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A traits-based model of species diversity

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A traits-based model of species diversity
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  EcologicalModelling288(2014)178–194 ContentslistsavailableatScienceDirect Ecological   Modelling  j   ournalhomepage:www.elsevier.com/locate/ecolmodel A   traits-based   model   of    species   diversity Robert   H.   Gardner ∗ ,Katharina   A.M.   Engelhardt,   Andrew    J.Elmore,   Dan   Cadol  AppalachianLaboratory,UniversityofMarylandCenterfor    EnvironmentalScience,Frostburg,MD21532,USA a   rti   c   le   i   nf   o  Articlehistory: Received6March2014Receivedinrevisedform4June2014Accepted10June2014 Keywords: MarshcommunitydevelopmentBiodiversitySpeciesrichnessSpatialmodelsLife-historytraitsTrade-offs a   b   s   t   ra   ct Modelswhich   usespecies-specifictrade-offs   of    life-historytraits   have   been   widely   usedtosimulate   sta-ble,   diverse   communities   of    sessile   organisms.   However,   the   preciseestimation   of    trade-off    parametersrequired   by   manymodelscannot   be   easily   realized   for   multiplespecies   livingwithin   rapidly   changingenvironments.   Wedeveloped   aspatially-explicit   model,   MCAP,   that   uses   empirically   estimated   param-eters   todefine   species-specific   life-history   functions.This   approachdidnotrequire   trade-offs   tobeexplicitlystated,   but   rather   intrinsicallyrepresented   trade-offs   withinthe   datastructure   defining   eachspecieslife-history   functions   (e.g.,age   or   size   dependent   changesinreproduction,   dispersal,establish-ment,   mortality   andgrowth).Theuseof    species-specificfunctionswith   empirically   estimated   parametersallowed   eachspecies   to   be   uniquelycharacterizedwith   subsequentestimationof    model   sensitivities   duetochanging   functional   forms   or   parametererrors.   Empirical   data   wasobtained   from   fieldobservationsand   experiments   for   16species   within   tidal   freshwater   marshcommunities   of    the   Chesapeake   Bay.   Modelresults   compared   with   these   data   showed   that   MCAP   realistically   represented   processesstructuring   thesetidal   marshcommunities.   Model   experiments   varying   weatherand   the   rangeof    habitatconditions   acces-sibleto   each   species   showed   that   patternsof    abundance   anddiversity   were   mostaffected   by   local   habitatconditions   and   neighborhood   interactions   among   competing   species.Thesimulation   approachusedinMCAP   waseffective   and   efficient,providing   acomprehensive   tool   forassessing   the   simultaneous   effectsof    changing   environmental   driversandspeciescomposition   onthe   persistenceandbiodiversity   of    marshcommunities.©   2014   Publishedby   ElsevierB.V. 1.Introduction Ecologistshavelongbeeninterestedinexplainingdriversof biodiversity,asking‘Howmanyspeciescananecosystemsupportandwhy?’(Hutchinson,1959;Rosenzweig,1995),‘Whatdrives therateofspeciesturn-overin   spaceandtime?’(Cowles,1899;Myersetal.,2013),and‘Inwhatwaysdoesbiodiversityaffectthefunctioningandstabilityofecosystems?’