The combined effects of biotic and abiotic stress on species richness and connectance

15 Pages·2017·1.57 MB·English

RESEARCHARTICLE
The combined effects of biotic and abiotic
stress on species richness and connectance
DevduttKulkarni*,FrederikDeLaender
LaboratoryofEnvironmentalEcosystemEcology,ResearchUnitinEnvironmentalandEvolutionaryBiology
(URBE),UniversityofNamur,Namur,Belgium
*[email protected],[email protected]
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a1111111111 Abstract
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Foodwebstructureandspeciesrichnessarebothsubjecttobiotic(e.g.predationpressure
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andresourcelimitation)andabioticstress(e.g.environmentalchange).Weinvestigatedthe
combinedeffectsofbothtypesofstressonrichnessandconnectance,andontheirrelation-
ship,inapredator-preysystem.Tothisend,wedevelopedamathematicaltwotrophiclevel
food-webmodeltoinvestigatetheeffectsofbioticandabioticstressonfoodwebconnec-
OPENACCESS tanceandspeciesrichness.Wefoundnegativeeffectsoftop-downandbottom-upcontrol
Citation:KulkarniD,DeLaenderF(2017)The onpreyandpredatorrichness,respectively.Effectsoftop-downandbottom-upcontrol
combinedeffectsofbioticandabioticstresson
werestrongerwheninitialconnectancewashighandlow,respectively.Bottom-upcontrol
speciesrichnessandconnectance.PLoSONE12
couldeitheraggravateorbuffernegativeeffectsoftop-downcontrol.Abioticstressaffecting
(3):e0172828.doi:10.1371/journal.pone.0172828
predatorrichnesshadpositiveindirecteffectsonpreyrichness,butonlywheninitialcon-
Editor:AndreaBelgrano,Sveriges
nectancewaslow.However,noindirecteffectsonpredatorrichnesswereobservedfollow-
lantbruksuniversitet,SWEDEN
ingdirecteffectsonpreyrichness.Top-downandbottom-upcontrolselectedforweakly
Received:March15,2016
connectedpreyandhighlyconnectedpredators,therebydecreasingandincreasingcon-
Accepted:February10,2017
nectance,respectively.Oursimulationssuggestabroadrangeofnegativeandpositiverich-
Published:March1,2017 ness-connectancerelationships,therebyrevisitingtheoftenfoundnegativerelationship
Copyright:©2017Kulkarni,DeLaender.Thisisan betweenrichnessandconnectanceinfoodwebs.Ourresultssuggestthat(1)initialfood-
openaccessarticledistributedunderthetermsof webconnectancestronglyinfluencestheeffectsofbioticstressonrichnessandtheoccur-
theCreativeCommonsAttributionLicense,which
renceofindirecteffectsonrichness;and(2)theshapeoftherichness-connectancerelation-
permitsunrestricteduse,distribution,and
shipdependsonthetypeofbioticstress.
reproductioninanymedium,providedtheoriginal
authorandsourcearecredited.
DataAvailabilityStatement:Allrelevantdataare
withinthepaperanditsSupportingInformation
files.
Introduction
Funding:DKwasfundedbyapostdoctoral
fellowshipfromtheCentred’e´tudesetde Foodwebstructureandspeciesrichnessarebothsubjecttobioticandabioticstress[1–2].
recherchesuniversitairesdeNamur,Universityof
Bioticstresscanoccurthroughpredation(top-downcontrolonprey),resourcelimitation
Namur,Belgium.FDLwasfundedbytheUniversity
(bottom-upcontrolonpredators),orthroughacombinationofboth(mixedcontrol[3]).
