a host–parasite model explains variation in liana infestation...

Journal of Ecology 20181062435ndash2445 wileyonlinelibrarycomjournaljecemsp|emsp2435

Received8December2017emsp |emsp Accepted26March2018DOI 1011111365-274512997

R E S E A R C H A R T I C L E

A hostndashparasite model explains variation in liana infestation among co- occurring tree species

Marco D Visser123 emsp|emspHelene C Muller-Landau3 emsp|emspStefan A Schnitzer4emsp|emsp Hans de Kroon2 emsp|emspEelke Jongejans2 emsp|emspS Joseph Wright3

1DepartmentofEcologyandEvolutionaryBiologyPrincetonUniversityPrincetonNewJersey2DepartmentsofExperimentalPlantEcologyandAnimalEcologyampPhysiologyRadboudUniversityNijmegentheNetherlands3SmithsonianTropicalResearchInstituteBalboaRepublicofPanama4DepartmentofBiologicalSciencesMarquetteUniversityMilwaukeeWisconsin

CorrespondenceMarcoDVisserDepartmentofEcologyandEvolutionaryBiologyPrincetonUniversityPrincetonNJEmailmarcodvissergmailcom

Funding informationNederlandseOrganisatievoorWetenschappelijkOnderzoekGrantAwardNumberNWO-ALW801-01-009DivisionofEnvironmentalBiologyGrantAwardNumberDEB0453665DEB0453445DEB0613666DEB0845071DEB1019436andDEB1558093

HandlingEditorDavidGibson

Abstract1 Lianasarestructuralparasitesoftreesthatreducethegrowthsurvivalandrepro-ductionoftheirhostsGiventhatco-occurringtreespeciesdifferstronglyintheproportionofindividualsthatareinfestedbylianas(lianaprevalence)lianascoulddifferentiallyimpacttreespeciesandtherebyinfluencetreecommunitycomposi-tionSurprisinglylittleisknownaboutwhatgovernsvariationinlianaprevalence

2 Hereweapplyanapproachinspiredbydiseaseecologytoinvestigatethedynam-icsoflianaprevalenceover11yearsonBarroColoradoIslandPanamaWefol-lowedthefateof1938 individualtreesfrom21treespecies recordingdeathsand change in liana infestation statusWith these datawe fit species-specificMarkovchainmodelstoestimatefourratescolonizationbylianas(analogoustodisease transmission) shedding or loss of lianas (analogous to host recovery)baselinemortalityofuninfestedtrees(baselinemortality)andadditionalmortalityofinfestedtrees(parasitelethality)

3 Modelsexplained58ofvariation in lianaprevalenceamongtreespeciesandrevealedthathostsheddingoflianasandparasitelethalitywerethemostimpor-tantcontributorsto interspecificvariationin lianaprevalenceatoursiteTheserateswerealsostronglyrelatedtoshadetolerancewithlight-demandingspecieshavinggreaterratesofsheddingandlethalityandlowerratesoflianaprevalenceAn indirect path analysis with a structural equationmodel revealed that bothgreaterratesof lianasheddingandliana-inducedlethalitycontributetotheob-servedlowerratesoflianaprevalenceforlight-demandingtreespecies

4 SynthesisOurapproachrevealedthattheprevalenceoflianainfestationamongtreespeciesisdrivenviaindirectpathwaysoperatingontheratesofsheddingandlethalitywhichrelatetotheability(orinability)oftreestoshedandortoleratelia-nasShade-toleranttreeshavegreaterproportionsoftreesinfestedbylianasbe-causetheyarebothlessabletoshedlianasandmoreabletotolerateinfestation

K E Y W O R D S

climbersgeneralistparasiteshostndashparasiteinteractionslianaprevalenceshadetolerancesusceptiblendashinfectedmodel

ThisarticlehasbeencontributedtobyUSGovernmentemployeesandtheirworkisinthepublicdomainintheUSA

copy2018TheAuthorsJournal of EcologypublishedbyJohnWileyampSonsLtdonbehalfofBritishEcologicalSociety

2436emsp |emsp emspenspJournal of Ecology VISSER Et al

1emsp |emspINTRODUC TION

Lianasmdashwoody climbersmdashare globally widespread highly diverseand play important roles in forest ecosystems (Putz amp Mooney1991 Schnitzer Bongers Burnham amp Putz 2015) Lianas canbe considered structural macroparasites of trees (Stevens 1987StewartampSchnitzer2017)Theytakeadvantageoftreestemsandbranchestogrowintothecanopywheretheytypicallydeploytheirfoliageabovetheirhoststhusgainingaccesstolightattheexpenseoftheirhosts(AvalosMulkeyampKitajima1999Putz1984a)whilesimultaneously competingwith hosts for below-ground resources(egDillenburgWhighamTeramuraampForseth1993)Asa con-sequencelianainfestationgenerallyhasstrongnegativeeffectsontreegrowthsurvivalandreproduction(ClarkampClark1990IngwellWrightBecklundHubbellampSchnitzer2010SchnitzerampBongers2002Wright Sun Pickering Fletcher amp Chen 2015) Lianas arealsoincreasinginabundanceinmanyNeotropicalforests(reviewedinSchnitzer2015Wrightetal2015)

Akeyquestion ishowlianas influencetherelativecompetitiveabilitymdashandultimately the relativeabundancesmdashof treespecies Intheoryhostspeciesthatarelessimpactedbyasharedparasitegainan advantage in competition (Holt Grover amp Tilman 1994) Theneteffectsoflianasonagiventreespeciesdependonhowsensi-tiveeachhostspeciesistoinfestation(lianatolerance)andontheproportionof itspopulationinfested(lianaprevalenceseeMuller-LandauampPacala2018Visseretal2018)Arecentstudyhasshownthattreespeciesdifferstronglyintheirtoleranceoflianainfestationwithespeciallyfast-growingandlight-demandingspeciesbeingleasttolerantoflianainfestation(Visseretal2018)Sympatrictreespe-ciesalsovaryconsiderablyintheproportionofindividualsinfestedwithlianaswithempiricalevidencesuggestingthatlight-demandingspeciesdisplaythelowestlevelsoflianaprevalence(ClarkampClark1990vanderHeijdenetal2008)

Hereweaskwhetherthenegativeeffectoflianasonhostpop-ulationsisgreaterforlight-demandingorforshade-tolerantspeciesAkeyissueistheinterpretationofthelowlianaprevalenceinlight-demandingspeciesArefewerindividualsoflight-demandingspeciesinfested because these species are able to avoid or shed infesta-tion (ashypothesizedbyClarkampClark1990Putz1984a1984bSchnitzer Dalling amp Carson 2000) Or are lianas less prevalentamonglight-demandingspeciessimplyduetosurvivorbiaswithin-festedindividualsdyingrapidlyanduninfestedindividualssurvivingleadingtoalowproportionofinfestedliveindividuals(ashypothe-sizedbyVisseretal2018)Thesetwopossibilitiesleadtooppositepredictionsabout the relative impactof liana infestation for light-demanding versus shade-tolerant host species To distinguish be-tweenthesetwopossibilitiesthecauseofinterspecificvariationinlianaprevalencemustbedetermined(Muller-LandauampPacala2018Visseretal2018)

Manystudiesassumethatvariationinlianaprevalenceamongtreespeciesreflectsvariationincolonizationandlossrates(egClarkampClark1990vanderHeijdenetal2008)whichinturnareattributed tovarying treedefencesagainst lianasHypothesized

tree defences include large leaves flexible trunks fast mono-podial growth and ant symbionts (Hegarty 1989 Putz 19801984a 1984b) which are all associated with fast-growing andlight-demanding species However liana prevalencewill dependnotonlyon colonization (transmission) and loss (shedding) ratesbut also on baseline host tree mortality and the effects of lia-nasonhostmortality (lethality) justasforanyotherparasiteorpathogen(AndersonampMay1982)Variationamongtreespeciesinlianaprevalencemayreflectinterspecificvariationinanyandalloftheserates

Variation in liana prevalence among tree species could be ex-plained in largepartbythedemographyofthehosttrees (Muller-LandauampPacala2018)First tree specieswith shorter life spanshave less timetobecome infestedandhenceshouldhavea lowerproportionofinfestedindividualsSecondspeciesthatexperiencehighermortalitywheninfestedshouldalsohavelowerproportionsinfestedbecausetheinfestedindividualsexitthepopulationfasterBoththesemechanismareplausible it iswellknownthatbaselinemortalityvariesextensivelyamongtreespecies(Conditetal2006)and the effects of lianas on host mortality differs greatly amongspecies (Visser etal 2018) Yet the idea that host demographymayshapeobserved interspecificvariation in liana infestationhasreceived almost no attention in the literature (Visser etal 2018)It isnotknownhowvariation in liana infestationamonghost treespecies relates tovariation in colonizationversus sheddingversushostdemographyDisentanglingtheseratesrequiresestimationofcolonizationand loss rates fromdynamicdataonchanges in lianainfestationsomethingnopreviousstudyhasdone

Here we apply models from disease ecology to explain theproportionoftreesinfestedbylianasin21tropicaltreespeciesonBarroColoradoIslandPanamaWeestimateratesofliana-freemor-tality liana-infestedmortality lianacolonizationand liana loss foreachspeciesfromfielddataWethenuseahostndashparasitemodeltopredictlianaprevalence(theproportionofindividualsinfested)foreach tree species and evaluate the accuracyof thesepredictionsWetestalternativehypotheses that interspecificvariation in lianaprevalenceispredominantlydrivenbyinterspecificvariationincolo-nizationandshedding(egPutz1980vanderHeijdenetal2008)orinhostdemographyspecificallybaselinehosttreemortalityandliana-induced lethality (afterMuller-LandauampPacala2018Visseretal2018)Wequantifytherelativecontributionsofinterspecificvariation in liana colonization rates liana shedding rates and treedemographytointerspecificvariationinlianainfestationFinallywetestwhetheranyoftheseratesandtheirintegrationintolianaprev-alencerelatetomeasuresofshadetoleranceacrosstreespecies

2emsp |emspMATERIAL S AND METHODS

21emsp|emspStudy site

Barro Colorado Island (9deg9primeN 79deg51primeW) Panama hosts a moisttropicalforestTemperatureaverages27degCandannualrainfallav-erages2650mm(since1929)withadryseasonbetweenJanuary

emspensp emsp | emsp2437Journal of EcologyVISSER Et al

andApril (Leigh 1999) Liana infestation data are from the 50-haForestDynamicsPlotonthecentreoftheislandandfour4-haplots

22emsp|emspTree and liana data

Weassessedthepresenceof lianas intreecrownsfor1781treesge20cmDBHinthe50-haplotin1996and2007(Ingwelletal2010Wrightetal2005)andforall1537treesge20cmDBHinfour4-haplotslocatednearthe50-haplotin2005and2015Foreachtreeweevaluatedcrownlianainfestationstatusfromthegroundusingbinoculars(detailsonfieldmethodologygiveninIngwelletal2010Visseretal2018)Weclassifiedeachtreeasliana-free(F)orliana-infested (I) inthe initialcensusandasF Iordead (D) inthefinalcensusForeachspecieswethenconstructedamatrixgiving thenumberof treesobserved foreachcombinationof theF I andDcategories inthetwocensusesThismatrixN0rarrthaselementsnij denotingthenumberofindividualsinitiallyinstatejattime0andinstateiattimet(years)withstatesorderedasFIandDinthecol-umnsandrowsThismatrixwasthebasisforoursubsequentmodelfitsForeachspecieswealsocalculatedobservedlianaprevalence(P)definedastheobservedproportionofindividualsinfestedintheinitialcensusasabasisforcomparisonagainstmodelpredictions

