducedSpreadofInvasiveSpeciesinAgriculturalLandscapes:InsightsfromthePotatoMothinEcuador

JournalofArtificialSocietiesandSocialSimulation 14(3)7

Received:27-Oct-2010Accepted:07-May-2011Published:30-Jun-2011

Abstract

Agent-basedmodels(ABM)areidealtoolstodealwiththecomplexityofpestinvasionthroughoutagriculturalsocio-ecologicalsystems,yetveryfewstudieshaveappliedtheminsuchcontext.InthisworkwedevelopedanABMthatsimulatesinteractionsbetweenfarmersandaninvasiveinsectpestinanagriculturallandscapeofthetropicalAndes.Ourspecificaimsweretousethemodel1)toassesstheimportanceoffarmers'mobilityandpestcontrolknowledgeonpestexpansionand2)touseitasaneducationaltooltotrainfarmercommunitiesfacingpestrisks.Ourmodelcombinedanecologicalsub-model,simulatingpestpopulationdynamicsdrivenbyacellularautomatonincludingenvironmentalfactorsofthelandscape,withasocialmodelinwhichweincorporatedagents(farmers)potentiallytransportingandspreadingthepestthroughdisplacementsamongvillages.Resultsofmodelsimulationrevealedthatbothagents'movementsandknowledgehadasignificant,non-linear,impactoninvasionspread,confirmingpreviousworksondiseaseexpansionbyepidemiologists.However,heterogeneityinknowledgeamongagentshadaloweffectoninvasiondynamicsexceptathighlevelsofknowledge.EvaluationsofthetrainingsessionsusingABMsuggestthatfarmerswouldbeabletobettermanagetheircropafterourimplementation.Moreover,byprovidingfarmerswithevidencethatpestspropagatedthroughtheircommunitynotastheresultofisolateddecisionsbutratherastheresultofrepeatedinteractionsbetweenmultipleindividualsovertime,ourABMallowedintroducingthemwithsocialandpsychologicalissueswhichareusuallyneglectedinintegratedpestmanagementprograms.

Keywords:Socio-EcologicalSystems,Farmers,InvasivePest,LongDistanceDispersion,Teaching

Introduction

1.1 Agriculturalsystemsarecomposedbytwointerlinkedandinterdependentsubsystems,thesocialandtheecologicalsubsystems,whichco-evolveandinteractatvariouslevelsandscales(Liu2007).Asaconsequence,thesesystemsarecharacterizedbycomplexspatio-temporaldynamicsandculturalvariation(Papajorgji2009).Themanagementofagriculturalinvasivepestsliesattheheartofsuchacomplexityaspestpropagationdependsonbothenvironmentalfeatures(e.g.climate,landscapestructure)andfarmers'behaviors(e.g.man-inducedpestdispersion)(Epanchin-Niell2010).Theproblemswithdealingwithmultipleactors,nonlinearity,unpredictability,andtimelagsininvadedagriculturalsystemssuggestthatagent-basedmodels(ABM)mayhaveanimportantroletoplayinthesustainabledevelopmentoffarmers'practicestofacethoseemergentthreats(Berger2001).AlthoughABMhaveincreasinglybeenappliedtophysical,biological,medical,social,andeconomicproblems(Bagni2002;Bonabeau2002;Grimm2005a)ithasbeen,toourknowledge,disregardedbyinvasivepestmanagementtheoryandpractice.

1.2 Intrinsicdispersalcapacitiesofagriculturalinvasivepest(inparticularinsects)arerarelysufficienttomakethemmajorthreatsatalargespatialscale.Inmostcases,invasivepestexpansionisdependentonlong-distancedispersal(LDD)events,akeyprocessbywhichorganismscanbetransferredoverlargedistancesthroughpassivetransportationmechanisms(Liebold2008).Thestudyofthedynamicsofpestdispersioninagriculturallandscapeisthereforecomparabletothatofdiseasecontagion:asdiseases,pestsaretransmittedfromaninfectedperson(farmer)toanotherwhowaspreviously"healthy",throughdifferentbiological,socialandenvironmentalprocesses(Teweldemedhin2004;Dangles2010).Severalstudieshaveshownthatthedynamicsofinfectionspreadinvolvespositiveandnegativefeedbacks,timedelays,nonlinearities,stochasticevents,andindividualheterogeneity(Eubank2004;Bauer2009;Itakura2010).Twofactorshaverevealedparticularlyimportanttopredictdiseasedynamics:(1)thenumberofencountereventsbetweeninfectedandhealthyindividuals,whichmainlydependsonindividuals'mobility(Altizer2006),and(2)thecontaminationratebetweeninfectedandhealthyindividuals,whichdependsonheterogeneoussusceptibilitiesofindividualstobeinfected(Moreno2002;Xuan2009).Similarly,thespreadofinvasivepeststhroughouttheagriculturallandscapewoulddependon(1)movementsoffarmerscarryinginfestedplantsorseedsintonewareasand(2)farmer'sknowledgetodetectthepest(pestcontrolknowledge),thereforeavoidingbeinginfestedandimpedingthecontaminationofnewareas(Dangles2010).

1.3 Borrowingfromdiseasecontagionliterature(e.g.Gong2007;Yu2010),wedeveloped,usingNetLogo(Wilensky1999),anABMtosimulatethespreadofaninvasivepotatoinsectpestinanagriculturallandscapeofthetropicalAndes.Ourmodelcombinedanecologicalsub-model,simulatingpestpopulationdynamicsdrivenbyacellularautomatonincludingenvironmentalfactorsofthelandscape,withasocialmodelinwhichweincorporatedagents(farmers)potentiallytransportingandspreadingthepestthroughdisplacementsamongvillages.Wethenusedourmodelfortwopurposes.First,werantheABMunder10levelsofagents'(farmers)movementsamongvillagesand7levelsofheterogeneityinfarmer'spestcontrolknowledge.Wecomparedtheresultingdiffusiondynamicsonthespeedofpestspread,whichrepresentsarelevantmetricsforinvasivepestmanagementbylocalstakeholders(e.g.thetimeavailableforagricultureofficialstorespondtothethreat).Second,weusedourABMasaneducationtooltoincreasefarmerawarenessontheimportanceofhuman-relatedLDDeventsofthepestswhichfosteredtheinvasionsoftheirvalley(seeDangles2010).WhilewespecificallyfocusedonaninvasiveinsectpestinthetropicalAndesinthispaper,ourapproachtounderstandtheinfluenceoffarmers'movementsandpestcontrolknowledgeonpestdynamicsandtotransferitthrougheducationalprogramswouldbeapplicabletoamuchwidergeographicandspeciesrange.