ofNamur(FSRImpulsionnel48454E1);https://
Whensufficientlystrong,bioticstresscanaffectrichness,e.g.whenhighpredatorrichness
www.unamur.be/.Thefundershadnoroleinstudy
design,datacollectionandanalysis,decisionto leadstoareductionofpreydiversity[4].Specieslosscanleadtosecondaryextinctions,and
publish,orpreparationofthemanuscript. thustochangesinfoodwebstructureandconnectance[5–6].Abioticstressoccurswhenenvi-
ronmentalgradientsexceedtolerancelimits,assuchimpactingfoodwebstructureandcon-
Competinginterests:Theauthorshavedeclared
thatnocompetinginterestsexist. nectance[7–13].Abioticstressorsincludetemperaturechangesandtoxicchemicals,which
PLOSONE|DOI:10.1371/journal.pone.0172828 March1,2017 1/15
Effectsofbioticandabioticstressonfoodwebs
canleadtoavarietyoflethalandsub-lethaleffects[14].Forinstance,changeintemperature
[15]orexposuretotoxicchemicals[16]candirectlyaffectphysiologicalprocessesleadingto
effectsondevelopment,reproductionandsurvival.Justlikebioticstressors,directeffectsof
abioticstressorscanchangerichness[7–11],causesecondaryspecieslossinmulti-trophic
foodwebs[17–19]andleadtotheappearanceordisappearanceoflinksbetweenspecies,
therebyaffectingconnectance[12,20].However,despitetheoverwhelmingevidenceofbiotic
andabioticstressaffectingrichnessandconnectance,thecombinedeffectsofbothtypesof
stressarefarlesswellstudied.
Sincethe1970s,speciesrichnessandconnectancehavebeenshowntorelateintimately.
Thismeansthatfoodwebscannotbetoocomplex,i.e.cannotcontainmanydirectspecies
interactions,andatthesametimehostmanyspecies[21,22].Thisfeatureisreflectedbymany
foodwebsandresultsinanegativerelationshipbetweenconnectanceandspeciesrichness:a
lowerproportionofthepotentialspeciesinteractionsisrealisedinricherfoodwebs.An
importantdriveroftherelationshipbetweenrichnessandconnectance,nexttospatialdynam-
ics[23],andthecapacityofspeciestochangetheirinteractionswithotherspecies(e.g.diet
shifts[24]),isthediversityofinteractiontypes[25].Thus,bioticstress,thetermusedinthe
presentpapertodenoteeffectsofspeciesinteractionsonspeciesrichness,bydefinitionplays
animportantroleinshapingtherichness-connectancerelationship.However,effectsofabiotic
stressonthisrelationshiparelesswellstudied.
Theobjectiveofthepresentpaperistoexaminethecombinedeffectsofbioticandabiotic
stressonrichnessandconnectance,andontheirrelationship,inapredator-preysystemrepre-
sentingabipartitegraph.Theapproachwefollowconsistsoftheorydevelopmentandmodel-
ling.Weproposeasimpletheoreticalframeworktoexplorethecombinedeffectsofbioticand
abioticstressonrichnessandconnectanceinbipartitegraphsmakingasetofwell-defined
assumptions.Wealsoformalizethisframeworkintoanewmodel,whichdiffersfromexisting
food-webmodellingapproaches[26–28]inthreeimportantways.First,themodelisrelatively
parameter-sparse:9parameterssufficetodescribehowrichnessandconnectancevaryalong
gradientsofbioticandabioticstress,regardlessofthenumberofspeciesincluded.Second,the
modelforthefirsttimeunifiestheeffectsthatabioticstressandbioticstresshaveonspecies-
levelfitness,assuggestedelsewhere[29–31],byusingthesamemathematicalformulationfor
bothtypesofstress.Third,themodelcombinesstochasticity(prevailingintheabsenceof
stress)withspeciesselection(prevailingathighbioticand/orabioticstress),acknowledging
theimportanceofbothstochasticanddeterministicdriversoffoodwebassembly[32].We
presentsimulationswithourmodel,representingafullfactorialdesignofthebioticstressor
type(threelevels:top-down;bottom-up;mixedcontrol),abioticstressortype(twolevels:
affectingpredatorreproduction;affectingpreyreproduction),andinitialconnectance(two
levels:lowandhigh).Undertop-downcontrol,predatorabundanceaffectedpreysurvival.
Underbottom-upcontrol,preyabundanceaffectedpredatorreproduction.Undermixed
controlbotheffectsoccurred.Usingthismodel,wefirstaskwhetherabioticstresscanindi-
rectlyalterdiversitybychangingbioticstresslevels,i.e.ifpredator(prey)richnessdecreases
(increases)followingabioticstressonpreyandpredators.Second,weevaluatethecorrespond-
ingchangesinconnectanceandtheconsequencesfortherichness-connectancerelationship.