(TilmanandDowning,1994;Cardinaleetal.,2012).Ongoingandpredictedglobalchangeisnowaddingurgencytothesequestions,callingforintegrativeapproachesthatforecasttheresponseof    communitiesandecosys-temstorapidlychanging,non-equilibriumenvironments(Webbetal.,2010).Thisparadigmshiftwillrequirea   newfocusontraits-basedapproaches(Kattgeetal.,   2011)that   canaccountfordynamicinteractionsamongspecieswithinchangingenvironments.Traits-basedapproachesmakeuseofunique,measureableattributesof organisms(McGilletal.,   2006),suchaslifehistory,morphologyandphysiology,topredictwhetherandhowspecies,populations, ∗  Correspondingauthor.Tel.:+13016897125;fax:+13016897200. E-mail   addresses: rhgardner@gmail.com,rgardner@umces.edu(R.H.Gardner). communitiesandecosystemsassemble,persistandadaptto   chang-ing   environmentalconditions(Webbetal.,   2010).Whileevolutionaryprocessesworktowardsmaximizingfitness(Haldane,1932),theycannotmaximizeallaspectsof    fitnesssimul-taneously(Law,1979),resultingintrade-offsamongattributes(TilmanandPacala,1993;Ben-Huretal.,2012).Theoreticalmod-elsshowthatthesetrade-offscanaloneproducestablecommunityassociations(Dislichetal.,2010).Simplemodelshavebeenexten-sivelystudied(LevinsandCulver,1971;NeeandMay,1992;Tilman,1994;Calcagnoetal.,   2006;PillaiandGuichard,2012)andevenshowcoexistencewithinhomogeneouslandscapes(Nattrassetal.,2012).Therelevanceof    theseresultsto   naturalcommuni-tiesdependsontheempiricalverificationwithinrealassemblages.However,criticalparametersformostsystemshavebeendiffi-culttoquantify(LevineandRees,2002)withrequiredlevelsof precisionbeyondwhatmay   bereasonablyachieved(Clark,2010).Thevariablenatureof    landscapehistoriesalsocausesmeasur-ableeffectsto   shiftinspaceandtimeaddingsignificantlytodatauncertainties(Burtonetal.,2010;Dziocketal.,2011;Rypeletal.,2012).Consequently,resultstodatehaveprovidedonlyweakandinconsistentconfirmationof    intraspecifictrade-offs( JakobssonandEriksson,2003),andthereforequestionthegeneralutilityof    precise http://dx.doi.org/10.1016/j.ecolmodel.2014.06.0060304-3800/©2014PublishedbyElsevierB.V.  R.H.Gardneretal./EcologicalModelling288(2014)178–194 179 trade-offsingeneratingstablepatternsof    coexistence(Limbergerand   Wickham,2011;ParrandGibb,2012).We   hypothesizethattheneedforfunctionaltrade-offs,suchasthefamiliardispersal-colonizationtrade-offs(e.g.,Ben-Huretal.,2012;PillaiandGuichard,2012),canberelaxedwhenmultipletraitsandspatialdynamicswithinheterogeneouslandscapesareconsidered(HigginsandCain,2002;Potthoffetal.,   2006;Buechietal.,2009;Dislichetal.,2010;Seifanetal.,   2012,2013).Eco-logicalprocessesthatmaintaindiversityforsessileorganismsareinherentlyspatial(GardnerandEngelhardt,2008):habitatsarespa- tiallycorrelated;competitionforresourcesis   mostintenseamongimmediateneighbors;dispersalisspatiallylimited;andmostdis-turbancesare   spatiallydiscreet,aggregatedevents.Consequently,spatialdynamicsresultinlocalaggregationsof    similarindividuals,whichhastheeffectofdecreasinglocal,inter-specificcompetitiveeffects(HartandMarshall,2009).Trade-offsremaingloballyimpor- tantbuttheirexactformulationandestimationmay   notberequiredwithinaspatiallydynamicframework(KneitelandChase,2004). Wedevelopedthetraits-based,spatially-explicitmodelMCAP(MarshCommunityAssemblyProgram)toallowcomparisonof spatialprocessesthat   structurecommunities,includingnichedifferences,habitatheterogeneity,discretedisturbances,andtem-porallyvariableenvironments.Mostspatialmodelshave,bynecessity,consideredonlya   fewspecies,a   fewspeciestraits,orfewprocesses,andmosttheoreticalmodelsarenot   parameterizedorvalidatedwithempiricaldata.InMCAP,wehavecombinedmanytraits,processesandscenariosusingasour   