Studysystem

2.1 Ourstudydealswiththepotatotubermoth(Teciasolanivora),aninvasivepestthathasspreadfromGuatemalaintoCentralAmerica,northernSouthAmericaandtheCanaryIslandsduringthepast30years(Puillandre2008).Thispestattackspotato(Solanumtuberosum)tubersinthefieldandinstorageandhasbecomeoneofthemostdamagingcroppestsintheNorthAndeanregion(Dangles2008).CommercialexchangesofpotatotubersatregionalandlocalscalesforbothseedingandconsumptionarethemaincausesfortherapidexpansionofthepestinallpartsoftheEcuadorianhighlands(2400-3500m.a.s.l).Theselandscapesarecharacterizedbyhighlyvariableenvironmentalandsocialconditionsduetosteepaltitudinalgradientsanddispersedhumansettlement,respectively.

Model

Overallstructureofthemodel

3.1 Thesocio-agronomicalframeworkofthemodelconsistsinthreekeyelements(Figure1):1)theagriculturallandscapecharacteristicsprovidedbyaGISenvironmentaldatabase(BiodiversityIndicatorsforNationalUse,MinisteriodelAmbienteEcuadorandEcoCiencia2005),2)theinsectpestpopulation,and3)thegroupsoffarmers.Pestdynamicsininteractionwithlandscapefeatures(e.g.landuse,climate)issimulatedthroughacellularautomaton(seethefollowingsub-section).Totransferthecellularautomatonintoanagent-basedsimulationmodelweincludedfarmersasagentsactingindividuallyuponpestdynamicsintheagriculturallandscape.PestsarethereforerepresentedasalayerinthecellularautomatonandfarmersasagentsintheABM.

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Figure1.Schematicrepresentationofthemodelstructure

Modelingpestdynamicsthroughcellularautomata

3.2 Thespatio-temporaldynamicsofpotatotubermothismodeledthroughasimplifiedversionofthecellularautomatondevelopedbyCrespo-Pérez(submitted).ThismodelwasdevelopedwiththeCORMASmodelingplatformandisdetailedinAppendix1.BrieflyitisbasedonbiologicalandecologicalrulesderivedfromfieldandlaboratoryexperimentaldataforT.solanivora'sphysiologicalresponsestoclimate.Mainprocessesincludemothsurvival(climatedependent),dispersalthroughdiffusionprocesses(densitydependent),andreproduction(climatedependent).Thismodelhasbeenvalidatedinastudyareaof20×20kmwithintheremotevalleyofSimiatugintheCentralEcuadorianAndes(seesection5)representedbyagridof1,600

cellswithacellsizeof0.25km2.

Modelinghuman-relatedpestdispersionthroughtheagent-basedmodel

3.3 TheABMaimsatsimulatingtheinfluenceoffarmersonthespatio-temporaldynamicsofthepotatomoth.Inthisparticularmodel,farmersareconsideredaspotentialagentsforpestLDD,forexamplewhentheycarryinfestedpotatosacksfromlocalmarketstotheirhome(otherinteractionswiththepest,suchascontrolbypesticide,arenotincludedinthismodel).TheirefficiencyasLDDagentsdependsontheirpestcontrolknowledge:thehighertheirknowledge,thelowertheprobabilitytheygettheirfieldinfestedafterpotatosackstransport(seebelow).

Agentprocessoverviewandscheduling

3.4 Agentprocessoverviewandschedulingarepresentedinfigure2.Agentsmovearoundonagridofcellswhoselevelofpestinfestationismodeledbythecellularautomaton(seeAppendix1).Duringeachmovementwithinasingletimeframeagentsturn"infested"(i.e.theirpotatocropsareinfestedbythemoth)orremain"non-infested"dependingontheirpestcontrolknowledgeandthepestinfestationinagivencell.Eachtimeframeisequaltoonemothgeneration(i.e.about2months)duringwhichagentscanmoveseveraltimesdependingontheirtraveldecisions.Agentswithhigherpestcontrolknowledge(e.g.knowinghowtorecognizemothdamagewhentheybuypotatosacksatthemarket)havealowerprobabilityofbecominginfested.Then,agentsmovefromonevillagetoanothertobuyand/orsellpotatoes.Agents'movementsfollowagravitymodel(Rodrigue2009),wheretheattractivenessofavillageicomparedtoavillagejisafunctionofbothpopulationsizeandcost-distancebetweenthem.Villageinfestationoccurswhenaninfestedagentmovestoanon-infestedvillage(carryinginfestedpotatosackswhichwillbeusedaspotatoseedsandtherebyinfestneighboringfields).Agentinfestationoccurswhenanon-infestedagentmovestoaninfestedvillage(buyinginfestedpotatoseedsacks),dependingonhispestcontrolknowledge(higherpestcontrolknowledgeleadstolowerprobabilityofbuyinginfestedsacks).

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Figure2.Agents'processesloopshowinghowfarmersinfluencepestinfestationspread.Thisloopisexecutedvarioustimesdependingonfarmers'travelingdecisionsduringeachtimeframe.

Designconcepts

3.5 Agentscansensethepestinfestationofthecellsbuttheydonotusethisinformationfortheirtravelingdecision.Instead,agentssensevillagepopulationsizeanddistancebetweenvillagessothattheyareabletoperceivetherelativecost/benefitofgoingtoeachvillagetosell/buytheircrop:(1)itislessexpensivetotraveltocloservillagesand(2)morepopulatedvillagesprovidehighercommercialopportunities.Asaresult,timeneededtoreachacompletepestinfestationintheareaemergesfromacombinationofpurelybiologicalpestdispersion,agents'movementsfromvillagetovillageandagent'spestcontrolknowledge.Amodelexampleisavailableonlineathttp://www.openabm.org.

Testingtheeffectofagents'movementandpestcontrolknowledgeonpestspreaddynamics

Effectofagents'movements

4.1 WeexaminedwithourABMhowthenumberofagents'movementspergenerationwouldimpactpestinvasiondynamics.Aswewereinterestedintheearlyphasesofinvasions,whichrepresentarelevantmetricsforinvasivepestmanagementbylocalstakeholders,weusedthetimeneededtoreach5%ofinfestedcellsasanoutcomevariable.