23emsp|emspEstimating liana colonization rates liana loss rates and tree mortality rates

Weusedtransitionmatricestoestimateprobabilitiespertimestep(definedbelow)ofmortalityinliana-freetrees(Mhereaftermortal-ity) additional mortality in liana-infested trees (L lethality con-strained to be ge0) liana colonization of liana-free trees (Ccolonization) and lossof lianas from liana-infested trees (R shed-dingakintoldquorecoveryrdquoinepidemiology)TheseparametersdefinethetransitionprobabilitiespertimestepForexampletheprobabil-ityoftransitioningfromliana-freetoliana-infestedistheproductofthesurvivalprobabilityofaliana-freeindividualandlianacoloniza-tionC(1minusM)(Figure1A)ThefulltransitionmatrixforstatechangesinasingletimestepAisthendefinedas

with statesorderedasF I andD incolumns for time0and rowsfortimetThezerosandoneinthefinalcolumnindicatethatdeathis anabsorbing stateRecruitmentofnew trees to thepopulationisnotconsideredTheestimatedtransitionmatrixfor2timestepsisAA (usingmatrixmultiplication)That is theprobability thatanindividual that is liana-free in time 0 is dead in time 2 is the sumoftheprobabilityittakespathsF0-F1-D2F0-I1-D2andF0-D1-D2(Figure1B)MoregenerallytheestimatedtransitionmatrixA(t)foratotalofttimestepsisdefinedbyA(t)=At

Thechoiceoftimestepdeterminesthepotentialnumberoftran-sitionsthatoccurinagiventimeThetimeintervalbetweenourcen-suses(10ndash11years)islongenoughforindividualtreestomakemultiple

transitions among states (Figure1B) and failure to account for thisbiasesestimates (FigureS1)We testedavarietyof time steps andfoundthatparameterestimatesconvergedasthedurationofthetimestepdecreasedwithlittlechangefortimestepssmallerthan1ndash2years(FigureS1)Thuswechose touseannual timestepswith10or11timestepsbetweenthetwocensuspointsdependingontheplot

(1)A=

⎛⎜⎜⎜⎝

(1minusC)(1minusM) R(1minus (M+L)) 0

C(1minusM) (1minusR)(1minus (M+L)) 0

M M+L 1

⎞⎟⎟⎟⎠

F IGURE 1emsp (a)DiagramoftheMarkovtransitionmodelusedtoexplainlianaprevalence(theproportionoftreesinfestedwithlianas)Eachtreepopulationisdividedintouninfestedindividuals(left)andliana-infestedindividuals(right)TreescanleavethepopulationthroughmortalityuninfestedindividualsdiewithprobabilityMpertimestepandinfestedindividualsdiewithprobabilityM+LUninfestedindividualsarecolonizedwithprobabilityCandthustransitiontoliana-infestedinonetimestepiftheysurviveandarecolonized(C(1minusM))Liana-infestedindividualsshedtheirlianas(ierecoverfrominfestation)withprobabilityRandthustransitiontoliana-freeinonetimestepiftheysurviveandlosetheirlianas(R(1minusMminusL)(B)Toestimatetheseratesfromdataformultiyearintervalsweneedtoaccountformultipletransitionsbetweentheliana-free(F)andtheliana-infested(I)stateThetotaltransitionprobabilityfromonestateattime0toanotherstateattime2isobtainedbysummingoverdifferentpossiblepathswiththerateofanygivenpathbeingtheproductoftheratesalongthepathForexampletheprobabilityofatreethatwasliana-freeattimezero(inF0)beingliana-infestedattime2(inI2)is(C(1minusM)(1minusR)(1minusMminusL)+(1minusC)(1minusM)C(1minusM)Failuretoaccountformultipletransitionswillyieldbiasedestimatesofrates(FigureS1)[Colourfigurecanbeviewedatwileyonlinelibrarycom]


Werestrictedouranalysestospeciesforwhichwehaddataforatleast49individualsinthecombineddatasetsbecausepreliminaryanalysesshowedthistobetheminimumsamplesizeprovidingcred-ibleestimatesforalltransitionprobabilities(definedconservativelyashavingconfidenceintervalslessthanthefullrangeofpossibleval-uesfrom0to1thatistherearesufficientdatatoatleastsomewhatreducetherangeofpossiblevalues)Foreachspeciesweobtainedmaximumlikelihoodestimatesofallrates(CRML)bysearchingfor the parameter combinations that maximized the multinomiallikelihood of the observed combinations of initial and final states(N)giventheexpectedtransitionprobabilities (A(t)=At)undertheparametervaluesTheparameterspacewassearchedusinggeneral-izedsimulatedannealing(XiangGubianSuomelaampHoeng2013)We estimated standard errors for eachmodel parameter throughnumerical approximation of the second partial derivative matrixof the log-likelihood function at themaximum likelihood estimate(Bolker2008)OurdataandtheR-scriptusedtofitthemodelsaregiveninthesupplementalmaterial(TextS1TableS1)

24emsp|emspPredicting the proportion of trees infested with lianas

Wecalculatedtheequilibriumlianaprevalence(proportioninfestedP)undertheMarkovmodel(A)foreachspeciesgivenitsestimatedcolonization sheddingmortality and lethalityWe calculated P astheasymptoticstablestatedistribution(iethedominantrightei-genvectorCaswell2001)usingthefirsttworowsandcolumnsofAModelpredictions(P)shouldbeclosetoobservedPifthepopula-tion isclosetoastablestateand ifnewrecruits (intothepopula-tionoftreesge20cmDBH)havesimilarprevalenceasthosealreadyin thepopulation (the secondassumption is requiredbecauseourmodelincludesnorecruitment)Modelperformancewasevaluatedby comparing observed (in the initial census) with predicted pro-portionsof liana-infested individualsacrossspecies (Pwith P)Wequantified performance using (a) the coefficient of determination(r2)ameasureofvarianceexplained(b)therootmeansquarederror(RMSE)ameasureofthetypicaldeviationbetweenpredictedandobserved (c) the difference between the predicted and observedmeans(Bias)ameasureofsystematicerrorand(d)thedifferencebetween predicted and observed standard deviations a measureofabilitytocapture interspecificvariation(∆σ)WealsoevaluatedinterspecificPearsoncorrelationsbetweenPandeachof the fourrates

25emsp|emspInvestigating the importance of different factors for interspecific variation in liana prevalence

We investigated the relative importance of interspecific variationincolonizationsheddingand lethalityforexplainingvariation in P amongspeciesTodothiswecomparedpredictionsundermodelsinwhich different combinations of parameterswere set either tospecies-specific or to species-averaged values Species-averagedvalueswere arithmeticmeans over all speciesWe calculated the

abovemetricsofmodelfit(r2RMSEBias∆σ)forallcombinationsofspecies-specificandspecies-averagedratesbutareespeciallyin-terestedinthefollowingcombinations

1 Full model including species-specific rates of all parameters(Ms Ls Rs Cs)

2 Treedemographyonlymodelmdashspecies-specificmortalityandle-thalityratesandspecies-averagedcolonizationandshedding(MsLs

CR)3 Colonizationandsheddingonlymodelmdashspecies-specificcoloniza-tion and shedding rates and species-averagedmortality and le-thalityrates( MLCsRs)

4 Species-specific values of one parameter and species-averagedvaluesoftheotherthree

5 Species-specificvaluesofthreeparametersandspecies-averagedvaluesofthefinalparameter

WealsonumericallycalculatedthesensitivityofPtosmallchanges(1)ineachunderlyingrateThecontributionofeachratetointerspe-cificvariationinequilibriumlianaprevalenceshouldbeproportionaltotheproductofthissensitivityandtheobservedinterspecificvarianceoftherateifthemodelappropriatelycapturesinterspecificvariationinprevalenceItisimportanttonotethatourmodelincludesnorecruit-mentandhencetheimportanceofthetreedemographyparametersmaychangeinamodelwithrecruitment

26emsp|emspRelating shade tolerance and liana infestation

Weevaluatedhowinterspecificvariationincolonizationsheddingliana-freemortality lethality and overall prevalencewere relatedtomeasuresofshadetoleranceAsshadetolerance isnotdirectlyobservable previous studies have used various proxies includinggrowthandmortalityratesofjuvenileandlargertreesorwoodden-sity (vanderHeijdenetal2008Visseretal2018Wrightetal2010)HereweusedtwoseparateapproachestocombineallthesemeasuresintometricsofshadetoleranceThefirstwastotestforbi-variatecorrelationsofashadeintoleranceindexwithRCLorP(weexcludedM from this analysisbecause the shade tolerance indexisderivedinpartfrommortality)Theshadeintoleranceindexwasdefinedasthefirstfactorscoreofaprincipalcomponentsanalysisincludingwooddensity(datafromWrightetal2010)mortalityandmeanrelativegrowthratesofsaplings(1ndash4cmDBH)andlargertrees(gt10cmDBHdatafromConditetal2006)ThefirstPCAaxisex-plained60ofthevariation(eigenvalue28among21species)withgreatervaluesindicatingincreasinglightrequirements(asinVisseretal2018)SignificancelevelswereBonferronicorrected

The second approachwas amultivariate latent variable analysisusingstructuralequationmodels (SEMs)Structuralequationmodelsareusefulformodellingunobservableconstructssuchasshadetoler-anceforrepresentinghypothesesofcasualrelationshipsandforquan-tifyingtherelativestrengthsofdirectandindirecteffectsinsystemswheremultipleprocessesoperate(GraceAndersonOlffampScheiner2010)Herewe constructedmultiple SEMs to (a) estimate a latent


construct resembling ldquoshade (in)tolerancerdquo using multiple imperfectindicators(b)testforrelationshipsbetweenCRMandLandthela-tentshadetolerancevariableand (c)quantifytherelative influencesof indirecteffectsofhostshadetoleranceon lianaprevalenceoper-atingviathepathwaysofCRMandLIneachSEMwerepresentedthehypothesizedcausaldirectandindirectrelationshipbetweenob-servedvaluesshadeintoleranceanditsindicatorsHerepathswereconstructed as follows wood density mortality and mean relativegrowthratesofsaplingsandtreesinformedalatentvariable(hereafterlatentSI)whichwasrelatedtoCRMandLwhichthenpredictedPCovariancebetween latentSIandthePwasalsoestimatedThefullmodelispresentedinFigureS2allotherevaluatedmodelsweresim-plersubsetsofthefullmodelWeincludedMhereasSEMsgenerallydonotrequiretheerrorstructurestobeindependentofoneanother(Fox2006)Weevaluated15differentmodelseachincludingdifferentcombinationsofwooddensityrelativegrowthratesandmortalitytoinformthelatentSIvariableThefitofeachSEMwasevaluatedbasedon χ2scoresandthegoodness-of-fit index(GFIWestTaylorampWu2012) To assess robustness of the results when different variablesinformthe latentSIweevaluatedagreementamongallmodelswithrespecttoourthreeSEMobjectives(above)WeconductedaMonteCarlosimulationforeachfittedSEMtoevaluatepowerandbiasandto determine reliability of predictions at our sample size (followingMutheacutenampMutheacuten2002codegiveninTextS2)SEMswerefitwiththelavaanpackage(Rosseel2012)