modelsystemforanexistingtidalfreshwatermarsh.Life-historyattributesandmodelparametershavebeenderivedfromongoingdatacollectionwithmodelpredictionsofplantcommunitystructurecomparedtofieldmeasurements.MCAPsimulatesthecommunitydynamicsofa   tidalfreshwa-termarshcommunitywith16specieslocatedin   themid-AtlanticregionoftheU.S.A.Thesespeciesvarywidelyin   theirlifehis-torytraitsincludinglongevity,size,reproductivemodeandoutput,dispersalmodeanddistancesmoved.Becausespeciesrichnessof thesemarsheswastractable,theentiresuiteofspeciesformingamarshplantcommunitywassimulatedandcomparedwithpat-ternsandprocessesobservedin   thefield.Elevationisadominantenvironmentalgradientaffectingplantestablishmentandpersis-tence(Woltersetal.,   2009)   andwasestimatedforMCAPusingremotesensingandgroundsurveys.Theelevationofmarshescon-stantlyshiftsthroughtime   duetosealevelriseandshort-termweathereventscausingerosionand/orsedimentationaswellastheaccumulationoforganicmatterwithtime(Redfield,1972;Kirwan etal.,2010).Plantsrespondto   thisshiftingelevationlandscapethroughchangesinbiomass,clonalspreadinperennials,germi-nationofannuals,andseedproduction(PetersonandBaldwin,2004).Thesecharacteristicsofmarshessuggesttheyareanidealsystemtobothparameterizeandtesttheoutcomesofatrait-basedmodelofspeciesdiversity.Wepresentherethemodelstructureandsolutionmethods,evaluatethesensitivityofresultsto   changingfunctionsandparameters,andthenassesstheeffectsofland-scapepatternandchangingenvironmentalconditionsonpatternsof    speciesabundanceandpersistence. 2.Methods TheMCAPmodeldynamicallysimulateschangesinmarshele-vation,temporalchangesinweatherandspeciespresenceandabundanceofthemarshplantcommunity(Fig.1).Flexiblefunc-tionsareusedto   describespecies-specificplantlifehistorytraitswhichgoverndispersal,fecundity,mortalityandestablishment.Eachfunctionhasbeendesignedto   beadaptableto   divergentlifehistories,tobeeasilyparameterizedfromempiricalinformation, Fig.1.   Outlineofcommunitymodelsolutionsequence. andtobeefficientlysolvedforrapidsolutionof    spatialdynamics.Theseobjectivesareaccomplishedbypre-solvingeachlife-historyfunctionandthenusingtable-lookupsto   determinethetemporalandspatialdynamicsof    eachgridcell.  2.1.Environmentaldrivers 2.1.1.Elevation Tidalmarshesaregeomorphiclandscapes(MyrickandLeopold,1963;Redfield,1972;PasternackandBrush,1998),   whichrespondto   fluctuationsinlocalsealevelovergeologictimethroughcom-plexfeedbacksthatdecreaserelativemarshsurfaceelevation(e.g.,decomposition,erosion,andsubsidence)or   increaserelativeeleva-tion(e.g.,biomassproduction,andsedimentinputs).Theelevationlandscapeofthemodelmarshwas   initializedwithaLightDetectionandRanging(LiDAR)baseddigitalelevationmodel(DEM)surveyedin2008.TheaccuracyofLiDARsurveysmaybeaffectedwhendensebiomassobstructsthemarshsurface(Wangetal.,2009), thereforeforeachgridcellthelowestLiDARreturnwasusedastheelevationforthatmarshsite.To   increaseaccuracy,we   con-ductedaRealTimeKinematic(RTK)GPSsurveyof    themarshin2012andusedthesedatato   establishtheelevationuncertaintyof    theLidar-basedelevation.DEMelevationswere8cmhigheronaveragethantheRTKmeasurementsowingtostandinglittercreatingfalsegroundreturns,withthemagnitudeof    thepositivebiasincreasingathighermarshelevations.Thisinaccuracy,thoughsmall,increasedtheavailabilityof    highmarshhabitat.Relativesur-faceelevationwas   updatedyearlybychangingtheelevationvalueof    eachgridcelltoaccountforthegeomorphicprocessesof    sedi-mentaccretionanderosion,andbydecreasingthevaluetoaccountforsealevelrise.Netaccretionrateasa   functionof    elevationrela-tivetosealevelwasestimatedfromrepeatsurveydataandSurfaceElevationTables(SETs)(Cahoonetal.,2002).Morrisetal.