Materialsandmethods
Theoryandmodeldescription
Thetheorywepresentcombinesstochasticprocesseswiththeeffectsofabioticandbiotic
stressorsondemographicrates,followingarecentlydevelopedapproach[9].Thestochastic
processesarebasedontheneutraltheoryofbiodiversity[33]andassumethatindividualshave
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Effectsofbioticandabioticstressonfoodwebs
identicalindividual-leveltraits,andthatchangesinrelativeabundanceinalocalcommunity
(thecaseweconsiderhere)onlyoccurthroughrandomdeath,reproduction,anddispersal.A
versionoftheneutralmodelonlyincludinglocalprocesseshasbeenpreviouslymodifiedto
includeabioticstresstakingintoaccountbothintra-andinterspecifictolerancevariability[9].
Inthepresentpaper,weextendedthismodeltoinclude(1)twocommunitiesoccupyingdis-
tincttrophiclevels(called‘prey’and‘predators’)(2)effectsofabioticstressonpreyandpreda-
torsurvivalandreproductionand(3)effectsofpredationandresourcelimitation(biotic
stress)onpreysurvivalandpredatorreproduction,respectively.Immigrationoccursbetween
aspatiallynon-explicitmainland(‘meta-community’)andthetwoconsideredlocalcommuni-
ties.Itsratedependsonanimmigrationprobabilitymandspecies-specificrelativeabundances
inthemainland.Abioticstressisassumedtonotaffectthemainland[9].
Death. Aspeciesjcanloseanindividualthroughdeathintwonon-mutuallyexclusive
ways:bychanceandbybioticstress(predation).Effectsofabioticstressondeathratescanbe
easilyconsidered,butareleftoutforsimplicity.Deathbychanceforspeciesj(or‘background
stochasticdeath’)issimplyN/N,whereN istheabundanceofspeciesjandN=∑N isthe
j j j
totalnumberofindividualswithintheconsideredcommunity.
Deathbypredationcanoccurwhenthecorrespondingbioticstresslevelsexceedthecorre-
spondingindividual-levelthresholds.Theprobabilitytodiebypredationiscalculatedby
dividingthenumberofindividualsfromspeciesjsusceptibletodeathbypredationbyallindi-
vidualsinthecommunity(i.e.allspecies)thataresusceptibletodeathbypredation.Inorder
tobesusceptible,c (thecriticalindividual-levelthresholdfordeathbypredation)shouldbe
p
exceededbythetotalpredatorabundancepred.Thisleadstothefollowingequation:
P(deathbychanceorpredationforspeciesj)
P½ðc>c Þ [ðpred>c Þ(cid:138)(cid:1)N N P½ðc>c Þ [ðpred>c Þ(cid:138)(cid:1)N
¼P m j p j j þP j (cid:0) P m j p j j
n ½P½ðc>c Þ [ðpred>c Þ(cid:138)(cid:1)N(cid:138) n N n ½P½ðc>c Þ [ðpred>c Þ(cid:138)(cid:1)N(cid:138)
i¼1 m i p i i i¼1 i i¼1 m i p i i
N
(cid:1)P j ð1Þ
n N
i¼1 i
where:
1
Pðpred>c Þ ¼1(cid:0) (cid:16) (cid:17) ð2Þ
p i 1þ pred spi
cp;50;i
c andc arethespecies-meanthresholdforspeciesj;s istheslope,representingintra-
m,50,i p,50,i pi
specifictolerancevariability;c isthecriticalindividual-levelthresholdfordeathbyabiotic
m
stress.Becausec isspecies-meantolerance,itisnotanindividual-levelparameter.Eq2
p,50,i
quantifieshowindividualswithinaspeciesdifferinsensitivitytopredation.Thesloperepre-
sentsthesteepnessofthisdistributionand,therefore,intraspecifictolerancevariability[9].