3emsp |emspRESULTS

Atotalof21speciesmetourminimumsamplesizecriteria(Nge49)Among-species means (ranges) of estimated annual rates were0040 (001ndash012) for colonization (C) 0031 (0003ndash021) for

shedding(R)0016(0003ndash0055)fortreemortality(M)and0021(0001ndash007)for lethality(LTableS2)Theobservedlianapreva-lence (P proportion of individuals infested) at the initial censusranged from 006 to 092 among these 21 species Liana preva-lence was negatively related to shedding and lethality weaklypositivelyrelatedtocolonizationandunrelatedtotreemortality(Figure2) The rate parameterswere not significantly correlatedwitheachother (FigureS3)Thesamplesizesfordifferentstatesandplotsforall21speciesaregiveninTablesS3andS4

Thefullmodelincorporatingallfourratesexplained58ofinter-specificvariationinPhadanRMSEof016(Table1Figure3A)andtendedtounderestimate theprevalenceof liana infestationby008(seeldquoBiasrdquoinTable1)Itcapturedthemagnitudeofinterspecificvari-ationinPwell(∆σ=001)ascanbeseenbycomparingthedistribu-tionsoftheobservedandpredictedPvalues(seeinsetinFigure3A)Modelsthatincludedoromittedspecies-specificvariationinparticularratesvariedgreatlyinexplanatorypower(Table1Figure3bc)Modelsincorporatingspecies-specific sheddingandcolonizationwhileomit-tinginterspecificvariationinhostdemographydidbetterthanthoseincorporatingspecies-specificdemographyandomittinginterspecificvariationinsheddingandcolonization(compareFigure3bc)Thesin-glemostinfluentialratewastherateatwhichtreesshedtheirlianasasevidencedbytheperformanceofmodelsthatincludedoromittedonly this parameter (shedding rateR Table1) The secondmost in-fluentialparameterinfluencinghosttreeabundancewaslethality(L)theliana-associatedadditionalmortalityrateTherateofcolonizationwas the thirdmost influential parameter howevermodels incorpo-rating species-specific shedding and colonization actually didworsethan those including only species-specific shedding (Table1) TheleastinfluentialparameterwasthemortalityofuninfestedindividualsOverallvariationinexpectedlianaprevalenceinthismodelamongourfocalspeciesappearstobedrivenprimarilybysheddingandlethality

F IGURE 2emspObservedvariationamong21co-occurringtropicaltreespeciesinlianaprevalence(theproportionofindividualsinfestedwithlianas)isunrelatedtointerspecificvariationinbaselinetreemortality(a)negativelyrelatedtolethalitymdashtheadditionalmortalitywheninfested(b)unrelatedtotherateofcolonizationbylianas(c)andnegativelyrelatedtotherateatwhichlianasarelost(d)ThesizeofeachcircleisproportionaltothespeciessamplesizeSignificantlinearrelationshipsareindicatedbysolidlines(showingordinarylinearregressions)withconfidenceintervals(95)givenbythedashedlinesThenegativerelationshipbetweensheddingandprevalence(d)remainedsignificant(p=0023)afterremovaloftherightmostoutlier(Cecropia insignis)withr2reducedto036TheBonferronicorrectedsignificancelevelwassetto0054=00125

001 003 005

02

04

06

08

02

04

06

08

02

04

06

08

02

04

06

08

Mortality (yearminus1)

r2 = 0 r2 = 039 r2 = 013 r2 = 041

000 002 004 006 008Lethality (yearminus1)

002 006 010Colonization (yearminus1)

000 005 010 015 020Shedding (yearminus1)

Obs

erve

d pr

eval

ence

(P)

(a) (b) (c) (d)


In our simple model liana prevalence is most sensitive to theratesofcolonizationandsheddingandsomewhatsensitivetolethal-itywithbackgroundtreemortalityhavingnoinfluence(FiguresS4andS5)At the same timemortality and lethalityvariedconsider-ablymore among tree species than did colonization and shedding(FigureS4b) The product of the sensitivity of liana prevalence toeach rate and interspecific variation in the rate predicted the rel-ative importanceof the rate inexplaining interspecificvariation inobserved P as expected if the model captures this variation well(FigureS4cd)

Hosttreeshadeintolerancewasnegativelyrelatedtolianaprev-alencepositivelywithsheddingandlethalityandunrelatedtocol-onization(Figure4)Lianaprevalencewasstronglyrelatedtoshadeintolerancewithlight-demandingspeciesshowinglowerprevalence(Figure4a r2=049 p=00003) Shade intolerance was also sig-nificantlypositively related to shedding rates (Figure4b r2=037p=00034) and lethality rates (Figure4c r2=030p=001)withmore shade-tolerant species showing lower shedding and lethal-ity Colonization was unrelated to the shade intolerance index(Figure4dr2=0002p=083)

All15structuralequationmodelsindicatedastrongandsignifi-cantlynegativerelationshipofprevalencewithlatentshadeintoler-ance(iepositivewithshadetolerance)andasignificantnegativerelationshipofprevalencewithsheddingandlethalityHowevernotallmodelswereunbiasedSimulationsshowedthatthetopfivemod-els(asrankedbytheGFI)hadlowbiasinparameterestimates(lt5)andhighpower(gt88TableS6)Biaswasmuchgreaterforthere-maining10SEMs(TableS6)indicatingthatwehadtoofewsamplestocrediblyestimatethesemodels

The best fitting structural equation model explained 64 ofinterspecific variation in liana prevalence (r2=0643 GFI=097χ2

df=6=15p=0958 Figure5 TableS7) Thismodel included onlyoneshadetoleranceindicatormdashtherelativegrowthratesoftreeslargerthan10cmDBHTheSEMpredictedthatshade-toleranttreeshavegreater levelsof lianainfestationbecausetheyhavelowersheddingandlethalityratesAnindirectpathwayanalysisshowedthatthiswasprimarilyduetosheddingwiththeindirecteffectofthelatentshadeintolerance on liana prevalence via shedding 44 larger than thepathwayvialethality(minus0221vsminus0153)ThetopfiveunbiasedSEMmodels all agreed in the relative rankingof the (indirect) pathways

Scenario r2 RMSE Bias ∆σ Range N

Fullmodel(MSLSRSCS)

058 016 008 001 [013ndash092] 4

Allexceptmortality( MLSRSCS)

058 016 008 001 [013ndash094] 3

Allexceptcolonization(MSLSRS

C)058 015 002 006 [014ndash092] 3

Sheddingandlethality( MLsRS

C)058 015 002 006 [014ndash092] 2

Onlyshedding( MLRSC)

054 017 003 009 [015ndash087] 1

Sheddingandmortality(MS

LRsC)

054 017 003 009 [015ndash087] 2

Sheddingandcolonization( MLRSCS)

047 018 009 003 [013ndash092] 2

Allexceptlethality(MSLRSCS)

047 018 009 003 [013ndash092] 3

Onlylianalethality( MLs

R C)041 019 011 018 [033ndash056] 1

Mortalityandlethality(MsLs

R C)041 019 011 018 [033ndash056] 2

Colonizationandlethality( MLS

RCs)028 022 015 008 [016ndash077] 2

Allexceptshedding(MSLS

RCS)028 022 015 008 [016ndash077] 3

Colonizationandmortality(MS

LRCs)010 024 015 009 [017ndash077] 2

Onlycolonization( MLRCs)

010 024 015 009 [017ndash077] 1

Onlymortality(MSLR

C)000 025 012 025 [049ndash05] 1

TABLE 1emspSummarystatisticsforalternativemodelsforinterspecificvariationinlianaprevalence(theproportionofindividualsinfestedwithlianas)Modelsdifferedinwhetherparticularratestookspecies-averagedorspecies-specificvalues(egCforspecies-averagedorCsforspecies-specificcolonizationrates)Statisticsarebasedoncomparingobserved(intheinitialcensus)withpredictedlianaprevalenceacrossspeciesModelsarecomparedintheircoefficientofdetermination(r2)rootmeansquarederror(RMSE)differencebetweenthepredictedmeanandobservedmeanprevalence(bias)anddifferencebetweenpredictedstandarddeviationandobservedstandarddeviation(∆σ)Thepredictedrangeofprevalence(range)isalsoshownasisthenumberofspecies-specificparameters(N)Theobservedmeanprevalencewas061theobservedstandarddeviationwas025andtheobservedrangewas006ndash092TableS5presentsthepredictedspecies-specificestimatesofprevalenceforeachmodel


withsheddingrankedfirstandlethalitysecondSheddingandlethalitywerealsosignificantlyrelatedtoshadetoleranceinallfiveofthetoprankedmodelsTheSEMpathcoefficientestimatedfortherelation-shipbetweenshadeintoleranceandcolonizationisjust021(Figure5)consistentwiththelackofapairwiserelationship(Figure4c)

4emsp |emspDISCUSSION

Theoveralleffectoflianasonatreepopulationdependsonboththe proportion of trees infested with lianas and the magnitude

of negative effects experienced by infested individuals bothof which vary greatly among tree species (Clark amp Clark 1990Toledo-Aceves 2014 van derHeijden etal 2008 Visser etal2018) This study is the first to explain variation in liana preva-lence among co-occurring tree species by integrating species-specific rates of colonization shedding baseline hostmortalityand lethality (ie additionalhostmortality associatedwith lianainfestation)Wefoundthat21tropicaltreespeciesvarywidelyinthe proportion of individuals infested by lianas (006ndash093) and58ofthisvariationcanbeexplainedbyjusttwoparameterstheratesofshedding(R)andlethality(L)Ofthefourratesshedding

F IGURE 3emspThefullmodelincludingspecies-specificratesofbaselinemortality(M)lethality(L)sheddingainfestation(R)andcolonizationbylianas(C)didwellatpredictingobservedinterspecificvariationinlianaprevalenceamong21co-occurringtropicaltreespecies(a)Incontrastamodelincorporatinginterspecificvariationonlyinmortalityandlethalitydidverypoorly(b)whileamodelincorporatinginterspecificvariationonlyinsheddingandcolonizationdidfairlywell(c)Pointsizereflectssamplesizesforindividualspeciesverticalgreylinesrepresent95confidenceintervalsofobservedproportionsThedashedgreylinerepresentsthe11lineTheinsetfiguresdisplaythedistributionsoftheobserved(solid)andpredicted(dashed)valuesoflianaprevalence

00 02 04 06 08 1000

02

04

06

08

10(a) Full model

Predicted

Obs

erve

d

r2 = 058

MsLsRsCs

ObservedPredicted

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08

10(b) Demography only

Predicted

r2 = 041

MsLsRC

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08

10(c) Colonization and shedding only

Predicted

r2 = 047

MLRsCs

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

F IGURE 4emspRelationshipsofshadeintolerancewithlianaprevalence(a)shedding(b)colonization(c)andlethality(d)amongour21focaltreespeciesSolidlinesindicatesignificantrelationshipsbasedonaBonferronicorrectedsignificancelevelof00125(0054)Dashedlinesrepresent99confidenceintervalsSymbolsizeisproportionaltosamplesizeornumberofindividualtreesassessedforeachspecies

minus2 minus1 0 1 2 3 4

02

04

06

08

Obs

erve

d pr

eval

ance

(P)

r2 = 049


She

ddin

g (R

)

0003

001

007

r2 = 037


Col

oniz

atio

n (C

)

001

003

01


000

002

004

006

008

Leth

ality

(L)

r2 = 03

shademinusintolerance indexShademinustolerant Light demanding

(a) (b) (c) (d)


wasthemostimportantthenlethalityandcolonizationwhereasuninfestedtreemortalitywasunimportantThesamerankingofparameterswasconfirmedbyfourseparateanalyses(a)Pearsoncorrelationbetweenestimatedratesandobservedproportionin-fested (PFigure2) (b)predictivepower (r2)whenonlyonevari-ablewasincluded(Table1)(c)thelossinr2whenonlyonevariablewas excluded (Table1) and (d) strength of indirect effects in amultivariatestructuralequationmodel(Figure5)