(2002) foundthattheelevation–accretionrelationshipcanbedescribedbya   cubicfunction,sosuchafunctionwas   fit   to   thefielddataandusedtorepresentannualsedimentationin   themodel.  180 R.H.Gardneretal./    EcologicalModelling288(2014)178–194  Table1 Functionsandparametersusedtodefinespecies-specificlife-historytraits.VariablenameNumericaltypePurposeFO/NV a id IntegerIdentificationnumber(usedasindex)1–100 name   Character(4)Characteridentifier(passive)‘speciesname’  f  ( C  )   Character(1)Function:definesprobabilityof    clonalspreadwithsize(m)   { F,L,T }  f  ( G )   Character(1)Function:defineschangeinplantheightwithage(m) { F,R,M }  f  ( K  )   Character(1)Function:definesthedispersalkernel { E,D,W }  f  ( M  )   Character(1)Function:defineschangeinmortalitywithage { C,S,E }  f  ( O )   Character(1)Function:definesestablishmentandgrowthresponsetoelevation { N,M,   W }  f(R)   Character(1)Function:defineschangeinfecunditywithage  { F,M,   L  }  A   IntegerParameter:maximumachievableage(y)1– ∼ 100 H    RealParameter:Maximumachievableheight(m)   0.1–large C    RealParameter:maximumprobabilityof    clonalspread0.0–1.0 R   RealParameter:maximumfecundity(totalnumberof    viableseeds)0.0–verylarge O   RealParameter:elevationformaximalgrowth(th)0.0–200  x   RealParameter:meandispersaldistance(pixelunits)for  f  ( K  )options { D,E } . 1– ∼ 25     RealParameter:dispersallimit(pixelunits)for  f  ( K  )   options { D,E }   1–large  g    RealParameter:proportionof  H  requiredforreproductionfor  f(R) options { M,L  } 0.5 s   RealParameter:functionshapefor  f  ( M  )option { [ { S } 0.01    RealParameter:exponentialdeclinefor  f  ( M  )option { E }  0.01  RealParameter:Meanseedterminalvelocity(m/s)for  f  ( K  )option { W }   Empiricallyestimated     RealParameter:standarddeviationof    seedterminalvelocity(m/s)for  f  ( K  )option { W } Empiricallyestimated ı   RealParameter:upperlimitof    seedsdensitieswithinlocal   seedlottery0.0–1.0    RealParameter:proportionofseedsgerminatingwhenlitteraccumulatesfollowingwinddisturbances0.0–1.0 a Functionsareindicatedby   theintegralsign(e.g.  f  ( K  )forthedispersalfunction);functionoptionsareincurlybrackets(e.g. { E } forexponentialdispersalkernelin  f  ( K  ));function   limitsarecapital,italic(e.g.,  A formaximalage);andspecies-specificparametersthat   areoption-dependentarelower-casesymbols(e.g., ı upperlimitonseeddensities.  2.1.2.Weather  Annualweatherconditionsmay   beusedtodeterminetheprob-abilityofgerminationandsubsequentestablishmentof    plantsinthespringandsummer.Datalinkingweatherto   these   probabilitiesarenotcurrentlyavailable.Therefore,weusedtwovectors, W  1, t  and W  2, t  ,torepresentprobabilitiesofgerminationandgrowthtoexaminepotentialweathereffectsonplantdynamics.Valuesfor W  1, t   weredistributedbetween0.0and1.0,definingtheprobabil-ityofgerminationindependentlyforeachgridcellbycomparisonwithauniformrandomnumber.Insimilarfashionestablishmentandtherateofplantgrowthwasseparatelydeterminedbyprob-abilitiesinthevector W  2, t   (seedetailsbelow).Optimalconditionsoccurredwhenvaluesof    W  =   1.0.Modelexperimentswithdifferentweatherconditionscanbe   formulatedbyvaryingthemeanandstandarddeviationof    W  andthetemporalcorrelationsbetweenspringandsummerweather, W  1, t   and W  2, t  .   