Thevalueof‘pred’dependsonfoodwebtopology,whichcanbeformalisedusingafood
web(or‘adjacency’)matrixf.Thisisa(q×q)matrix(qspeciesintotal,includingallpreyand
predatorspecies).Thefirstkrowsandcolumnsrepresentthekpreyspecies;theremainingq-
krowsandcolumnsrepresentpredators.Foreverypredatorjeatingapreyi,a‘1’isplacedat
thecorrespondingelementf[i,j].Iforganisedinthisway,‘pred’forspeciesjisthejthelement
ofthematrixproductf×n,wherenisthe(q×1)vectorofallqspeciesabundances.Foratop
predator,predwillalwaysequalzerosothatEq1simplycollapsestobackgroundmortality
(thesecondterminEq1).
Reproduction. Aspeciesjcangainanindividualthroughimmigration(seefirstpara-
graphof‘Materialandmethods‘)orthroughreproduction.Theprobabilitythatanindividual
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Effectsofbioticandabioticstressonfoodwebs
fromspeciesjreproducesisgivenbydividingthenumberofindividualsfromspeciesjeligible
forreproductionbyallindividualsinthecommunity(i.e.fromallspecies)thatareeligiblefor
reproduction.Anindividualiseligibleforreproductionwhenbiotic(resourcelimitation)and
abioticstressdonotimpedethis.Bioticstress(resourcelimitation)occurswhenthetotal
amountofresource,i.e.thesummeddensitiesofallpreyavailabletoindividualofspeciesj,is
lowerthanc (criticalthresholdforreproductionimpairmentbyresourcelimitation).Abiotic
f
stressoccurswhentheabioticstresslevelcexceedsc (criticalthresholdforreproduction
r
impairmentbyabioticstress).Thisleadsto:
P(anindividualfromspeciesjreproduces)
Pððresource>cÞ \ðc<cÞÞ(cid:1)N
¼P f j r j j ð3Þ
n ½Pððresource>cÞ \ðc<cÞÞ(cid:1)N(cid:138)
i¼1 f i r i i
where:
1
Pðresource>cÞ ¼1(cid:0) (cid:16) (cid:17) ð4Þ
f i 1þ resource sfi
cf;50;i
1
Pðc<cÞ ¼ (cid:16) (cid:17) ð5Þ
r i sri
1þ c
cr;50;i
Again,c andc arethespecies-meanthresholds;s istheslope,representingintra-
f,50,i r,50,i ri
specificvariability.Becausec andc arespecies-meantolerances,theyarenotindividual-level
f r
parameters.Eqs4and5quantifyhowindividualswithinaspeciesdifferinsensitivityto
resourcelimitationandabioticstressrespectively.Thesloperepresentsthesteepnessofthis
distributionandthereforeintraspecifictolerancevariability[9].Resourceissimplythejthele-
mentofthematrixproductfTxn,withfandnasinsection‘Death’.Forspeciesthatsufferno
resourcelimitation,thisequationsimplifiesto:
P(anindividualfromspeciesjreproduces)
Pðc<cÞ (cid:1)N
¼P r j j ð6Þ
n ½Pðc<cÞ (cid:1)N(cid:138)
i¼1 r i i
Biodiversitydynamics. Biodiversitydynamicswithinonecommunityweremodelledas:
PðN þ1jNÞ¼½1(cid:0) PðdeathÞ(cid:138)(cid:1)½½1(cid:0) m(cid:138)(cid:1)PðreproductionÞþm(cid:1)PðmainlandÞ(cid:138) ð7Þ
j j
PðN (cid:0) 1jNÞ¼PðdeathÞ(cid:1)½½1(cid:0) m(cid:138)(cid:1)½1(cid:0) PðreproductionÞ(cid:138)þm(cid:1)½1(cid:0) PðmainlandÞ(cid:138)(cid:138) ð8Þ
j j
withP(mainland)therelativeabundanceofspeciesjinthemainland.