4.2 Wefoundthatincreasingfrom1to10thenumberofagents'movementsinthelandscapehadanegativeexponentialeffectonthespreadoftheinvasivepest(Figure3andanimationinAppendix2).Invasionspeedwasparticularlyincreasedupto4movementsandthentendedtostabilize.Asexpected,theeffectofagents'movementoninvasionspeedwasintensifiedbythenumberofagentslocatedonthelandscape,butonceagainthiseffectwasnotlinear:insectpestdynamicswasspeededupwhenaddingupto10agentsbutremainedroughlyunchangedforthe10followingones.Foranintermediatescenario(4movements,10agents),thespeedofinvasionwastwicefasterthatofapurelybiologicalspread(i.e.throughinsect'sdispersioncapabilitiesalone).Weareawarethatthespatialconfigurationofoursociallandscape(seethefrequencyofinfestedfarmermovementsinFigure4)likelyinfluencedourresults.Furtherstudiesincludingrandomlygeneratedsociallandscapescouldhelptoquantifythiseffectonagents'movementsandsubsequentpestinfestationdynamics.

Figure3.Influenceofagents'movements(perpestgeneration)onpestinfestationdynamicsfordifferentagentdensities(n=2to20).Thedashedlinerepresentstimeneededtoreach5%ofinfestedcellswithoutagents(purely"biological"spread).

4.3 Ourresultshighlighttheimportanceofinsectpestpassivetransportationbyhumanswhichallowsinvasivepeststomakelong-distancedispersaljumps.Eventhoughseveralauthorshaveacknowledgedthesignificanceofthistypeofdispersalforspeciesspread,(e.g.,Bossenbroek2001;Suarez2001)itsinclusioninmodelsstillposesdifficultiesformodelers(Pitt2009).Mostdispersalmodelsarebasedonempiricallymeasuredratesofpestdispersal,whileinthecaseofLDDeventsitwouldbemoreusefultomodelhumanbehaviorstobetterunderstandpestinvasiondynamics.Inthiscontext,ABMofferaninterestingyetpoorlyusedmethod,tobeappliedtothevastfieldofbiologicalinvasions(seeLuo2010andVinatier2009foroneoftherarestudyonexoticspeciesusingABM,althoughintheircase,agentsaretheinvasivespecies).ResultsofourABMsimulationsfurtherrevealednonlinearprocessesbetweenfarmers'behavior(e.g.movement)anddensitiesandpestspread,asalreadyshownfordiseaseexpansionbyepidemiologicmodels(e.g.Gong2007).Thissuggeststhatagoodunderstandingofsocialnetworkstructureswouldbeakeysteptobetterpredictpestinvasionspeedinhumandominatedlandscapes.Inthiscontext,ecologistswouldgaininfollowingthepathtracedbyepidemiologistswithABMtobetterunderstandthedynamicsofinvasivepests.

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Figure4.FrequencyofvisitsofinfestedagentsforeachvillageandmapoftheSimiatugvalleywithagents'movementsandvillageslocation.

Effectofagent'sheterogeneityinpestcontrolknowledge

4.4 WethenexploredwithourABMhowagents'pestcontrolknowledge(rankedfrom0to100)wouldimpactpestpropagationdynamics.Aspestcontrolknowledgewasusuallyvariableamongfarmers(Dangles2010),wewereinterestedinexaminingtheinfluenceofheterogeneouslevelsamongagentsonpestspreaddynamics.Toachievethisgoal,wetested7levelsofheterogeneity(standarddeviation=0,5,10,15,20,25,30)around10meanvaluesofpestcontrolknowledge(mean=0to100).Foreachsimulation,agents'pestcontrolknowledgelevelswererandomlychosenfromaNormaldistribution,N(mean,standarddeviation).

4.5 Oursimulationsrevealedthatagents'pestcontrolknowledgehadasignificanteffectonpestinvasiondynamics(Figure5andanimationinAppendix2).Inallsimulations,loweragents'pestcontrolknowledgeledtohigherinvasionspeed,almosttwicefasterthanintrinsicpestdispersionspreadforhighestinfectivityvalues.Agents'movementhadaworseningeffect,withfasterinvasionoccurringforhigheragent'smobility.Agents'heterogeneityinpestcontrolknowledgehadaweakeffectonpestdynamics,especiallyforhighagents'mobility(6and4).However,heterogeneityinknowledgedidintroducesomesochasticityininvasiondynamicswhenagentsseldommoved.

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Figure5.Influenceofagents'pestcontrolknowledge(means)andheterogeneity(standarddeviation=0to30%)onpestinfestationdynamicsforthreefrequenciesofmovements(2,4,and6).

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Thedashedlinerepresentstimeneededtoreach5%ofinfestedcellswithoutagents(purely"biological"spread).

4.6 Asreportedbyepidemiologistsfordiseasespread(e.g.,Newman2002),ourresultsshowedthatagents'pestcontrolknowledgehadanimportantimpactonthedynamicsofpestinvasionspread.Thissuggeststhatfarmers'pestcontrolknowledgewouldbeakey,yetpoorlystudied,variabletotakeintoaccountformodelingpestinvasionsinagriculturallandscapes.Lessexpectedly,wefoundthatheterogeneityofknowledgeamongagentshadarelativelyweakeffectonpestdynamics,especiallyforhighmobilitylevelsofagents.Thiscontrastwithepidemiologicalmodelswhichhavegenerallyshownthatheterogeneouspopulationsenhancethespreadofinfectionsaswellasmakethemhardertoeradicate(forareviewseeAnderson1992).Onepotentialexplanationisthatthelimitednumberofvillagesusedinourstudyandtheabsenceofspatialclustersfavorinfestationmixtureamongagentsandrapidlysmoothupitsimpactoninvasionspreaddynamics.However,ourresultsshowedthatwhenallagentsare"healthy"(pestcontrolknowledge=100),anyadditionofagentswithlowerlevelsofknowledgewillconsiderablyspeeduppestdynamics(especiallyathighlevelsofmovements),therebyconfirmingpredictionsofdiseasespreadtheory.