Our results lead us to reject both of our original hypothesesNeither interspecific variation in host demography alone nor col-onizationandsheddingaloneexplainmostof thevariationamongtreespeciesinlianaprevalence(Figure3Table1)Rathertheratesofsheddingincombinationwithlethalityexplaininterspecificvari-ation in the prevalence of liana infestation in trees in this forestFurthermore we show that shade intolerance correlates stronglywith shedding and lethality light-demanding tree species tend tohavehigher ratesofbothsheddingand lethality (Figures4and5)andthisjointlyleadsthemtohavelowerproportionsofindividualsinfestedbylianas(Figure5)

41emsp|emspThe mechanisms underlying interspecific variation in liana prevalence

Traits such as flaky bark (bark shedding) the ability to dropbranches(self-pruning)trunkbranchflexibilityandlongleavesare

hypothesizedtoinfluencetheabilityoftreespeciestoresistcolo-nizationor shed lianas and thus their lianaprevalence (eg Putz1984b)Consistentwiththishypothesispreviousstudiesreportedthatlianaprevalenceisnegativelycorrelatedwithseveralhosttreearchitectural traits branch-free bole-height smooth bark longerleaves and lowwooddensity (BalfourampBond1993CampbellampNewbery1993Putz1980vanderHeijdenetal2008)Thesecor-relationsalonehoweverdonotrevealwhetherthetraitsinfluencetheprevalenceof lianainfestationviacolonizationsheddingandorotherratesAmoremechanisticunderstandingcouldbegainedbyevaluatinghowdynamicallyestimatedrates(ieRCLandM)relatetotraits

The two most influential rates heremdashshedding and lethalitymdashwerebothassociatedwithshadetoleranceandthismayhelpnar-rowdownwhichtraitsinfluencelianaprevalenceLight-demandingtreespecieshavelongbeenknowntohaverapidleafturnovertimesandhighlevelsofself-pruningofshadedleavesandbranches(ZonampGraves1911)Thesetraitsarealllikelytoincreaseratesoflianashedding(egPutz1980)FurthermoreVisseretal(2018)hypoth-esizedthatfast-growingtreespeciesarelesstolerantoflianainfes-tationastheytendtohaveshallowercrowns(vertically)withlowerleaf area indices causing a greater proportional displacement oftotalleafareaduetoinfestationThesetwoobservationsarelinkedGreaterratesofbranchsheddingleadtoshallowercrownsandlowerleafareaindicesHencetheverytraitsthatincreasesheddingmay

F IGURE 5emspThebestfittingstructuralequationmodel(SEM)among15candidatemodelsusingdifferentindicatorvariablesforshadetolerance(fullmodelshowninFigureS2)TheSEMshowsthehypothesizedpathsthroughwhichthedegreeofshadeintolerance(SI)influenceslianaprevalenceviasheddingcolonizationlethalityandmortalitySquaresindicateobserved(measured)variablesandthecircleidentifiestheonelatentvariableThecolourthicknessandshadingindicatethedirectionsizeandsignificanceofeachpathloadingRespectiveestimatesofloadingsizearegivennexttoeachconnectinglinewithstandarderrorsinparenthesesandasterisksindicatesignificance(95CIdonotoverlapwithzero)Thedouble-headedarrowbetweenSIandprevalenceindicatesthatnodirectrelationshipwashypothesizedorfitbutratheronlythecovariancebetweenvariableswasestimated[Colourfigurecanbeviewedatwileyonlinelibrarycom]

RGR

SI

Shedding Lethality Colonization Mortality

Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)


simultaneouslyincreaselethalityWedidnotfindasignificantcor-relationbetweensheddingandlethality(FigureS3)butbothfactorsare significantly related to shade tolerance (Figures4 and 5) Thestrongpositivelinksofshadeintolerancewithsheddingandlethalityalsohint that theabove traitsmaynotbeadaptations specificallyfor interactionswith lianas light is a principle limiting resource intropicalforestsandthesetraitsmaybeshapedsimplybyshadetol-erancestrategy

Our model shows that the prevalence of liana infestation ishighly sensitive to the rateofhostcolonization (FiguresS4aandS5)However estimated colonization varied little among species(FigureS4b)andthusplayedasmallroleinexplaininginterspecificvariation in prevalence (FigureS4d) The relatively low varianceincolonizationratesobservedamongtreespeciesmight indicatethat colonization is largely a chance occurrence and is mostlyunrelated to host tree traits Lianas infest trees either from theground up or laterally growing from an infested neighbour (vanderHeijdenetal 2008)whichmeans that the rateof coloniza-tionmaybelargelydependentonlocallianaabundanceIndividualcanopylianasinfestanaverageof16treesonBCI(Putz1984a)and instances of lateral (crown to crown) infestation depend onhowmanyadjacenttreescarrylianas(vanderHeijdenetal2008)Colonizationwillalsolikelydependonthelife-historystrategiesofthelianaspresentForexamplelianaspeciesdifferinmanytraitsincluding the average number of host trees an individual infests(IchihashiampTateno2011)Weexpectthattherateofcolonizationwilldependmoreonthedensityof lianasintheforestthepres-enceof infestedneighboursandon theaggregate traitsof locallianaspeciesthanonhostspeciesidentityandtraitsThishypoth-esismayexplaintherelativelowvariabilityandpredictivepoweroflianacolonizationamongtreespeciesItmayalsointroduceerrorintoourestimatesofcolonizationratesforindividualtreespeciesBetterspecies-specificestimatesthatmaycorrelatewithspecies-specifictraitscouldemergefrommodelsthatalsoincludeeffectsofneighbourhoodlianadensity

Tropical treespeciesvarycontinuouslyalonganaxis from lowmortality and slow growth towards fast growth and highmortal-ity (GilbertWrightMuller-Landau Kitajima ampHernandeacutez 2006Wrightetal2010)Weinitiallyexpectedthatbecauselongerlivedhostshavealongertimeperiodduringwhichtheycanbecomein-fested theywould have higher prevalence Yet the baseline (un-infested) treemortality ratewas the least influentialparameter inexplaininglianaprevalenceThelackofinfluenceofbaselinemortal-ityinourMarkovchainmodelatitscurrentparameterizationcouldchangeiftreerecruitmentisincludedintothemodelInsuchamodelbaselinemortalitycanbeexpectedtonegativelyaffectequilibriumprevalenceinamodelwithaconstantinfluxofliana-freeindividu-als inwhich colonization exceeds shedding Surprisingly howeverourempiricalanalysesalsoshowedthatbaselinemortalitywasun-correlatedwith prevalence across species and thatmortality hadtheweakest influenceofany rate inourpathanalysesMoreoverthe path analysis estimated a positive relationship between mor-tality and prevalence which is the opposite of what is expected

mechanisticallywhencolonization ratesexceedshedding rates (astheydofor14ofour21species)Wehypothesizethatsheddingmaymasktheeffectoftreelongevity(theinverseofmortality)Sheddingratesareindependentoftreemortality(FigureS3)andlargeenoughtorenderanyaccumulationeffectundetectable

5emsp |emspCONCLUSIONS AND FUTURE DIREC TIONS

Lianas are a globallywidespread and diverse plant group that arevitalcomponentsofforestecosystems(SchnitzerampBongers2002)with profound impacts on tree population dynamics (Visser etal2018)ecosystemprocessesincludingcarbonsequestration(vanderHeijdenPowersampSchnitzer2015)andanimaldiversity(Yanoviak2015) Yetwe know little about themechanisms that govern theprevalence of liana infestation at any given site (Muller-LandauampPacala2018)Hereweappliedamodellingapproachbasedonsimpleprinciplesofdiseaseecologythatexplainedthemajorityofvariationintheproportionoftrees infestedwith lianasamongco-occurringtropical treespeciesTheprevalenceof liana infestationwas predicted by asymptotic stable stage distributions calculatedfrom observed species-specific transition rates (Figures2 and 3)Of the four transition rates sheddingand lethalitywere themostimportant in explaining interspecific variation in liana infestationprevalenceWeshowthattheprevalenceoflianainfestationisposi-tivelyrelatedtoshadetoleranceviaindirectpathwaysoperatingontheratesofsheddingandlethality(Figures4and5)Ourworkdem-onstratesthatanepidemiologicalapproachprovidesmanyinsightsandasoundbasisforfurtherexplorationofthefactorsthatregulatelianapopulations

Futureworkshouldinvestigatehowfunctionaltraitsofbothli-anasandtreesinfluencetheirinteractionsOurworksuggestthatthisshouldincludetraitsthatinfluencethelikelihoodofsheddingalianasuchasbarkflakingandbranchabscissionaswellastheirin-teractionwithlianaclimbandgrowthstrategies(egtendriltwin-ingorrootclimbingIchihashiampTateno2011)Whichlianatraitsmediate the impact lianashaveontheirhosts isalsoof interestA seminal study in temperate forests showed that co-occurringlianaspeciescanvarygreatlyintheirinteractionswithhosttreesand thus in their impactsonhost growthand survival (IchihashiampTateno2011)andthereiseveryreasontoexpectthatsimilarvariationexistsamong the162co-occurring liana speciesatourstudysite(Schnitzeretal2012)Itwouldbeusefultoinvestigatewhich traitsof lianas are associatedwith this strategic variationin ldquovirulencerdquo For instance gap-dependent or light-demandinglianasmaybe inclined togrowmorevigorouslyexploitinghostsmore intenselyandcausinggreater lethality rates Indeed somelianas thrivedespite the lossofa treehost suppressing treere-cruitmentand regeneration ingaps fordecades (Schnitzeretal2000 Tymen etal 2016) Therefore future work that focusesonlianatraits(sensuIchihashiampTateno2011)inadditiontotreetraits while correcting for habitat and spatial neighbourhoods


isneeded togenerateamechanisticunderstandingofhow lianatraits interactwith tree traits to shape the abundance of lianasand trees across a landscapeWe conclude that the theoreticalandempiricalaspectsoflianapopulationcommunityandevolu-tionarydynamicsareseverelyunderdevelopedandprovidefertilegroundforfurtherstudy

ACKNOWLEDG EMENTS

We thankDavidBrassfield for help in the field and Steve PacalaforhelpfuldiscussionThisstudywassupportedbytheNetherlandsOrganization for Scientific Research (NWO-ALW 801-01-009MDV) the Carbon Mitigation Initiative at Princeton University(MDV)andtheHSBCClimatePartnership(HCM-L)ThedatasetswerecollectedwithfundingfromtheNationalScienceFoundation(DEB0453445toHCM-L0453665toSJW061366608450711019436amp1558093toSAS)theSmithsonianTropicalResearchInstitute theCentre for Tropical Forest Science the JohnD andCatherineTMacArthurFoundationtheMellonFoundationandtheSmallWorldInstituteFund

AUTHORSrsquo CONTRIBUTIONS

MDV HCM-L and SJW designed the study analysedthe data and built the models MDV HCM-L and SJWwrote the first draft MDV HCM-L SAS SJW EJ and HdeK all contributed substantial revisions All authors gave finalapprovalforpublication

DATA ACCE SSIBILIT Y

Data available from the Smithsonian DSpace Repository httpsdoiorg1025570stri1008835383(VisserampWright2018)andinthesupportingmaterial(TextS1andS2TableS1)orwerepublishedpreviously