NotethatEqs7and8arenotcomplements.Indeed,theabundanceofaspeciescanalso
stayconstantwithprobability1−P(N +1|N)−P(N −1|N).
j j j j
SubstitutingthedifferentprobabilitiesinEqs7and8withthosepresentedinEqs1–3,we
cannowspecifybiodiversitydynamicsofonecommunitythatisexperiencingbioticandabi-
oticstressasasetoftwoequationsthatgivetheprobabilityofaspeciesjtoincreaseand
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Effectsofbioticandabioticstressonfoodwebs
decreasewithoneindividual,respectively:
" " ##
P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N N P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N N
PðNþ1jNÞ¼ 1(cid:0) P m j j p j j þP j (cid:0) P m j j p j j (cid:1)P j
j j n ½P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N(cid:138) n N n ½P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N(cid:138) n N
i¼1 m i i p i i i¼1 i i¼1 m i i p i i i¼1 i
" " # #
PðððfTxnÞ >cÞ \ðc<cÞÞ(cid:1)N
(cid:1) ð1(cid:0) mÞ(cid:1) P j f j r j j þm(cid:1)P ð9Þ
n ½PðððfTxnÞ >cÞ \ðc<cÞÞ(cid:1)N(cid:138) j
i¼1 i f i r i i
and
" #
P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N N P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N N
PðN(cid:0) 1jNÞ¼ P m j j p j j þP j (cid:0) P m j j p j j (cid:1)P j
j j n ½P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N(cid:138) n N n ½P½ðc>c Þ [ððf(cid:2)nÞ >c Þ(cid:138)(cid:1)N(cid:138) n N
i¼1 m i i p i i i¼1 i i¼1 m i i p i i i¼1 i
" " # #
PðððfTxnÞ <cÞ \ðc>cÞÞ(cid:1)N
(cid:1) ð1(cid:0) mÞ(cid:1) P j f j r j j þm(cid:1)ð1(cid:0) PÞ ð10Þ
n ½PðððfTxnÞ <cÞ \ðc>cÞÞ(cid:1)N(cid:138) j
i¼1 i f i r i i
Modelsimulations
WeimplementedEqs9and10foronecommunityofpreyspeciesandonecommunityof
predatorspecies(fourequationsintotal).Preyservedasresourceforpredatorsbutwerethem-
selvesnotresourcelimited(asinEq2).Predatorswerenotpredated.Weranthismodelina
fullfactorialdesignofthreefactors(typeofabioticstress,typeofbioticstressandinitialcon-
nectance)(Table1).Weconsideredthreelevelsofabioticstress:noabioticstressonpreyor
predators,abioticstressaffectingpreyreproductiononly,orabioticstressaffectingpredator
reproductiononly.Weconsideredthreelevelsofbioticstress:top-downcontrol(predation
pressurereducespreysurvival),bottom-upcontrol(resourcelimitationreducespredator
reproduction),orboth.Weconsideredtwolevelsofinitialconnectance:low(0.05andhigh
(0.20).WecalculatedconnectanceasL/(S ×S ),whereListhenumberoflinks,S is
prey pred prey
preyrichnessandS ispredatorrichness.Preycannoteatpredatorsorotherpreyandpreda-
pred
torscannoteatotherpredators.Theaveragenumberoflinksperspeciesforinitialconditions
can,therefore,becalculatedas50×50×0.05i.e.125(low)and50×50×0.2i.e.500(high).Inliter-
ature,connectanceisgenerallycalculatedfornon-bipartitefoodwebswiththeformulaL/S2,
whereListhenumberoflinksandSisthetotalnumberofspecies[26,34–37].Therangeof
connectanceusedinoursimulations(0.05–0.2),evenafterrecalculationusingtheformulaL/
S2,correspondstotherangesobtainedinliteraturefornon-bipartitefoodwebs(0.026–0.315
[26],0.061–0.32[35],0.026–0.122[36]and0.016–0.33[38]).
Percombinationoffactorlevels,Eqs9and10werenumericallycalculatedandupdatedper
timestepforeverypreyspeciesbutonlyperfourtimestepsforeverypredatorspeciestosimu-
lateslowercommunitydynamicsforpredators[39].Assuch,theprobabilitiesforabundance
increaseanddecreasewereobtainedforeveryspeciesbysolvingEqs9and10,respectively.
EventhoughallpreyspeciesusethesameimplementationsofEqs9and10,theirtolerancesto
thestressors,theirconnectionstopredators,andtheirrelativeabundanceinthemainlandwill
bedifferent.So,species-specificsolutionswillbeobtained.Thesameholdsforpredators.Per
timestep(prey)orfourtimesteps(predators),onespecieswasdrawnpercommunityasa
weightedsamplewiththeprobabilitygivenbyEq9.Theabundancesofthesetwospecieswere
increasedwithone.Next,onespecieswasdrawnpercommunityasaweightedsamplewith
theprobabilitygivenbyEq10.Theabundancesofthesetwospeciesweredecreasedbyone.