Ideallyvaluesfor W  shouldbeestimateddirectlyfromweatherrecordsasa   percentiledeviationfromconditionswhichproduceoptimalgerminationandgrowthconditions.  2.2.Communitymodel Thesimulationof    communitydynamicsof    MCAPwerebasedonthespatially-explicitmodelCAPS(PlotnickandGardner,2002;GardnerandEngelhardt,2008;MinorandGardner,2011)withanumberofkeyextensions.MCAPisafine-grained,spatialmodelwiththeprobabilityof    plantestablishmentafunctionof    fecundity,seeddispersalandclonalgrowth,habitatsuitability,neighborhoodcompetition,weather,disturbancesandage-specificratesof    mor-tality.UnlikeCAPS,MCAPusesa   detailedspecificationof    speciestraitsandspeciesinteractionstodeterminethebiologicalproper-tiesofacommunityastheychangeintimeandspace.ThesolutionschemeforMCAPis   outlinedinFig.1.   Eachyear,every0.2mgridcellwasexaminedforplantoccupancy.If    thesitewasoccupied,mortalitywassimulatedasafunctionofage(seedetailsbelow).Iftheplantsurvived,itwasallowedto   growasafunctionofplantage,weather,andhabitat.Competitionforestab-lishmentatvacantsites(gridcells)wasperformedasafunctionof propagulenumbers(seebelow).Iftheweatherwas   conducivetogermination,newplantswereestablished.However,ifsub-optimalspringweatherconditionsoccurredthatdidnotallowgermina-tion,a   clonallotteryfrom8neighborswas   performedandinvadingclonalrametswereallowedtogrow.Thespecies-specificlife-historyfunctionsandparametersaredefinedin   Table1andvariablesforprogramcontrolin   Table2.Thevaluesformodelparametervaluesforthe16speciessimu-latedaregiveninTable3.We   nextprovidedetailsregardingeachof    thedynamiclife-historyfunctionsin   MCAP,includingspecieslife-historytraitsof    growth  f  ( G ),clonalspread  f  ( C  ),reproductivepotential  f  ( R ),mortality  f  ( M  )   habitatoptima  f  ( O )anddispersal  f  ( K  ).Eachfunctionmay   takeondifferentformsdependingonthenatureof    eachspecieslife   historyattribute.Noneofthefunctionsrequiredataonthespeciesabundanceorlife-historytraitsofotherspecies. Fig.2. Age-dependentprobabilityofmortalityfortheasymptotic { S } andexpo-nentially   declining { E }   optionsof     f  ( M  ) . Theshapeof    theexponentialfunctionwascontrolledby   theparameter   whiletheshapeoftheasymptoticfunctionwascon-trolled   by   the   parameter s (Table2) .  R.H.Gardneretal./EcologicalModelling288(2014)178–194 181  Table   2 Variablesforprogramcontrol.ParameterTypePurposeSimulationcontroliseedIntegerRandomnumberseed(negative)nrepIntegerNumberof    replicationssimlenIntegerLengthof    thesimulationinyearsSpeciescharacteristics a spparmfile.csvCharacterDefaultparameterinputfile(readsnumberofspeciesfromthe   numberof rowsof    parameters)asgiveninTable1.Map   characteristicsmaptypeCharacterFilenamemapnameCharacterInputmap   nameirow,jcolIntegerMap   size–   rowsandcolumnsmin elevation RealMinimumelevationforplantgrowth(m)max   elevationRealMaximumelevationforplantgrowth(m)MainlandspeciesalphaRealAvaluebetween0.0and1.0forPearsonlognormalabundancesonmainlanddistanceRealValuebetween0.0(infinitelyfar)and1.0   (verynear)forrelativedistance.Speciesinitializationinitializationtype   Character r  =randomlocationsWeatherdescriptorsweatherRealSpringandsummerweatherrepresentedasa   valuebetween0.0and1.0representingdegreeofoptimalconditions.Disturbanceparameters w RealThresholdsizeof    plantssubjecttoblow-down(m) a ,   b  Real   Majorandminoraxesof    blow-downellipse(m)    RealPoissonmeanforthenumberofblow-downeventsper   year. a DatasetdescriptionforspeciescharacteristicsfoundinTable1. Therefore,eachuniquelyrespondstolocalcompetitionandchang-ingenvironmentalconditions.  