ORCID

Marco D Visser httporcidorg0000-0003-1200-0852

Helene C Muller-Landau httporcidorg0000-0002-3526-9021

Hans Kroon httporcidorg0000-0001-6151-3561

Eelke Jongejans httporcidorg0000-0003-1148-7419

S Joseph Wright httporcidorg0000-0003-4260-5676

R E FE R E N C E S

Anderson R M amp May R M (1982) Coevolution of hosts andparasites Parasitology 85 411ndash426 httpsdoiorg101017S0031182000055360

AvalosGMulkeySampKitajimaK (1999)LeafopticalpropertiesoftreesandlianasintheoutercanopyofatropicaldryforestBiotropica31517ndash520httpsdoiorg101111j1744-74291999tb00395x

BalfourDAampBondWJ(1993)Factorslimitingclimberdistributionandabundance inaSouthernAfricanforestJournal of Ecology8193ndash100httpsdoiorg1023072261227

Bolker B M (2008) Ecological Models and Data in R Princeton NJPrincetonUniversityPress

CampbellEJFampNewberyDM(1993)Ecologicalrelationshipsbe-tweenlianasandtreesinlowlandRainForestinSbahEastMalaysiaJournal of Tropical Ecology 9 469ndash490 httpsdoiorg101017S0266467400007549

CaswellH (2001)Matrix population models Construction analysis and interpretation(2nded)SunderlandMASinauerAssociates

ClarkDBampClarkDA(1990)DistributionandeffectsontreegrowthoflianasandwoodyhemiepiphytesinaCostaRicantropicalwetfor-estJournal of Tropical Ecology6321ndash331httpsdoiorg101017S0266467400004570

ConditRAshtonPBunyavejchewin SDattarajaH SDavies SEsufaliShellipZillioT(2006)Theimportanceofdemographicnichesto tree diversity Science 313 98ndash101 httpsdoiorg101126science1124712

DillenburgLRWhighamDFTeramuraAHampForsethIN(1993)EffectsofbelowgroundandabovegroundcompetitionfromthevinesLonicera-Japonica and Pathenocissus-Quinquefolia on the growth ofthetreehostLiquidambar-Styraciflua Oecologia9348ndash54httpsdoiorg101007BF00321190

FoxJ(2006)StructuralequationmodelingwiththeSEMpackageinRStructural Equation Modeling13465ndash486httpsdoiorg101207s15328007sem1303_7

Gilbert B Wright S J Muller-Landau H C Kitajima Kamp Hernandeacutez A (2006) Life history trade-offs in tropi-cal trees and lianas Ecology 87 1281ndash1288 httpsdoiorg1018900012-9658(2006)87[1281LHTITT]20CO2

GraceJBAndersonTMOlffHampScheinerSM(2010)Onthespecificationof structural equationmodels forecological systemsEcological Monographs8067ndash87httpsdoiorg10189009-04641

HegartyEE(1989)Vine-hostinteractionsInFEPutzampHAMooney(Eds) Ecology of lianas (pp 357ndash375) New York NY CambridgeUniversityPress

Holt R D Grover J amp Tilman D (1994) Simple rules for inter-specific dominance in systems with exploitative and apparentcompetition The American Naturalist 144 741ndash771 httpsdoiorg101086285705

IchihashiRampTatenoM(2011)Strategiestobalancebetweenlightac-quisitionandtheriskoffallsoffourtemperatelianaspeciesToover-tophostcanopiesornotJournal of Ecology991071ndash1080httpsdoiorg101111j1365-2745201101808x

IngwellLLWrightSJBecklundKKHubbellSPampSchnitzerSA (2010) The impact of lianas on10 years of tree growth andmortalityonBarroColoradoIslandPanamaJournal of Ecology98879ndash887httpsdoiorg101111j1365-2745201001676x

LeighE(1999)Tropical forest ecology A view from Barro Colorado Island NewYorkNYOxfordUniversityPress

Muller-LandauHCampPacalaSW(2018)Whatdeterminestheabun-danceof lianas InADobsonBHoltampDTilman (Eds)Unsolved problems in ecologyPrincetonNJPrincetonUniversityPress

MutheacutenLKampMutheacutenBO(2002)HowtouseaMonteCarlostudytodecideonsample sizeanddeterminepowerStructural Equation Modeling A Multidisciplinary Journal 9 599ndash620 httpsdoiorg101207S15328007SEM0904_8

Putz F (1980) Lianas vs trees Biotropica 12 224ndash225 httpsdoiorg1023072387978

PutzFEF(1984a)ThenaturalhistoryoflianasonBarroColoradoIslandPanamaEcology651713ndash1724httpsdoiorg1023071937767

PutzFE(1984b)HowtreesavoidandshedlianasBiotropica1619ndash23httpsdoiorg1023072387889


PutzFEampMooneyHA(1991)The biology of vinesCambridgeUKCambridgeUniversityPress

RosseelY(2012)lavaanAnRpackageforstructuralequationmodel-ingJournal of Statistical Software481ndash36

Schnitzer S A (2015) Increasing liana abundance in neotropical for-ests Causes and consequences In S A Schnitzer F BongersR J Burnham amp F E Putz (Eds) Ecology of lianas (pp 451ndash464)ChichesterUKJohnWileyampSons

SchnitzerSampBongersF (2002)Theecologyof lianasandtheirrolein forests Trends in Ecology amp Evolution 17 223ndash230 httpsdoiorg101016S0169-5347(02)02491-6

SchnitzerSABongersFBurnhamRJampPutzFE(2015)Ecology of lianasOxfordUKWiley-Blackwellhttpsdoiorg1010029781118 392409

Schnitzer S A S Dalling JW J amp CarsonWW P (2000) Theimpact of lianas on tree regeneration in tropical forest can-opy gaps Evidence for an alternative pathway of gap-phaseregeneration Journal of Ecology 88 655ndash666 httpsdoiorg101046j1365-2745200000489x

SchnitzerSASAManganSASADallingJWJWBaldeckCACAHubbellSPSPLedoAAhellipYorkeSRSR(2012)Lianaabundance diversity and distribution on Barro Colorado IslandPanama PLoS ONE 7 e52114ndashe52114 httpsdoiorg101371journalpone0052114

StevensGC(1987)LianasasstructuralparasitesTheBursera simaruba exampleEcology6877ndash81httpsdoiorg1023071938806

Stewart T E amp Schnitzer S A (2017) Blurred lines between com-petition and parasitism Biotropica 49 433ndash438 httpsdoiorg101111btp12444

Toledo-Aceves T (2014) Above- and belowground competition be-tween lianas and trees In S Schnitzer F Bongers R BurnhamampFPutz (Eds)Ecology of lianas (pp147ndash163)ChichesterUK JohnWileyampSonsLtd

TymenBReacutejoul-MeacutechainMDallingJWFausetSFeldpauschTRNordenNhellipChaveJ(2016)Evidenceforarrestedsuccessionin a liana-infestedAmazonian forest Journal of Ecology104 149ndash159httpsdoiorg1011111365-274512504

van der Heijden G M F Healey J R Phillips O L van derHeijden G M F Healey J R amp Phillips O L (2008)Infestation of trees by lianas in a tropical forest in AmazonianPeru Journal of Vegetation Science 19 747ndash756 httpsdoiorg1031702008-8-18459

van der Heijden G M Powers J S amp Schnitzer S A (2015)Lianas reduce carbon accumulation and storage in tropical for-estsProceedings of the National Academy of Sciences of the United States of America 112 13267ndash13271 httpsdoiorg101073pnas1504869112

VisserMDampWrightS J (2018)Data fromAhost-parasitemodelexplains variation in liana infestation among co-occurring tree

species Smithsonian DSpace Repository httpsdoiorg1025570stri1008835383

VisserMDWrightSJMuller-LandauHCJongejansEComitaLSdeKroonHampSchnitzerS(2018)TreespeciesvarywidelyintheirtoleranceforlianainfestationAcasestudyofdifferentialhostresponse to generalist parasites Journal of Ecology 106 781ndash794httpsdoiorg1011111365-274512815

WestSGTaylorABampWuW(2012)Modelfitandmodelselec-tioninstructuralequationmodelingInRHHoyle(Ed)Handbook of structural equation modeling(pp209ndash234)NewYorkNYGuilfordPress

WrightSJJaramilloMAPavonJConditRHubbellSPampFosterRB(2005)ReproductivesizethresholdsintropicaltreesVariationamongindividualsspeciesandforestsJournal of Tropical Ecology21307ndash315httpsdoiorg101017S0266467405002294

WrightSJKitajimaKKraftNJBReichPBWrightIJBunkerD E hellip Zanne A E (2010) Functional traits and the growth-mortalitytrade-offintropicaltreesEcology913664ndash3674httpsdoiorg10189009-23351

WrightSSun IPickeringMFletcherCampChenY (2015)Long-termchangesinlianaloadsandtreedynamicsinaMalaysianforestEcology9627482757

XiangYGubianSSuomelaBampHoengJ (2013)Generalizedsim-ulated annealing for global optimization The GenSA Package R Journal513ndash28

YanoviakSP(2015)EffectsoflianasoncanopyarthropodcommunitystructureInSASchnitzerFBongersRJBurnhamampFEPutz(Eds)Ecology of lianas(pp343ndash361)ChichesterUKWileyOnlineLibrary

ZonRampGravesHS(1911)Light in relation to tree growthWashingtonDC US Dept of Agriculture Forest Service httpsdoiorg105962bhltitle66218

SUPPORTING INFORMATION

Additional supporting information may be found online in theSupportingInformationsectionattheendofthearticle

How to cite this articleVisserMDMuller-LandauHCSchnitzerSAdeKroonHJongejansEWrightSJAhostndashparasitemodelexplainsvariationinlianainfestationamongco-occurringtreespeciesJ Ecol 20181062435ndash2445 httpsdoiorg1011111365-274512997

Supporting information

A host-parasite model explains variationin liana infestation among co-occurring

tree species

Marco D Visserlowast123 Helene C Muller-Landau3 Stefan ASchnitzer4 Hans de Kroon2 Eelke Jongejans2 and Joe Wright3

1Department of Ecology and Evolutionary Biology PrincetonUniversity

2Department of Experimental Plant Ecology Nijmegen University3Smithsonian Tropical Research Institute Republic of Panama

4Department of Biological Sciences Marquette University

April 11 2018

lowastmvissersciencerunl

1

S1 SUPPLEMENTAL TABLES

S1 Supplemental tables

2


species code FF FI FD IF II IDAlchornea costaricensis ALCHCO 5 3 1 16 70 15Anacardium excelsum ANACEX 21 3 1 3 30 4Brosimum alicastrum BROSAL 28 10 3 5 28 12Cecropia insignis CECRIN 102 14 51 5 1 4Cordia alliodora CORDAL 26 8 6 4 5 9Eugenia oerstediana EUGEOE 9 1 8 2 10 19Guarea guidonia GUARGU 5 2 1 3 32 9Gustavia superba GUSTSU 39 5 3 11 62 6Hieronyma alchorneoides HYERAL 11 5 1 6 24 3Jacaranda copaia JAC1CO 135 26 18 11 30 13Macrocnemum roseum MACRGL 10 8 2 5 42 7Protium tenuifolium PROTTE 10 7 1 5 68 12Quararibea asterolepis QUARAS 11 3 1 9 26 3Simarouba amara SIMAAM 44 14 23 7 19 33Spondias radlkoferi SPONRA 24 2 4 4 17 9Tabernaemontana arborea TAB2AR 1 2 2 1 19 17Tetragastris panamensis TET2PA 4 3 1 2 76 15Trichilia tuberculata TRI2TU 13 6 6 20 53 34Virola sebifera VIROSE 7 3 5 4 30 19Virola surinamensis VIROSU 16 4 2 4 23 12Zanthoxylum ekmanii ZANTBE 43 20 16 4 10 8