Thisprocedureassumes“zerosumdynamics”i.e.thenumberofindividualspercommunity
staysconstantandateachtimestep,1individualpercommunityiskilledandreplacedbya
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Effectsofbioticandabioticstressonfoodwebs
Table1. Modelparametersintheirinitialstate.
Description Parameter Level Values
Totalnumberofspecies(Constant) n Community 100(50predators;50prey)
Numberofindividuals:multipleofn(Variable) N Community n×5
Levelofabioticstressor(Constant) c Community 0or100
Lowerandupperlimitsofuniformdistributionofimmigrationrate(Variable) m ;m Individual 1E-01;1.5E-01(low),2E-01;3E-01(high)
min max
Lowerandupperlimitsofcriticalreproductionthreshold(Variable) c ;c Individual 5E1;1.5E2
rmin rmax
Lowerandupperlimitsoffoodlimitationandpredationthresholds(c values c ;c ; Individual 1E-10;1E-10;10;40(top-downcontroland
f fmin fmax
constantandc valuesvariablefortop-downcontrol;c valuesvariableandc predationpressure,nofoodlimitation)
p f p
valuesconstantforbottom-upcontrol)[39]
c ;c 10;40;1E10;1E10(bottom-upcontroland
pmin pmax
foodlimitation,nopredationpressure)
Lowerandupperlimitsoftheslopeofthestressresponsefunction(Constant) minslope; Individual 3;3
[42] maxslope
Initialconnectance(Initialconnectanceisconstant;realisedconnectanceis Connectance Community Low(0.05)High(0.2)
variable)[23,35,36,38]
doi:10.1371/journal.pone.0172828.t001
“new”individual.Becausethemodelisdynamic,communitycompositionandabundanceof
bothpreyandpredatorschangeovertime.Thisimpliesthatthelevelsofbioticstressalso
changeovertime,whileabioticstressisconstantthroughtime.
Percombination,themodelwasrun(i.e.theprobabilitieswerecalculated)for15000time
steps,using5000iterations.These5000iterationsdifferedinthespecies-meantolerances
(Table1).Initialspeciesabundances(andthereforeinitialrichness)wereequalacrossallcom-
binationsanditerations.Food-weblinksweresetatrandomwiththeinitialconnectanceas
theonlyconstraint.Linksbetweentwospeciesdisappearwhenoneofthespeciesgoesextinct
locallybutreappearwhenthisspeciesrecolonizesthelocalcommunityfollowinganimmigra-
tionevent.Nonewlinksarecreated.Foreverycombinationanditerationwecalculatedthe
finalpreyandpredatorrichnessaswellasfinalconnectance.ThemodelwascodedinPython
(2.7.10).
Toassesstherobustnessofthesimulationstotheselectedimmigrationprobabilitym,we
performedallsimulationsfortwodifferentvaluesofm(Table1).Allfigureswereprepared
usingR[40].Statisticaltestswerenotusedtointerpretmodelsimulationresultsashasbeen
recommendedrecently[41].
Results
Becauseresultswerequalitativelysimilarbetweenlower(Figs1–4)andhigherimmigration
probabilitiesm(S1–S4Figs),onlytheformeraredescribedanddiscussedbelow.
Richness
Preyrichness. Intheabsenceofabioticstress,preyrichnessunderbottom-upcontrolcan
beconsideredareference(unstressed)situation,sincepreyalsodonotexperienceanybiotic
stressunderbottom-upcontrol.Thus,preyrichnessisonlydeterminedbydispersallimitation.
Comparedtothisreference,top-downandmixedcontroldecreasedpreyrichness(Fig1).
Mixedcontrolcausedreductionsofpreydiversitythatweremoreseverewheninitialconnec-
tancewaslow.
Whenabioticstressaffectedprey,preyrichnesswasreduced,butonlyinabsenceofbiotic
stressonprey(bottom-upcontrol).Whenabioticstressaffectedpredators,preyrichness
increasedundertop-downcontrol,butonlyatlowinitialconnectance.Athighinitialconnec-
tance,noindirecteffectonpreyrichnesswasobserved.
