人体组织解剖学Allee effects in multi-prey systems

Ecology,91(1),2010,pp.286–292

Ó2010bytheEcologicalSocietyofAmerica

Predator-mediatedAlleeeffectsinmulti-preysystems

BRUCEN.MCLELLAN,1ROBERTSERROUYA,1,2HEIKOU.WITTMER,3,4

1

AND

STANBOUTIN2

BritishColumbiaMinistryofForestsandRange,RPO#3,P.O.Box9158,Revelstoke,BritishColumbiaV0E3K0Canada

2

DepartmentofBiologicalSciences,UniversityofAlberta,Edmonton,AlbertaT6G2E9Canada

3

Wildlife,Fish,andConservationBiology,UniversityofCalifornia,OneShieldsAve.,Davis,California95616USA

Abstract.Alleeeffectscanhavesigni?cantconsequencesforsmallpopulationsandunderstandingthecausalmechanismsforsucheffectsisimportantforguidingconservationactions.Oneproposedmechanismisthroughpredation,inwhichatypeIIfunctionalresponseleadstoincreasingpredationratesaspreynumbersdecline.However,modelstosupportthismechanismhaveincorporatedonlyasingledecliningpreyspeciesinthefunctionalresponse,whichisprobablyanoversimpli?cation.Wereevaluatedthepotentialforpredator-mediatedAlleeeffectsinamulti-preysystemusingHolling’sdiscequation.Wealsousedempiricaldataonalargeherbivoretoexaminehowgroupingbehaviormayin?uencethepotentialforpredation-mediatedAlleeeffects.Resultsbasedonamulti-preyexpressionofthefunctionalresponsepredictthatAlleeeffectscausedbypredationonrelativelyraresecondarypreymaynotoccurbecausehandlingtimeoftheabundantpreydominatesthefunctionalresponsesuchthatsecondarypreyarelargely‘‘bycatch.’’However,apredator-mediatedAlleeeffectcanoccurifsecondarypreyliveingroupsandif,asthepopulationdeclines,theiraveragegroupsizedeclines(arelationshipseeninseveralspecies).Insuchacase,therateatwhichthenumberofgroupsdeclinesislessthantherateatwhichthepopulationdeclines.Thustherateatwhichapredatorencountersagroupremainsrelativelystable,butwhenapredatorkillsoneanimalfromsmallergroups,thepredationrateincreases.Theseresultshighlighttheneedtoevaluaterisksassociatedwithpotentialchangesingroupsizeaspopulationsdecline.

Keywords:Alleeeffect;apparentcompetition;conservation;functionalresponse;mountainecotypewoodlandcaribou;predator–preyinteractions;Rangifertaranduscaribou;socialorganization;southeasternBritishColumbia,Canada.

INTRODUCTION

Understandingmechanismsaffectingsmallpopula-tionsiscriticalforimplementingeffectiveconservationactions.OfparticularimportanceforconservationarepossibleAlleeeffects(orinversedensitydependence)thatcausethepercapitagrowthratetodeclineaspopulationsbecomesmaller(Alleeetal.1949,Cour-champetal.1999,Stephensetal.1999).Alleeeffectsgreatlyexacerbateextinctionriskunlessappropriatemanagementisapplied.

DocumentedmechanismscausingAlleeeffectsincludeaninsuf?cientnumberofconspeci?csforef?cientreproductionorpredatoravoidance(Courchampetal.1999,2008,Stephensetal.1999).Severalstudieshaveconcludedthatapredator-mediatedAlleeeffectmaybecommonwhenapredatordisplaysatypeIIfunctionalresponseincombinationwith,orinparticularwithout,anumericalresponsetodeclinesinthedensityoftherarepreyspecies(Sinclairetal.1998,Cantrelletal.2001,GascoigneandLipcius2004,Wittmeretal.2005b,Anguloetal.2007,Courchampetal.2008).Thelackof

Manuscriptreceived18February2009;revised28April2009;accepted30April2009.CorrespondingEditor:M.Festa-Bianchet.

4Correspondingauthor.E-mail:huwittmer@ucdavis.edu

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anumericalresponsebythepredatorcouldarisewheretherarepreyspeciesisdeclining,butbecauseitisaminorcomponentinthedietofthepredator,thepredatorshowsnochangeinnumberassociatedwithitsdecline.Ithasbeensuggestedthatundersuchascenario,thetypeIIfunctionalresponsealoneiscapableofcreatinganescalatingmortalityrateofpreyastheirnumbersdecline,thuscausinganAlleeeffect(Sinclairetal.1998,GascoigneandLipcius2004).