Table S1 The focal tree species their codes (used in table S5) and their ob-served frequencies of different combinations of initial and final states Codes FI and D represent liana-free liana-infested and dead individuals respectivelyCode combinations represent states in initial and final censuses conducted 10or 11 years apart (eg FF represents liana-free in both censuses) These datawere used to estimate the transition rates

3

S1

SUPPLEMENTALTABLES

species C R M LAlchornea costaricensis 0054 (00150171) 0026 (00140047) 0011 (00010158) 0006 (00682)Anacardium excelsum 0014 (00040045) 001 (00030031) 0004 (0004) 0008 (00010053)Brosimum alicastrum 0037 (0019007) 0017 (00070043) 0004 (00071) 0029 (00120068)Cecropia insignis 0035 (00060169) 0216 (00230764) 0033 (00190056) 0038 (0001067)Cordia alliodora 0046 (00190106) 0055 (00170164) 0005 (00249) 0079 (00290197)Eugenia oerstediana 0013 (00020096) 0016 (00040067) 0055 (00250116) 0038 (00070191)Guarea guidonia 0036 (00090143) 001 (00030033) 0012 (00010152) 0011 (00238)Gustavia superba 0013 (00050032) 0017 (00090031) 0006 (00020022) 0001 (00758)Hieronyma alchorneoides 0043 (00170107) 0027 (00110063) 0005 (00082) 0005 (00351)Jacaranda copaia 0022 (00150033) 0032 (00170058) 0009 (00050017) 0021 (00080054)Macrocnemum roseum 0063 (0030129) 0015 (00060037) 0009 (00010074) 0005 (00535)Protium tenuifolium 0057 (00260119) 0009 (00030022) 0003 (00289) 0012 (00030056)Quararibea asterolepis 0028 (0008009) 0033 (00160067) 0007 (00010067) 0002 (00998)Simarouba amara 004 (00220071) 0029 (00130064) 0025 (0012005) 0062 (00310119)Spondias radlkoferi 001 (0002004) 002 (00070053) 0013 (0004004) 0024 (00060085)Tabernaemontana arborea 0116 (00220427) 0008 (00010069) 0044 (00030418) 0016 (00976)Tetragastris panamensis 0057 (00170169) 0003 (00010014) 0012 (00010173) 0005 (00823)Trichilia tuberculata 0048 (00190113) 0038 (00220064) 0025 (00080074) 0015 (00010153)Virola sebifera 0038 (00120121) 0015 (00050041) 0039 (00130111) 0005 (00997)Virola surinamensis 0027 (0010073) 0016 (00060043) 0006 (00073) 0032 (0012008)Zanthoxylum ekmanii 0051 (00290087) 0038 (00130109) 0017 (00060044) 0032 (00070137)

Table S2 Species-specific estimated rate parameters (all per year) with their 95 confidence intervals Columns refer tospecies colonization (C) shedding (R) mortality (M) and lethality (L)

4

S1

SUPPLEMENTALTABLES

FF FI FD IF II ID TotalAVA 026 (65) 0012 (3) 0032 (8) 014 (35) 046 (115) 0092 (23) 249

DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938

Table S3 The plots at which trees were observed and the proportions of trees in different combinations of initial and finalstates by plot with numbers of trees actually observed in parentheses See caption to Table S1 for further explanation

5

S1

SUPPLEMENTALTABLES

AVA DRAYTON FDP PEARSON ZETEKAlchornea costaricensis 44 (1) 78 (088) 8794 (093) 33 (1) 01 (0)Anacardium excelsum 00 (0) 56 (083) 1122 (05) 2134 (062) 00 (0)Brosimum alicastrum 01 (0) 58 (062) 3872 (053) 01 (0) 24 (05)

Cecropia insignis 00 (0) 09 (0) 9157 (0057) 00 (0) 111 (0091)Cordia alliodora 16 (017) 04 (0) 1038 (026) 22 (1) 58 (062)

Eugenia oerstediana 49 (044) 00 (0) 2538 (066) 11 (1) 11 (1)Guarea guidonia 1215 (08) 1519 (079) 00 (0) 1415 (093) 33 (1)Gustavia superba 5786 (066) 916 (056) 00 (0) 712 (058) 612 (05)

Hieronyma alchorneoide 56 (083) 01 (0) 2131 (068) 712 (058) 00 (0)Jacaranda copaia 01 (0) 818 (044) 36185 (019) 612 (05) 417 (024)

Macrocnemum roseum 44 (1) 1922 (086) 713 (054) 2435 (069) 00 (0)Protium tenuifolium 44 (1) 5561 (09) 00 (0) 2234 (065) 44 (1)

Quararibea asterolepis 910 (09) 1425 (056) 00 (0) 03 (0) 1515 (1)Simarouba amara 12 (05) 45 (08) 47116 (041) 12 (05) 615 (04)

Spondias radlkoferi 1933 (058) 12 (05) 00 (0) 1024 (042) 01 (0)Tabernaemont arborea 22 (1) 00 (0) 00 (0) 11 (1) 3439 (087)

Tetragastris panamensis 11 (1) 5459 (092) 11 (1) 2629 (09) 1111 (1)Trichilia tuberculata 3643 (084) 1616 (1) 00 (0) 919 (047) 4654 (085)

Virola sebifera 913 (069) 2124 (088) 00 (0) 914 (064) 1417 (082)Virola surinamensis 58 (062) 1623 (07) 11 (1) 920 (045) 89 (089)

Zanthoxylum ekmanii 01 (0) 03 (0) 2191 (023) 00 (0) 16 (017)

Table S4 Variation among sites and species in sample sizes and liana prevalence (initial census) Entries are number ofindividuals infested total number of individuals (liana prevalence in parentheses) for each species and plot

6

S1

SUPPLEMENTALTABLES

ALCHCO ANACEX BROSAL CECRIN CORDAL EUGEOE GUARGU GUSTSU HYERAL JAC1CO MACRGLFull model (Ms Ls Rs Cs) 0661 0512 0552 0126 0300 0221 0737 0421 0602 0328 0802

Only mortality (Ms L R C) 0496 0496 0496 0494 0496 0492 0495 0496 0496 0496 0496Only liana lethality (M Ls R C) 0547 0540 0469 0440 0328 0439 0528 0562 0551 0496 0551

Only shedding (M L Rs C) 0533 0721 0616 0149 0375 0628 0716 0617 0526 0490 0647Only colonization (M L R Cs) 0578 0235 0468 0453 0530 0221 0466 0217 0513 0330 0621

All except mortality (M Ls Rs Cs) 0661 0511 0551 0126 0298 0226 0737 0421 0602 0327 0802All except lethality (Ms L Rs Cs) 0617 0388 0589 0131 0406 0297 0687 0290 0545 0327 0764All except shedding (Ms Ls R Cs) 0620 0283 0442 0394 0366 0175 0501 0291 0567 0332 0661

All except colonization (Ms Ls Rs C) 0590 0778 0583 0143 0271 0543 0760 0697 0586 0492 0717Shedding and colonization (M L Rs Cs) 0617 0386 0587 0131 0406 0301 0687 0289 0544 0326 0764

Shedding and mortality (Ms L Rs C) 0534 0722 0617 0149 0375 0625 0717 0618 0527 0491 0648Shedding and lethality (M Ls Rs C) 0590 0777 0582 0143 0269 0550 0760 0697 0586 0491 0717

Colonization and mortality (Ms L R Cs) 0578 0236 0469 0452 0531 0218 0466 0218 0514 0331 0622Colonization and lethality (M Ls R Cs) 0620 0282 0441 0396 0364 0178 0501 0291 0567 0331 0661

Mortality and lethality (Ms Ls R C) 0547 0540 0471 0438 0330 0434 0529 0562 0551 0496 0551

PROTTE QUARAS SIMAAM SPONRA TAB2AR TET2PA TRI2TU VIROSE VIROSU ZANTBEFull model (Ms Ls Rs Cs) 0843 0451 0372 0200 0927 0941 0517 0707 0451 0490

Only mortality (Ms L R C) 0496 0496 0494 0495 0493 0495 0494 0493 0496 0495Only liana lethality (M Ls R C) 0525 0561 0371 0487 0511 0549 0516 0551 0459 0460

Only shedding (M L Rs C) 0741 0478 0507 0588 0755 0871 0452 0648 0633 0452Only colonization (M L R Cs) 0592 0395 0491 0167 0767 0592 0544 0481 0383 0563

All except mortality (M Ls Rs Cs) 0843 0451 0374 0200 0928 0941 0517 0708 0449 0490All except lethality (Ms L Rs Cs) 0822 0380 0502 0209 0924 0920 0499 0632 0511 0518All except shedding (Ms Ls R Cs) 0616 0471 0365 0161 0772 0634 0563 0539 0347 0531

All except colonization (Ms Ls Rs C) 0781 0541 0377 0578 0775 0916 0470 0718 0584 0421Shedding and colonization (M L Rs Cs) 0821 0379 0503 0209 0925 0920 0500 0634 0510 0518

Shedding and mortality (Ms L Rs C) 0742 0479 0507 0588 0752 0871 0452 0646 0634 0452Shedding and lethality (M Ls Rs C) 0780 0541 0378 0577 0777 0916 0471 0718 0583 0421

Colonization and mortality (Ms L R Cs) 0593 0395 0490 0167 0766 0592 0543 0480 0384 0563Colonization and lethality (M Ls R Cs) 0616 0471 0367 0161 0772 0634 0563 0539 0346 0531

Mortality and lethality (Ms Ls R C) 0526 0561 0369 0487 0510 0549 0516 0551 0460 0460

Table S5 Predicted liana prevalence for all species and all models Species codes are defined in table S1

7

S1

SUPPLEMENTALTABLES

GFI χ2 df Latent variable indicators Mean paramerer bias Mean bias in parameter sd Power1 0975 1517 6000 STI = rgr -0008 -0046 08912 0962 2380 6000 STI = rgrsap -0021 -0046 08963 0959 2416 6000 STI = mrtsap 0035 -0044 08974 0951 3384 6000 STI = mrt -0031 -0044 08895 0929 4606 6000 STI = wd -0002 -0047 08916 0905 8145 10000 STI = rgrsap + mrtsap 12529 6121 09177 0888 8555 10000 STI = rgr + rgrsap 19096 0296 08828 0886 12677 10000 STI = rgr + mrt 2980 0449 08279 0866 12093 10000 STI = mrt + mrtsap 40774 0661 0905

10 0834 20441 16000 STI = rgr + rgrsap + wd -14394 0256 086411 0808 25362 16000 STI = rgr + mrt + wd -43400 0708 083312 0791 28363 16000 STI = rgrsap + mrt + wd -32120 64325 092813 0757 30624 16000 STI = mrt + mrtsap + wd -27476265 1322 078014 0682 54628 23000 STI = rgr + rgrsap + mrt + mrtsap 0143 0114 087615 0658 65927 31000 STI = rgr + rgrsap + mrt + mrtsap + wd 24060 0113 0875

Table S6 Fit statistics for 15 alternative structural equation models with different indicators for the latent variable STI -representing the unobservable construct shade tolerance Recall that higher values of STI are associated with lower shade-tolerance The columns GFI χ2 and df are the goodness of fit index the χ2 statistic and the degrees of freedom (from thelavaan package see below) respectively The columns mean parameter bias and mean bias in parameter sd refer to the meanproportional bias in the estimated parameter and corresponding standard deviation after 1000 simulations respectively Thecolumn power refers to the proportion of instances that a parameter was within 95 CI of the true parameter Indicatorsinclude wood density (wd) the growth rates and mortality of tree gt 10 cm dbh (rgr amp mrt) and the growth rates and mortalityof saplings gt1 and lt4 cm dbh (rgrsap amp mrtsap) In lavaan degrees of freedom is calculated as the number of the unique valuesin the variance-covariance matrix minus the number of free parameters The exact equation is df = n(n+ 1)2minus tminus f(f + 1)2where n is the number of variables t is the number of free parameters and f is the number of fixed exogenous variables