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Effectsofbioticandabioticstressonfoodwebs
Fig1.Preyrichnessunderstress.Bioticstress(top-down,bottom-upormixedcontrol)andabioticstress(none,AS
onprey,ASonpredators)atlowandhighinitialconnectance.
doi:10.1371/journal.pone.0172828.g001
Predatorrichness. Inabsenceofabioticstress,predatorrichnessundertop-downcontrol
canbeconsideredanunstressedsituation,sincepredatorsalsodonotexperienceanybiotic
stressundertop-downcontrol.Thus,bottom-upcontrolreducedpredatorrichnessanddidso
mostwheninitialconnectancewaslow.Mixedcontrolhadnocleareffectonpredatorrichness
(Fig2).
Adirectnegativeeffectofabioticstressonpredatorrichnesswasfound,butthiseffectwas
onlypronouncedinabsenceofbioticstressonpredators(top-downcontrol),regardlessofini-
tialconnectance.Whenabioticstressaffectedpreyandbottom-upcontrolprevailed,asmall
negativeindirecteffectonpredatorrichnessoccurredbutonlyathighinitialconnectance.
Connectance
Whetherornotabioticstresswaspresent,connectancewasalwayslowerundertop-down
thanunderbottom-upcontrol(Fig3).Connectancewaslowestundermixedcontrolatlow
initialconnectancecomparedtotop-downandbottom-upcontrolbuthigherthanthatunder
top-downcontrolathighinitialconnectance.Overall,abioticstressdidnotmarkedlychange
connectance.Onlywhenabioticstressaffectedpredatorswasconnectancehigher(lower)
undertop-downcontrolwheninitialconnectancewaslow(high).
Inabsenceofabioticstress,top-downcontroldecreasedthenumberofpredatorsperprey
(S5Fig)whilebottom-upcontrolslightlyincreasedthenumberofpreyperpredator.Mixed
controldecreasedthenumberofpredatorsperpreyaswellthenumberofpreyperpredator
andbothwereverylowatlowinitialconnectance.
Bothtypesofabioticstressreducedthenumberofpreyperpredatorunderbottom-upcon-
trol(S6Fig).Undertop-downcontrol,abioticstressaffectingpredatorsreducedthenumber
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Effectsofbioticandabioticstressonfoodwebs
Fig2.Predatorrichnessunderstress.Bioticstress(top-down,bottom-upormixedcontrol)andabioticstress
(none,ASonprey,ASonpredators)atlowandhighinitialconnectance.
doi:10.1371/journal.pone.0172828.g002
Fig3.Connectanceunderstress.Bioticstress(top-down,bottom-upormixedcontrol)andabioticstress(none,AS
onprey,ASonpredators)atlowandhighinitialconnectance.
doi:10.1371/journal.pone.0172828.g003
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Effectsofbioticandabioticstressonfoodwebs
Fig4.Therelationshipbetweenconnectanceandtotalrichness(preyandpredatorstogether)understress.
Bioticstress(top-down,bottom-upormixedcontrol)andabioticstress(none,ASonprey,ASonpredators)atlowand
highinitialconnectance.
doi:10.1371/journal.pone.0172828.g004
ofpredatorsperprey(S7Fig).Undermixedcontrol,abioticstressdidnotchangethenumber
ofpreyandpredatorsperpredatorandprey,respectively(S6andS7Figs).
Relationshipbetweenconnectanceandrichness
Theshapeoftherelationshipbetweenconnectanceandtotalrichness(allspecies,including
predatorsandprey)wasstronglyinfluencedbyinitialconnectanceandthetypeoffood-web
control,butwasrobusttothetwotypesofabioticstressconsideredhere.Atlowinitialconnec-
tance,irrespectiveofthepresenceorabsenceofabioticstress,connectanceremainedconstant
underbottom-upcontrolandshowedaweakpositiverelationshipundertop-downandmixed
controlswithincreasingtotalrichness.Athighinitialconnectance,wefoundapositivesatu-
ratingrelationshipbetweenconnectanceandrichnessundertop-downandmixedcontrol
(Fig4).