2.2.1.Mortality Theprobabilityof    naturalmortality, m i ,   forspecies i wasdeter-minedannuallyforeachplantateachgridcellbythefunction  f  ( M  )(Table1).Theoptionsforthemortalityfunction(denotedbycurlybrackets)wereeitherconstantwithage { C } ,asigmoidformwithage { S } ,orexponentiallydecliningwithage { E } (Fig.2).Theexponentialoptionwasdefinedas m i  = e a i whilethesigmoidoptionwasdefinedas m i  = a 0 . 5 i  e sa i where a i  iscurrentageforspecies i .   Options { C } and { S } weretheonlytwomortalityoptionsusedforthe16marshspeciessimula-tionswith s   =0.01(Table3).Theparameterforexponentialdecline,   ,wasusedinsensitivitytests(   =   0.01).Mortalityeventswereindependentlydeterminedforeachgridcellandyearbycompar-ingthevalueof    m i  foreachgridcelleachyeartoa   uniformrandomnumber( urn )   withdeathoccurringif  urn < m i  ortheagelimit,  A i ,wasreachedforspecies i .  2.2.2.Growth Species-specificgrowthratesweredeterminedbythemaximalpotentialgrowthin   plantheight, h i ,asdeterminedby  f  ( G ).Thisfunctiongenerateda   realizedgrowthrate, h i  ,forspecies i ateachgridcellandyearasafunctionof    summerweather, W  2, t  ,   andlocalhabitatconditions, o i .Thefunctionoptionsfor  f  ( G )wereeither:instantaneous { F } to   maximumheight, H  i  (e.g.,annualplants);rapidgrowth { R  } potentiallyreaching H  i  in2years( h i = H  i /2);ormoderategrowth { M } reachingmaximumheightunderoptimalconditionsin4years( h i = H  i /4).Theyearlyrealizedgrowth( h i  )   of eachspecies i ateachlocation  j   isthus: h i  =h i × W  2, t  × o i ,   where o i  istheestimatinghabitatoptimaatlocation  j   determinedby  f  ( O )describedbelow.Thepotentialinteractiveeffectsofweatherandsup-optimalhabitatconditionsmay   preventindividualsfromreachingreproductivematurity(e.g., W   2,t  × o i =0.25)beforemaxi-mum   age,  A i ,occurs.  2.2.3.Reproduction Themaximumreproductivepotentialforeachspecies, R i (Table1),is   anidealnumberrepresentingthemaximumnumberofviableseedsthatcouldbeproducedandsubsequentlydispersed.Thisprocessresultsin   anewindividualof    species i ata   givengridcell(i.e.,onlyviableseedsaresimulated).Therealizedlevelof fecundity, r  i ,variesforeachspeciesdependingonmaturationas  Table3 Parametervaluesforspeciesusedinthemarshcommunitysimulations.ThevariablesaredefinedaregiveninTable1.IdName  f  ( C  )  f  ( G )  f  ( K  )  f  ( M  )  f  ( O )  f  ( R )  AH    CROg    1ACCA(Acoruscalamus)TRE   SMM751.581.00.02.600.75nana2   AMCA(Amaranthuscannabinus)CRWCNL11.550.01401.340.41.7930.083   BILA( Bidenslaevis )CRWCWL11.80.01501.580.51.8150.0544   HIMO(Hibiscusmoscheotus)LMWSNM101.520.5   501.940.33.3680.1765   IMCA(Impatienscapnesis)CRWCWM11.570.07002.180.203.1490.0736   IRVE(Irisverticillata)LRWSMM251.221.0102.360.65.00.27   LEOR(Leersiaoryzoides)CFWCMM21.520.6   3501.820.32.120.0628   NULU(Nupharlutea)LFE   SNM51.20.4   100.800.90nana9   PEVI( Peltandravirginica )LRDCMM61.420.6   1001.700.40nana10   POAR(Polyganumarifolium)CMWCNF12.930.01501.460.42.9260.11411POCO(Pontedariacordata)LME   SNM251.551.011.100.2nana12SALA(Sagittarialatifolia)LMWCNM31.0   0.0501.220.21.3330.04813SCFL( Schoenoplectusfluviatilis TFWSMM202.21.01252.480.32.7160.32614SPEU(Sparganiumeurycarpum)CFWCMM21.490.6   3502.060.32.50.115TYAN( Typhaangustifolia )TRWSWM102.741.075   2.750.601.1230.3416ZIAQ(  Zizaniaaquatica )CRWCNM12.960.01500.950.52.0180.121  182 R.H.Gardneretal./    EcologicalModelling288(2014)178–194 specifiedby  f  ( R )(Table1).Theoptionswere:instantmaturation(annualplants)withconstantvaluesof    r  i  forallplantheights { C } ;linearlyincreasing r  i  withheight { L  } ;ora   step-functionresponse { M } were r  i = R i  oncea   criticalplantsizehasbeenreachedasdeter-minedby  g  i × H  i .  