8

S1

SUPPLEMENTALTABLES

SEM variable type Response Dependent Coefficient se z p value

Latent variable Latent shade tolerance Relative growth rate (ge10cm dbh) 1000 0000

Direct pathways (regressions)

R Latent shade tolerance 0427 0197 2165 001518L Latent shade tolerance 0591 0176 3361 000039C Latent shade tolerance 0210 0213 0985 01622M Latent shade tolerance 0406 0199 2034 0021Observed prevalence R -0517 0113 -4565 0Observed prevalence L -0259 0127 -2045 002043Observed prevalence C 0295 0105 2816 000243Observed prevalence M 0211 0112 1882 002993

Estimated covariance Latent shade tolerance Observed prevalence -0302 0166 -1813 003492

Table S7 Estimated path loadings or coefficients their standard errors z-values and p-values for each hypothesized path inthe best SEM (depicted in Fig 6)

9

S2 SUPPLEMENTAL FIGURES

S2 Supplemental Figures

1 2 5 10 20

000

001

002

003

004

005

T (number of transitions)

rate

CRML

Figure S1 Relationships between annual transition rates estimated for all treescombined (solid lines) and the number of time steps (T) into which the censusinterval is divided The dashed lines show the estimates for annual time steps(as used in the main analyses) which corresponds with T=10 for our 10-yearcensus interval

10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086

rgr rgrs mrt mrts wd

R L C M

obs

STI

Figure S2 Diagram for the full structural equation model The 14 alternativemodels that were fit were simpler subsets of this model including a smaller num-ber of indicator variables for the index of shade-intolerance (STI) The down-ward pointing arrows show the hypothesized paths through which the degree ofshade-tolerance influences liana prevalence via shedding colonization lethalityand mortality Upward pointing arrows show which variables influenced the es-timation of the latent STI variable Squares indicate observed (measured) vari-ables and the circle indicates the one latent variable The color thickness andshading indicate the direction size and significance of each path loading Thedouble-headed arrow indicates that no direct causal relationship was hypothe-sized or fit but rather only the covariance between variables was estimated

11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

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006

008

01

0 005 01 015 02 025

0

002

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006

008

01

0 002 004 006 008 01 012 014

0

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01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

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006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C

Figure S3 Univariate distributions of the rate parameters across species (diagonal) and bivariate correlations among theseparameters The blue lines show the trend among variables after accounting for uncertainty in both axis and represent thefirst axis of a principle component analysis (scatterplots) The lower half matrix of the plot shows the corresponding correlationtests including 9875 confidence intervals (Bonferroni corrected for 6 tests)

12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

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8

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oniz

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ddin

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ality

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)

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D

Var

ianc

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ned

in P

00

01

02

03

04

Figure S4 The four rates used to predict liana prevalence in our matrix model varied in (A) sensitivity of predicted lianaprevalence (P ) to the rate (B) variation in the estimated rate among our 21 focal species (estimated as the coefficientof variation standard deviation mean) (C) the product of sensitivity and variation an indicator of expected explanatorypower and (D) actual r2 values for ordinary linear regressions between estimated species-specific rates and observed prevalence(P ) among our 21 species The product of sensitivity and variability for each rate accorded well with their pairwise correlationswith prevalence (Fig 2) as well as with the explanatory power of different models (Table 1) The four rates are the rate ofcolonization of uninfested trees by lianas the rate at which infested trees recover from or lose their lianas the mortality rateof uninfested trees and the additional mortality rate or lethality caused by liana infestation

13


002 006 010

minus20

minus10

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Colonization

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ity

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minus10

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i

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00 01 02 03 04 05

minus20

minus10

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sitiv

ity(dP

i

dAij)

rate

Figure S5 Sensitivity of the predicted liana prevalence (P ) to the rates ofcolonization (C) shedding (R) baseline mortality (M) and additional mortalitywhen infested (lethality L) The vertical axis shows the change in the proportioninfested due to small changes of +1 in each rate The vertical axis rangeis identical across all panels for easy comparison The left column of panelsshows sensitivity when increasing each rate by 1 and keeping all other ratesconstant Grey lines show the trajectories for each species and the green lineshows the mean trajectory over all 21 species The center column of panels showssensitivity to small iterations of the focal rate while keeping the other rates attheir estimates for each species (black dots) The green line is a smoothedmoving average The right column of panels shows sensitivity to small changesof the focal rate plotted against the predicted proportion infested In the middleand right columns the sizes of the black dots are proportional to sample sizesor the number of individual trees assessed and the black horizontal and verticallines indicate the mean rate and mean sensitivities over all species

14

Visser-et-al_2018b_JEcol

Visser-et-al_2018b_JEcol_S1


1emsp |emspINTRODUC TION

Lianasmdashwoody climbersmdashare globally widespread highly diverseand play important roles in forest ecosystems (Putz amp Mooney1991 Schnitzer Bongers Burnham amp Putz 2015) Lianas canbe considered structural macroparasites of trees (Stevens 1987StewartampSchnitzer2017)Theytakeadvantageoftreestemsandbranchestogrowintothecanopywheretheytypicallydeploytheirfoliageabovetheirhoststhusgainingaccesstolightattheexpenseoftheirhosts(AvalosMulkeyampKitajima1999Putz1984a)whilesimultaneously competingwith hosts for below-ground resources(egDillenburgWhighamTeramuraampForseth1993)Asa con-sequencelianainfestationgenerallyhasstrongnegativeeffectsontreegrowthsurvivalandreproduction(ClarkampClark1990IngwellWrightBecklundHubbellampSchnitzer2010SchnitzerampBongers2002Wright Sun Pickering Fletcher amp Chen 2015) Lianas arealsoincreasinginabundanceinmanyNeotropicalforests(reviewedinSchnitzer2015Wrightetal2015)

Akeyquestion ishowlianas influencetherelativecompetitiveabilitymdashandultimately the relativeabundancesmdashof treespecies Intheoryhostspeciesthatarelessimpactedbyasharedparasitegainan advantage in competition (Holt Grover amp Tilman 1994) Theneteffectsoflianasonagiventreespeciesdependonhowsensi-tiveeachhostspeciesistoinfestation(lianatolerance)andontheproportionof itspopulationinfested(lianaprevalenceseeMuller-LandauampPacala2018Visseretal2018)Arecentstudyhasshownthattreespeciesdifferstronglyintheirtoleranceoflianainfestationwithespeciallyfast-growingandlight-demandingspeciesbeingleasttolerantoflianainfestation(Visseretal2018)Sympatrictreespe-ciesalsovaryconsiderablyintheproportionofindividualsinfestedwithlianaswithempiricalevidencesuggestingthatlight-demandingspeciesdisplaythelowestlevelsoflianaprevalence(ClarkampClark1990vanderHeijdenetal2008)

Hereweaskwhetherthenegativeeffectoflianasonhostpop-ulationsisgreaterforlight-demandingorforshade-tolerantspeciesAkeyissueistheinterpretationofthelowlianaprevalenceinlight-demandingspeciesArefewerindividualsoflight-demandingspeciesinfested because these species are able to avoid or shed infesta-tion (ashypothesizedbyClarkampClark1990Putz1984a1984bSchnitzer Dalling amp Carson 2000) Or are lianas less prevalentamonglight-demandingspeciessimplyduetosurvivorbiaswithin-festedindividualsdyingrapidlyanduninfestedindividualssurvivingleadingtoalowproportionofinfestedliveindividuals(ashypothe-sizedbyVisseretal2018)Thesetwopossibilitiesleadtooppositepredictionsabout the relative impactof liana infestation for light-demanding versus shade-tolerant host species To distinguish be-tweenthesetwopossibilitiesthecauseofinterspecificvariationinlianaprevalencemustbedetermined(Muller-LandauampPacala2018Visseretal2018)

Manystudiesassumethatvariationinlianaprevalenceamongtreespeciesreflectsvariationincolonizationandlossrates(egClarkampClark1990vanderHeijdenetal2008)whichinturnareattributed tovarying treedefencesagainst lianasHypothesized

tree defences include large leaves flexible trunks fast mono-podial growth and ant symbionts (Hegarty 1989 Putz 19801984a 1984b) which are all associated with fast-growing andlight-demanding species However liana prevalencewill dependnotonlyon colonization (transmission) and loss (shedding) ratesbut also on baseline host tree mortality and the effects of lia-nasonhostmortality (lethality) justasforanyotherparasiteorpathogen(AndersonampMay1982)Variationamongtreespeciesinlianaprevalencemayreflectinterspecificvariationinanyandalloftheserates

Variation in liana prevalence among tree species could be ex-plained in largepartbythedemographyofthehosttrees (Muller-LandauampPacala2018)First tree specieswith shorter life spanshave less timetobecome infestedandhenceshouldhavea lowerproportionofinfestedindividualsSecondspeciesthatexperiencehighermortalitywheninfestedshouldalsohavelowerproportionsinfestedbecausetheinfestedindividualsexitthepopulationfasterBoththesemechanismareplausible it iswellknownthatbaselinemortalityvariesextensivelyamongtreespecies(Conditetal2006)and the effects of lianas on host mortality differs greatly amongspecies (Visser etal 2018) Yet the idea that host demographymayshapeobserved interspecificvariation in liana infestationhasreceived almost no attention in the literature (Visser etal 2018)It isnotknownhowvariation in liana infestationamonghost treespecies relates tovariation in colonizationversus sheddingversushostdemographyDisentanglingtheseratesrequiresestimationofcolonizationand loss rates fromdynamicdataonchanges in lianainfestationsomethingnopreviousstudyhasdone

Here we apply models from disease ecology to explain theproportionoftreesinfestedbylianasin21tropicaltreespeciesonBarroColoradoIslandPanamaWeestimateratesofliana-freemor-tality liana-infestedmortality lianacolonizationand liana loss foreachspeciesfromfielddataWethenuseahostndashparasitemodeltopredictlianaprevalence(theproportionofindividualsinfested)foreach tree species and evaluate the accuracyof thesepredictionsWetestalternativehypotheses that interspecificvariation in lianaprevalenceispredominantlydrivenbyinterspecificvariationincolo-nizationandshedding(egPutz1980vanderHeijdenetal2008)orinhostdemographyspecificallybaselinehosttreemortalityandliana-induced lethality (afterMuller-LandauampPacala2018Visseretal2018)Wequantifytherelativecontributionsofinterspecificvariation in liana colonization rates liana shedding rates and treedemographytointerspecificvariationinlianainfestationFinallywetestwhetheranyoftheseratesandtheirintegrationintolianaprev-alencerelatetomeasuresofshadetoleranceacrosstreespecies

2emsp |emspMATERIAL S AND METHODS

21emsp|emspStudy site

Barro Colorado Island (9deg9primeN 79deg51primeW) Panama hosts a moisttropicalforestTemperatureaverages27degCandannualrainfallav-erages2650mm(since1929)withadryseasonbetweenJanuary










(1)A=

⎛⎜⎜⎜⎝



M M+L 1

⎞⎟⎟⎟⎠




















3emsp |emspRESULTS





001 003 005

02

04

06

08

02

04

06

08

02

04

06

08

02

04

06

08


r2 = 0 r2 = 039 r2 = 013 r2 = 041




Obs

erve

d pr

eval

ence

(P)