Teachingwiththemodel

5.1 Inasecondstep,weusedourABMasaneducationaltooltoteachfarmersaboutpotentialinvasionrisksresultingfromindividualbehaviors.TeachingactivitieswererealizedinFebruary2009attheAgricultureandTechnologyCollegeoftheSimiatugvalleyinthecentralEcuadorianAndes.Thisparishiscomprisedofroughly45kichwacommunitieslivingbetween2800mand4250mofaltitude,thatsharesimilarcharacteristicsintermsofsocialorganization,dateofestablishment,andagriculturalpractices.Currently,about25,000people,mainlysubsistenceandmarket-orientedfarmers,liveintheSimiatugparish.Themainagriculturalproductsarepasture,cereals(barley),legumes(favabean)andpotatoesaswellascattleandsheep(seemoredetailsinDangles2010).Althoughtheremotenessofthevalleyprotectsitagainstmothinvasion,increasingcommercialexchangesfromandtoSimiatugarecurrentlyincreasingtheriskofmothintroduction.Localfarmerswerethereforeinterestedinlearningaboutpotentialrisksassociatedwiththepestandhowtocontroltheirspreadinthevalley.

Modelintroductiontothefarmers

5.2 Introductionofthemodelsandvariablerepresentationtothefarmershasbeenalongprocessthatbeganwiththeeducationalprogramsetupin2007(Dangles2010,seethetimelineofthegroundworkinFigure6).

Figure6.Timelineofthegroundworkpriortotheteachingsession

5.3 Forthisprogram,weheldanegotiationsessiontoinsurethatteachingwasdrivenbyfarmers'interestsfollowedbyatrainingsessiononintegratedpestmanagementandonparticipatorymonitoringofpotatomothinthevalley.Afterthedataanalysissession,farmershadacquiredaratherclearconnectionbetweenpestabundanceandairtemperature,villagesizeandremoteness(seeDangles2010,foradetaileddescriptionofthesessionswithfarmers).Thisinitialprocessallowedustointroduceourmodelinasecondstepandtouseitasateachingtool.Farmerswereyoung(17to25yearsold)andshowedinnateinterestin"playing"withthecomputersandseeingsimulations(anInternetcaféjustopenedinSimiatugtheyearbeforestartingtheABMteachingsession).Themodelwaspresentedasawaytobetterunderstandaresultthatfarmersthemselveshadfound:theimportanceofLDDinmothdispersion(seeDangles2010).

Modelparameterization

5.4 Forteachingpurposes,farmerswereseparatedintotwo,"blue"and"red"teams;havingtwoteamsthatcompeteforminimizationofpestpresenceinthevalleystimulatedenthusiasmamongfarmers.Eachmemberoftheteamwasaskedtofillaquestionnaireincluding20items,10onbasicissues(biologyandecologyofthepest)and10onappliedissues(pestmanagement).Afacilitatorhelpedtheplayerstofillinthesequestionnaires.Basedonfilledquestionnaires,webuilta"pestcontrolknowledgeindex"foreachfarmer,whichcorrespondedtothepercentofquestionsansweredcorrectly.Farmerswerealsoaskedtoanswerquestionsabouttheirtravelbehaviorinthevalley(destinationandfrequencies).Villages'locationsandpopulationsizesweredefinedbyfarmersusingmaps(seefigure7).Environmentaldatasuchastemperatureorprecipitationwereupdatedusingrealvaluesintheconsideredarea(DanglesandCarpio,unpublisheddataprovidedwiththemodelintheopenabm.orgwebsite).

Figure7.Teachingwithanagent-basedmodelinanagriculturalvalleyofEcuador

Playingandlearningwiththeagent-basedmodel

5.5 Onceinputdatawerecollectedandsetup(Table1),weranthemodelandregisteredthespreadofthepestthroughoutthevalley.Inallsimulations,agentsarerandomlylocatedatthebeginningoftherun.

Table1:Parametersandsimulationresultsofthegamingsessionwithfarmers

Parameters Parametersvaluesusedforthegaming Parametersvaluesattheendofthegaming

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session sessionParameterizationNumberoffarmers(agents) 10 10Numberofagents'movementspertimeframe(pestgenerations)

6 3

Pestcontrolknowledge(followingaNormaldistribution~N(mean,sd))

<n(0.4;0.1) <n(0.8;0.1)

ResultsTimeneededforcompleteinfestation(pestgeneration) 39 45

5.6 Ourmodeloutputcoulddistinguishbetween1)cellsinfestedduetoLDDeventsmadebytheblueteam,2)cellsinfestedbyredteamLDDand3)cellsinfestedbyinsect'sowndispersalcapabilities(seehttp://www.openabm.org;see"pestdispersion"byinnomip).EachteamwasthereforeabletovisualizeitsrelativeimpactonmothdispersionthroughouttheSimiatugvalleythroughthemaincolorofaspatialinterfacerepresentingthelandscape.Theywerefurtherinvitedto"play"withthesimulationinterfacebychangingLDDandthepestcontrolknowledgevaluesandtoseetheconsequencesintermsofmothspreadthroughouttheirvalley.Asynthesisoftheprocessesinvolvedintheteachingsession(includingrequiredtime)isgiveninTable2.

Table2:Processesandtimerequiredforteachingandlearning

Gamingsessionprocess Mainactivities TimespentIntroduction Overallpresentationofallactors 1hourComputerpresentation Presentationofcomputersimulationutility 30minutesModeladoption:buildingcommunitymap(villagesandpopulations)

Presentationofthespatialrepresentationofthemodel 30minutes

Modelinputvariables(interviews) Modelparameterization 1hourModeloutputvariables Runningthemodelwiththetwoteams,resultpresentationanddiscussion 1hourPlayingsession1:farmermovementsandpestinfestationspread

Farmerteamsmodifyagents'movementsandvisualizeconsequencesonpestspreading

30minutes

Playingsession2:farmerknowledgeandpestinfestationspread

Farmerteamsmodifyagents'pestcontrolknowledgeandvisualizeconsequencesonpestspreading

30minutes

Conclusionandevaluation Generaldiscussionwithfarmersandinterviews 1hour

Modeladoption

5.7 Becauseparticipantswereyoungfarmerswehadnoproblemrelatedtopotentialtechnical,cultural,knowledgeorattitudebarriers.Oneofthemaindifficultiesrelatedtomodeladoptionturnedouttobethespatialrepresentationoffarmer'svillages,whichwaspartiallysolvedbybuildingwiththemadigitalmapoftheirvalley.Anotherdifficultywasthatfarmershadahardtimeinassociatinggridcellcolorswiththepresenceofmoths.Unfortunately,wecouldnotfixthisproblemduringtheteachingsessionandthiswasprobablyoneofthemaindrawbacksofourapproach.However,sincethisdate,weimprovedthesimulationtointegratethedrawingofmothsspreadingonthecellularautomatagridinasimplemodelaimedatimprovingitsadoption(seehttp://www.openabm.orgsee"pestdispersionversion1"byinnomip).