PLOSONE|DOI:10.1371/journal.pone.0172828 March1,2017 9/15
Effectsofbioticandabioticstressonfoodwebs
Discussion
Preyrichness
Abioticandbioticstress(top-downcontrol)haddirectnegativeeffectsonpreyrichness,
whichconfirmsempiricalfindings[43–45]andresultsfromarecentmeta-analysis[4],respec-
tively.Effectsofbioticstressonpreyrichnessweremoresevereunderhighthanunderlowini-
tialconnectance,becausepreywerebydefinition–onaverage–connectedtomorepredators
underhighinitialconnectance.Theeffectsofmixedcontrolonpreyrichnessillustratesthat
bottom-upcontrolcanaggravateorbuffernegativeeffectsoftop-downcontrolonpreyrich-
ness,dependingonwhetherinitialconnectanceisloworhigh,respectively.
Foodwebinteractionsareknowntocauseindirecteffectsofabioticstressonthedensity
ofnon-targetcommunities[17],butindirecteffectsonrichnesshavebeenlesswellstudied
[4].Empiricalstudiesthathavemanipulatedpredatordiversitydoexist[26,46–48], butit
isoftendifficulttomanipulatediversitywithoutmanipulatingdensitysothatisolating
effectsofrichnessfromdensityeffectsbecomesdifficult.Inourtheoreticalstudy,we
wereabletoonlymanipulatepredatorrichnessbecausethemodelpostulatesaconstant
sizeofthepredatorcommunity.Ourresultsthereforeillustrateindirecteffectsonprey
diversity(Figs1and2)thatareonlyduetoabioticstressaffectingpredatordiversityand
notdensity.
Connectanceisconsideredaproxyforresistanceoffood-webstoindirecteffectsondensity
[5,26].Foodwebswithlowconnectanceareextremelysensitiveandmorepronetoselective
lossofhighlyconnectednodesthanfoodwebswithhighconnectance[26].Ourresultssuggest
thatconnectancealsoincreasesresistanceagainstindirecteffectsonrichnessbecausewefind
thathigherinitialconnectanceincreasedresistanceofpreydiversitytoindirecteffectsofabi-
oticstressonpredators.
Wedidnotfindindirecteffectsonpreyrichnessundermixedcontrol(Fig1).Whenabiotic
stressaffectedpredators,thesubsequentincreaseinpreyrichnessresultedinahighernumber
ofpreyspeciesavailabletopredators,whichapparentlyresultedinastabilizingfeed-back
mechanism.Thisshowsthatundermixedcontrol,ourframeworkpredictsnon-additive
effectsofbioticandabioticstressinbipartitegraphs.
Predatorrichness
Abioticandbioticstress(bottom-upcontrol)decreasedpredatorrichness,whichcorresponds
toempiricalfindings[49].Effectsofbioticstresswasmorepronouncedatlowthanathighini-
tialconnectance(Fig2)becausepredatorshavefewerfeedingoptionsatlowerinitialconnec-
tanceandthusexperiencehigherbioticstress.Empiricalresults[50]forbottom-upcontrolon
predatordensitysuggestsimilarmechanisms.Theeffectsofmixedcontrolonpredatorrich-
nessillustratethatthenegativeeffectsofbottom-upcontrolonpredatorrichnessare(partly)
offsetbyfeedbackmechanismsfromtop-downcontroloffewerpredatorspeciesonprey.This
mechanismoccurredregardlessofinitialconnectance.
Wedidnotfindstrongsupportforindirecteffectsofabioticstressonpredatorrichness
(Fig2).Underbottom-upcontrol,abioticstressonpreyonlyslightlyreducedpredatorrich-
nessandonlywheninitialconnectancewashigh.Thiscanbeexplainedbythefactthatbot-
tom-upcontrolselectsforpredatorsfeedingonmultiplepreyspecies.Becausetheprobability
tobeconnectedtoatolerantprey(thatcancompensatefordensitylossofsensitivepreyspe-
cies)increaseswiththenumberofpreyspeciesinthediet,bottom-upcontroleffectively
reducestheprobabilityforindirecteffects.
PLOSONE|DOI:10.1371/journal.pone.0172828 March1,2017 10/15