(a) (b) (c) (d)








Fullmodel(MSLSRSCS)

058 016 008 001 [013ndash092] 4


058 016 008 001 [013ndash094] 3


C)058 015 002 006 [014ndash092] 3


C)058 015 002 006 [014ndash092] 2


054 017 003 009 [015ndash087] 1


LRsC)

054 017 003 009 [015ndash087] 2


047 018 009 003 [013ndash092] 2


047 018 009 003 [013ndash092] 3


R C)041 019 011 018 [033ndash056] 1


R C)041 019 011 018 [033ndash056] 2


RCs)028 022 015 008 [016ndash077] 2


RCS)028 022 015 008 [016ndash077] 3


LRCs)010 024 015 009 [017ndash077] 2


010 024 015 009 [017ndash077] 1

Onlymortality(MSLR

C)000 025 012 025 [049ndash05] 1








00 02 04 06 08 1000

02

04

06

08

10(a) Full model

Predicted

Obs

erve

d

r2 = 058

MsLsRsCs

ObservedPredicted

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 041

MsLsRC

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 047

MLRsCs

00 02 04 06 08 1000

02

04

06

08

10

00 05 10



02

04

06

08

Obs

erve

d pr

eval

ance

(P)

r2 = 049


She

ddin

g (R

)

0003

001

007

r2 = 037


Col

oniz

atio

n (C

)

001

003

01


000

002

004

006

008

Leth

ality

(L)

r2 = 03


(a) (b) (c) (d)









RGR

SI


Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)











ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

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SUPPLEMENTALTABLES












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SUPPLEMENTALTABLES


















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SUPPLEMENTALTABLES




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SUPPLEMENTALTABLES







9



1 2 5 10 20

000

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rate

CRML


10


minus009

018021

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056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

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0 001 002 003 004 005 006 007

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003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14












(1)A=

⎛⎜⎜⎜⎝



M M+L 1

⎞⎟⎟⎟⎠




















3emsp |emspRESULTS





001 003 005

02

04

06

08

02

04

06

08

02

04

06

08

02

04

06

08


r2 = 0 r2 = 039 r2 = 013 r2 = 041




Obs

erve

d pr

eval

ence

(P)

(a) (b) (c) (d)








Fullmodel(MSLSRSCS)

058 016 008 001 [013ndash092] 4


058 016 008 001 [013ndash094] 3


C)058 015 002 006 [014ndash092] 3


C)058 015 002 006 [014ndash092] 2


054 017 003 009 [015ndash087] 1


LRsC)

054 017 003 009 [015ndash087] 2


047 018 009 003 [013ndash092] 2


047 018 009 003 [013ndash092] 3


R C)041 019 011 018 [033ndash056] 1


R C)041 019 011 018 [033ndash056] 2


RCs)028 022 015 008 [016ndash077] 2


RCS)028 022 015 008 [016ndash077] 3


LRCs)010 024 015 009 [017ndash077] 2


010 024 015 009 [017ndash077] 1

Onlymortality(MSLR

C)000 025 012 025 [049ndash05] 1








00 02 04 06 08 1000

02

04

06

08

10(a) Full model

Predicted

Obs

erve

d

r2 = 058

MsLsRsCs

ObservedPredicted

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 041

MsLsRC

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 047

MLRsCs

00 02 04 06 08 1000

02

04

06

08

10

00 05 10



02

04

06

08

Obs

erve

d pr

eval

ance

(P)

r2 = 049


She

ddin

g (R

)

0003

001

007

r2 = 037


Col

oniz

atio

n (C

)

001

003

01


000

002

004

006

008

Leth

ality

(L)

r2 = 03


(a) (b) (c) (d)









RGR

SI


Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)











ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14





















3emsp |emspRESULTS





001 003 005

02

04

06

08

02

04

06

08

02

04

06

08

02

04

06

08


r2 = 0 r2 = 039 r2 = 013 r2 = 041




Obs

erve

d pr

eval

ence

(P)

(a) (b) (c) (d)








Fullmodel(MSLSRSCS)

058 016 008 001 [013ndash092] 4


058 016 008 001 [013ndash094] 3


C)058 015 002 006 [014ndash092] 3


C)058 015 002 006 [014ndash092] 2


054 017 003 009 [015ndash087] 1


LRsC)

054 017 003 009 [015ndash087] 2


047 018 009 003 [013ndash092] 2


047 018 009 003 [013ndash092] 3


R C)041 019 011 018 [033ndash056] 1


R C)041 019 011 018 [033ndash056] 2


RCs)028 022 015 008 [016ndash077] 2


RCS)028 022 015 008 [016ndash077] 3


LRCs)010 024 015 009 [017ndash077] 2


010 024 015 009 [017ndash077] 1

Onlymortality(MSLR

C)000 025 012 025 [049ndash05] 1








00 02 04 06 08 1000

02

04

06

08

10(a) Full model

Predicted

Obs

erve

d

r2 = 058

MsLsRsCs

ObservedPredicted

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 041

MsLsRC

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 047

MLRsCs

00 02 04 06 08 1000

02

04

06

08

10

00 05 10



02

04

06

08

Obs

erve

d pr

eval

ance

(P)

r2 = 049


She

ddin

g (R

)

0003

001

007

r2 = 037


Col

oniz

atio

n (C

)

001

003

01


000

002

004

006

008

Leth

ality

(L)

r2 = 03


(a) (b) (c) (d)









RGR

SI


Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)











ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14










Fullmodel(MSLSRSCS)

058 016 008 001 [013ndash092] 4


058 016 008 001 [013ndash094] 3


C)058 015 002 006 [014ndash092] 3


C)058 015 002 006 [014ndash092] 2


054 017 003 009 [015ndash087] 1


LRsC)

054 017 003 009 [015ndash087] 2


047 018 009 003 [013ndash092] 2


047 018 009 003 [013ndash092] 3


R C)041 019 011 018 [033ndash056] 1


R C)041 019 011 018 [033ndash056] 2


RCs)028 022 015 008 [016ndash077] 2


RCS)028 022 015 008 [016ndash077] 3


LRCs)010 024 015 009 [017ndash077] 2


010 024 015 009 [017ndash077] 1

Onlymortality(MSLR

C)000 025 012 025 [049ndash05] 1








00 02 04 06 08 1000

02

04

06

08

10(a) Full model

Predicted

Obs

erve

d

r2 = 058

MsLsRsCs

ObservedPredicted

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 041

MsLsRC

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 047

MLRsCs

00 02 04 06 08 1000

02

04

06

08

10

00 05 10



02

04

06

08

Obs

erve

d pr

eval

ance

(P)

r2 = 049


She

ddin

g (R

)

0003

001

007

r2 = 037


Col

oniz

atio

n (C

)

001

003

01


000

002

004

006

008

Leth

ality

(L)

r2 = 03


(a) (b) (c) (d)









RGR

SI


Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)











ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14









00 02 04 06 08 1000

02

04

06

08

10(a) Full model

Predicted

Obs

erve

d

r2 = 058

MsLsRsCs

ObservedPredicted

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 041

MsLsRC

00 02 04 06 08 1000

02

04

06

08

10

00 05 10

00 02 04 06 08 1000

02

04

06

08


Predicted

r2 = 047

MLRsCs

00 02 04 06 08 1000

02

04

06

08

10

00 05 10



02

04

06

08

Obs

erve

d pr

eval

ance

(P)

r2 = 049


She

ddin

g (R

)

0003

001

007

r2 = 037


Col

oniz

atio

n (C

)

001

003

01


000

002

004

006

008

Leth

ality

(L)

r2 = 03


(a) (b) (c) (d)









RGR

SI


Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)











ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14











RGR

SI


Prevalence

1 (0)

ndash0302 (0166)

0427 (0197) 0591 (0176) 021 (0213) 0406 (0199)

minus0517 (0113)

minus0259 (0127) 0295 (0105)

0211 (0112)











ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14













ACKNOWLEDG EMENTS






ORCID






R E FE R E N C E S




















































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14
































tree species





April 11 2018


1



2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14





2




3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14






3

S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S1

SUPPLEMENTALTABLES



4

S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S1

SUPPLEMENTALTABLES


DRAYTON 015 (49) 0058 (19) 0036 (12) 0046 (15) 052 (172) 019 (62) 329FDP 041 (352) 011 (94) 012 (99) 0057 (49) 02 (169) 011 (96) 859

PEARSON 026 (70) 0073 (20) 004 (11) 0062 (17) 049 (135) 0073 (20) 273ZETEK 012 (28) 0057 (13) 011 (26) 0066 (15) 037 (84) 027 (62) 228

Total 564 149 156 131 675 263 1938


5

S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S1

SUPPLEMENTALTABLES












6

S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S1

SUPPLEMENTALTABLES


















7

S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S1

SUPPLEMENTALTABLES




8

S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S1

SUPPLEMENTALTABLES







9



1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14





1 2 5 10 20

000

001

002

003

004

005


rate

CRML


10


minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14




minus009

018021

026

minus026minus035

minus049

053

056

068

071

minus071

085086


R L C M

obs

STI


11

S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S2

SUPPLEMENTALFIG

URES

0 002 004 006 008

Den

sity

0 001 002 003 004 005 006 007

0

002

004

006

008

01

0 005 01 015 02 025

0

002

004

006

008

01

0 002 004 006 008 01 012 014

0

002

004

006

008

01

r2 = 00299875 CI (r) [minus0395 0641]

L ~ M

0 001 002 003 004 005 006

Den

sity

0 005 01 015 02 025

0

001

002

003

004

005

006

007

0 002 004 006 008 01 012 014

0

001

002

003

004

005

006

007

r2 = 01129875 CI (r) [minus0236 0734]

L ~ R

r2 = 00419875 CI (r) [minus0365 0661]

M ~ R

0 005 01 015 02 025

Den

sity

0 002 004 006 008 01 012 014

0

005

01

015

02

025

r2 = 00059875 CI (r) [minus0577 0478]

L ~ C

r2 = 00469875 CI (r) [minus0356 0667]

M ~ C

r2 = 00079875 CI (r) [minus0588 0464]

R ~ C

0 002 004 006 008 01 012

Den

sity

L

L

M

M

R

R

C

C


12

S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



S2

SUPPLEMENTALFIG

URES

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

A

Mea

n ab

solu

te s

ensi

tivity

0

2

4

6

8

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

B

Coe

ficie

nt o

f var

iatio

n (

)

0

50

100

150

200

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

C

Exp

ecte

d co

ntrib

utio

n to

inte

rspe

cific

var

iatio

n

0

2

4

6

8

10

Col

oniz

atio

n

She

ddin

g

Mor

talit

y

Leth

ality

D

Var

ianc

e ex

plai

ned

in P

00

01

02

03

04


13


002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14




002 006 010

minus20

minus10

0

10

20

Colonization

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 005 010 015 020

minus20

minus10

0

10

20

Shedding

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

001 003 005

minus20

minus10

0

10

20

Mortality

Sen

sitiv

ity

02 04 06 08

minus20

minus10

0

10

20

000 002 004 006 008

minus20

minus10

0

10

20

Lethality

Sen

sitiv

ity

rate

02 04 06 08

minus20

minus10

0

10

20

proportion infested

00 01 02 03 04 05

minus20

minus10

0

10

20S

ensi

tivity

(dPi

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

00 01 02 03 04 05

minus20

minus10

0

10

20

Sen

sitiv

ity(dP

i

dAij)

rate


14



a host–parasite model explains variation in liana infestation...

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