Benefitsofmodel-basedteachingtofarmers

5.8 Attheendofthesessionwere-evaluatedparticipantpestcontrolknowledgeonbasicandpracticalmothcontrolissueswiththesame20-itemindicatorsquestionnaire(seeabove).Themeanpestcontrolknowledge(percentofquestionsansweredcorrectly)increasedfrom40±10(basic)and40±20(practical)atthebeginningofthesessionto80±10(basic),and80±10(practical)attheendofthesession,suggestingthatfarmerswouldbeabletobettermanagepestrisksaftertheteachingsessions.Asawhole,oureducationalprogram(2007-2009)indeedenhancedlocalawarenessabouttheneedtocontrolthepestsbeforetheybecametoonumerousandcoveredthewholelandscape.ThemainspecificmanagementdecisiontakenbyfarmerswasapromisetosystematicallycheckformothinfestationwhenbuyingpotatotubersintheSimiatugmarketbeforetransportationtotheircommunity(seealsoDangles2010).Althoughfarmersvouchedformodel'sattractivenessandusefulnesstolearnaboutpestproblems,itremainedhardtoquantifyknowledgeenhancementspecificallyduetotheABMasopposedtothatduetotherestoftheeducationalparticipatoryprogram.However,webelievethattheuseofABMandcomputerssignificantlycomplementedoureducationalprogramonpestmanagementinthevalleyasithadaclearconsequenceinenhancingyoungfarmers'interestinagriculturalissues.TheCollegeofSimiatugindeedsufferedfromanincreasinglackofinterestfromstudentsofagriculturedisciplinesinfavoroftechnical/computationalones.OurprogramshowedyoungfarmersthatbothdisciplinescouldbemergedandthattheycouldfindthroughtheInternet(http://www.innomip.ird.fr)computationaltoolstoincreasetheirknowledgeonpestmanagement.OurstudyisapreliminaryapproachintheuseofABMforpestmanagementissues.Furthereffortsshouldbedonetooptimizemodeladoptionprocesssuchastheearlyidentificationofgapsinfarmers'knowledge(Wilson2009),theconsiderationofpeak-laborperiods(White2005)orthesocialnetworkoflearners(Boahene1999).

5.9 AnotherachievementofABMwasthat,byprovidingfarmerswithevidencethatpestspropagatedthroughtheircommunitynotastheresultofisolateddecisionsbyindividualsbutratherastheresultofrepeatedinteractionsbetweenmultipleindividualsovertime,ourABMpointedatkeypsychologicalandsocialissues,highlyrelevantforefficientmanagementofinvasivepests(Peshin2008).ABMmaythereforebeapowerfultooltoadvancetheapplicationofsocialpsychologytheorybystakeholdersinruralcommunities( Smith2007)andtochangeindividualattitudes(Jacobson2006).Thissuggeststhatnewapproachesinpestmanagementextensionpracticesshouldincludetopicssuchasgroupdecisionmaking,intergrouprelation,commitment,andpersuasionwhichdealdirectlywithhowotherfarmersinfluenceone'sthoughtsandactions(Mason2007;Urbig2008).Byexamininggroup-andpopulation-levelconsequencesoninvasionprocess,agent-basedmodelingmaythereforerevealsasapowerfulpedagogicalapproachtochangebehaviorsacrosslargepopulations,alonglastingissueinpestmanagementoutreachprogramsworldwide(Feder2004).

Conclusion5.10 Weshowedinthisstudythatagent-basedmodelingmaybeapowerfultooltosimulateinvasivepestspreadinhumandominatedlandscapes.Oursimulationsfurtherrevealedthatboth

farmers'movementsandpestcontrolknowledgecouldsignificantlyimpactinvasionspeedandshouldbeconsideredaskeyvariablestobetterpredictpestinvasiondynamicsinagriculturallandscapes.RegardingtheuseofABMaseducationaltools,wefoundthatnewtechnologies(computers)increasedtheinterestofyoungfarmersinlearningabouthowtobetterfacepestproblems.AlthoughwewouldneedtodesignproperstudiestobetterunderstandthespecificwaysABMfosterslearningprocesses,theintroductionofABMintolearningenvironmentslocatedinremoteplacesmaypromisetoimproveeducationoffarmers,especiallyyoungones.Forexample,ABMcanbeintegratedintointeractivewebsitesorburnedonaCDandbeavailabletofarmercommunitiesinwhichtechnologyaccessincreasesrapidlythankstogovernmentalinitiatives.Inviewofthegrowingthreatmadebyemergentinsectpestsworldwide,especiallyinremoteandpoorlocalities,furthereffortstoincludecost-efficientABMintointegratedpestmanagementprogramsmayrepresentapromisinglineofresearchandapplications.

Appendix1:DescriptionofthecellularautomatonusedtosimulatethepestusingtheODDprotocol

A1.1 ThemodeldescriptionfollowstheODDprotocolfordescribingindividual-andagent-basedmodels(Polhilletal.2008;Grimmetal.2006;Grimm&Railsback2005b)andcellularautomaton(Grimmetal.2006,appendixAp136-147).Notethatinthecaseofcellularautomaton,someofthedesignconceptsoftheODDprotocoldonotapply.ThemodelwasdevelopedusingCORMAS(CIRAD,France,http://cormas.cirad.fr)basedontheVisualWorksprogrammingenvironment(CincomSmalltalk,http://www.cincomsmalltalk.com).

OVERVIEW

Purpose

A2.1 TheSimPolillamodelwasdevelopedtodescribetheinvasionanddiffusionofthepotatotubermoths(PTM)(Teciasolanivora,PhthorimaeaoperculellaandSymmetrischematangolias,Gelechiidae,Lepidoptera),tinymothsthatinvadedtheagriculturallandscapeoftheNorthAndeanregioninthelastdecades.Thelarvaeofthesemothsareseriouspestsofpotatoes,oneofthemainfoodcropsoftheregion.Asecondobjectiveofthemodelwastomakepredictionandgeneratemapsofinvasionriskforlocalfarmercommunities.ThemodelwasdevelopedandvalidatedinapilotregionofcentralEcuadorbutwasbuilttobeapplicabletoamuchwidergeographicrangeinNorthAndes.