2.2.4.Dispersal Patternsofseeddispersalmay   varywidelyamongspecies.ThereareseveraldispersaloptionsimplementedinMCAPvia   thedis-persalfunction  f  ( K  )(Table1).   Weused3dispersalkernelsforsimulationsreportedhere:Winddispersal { W }   withvariabledis-tancesdependentonplantheight,windspeedandcanopystructure(seedetailsbelow);oroptions { E } and { D } whichwereheight-independentempiricalfunctionsusingtheexponentialandinversedistancedispersalformulations,respectively.Options { E } and { D } aremostsuitableforsmaller,annualplantslackingwind-dispersedseeds.Thesetwo   height-independentdispersalkernelsrequiretwoparameters:  x ,themeandispersaldistanceand   ,   themaximumdispersaldistance(bothin   gridcellunitsof    0.2m,   Table1).Thewinddispersalalgorithmis   basedon   a   2-DballisticmodeldevelopedbyNathanetal.(2001)asimplementedbyStephenson etal.(2007).We   modifiedthismethodtoincludetheturbulenceeffectsofleafareaasestimatedbyRaupach(1994).   Thecompu-tationalexpenseof    simulatingthefateofeachseeddispersedbywindwasreducedtomanageablelevelsbyestimatingspatially-dependentdispersalprobabilitiesusingMonteCarlomethods.BeforeMCAPsimulationsbegan,250,000estimatesof    dispersaldis-tanceswereperformedusingthewinddispersalalgorithm, WSD ,for10classesofplantheight, q  j ,overtheintervals  gH  i  to   H  i .Thewinddispersalalgorithmforeachlevelof    q  j  was: WSD   = 0 . 3 U  (0 . 4 v  )  ×  ( q  j − d ) × ln  ( q  j −   d )( e 1  z  o )  +  z  o  where U  ismaximumsustainedwindspeed(m/s)duringdis-persaleventsandwasnormallydistributedwithmeanof6.0andstandarddeviationof9.0; q  j  isplantheightclass(  j ),  j   =   1,10; LA =leaf area,normallyvariedfromglobalestimatesformarshcommunities(Scurlocketal.,2001)withmeanof    6.34andstandarddeviationof 2.29; v  istheverticalvelocity(m/s)of    fallingseeds,normallyvariedwithmeanandstandarddeviationestimatedfromdata(Table3)(Caplatetal.,2012).Thevaluesusedforwindspeedweregreaterthanmeasureddailyaverages(mean0.9m/s,standarddeviation1.1m/s)butareintendedtorepresentcharacteristicwindsduringdispersalevents.Thevariables  z  o and d   aresurfaceroughnesslengthandzero-planedisplacement,respectively,representingsurfaceturbulenceeffects.Eqs.(4)and(8)of    Raupach(1994)give  z  o  =  1 . 0 − dH  i  × e − 1 . 1403 d =  1 . 0 −  (1 . 0 − e −√  7 . 5 × LA ) √  7 . 5 × LA  × H  i Eachsolutionof    WSD   isperformedbyrandomlyvarying U  , LA and v  (normallydistributedwithmeansandstandarddeviationsaslistedabove)andthenestimatingthedispersaldistanceforasingleseed.The1-dimensionalMonteCarlorealizationsof  WSD (N=250,000)weredistributedovera   2-dimensionalsurfacebyselectingarandomangleovertheinterval0.0–2  foreachdispersalevent.Acumulativeprobabilitydistribution, cdf  ,wasthenformedbysummationandnormalizationtoobtaintheprobabilityof    a   seedbeingdispersedfromtheparentplantto   eachneighborhoodgridcell.Duringsubsequentsimulationofcommunitydynamicsthis cdf  ,whichsummarizesvariationin   windandcanopyheight,providedtheprobabilityofdispersalforwinddispersedseedswithouttheneedtoregeneratewinddispersalevents.  