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Statevariablesandscales

A2.2 ThemodelisbasedonbiologicalandecologicalrulesderivedfromfieldandlaboratoryexperimentaldataforthethreePTMspecies(Dangles&Carpio2008;Danglesetal.2008;Roux&Baumgärtner1997).TheSimiatugvalley,usedasapilotregiontobuildthemodel,islocatedintheprovinceofBolívar,inthecentralhighlandsofEcuador.Wefocusedonastudyareaof40×

40kmrepresentedbyagridof6,400cellswithacellsizeof0.25km2.Eachcelliischaracterizedbyitsqualityofhabitatnii.e.thequantityoffoodresourcesavailableforthemothlarvae.Weconsiderthatniwasfixedto0or1dependingonthelanduse(i.e.cropsorotherusessuchaswoodsorhighlands).Eachcellisalsocharacterizedbyarangeoftemperaturevalues(meanTmoyi,maximumTmaxiandminimumTminiin°C),amonthlyamountofprecipitationPi;j(inmm),andameanelevationαi(m.a.s.l.).

Table1:FullsetofstatevariablesinSimPolilla

Nameofvariable Units

Habitat Qualityofhabitatofcelli ni

Temperature Averagemeantemperatureover30yearspercelli Tmoyi ºC

Averageminimumtemperatureover30yearspercelli Tmini ºC

Averagemaximumtemperatureover30yearspercelli Tmaxi ºC

Precipitation Averageprecipitationamountover30yearspercelliandpermonthj Pi;j mm

Elevation Elevationonthestudyzonepercelli αi m

PTMspecies Levelofinfestationofjuvenilesdensityofspeciekpercelli(k=1,2,3;T.solanivora,P.operculella,S.tangolias,respectively)

Jk;i Number

Levelofinfestationofadultsdensityofspeciekpercelli(k=1,2,3;T.solanivora,P.operculella,S.tangolias,respectively)

Ak;i Number

Levelofinfestationofgravidfemalesdensityofspeciekpercelli(k=1,2,3;T.solanivora,P.operculella,S.tangolias,respectively)

Gk;i Number

Distancecoveredbyamoth Distancecoveredbyamoth d Meters

A2.3 Thehigher-levelentitiesarebasedonthenumberofgravidfemalesofthethreePTMspecies.EachtimesteprepresentsonePTMgenerationbasedonT.solanivoralifecycleduration(i.e.about3monthsat15°C).AnadjustmentismadeonthetwootherspeciessothateachstepcorrespondstoonePTMgeneration.The500×500mscaleforcellswaschosenforfittingthelevelofprecisionwehaveconcerningPTMdispersion,basedonavailableknowledgeonmothdispersion(Cameronetal.2002b).Temperatures,precipitationsandelevationshavea1per1kmresolution.Insideasquareoffourcells,theseparametershavethesamevalue.

Processoverviewandscheduling

A2.4 Inthissection,webrieflydescribetheprocessesandschedulingofourmodel.Detailsaregiveninthesubmodelssection.Eachprocessispresentedaccordingtoitssequenceproceedingandintheorderatwhichstatevariablesareupdated.EachtimestepisoneT.solanivorageneration.

Table2:ProcessesofSimPolillamodel

Process SubmodelsStatevariablesupdate StatevariablesupdateStochastictemperature StochastictemperatureStochasticrainfall StochasticrainfallPTMmortality Crudemortality

TemperaturedependentmortalityPrecipitationdependentmortality

PTMdispersal NeighbourhooddispersalPTMreproduction Matingrate

SexratioTemperaturedependentfecundity

Process:statevariablesupdate

A2.5 Eachstatevariablecorrespondingtorealdata(AlmanaqueElectrónicodeEcuadorbyAlianzaJatunSacha-CDC,digitisedbyDINAREN,2003;Hijmansetal.2005),isimportedfromindividualfiles(oneperlayer),sothatSimPolillamaybeeasilyadaptedtootherregions.

Process:stochastictemperature

A2.6 Meantemperatureistransformedaccordingtoastochasticfactor(Box&Muller1958).

Process:stochasticrainfall

A2.7 Twoconsecutivemonthlyprecipitationsarerandomlychosenduringagivenstep.

Process:PTMmortality

A2.8 PTMpopulationisupdatedaccordingtocrude,temperatureandprecipitationmortality.

Process:PTMdispersal

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A2.9 PTMdispersethroughtheterritoryfromonecelltoanotherbydiffusion.

Process:PTMreproduction

A2.10 PTMpopulationsareupdatedaccordingtobiologicalrules(matingrate,sexratio,fecundity).AcorrectionismadeoverfitnessonthetwootherPTMspeciestoadjusttimestepbasedonT.solanivoralifecycle.

DESIGNCONCEPTS

A3.1 InSimpolillamodel,moths'implicitobjectiveistoinfesttheconsideredlandscapebymaximizingdispersalspeed.Emergentkeyresultsarelevelofinfestationineachcellandinfestationspeed.Interspecificinteractionsarenottakenintoaccountinthismodelandastochasticfactorovertemperatureandrainfallsareincludedmimicactualclimaticvariation.

DETAILS

Initializationandinput

A4.1 TheenvironmentisbasedontheSimiatugagriculturalregion(Bolivar,centralpartofEcuadorianAndes),withtemperature,precipitationandelevationfromavailabledatawitha1km2

resolution(Hijmansetal.2005).QualityofhabitatisbasedonGISinformationaboutlandusewitha0.25km2resolution(AlmanaqueElectrónicodeEcuadorbyAlianzaJatunSacha-CDC,digitisedbyDINAREN,2003).Thecellularautomatonisa4-connexsquareshapedgrid,withclosedboundariesasweareconsideringanexistinggeographicallocation.Atthebeginningofeachsimulation,PTMinoculumsareplacedintheSimiatugvillageandspreadisobservedandrecordedforeachspecies.

Submodels

A4.2 Inthissectionwedescribethesubmodelsgivenintable2.

ClimaticdriverofPTMdynamic

Temperature

A4.3 Inordertofeedthemodelwithrealclimatevariables,wechosetointroduceastochasticfactorTstochasticinthemodel(seealsoSikderetal.2006)thatallowedustoobtainbymultiplicationastochastictemperatureincelliTStoi .

A4.4 WeusethepolarformoftheBox-Mullertransformation(Box&Muller1958),togenerateaGaussianrandomnumber,basedonclimaticdatafromtheregion(seeDanglesetal.2008,appendixA).RandomnumberusedisbasedonrandomprocedureinVisualWoks(VisualWorks®NonCommercial,7.5ofApril16,2007.Copyright©1999-2007CincomSystems,Inc.AllRightsReserved.).

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Thestochastictemperaturereplacesaveragetemperatureinallequationsbellow.

Precipitation

A4.5 Asfortemperature,wechoosetointroduceastochasticfactortoobtainastochasticprecipitationPStoi.Usingarandomnumberjfrom1to12(VisualWorks®NonCommercial,7.5ofApril16,2007.Copyright©1999-2007CincomSystems,Inc.AllRightsReserved.),wetaketheaverageofthemonthlyamountofprecipitationPi;jcorrespondingtotherandomnumberandthefollowing.

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PTMlifedynamics

A4.6 Dataondevelopmentandsurvivalforimmaturestages(eggs,larva,andpupa)andonfecundityforadultswereacquiredfromtwosources.FirstweusedpublisheddatafromlaboratoryexperimentsperformedintheAndeanregion(Notzetal1995;Danglesetal.2008).Secondweuseddataobtainedwithinthelast8yearsattheEntomologyLaboratoryatthePUCE(Pollet,Barragan&Padilla,unpublisheddata).Forthesetwosources,onlydataacquiredunderconstanttemperatures(±2°C)wereconsidered.Inallstudies,relativehumidityrangedfrom60to90%,valuesaboveanyphysiologicalstress.

Crudemortality

A4.7 Overallforceofmortalityamongapopulationisthesumofcrudecause-specificforces.Hereweconsiderinnatemortality(λi),dispersalrelatedmortality(λd)andpredation(λe)(seeRoux1993;Rouxetal.1997)forP.operculella.

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A4.8 Innatemortalityisnottakenintoaccountusingequation(3),becauseatemperaturedependentparameterfitsbettertorealitythanλi(seebellow).

A4.9 WearealsoconsideringseparatelysurvivalratewithpredationSPredationbybirds,spiders,antsandotherspredatorsfortheadultstagefollowingequation(4)(Tanhuanpääetal.2003).Levelofpredation_iscalesfrom0to10(ie10thelower,0thehigherlevel),inordertosimulatedifferentscenarios,fromtheorytoreality.

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Temperaturedependentmortality

A4.10 Temperatureisthemostbasiccontrollerinpoikilothermicorganisms(Zaslavskietal.1988).SurvivalrateunderlaboratoriesconditionshasbeenstudiedforthethreePTMspecies,usingatemperaturedependentkineticmodel.

A4.11 WeusedthefollowingequationtocalculatethesurvivalrateSDforeachstageateachtemperatureforwhichdatawereavailable:

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withSTthetotalsurvivalatthegivenstage,expressedasaproportion,andDDthedaystodevelopment.FollowingRoux(1993),weappliedtheSharpeandDeMichelmodel(eq.5)tothesurvival-responsetotemperatureasinequation6:

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witha,b,c,d,e,andftheequationparameterstobeestimated.

Table3:Parametervaluesofthekineticmodel(equation7)describingthestagespecificsurvivalrateSD(T)responseofthethreeinvasivePTMspecies(T.solanivora,P.operculella,andS.tangolias)toconstanttemperatures.NotethattemperatureisgiveninKelvindegrees.

Species Instar a b c d e fS.tangolias Egg 0,834 10,94 -234000 282,4 616600 304,1

Larva 0,694 -236,3 -420300 283.1 1551000 305,6Pupa 0,882 39,93 -992700 282,9 1110000 304,7

P.operculella Egg 0,917 50 -200000 283.3 400000 310.1Larva 0,950 -150 -400000 284.4 900000 310.0Pupa 0,960 50 -800000 283.1 700000 312.2

T.solanivora Egg 0,822 -758,5 -212100 281,9 405200 303,8Larva 0,758 -180,2 -475700 282,7 1298000 301,5Pupa 0,900 -73,72 -1263000 286,5 1095000 306,3

A4.12 Fortemperatureshigherthan13°C,P.operculellaimmaturestagesshowedhighersurvivalrates(0.9-1.0)andtolerancetohightemperatures(upto37°C)thanthetwootherspecies.BothT.solanivoraandS.tangoliashadaslightlybettertolerancetolowtemperaturesthanP.operculella.

Precipitationdependentmortality

A4.13 Precipitationsplayaminorbutsignificantroleinmothsurvivalrate(Wakisakaetal.1989;Koborietal.2003).BecauseeachinsectstageisconcernedandbecausenostudieshavebeenconducedonPTM,weuseacorrectingfactoronsurvivalrate.ThisrateisdependentontheamountofprecipitationsinmmovertwomonthsrandomlychosenontheGISdatabase(SICAGRO).Thecorrectingfactorisadjustedfromhypotheticalrelationshipbaseduponavailableknowledge.

Neighborhooddispersal

A4.14 WeconsiderthatthefractionofPTMleavingacellisdependentonadultpopulationdensityandqualityofhabitatniwithinthecell(seealsoBendoretal.2006;BendorandMetcalf2006b;Eizaguirreetal.2004).PTMdonothaveaperceptionoftheenvironmentsituatedinaneighborhoodcell.AccordingtoBendoretal.,weassumethatemigrationrate(ye),followsans-shapedcurve,whichlevelsoutasitapproachesthemaximumdensity(carryingcapacity).DensityisafractionofK,carryingcapacity(0<density<K).

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A4.15 WeassumedthatPTMcantravelupto200mawayfromtheiroriginduringageneration(larvaecanhardlymoveto1mandadults'lifetimeisveryshort).TheprobabilityofaPTMtocoveradefineddistance(yd)isadecreasingfunctionofemigrationrate.ThisfunctionmaycertainlyoverestimatePTMdispersalbutwepreferoverestimationthanbelowestimation(Cameronetal.2002a;2002b).

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A4.16 Asourunitcellis0.25km2,eachmigratingPTM,dependingonitspositiononthesquare,andondistancecoveredd,hasaprobability(yeR)ofcrossingthecellboarder.WeassumethatPTMmoveinsidethecelleitherhorizontallyorvertically.ThisassumptionmaycertainlyoverestimatePTMdispersalbutwepreferoverestimationthanbelowestimation(Cameronetal.2002a;2002b).