2.2.5.Habitat  Therangeofelevationsthatsupportplantgrowthforeachspeciesweredescribedbythehabitatfunction  f  ( O ),withtheopti-mumelevationforgrowthspecifiedby O i  (Table1).Site-specificprobabilitiesofestablishment, o i ,weregeneratedby  f  ( O )foreachspeciesasa   functionof    marshelevation.Valuesof    o i  werethenusedtomodifytheprobabilityofestablishmentintheseedlot-tery(seedescriptionbelow).Threeoptionswereavailablewithin  f  ( O ),allgeneratedfromthenormaldistribution:Anarrowrangeof    suitableelevations { N } havinga   coefficientofvariation(CV)of 5%; { M } a   moderaterangewitha   CVof    10%;orawiderange { W } witha   CV=   25%.Fig.3(solidline)illustratesthenormalizedhabi-tatsuitabilityforeachspecieswithconsiderableoverlapamonghigh-marshspecies(e.g.,TYANandACCA),mid-marsh(e.g.,PEVIandSPEU)andlow-marshspecies(e.g.,NULU,ZIAQ).Eachdis-tributionwasnormalizedsothatthemostoptimalelevationforeachspecies(inputparameter O i )   hadaprobabilityof    occupancy( o i )of1.0.Thenormaldistributionhasinfinitetailssovaluesof  o i <0.0001or   o i >0.9999weresetto   zerotopreventcompleteoccu-pancyacrossallhabitatelevationsfora   givenspeciesintheabsenceofcompetition.  2.2.6.Competitionfor    establishment  Successfulseedgerminationwas   independentlydeterminedateachgridcellbya2-stepprocess.Foreachyear t  ,thespringweathervalue W  1, t   setstheprobabilityforseedgerminationandestab-lishmentforthatyear.At   eachemptygridcellauniformrandomnumber( urn )   was   selectedandif    urn <   W 1, t  ,seedgerminationatthatgridcellwouldoccur.CompetitionforplantestablishmentthencommencedusingtheseedlotterymethodsasdescribedbyLavoreletal.(1994)andPlotnickandGardner(2002)and implementedinCAPS(GardnerandEngelhardt,2008).Seedswereaccumulatedfromneighboringgridcellsoccupiedbyreproduc-tivelymatureindividuals.Severaladjustmentstothenumberof viableseedsparticipatinginthelotteryforestablishmentwereper-formedincluding:Additionof    seedsduetolong-distancedispersal(i.e.,a   seedbath)simulatedbymultiplyingmap-wideabundanceforeachspecies i by R i ×   0.002;densitydependenteffectsreducingseednumbers(describedin   thenextparagraph);andadjustmentsintheprobabilityofestablishmentforeachspeciesasafunctionofspecies-specifichabitatoptima, o i ,forthatgridcellelevation.Thewinneroftheseedlotterywasthenrandomlydetermined,thespeciesidentificationnumber id forthatlocationwas   settothewinningspeciesnumber,theageandheightclasssetto   1,andthepropagulesourcewassetto‘s’.Densitydependenteffectsaredominantdriversof    commu-nitydynamicsinmarshes(BertnessandYeh,1994).Forexample,higherdensityof    plantsincreasescompetitionforlight,whichdecreasesthesurvivalof    seedlings(Proffittetal.,2005;Kulletal.,2011).Higherproductivitymayalsoincreaseplantlittercoverthatmulchesthesoilsurface,interferingwithgerminationandseedlingsurvival(FarrerandGoldberg,2009)orenhancingrecruitmentthroughcaptureof    seeds(LambrinosandBando,2008)   andnutrientamendments(Meisneretal.,2012).MCAPonlyconsiderednegativedensitydependenceintheformof    competitionforestablishmentalthoughothereffects,includingfacilitation,couldbeincluded.Densitydependentestablishmenteffectswererepresentedwithineachgridcellusingasimple,singleparameterderivedfromthefamiliarMichaelis–Mentonfunction: S  i  =  ı i R i  S i  ı i R i  − 1 + S i  ,
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