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Reproduction

Matingrate

A4.17 Matingrateiscorrelatedwithage,sexratioandweighofindividuals,butalsowithdistancefromoneindividualtoanother(Makeeetal.2001;Cameronetal.2004).Nospecificstudieshavebeenmadeonmatingrateundernaturalconditions,andlaboratorymeasurementsmayfrequentlyrepresentanoverestimationofthenaturalsituationbecauselaboratoryfemaleshavelittleopportunitytoavoidmating(Reinhardtetal.2007).However,asourcellsare500mlong,andthankstofieldobservation,weknowthatpheromonesworksatleastona200mradius,andweassumethatwithinacell,matingrateisequaltoonenomatterthedensity.

Sexratio

A4.18 AmongPTMpopulation,sexratiohasbeenstudiedandis1:1(Saour1999).Afterdispersal,theremainingadultpopulation,combinedwiththematingrateandthesexratiogivethegravidfemalespopulation.

PTMfecundity

A4.19 Althoughenergy-partitioningmodelshavebeendevelopedtoexplaintheshapeofinsectfecundityasafunctionofaging(Kindlmannetal.2001),wearenotawareofanymechanisticmodelsthatdescribesinsectfecundityasafunctionoftemperature.Severalprobabilisticnon-linearmodelstofitinsectfecundityacrosstemperaturehavebeenproposedintheliterature(Roux1993;Lactinetal.1995;KimandLee2003;Bonatoetal.2007),butnoneofthemgaveussignificantresultswithourdata(r<0.35,Fstat<2.01).Wethereforeusedweightedleastsquare(WLS)regressiontofindthebestmodelthatfitsourfecunditydataacrosstemperature.WLSregressionisparticularlyefficienttohandleregressionsituationsinwhichthedatapointsareofvaryingquality,i.e.thestandarddeviationoftherandomerrorsinthedatamaybenotconstantacrossalllevelsoftheexplanatoryvariables,whichcouldbethecase.Forthethreetubermothspecies,thebestfitwasobtainedwiththeWeibulldistributionfunction,whichhaslongbeenrecognizedasusefulfunctiontomodelinsectdevelopment(Wagneretal.1984).

A4.20 TheeffectoftemperatureuponfecunditywaswelldescribedbytheWeibulldistributionfunctions(r2=0.75,0.83,and0.91forT.solanivora,S.tangoliasandP.operculella,respectively).ResultsshowedmarkeddifferencesamongPTMspecies,bothintermsoftotalnumbersofeggslaidperfemalesandoptimalfecunditytemperature:thehighestfecunditywasfoundinT.solanivora,withabout300eggs/femaleat19°C,followedbyS.tangolias(220eggs/femaleat15°C)andP.operculella(140eggsat23°C).

Appendix2:Animations

A5.1 Thefollowinganimationsillustratesimulationsinwhichblueandredfigurinesrepresentsagents,andblueandredlinksagents'movementsfromvillagetovillage.Thenumberinthetoprightcornercorrespondstothenumberoftimeframeandthebackgroundcolortothepestinfestation(black:nopestinfestation;green:pestinfestationduetopurelybiologicaldiffusion;redandblue:pestinfestationduetoaninfestedagentmovement).Attheendofeachanimatedsimulation,theareatotherightremainsuninfected.Thisareacorrespondstohigherelevationswherethepestcannotsurvive.

FigureA-2.Animatedsimulationsshowingtheeffectofagents'movementsonthepestspreadwith2movementspertimeframeand6movementspertimeframe.Thepestinfestationisquickerwhenagentsmovemore.

FigureA-3.Simulationsshowingtheeffectofagents'pestcontrolknowledgewithoutheterogeneityonthepestspreadwithameanpestcontrolknowledgeof0and100.Whenthepestcontrolknowledgeishigh,thepestcanonlydispersethroughdiffusion(i.e.veryslowly),comparedtoasimulationwhenpestcontrolknowledgeislow,wheretheagents'behaviorsleadtoafull

infestationbylongdistancedispersaleventsfromvillagetovillage.

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FigureA-4.Animatedsimulationofthegamesession.ParametersarepresentedinTable1.Thesimulationrantoreachfullinfestationofthelandscapesuitableforthepest.Integratingrealdistributionofpestcontrolknowledge(Normaldistribution),weobservedthatalmostallthelandscapeisinfestedduetolongdistancedispersalevents.Itrevealedtheimportancetofocuson

pestcontrolknowledgereinforcementtoreducetheincidenceofthepestatthelandscapelevel.

Acknowledgements

Wethanktwoanonymousreviewersfortheirhelpfulcommentsonapreviousversionofthiswork.WearegratefultoClaireNicklin,fromtheMcKnightFoundation,forthelinguisticrevisionofthemanuscript.WealsothankCarlosCarpioandMarioHererrafortheirtechnicalsupportandallfarmersinvolvedinthisprocess.ThisstudywaspartoftheresearchconductedwithintheprojectInnovativeApproachesforintegratedPestManagementinchangingAndes(C09-031)fundedbytheMcKnightFoundation.VCPreceivedthefinancialsupportoftheDirectionSoutienetFormationoftheIRDthroughaPh.D.grant(2009-2011).

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AbstractIntroductionStudy systemModelOverall structure of the modelModeling pest dynamics through cellular automataModeling human-related pest dispersion through the agent-based modelAgent process overview and schedulingDesign concepts

Testing the effect of agents' movement and pest control knowledge on pest spread dynamicsEffect of agents' movementsEffect of agent's heterogeneity in pest control knowledge

Teaching with the modelModel introduction to the farmersModel parameterizationPlaying and learning with the agent-based modelModel adoptionBenefits of model-based teaching to farmers

ConclusionAppendix 1: Description of the cellular automaton used to simulate the pest using the ODD protocolOVERVIEWPurposeState variables and scalesProcess overview and schedulingProcess: state variables updateProcess: stochastic temperatureProcess: stochastic rainfallProcess: PTM mortalityProcess: PTM dispersalProcess: PTM reproduction

DESIGN CONCEPTSDETAILSInitialization and inputSubmodelsClimatic driver of PTM dynamicTemperaturePrecipitation

PTM life dynamicsCrude mortalityTemperature dependent mortalityPrecipitation dependent mortalityNeighborhood dispersalReproductionMating rateSex ratioPTM fecundity

Appendix 2: AnimationsAcknowledgementsReferences