Intheirrecentbookentitled‘‘Alleeeffectsinecologyandconservation,’’Courchampetal.(2008:109)pointout‘‘althoughsinglespeciesmodelshavebeenveryusefulforunderstandingAlleeeffects,theirfailuretoaccountforinterspeci?crelationshipsisinmanycasesanoversimpli?cation.’’Weagreethatthisisthecasewhenconsideringpredator-mediatedAlleeeffects.Al-thoughtheimplicationsofvariouscombinationsoffunctionalandnumericalresponseshavebeendiscussedindetail(e.g.,Holling1959a,OatenandMurdoch1975,Messier1995),theseinvestigationswerebasedonsingle-preysystemsoratleastwerefocusedonthedominantpreyspeciesinthesystem.However,thepotentialforanAlleeeffectisonlyrelevanttopreythatareasmallcomponentofthetotalbiomassavailabletothepredatorinthemulti-preysystem.Otherwise,thepredatorwouldprobablyshowaconventionalnumer-icalresponse,negatingthepotentialforanAlleeeffect.

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Ourobjectivesaretwofold.First,wereevaluatepredictionsinvolvingpredator-mediatedAlleeeffects(Messier1995,Sinclairetal.1998,GascoigneandLipcius2004)byincludingmultiplepreyspeciesinthefunctionalresponse.Weareinterestedinthesituationinwhichpredatorsforageondecliningrareprey(i.e.,secondaryprey)butspendthemajorityoftheirtimeeatingmoreabundantprimaryprey(BergerudandElliot1986,Seip1992,Robinsonetal.2002,Wittmeretal.2005b).Othershaverecognizedthattherelationshipbetweenpredatorsandpreydependsnotonlyontheirabundance,butalsoonthesocialorganizationofthevariousspeciesinvolved(e.g.,Hamilton1971,Fryxelletal.2007).Therefore,oursecondobjectivewastoexaminehowgroupsizechangeswithpopulationdensityandhowthis,inturn,affectspredationratesunderscenariosofdecliningsecondaryprey.Weusedatafromtheendangeredmountainecotypeofwood-landcaribou(Rangifertaranduscaribou),whichisdeclininginnumbersovermostofitsdistribution(Wittmeretal.2005a).

METHODS

Functionalresponsemodel

Ifpreydidnotliveingroupsandwerepartofasingle-predator–single-preysystem,thetypeIIfunctionalresponseofthatpredatorwouldfollowthe‘‘discequation’’ofHolling(1959b):

yaNTt¼

1þaNTð1Þ

h

whereytisthetotalnumberofpreykilledperpredatoroveratotalperiodoftimeT,aisthesearchingrateofthepredator,Nisthepreydensity,andThisthehandlingtimethatincludeschasing,killing,consuming,anddigestingoneprey.Themortalityrateofthepreycausedbypredation(i.e.,predationrate)canthenbedeterminedfromthenumberofpreykilleddividedbythepreypopulationsize(Messier1994).Thenumberofpreykilledisreferredtoasthe‘‘totalresponse’’andissimplytheproductofthefunctionalandnumericalresponse(Holling1959a,Messier1994).

Ifthereismorethanonepreyspecies(inthefollowingexampleweusetwopreyspecies)and,forsimplicity,allpreyspecieshavethesamehandlingtime,Nbecomesthesumofthenumberofeachspecies(sensuAbrams1990),and

yaðNt¼

1þN2ÞT

1þaðNð2Þ

1þN2ÞTh

whereytisnowthetotalnumberofbothpreyspecieskilledperpredator.If,forthissimplemodel,weassumethatthepredatorencounterspreyinproportiontotheirabundanceand,onceencountered,theprobabilityofkillingisthesameforeachspecies,thenwecandivideytintoy1andy2,thenumbersofeachpreyspecieskilled,basedontheirrelativeabundance.

Preylivingingroups

Ifoneofthespeciesisfoundingroups,thenNiisthenumberofgroups,notindividuals.Whatiscriticalinthegroup-sizecomponentofourmodelisthatweassumetheprobabilityofasearchingpredatorencounteringagroupisequaltoencounteringanindividual(seeHuggard1993)andthepredatorkillsonlyonegroupmemberatatime.Theseassumptionsareunlikelytrueforallpredator–preysystems,butaremorelikelytoholdwhenthesecondarypreyarerareandexistinsmallgroups(whereAlleeeffectsareexpressed)andhandlingtimeisofsuf?cientdurationtoenablesurvivingmembersofthegrouptoeffectivelyescape(e.g.,Huggard1993,Hebble-whiteandPletscher2002,Fryxelletal.2007,Coleman2008).Forgroupsizesandthusnumberofgroups(Ni)usedinEq.2toestimatepredationratesatvariouspopulationsizes,we?rstusedtherelationshipbetweentheaveragepopulationsizedeterminedbyWittmeretal.(2005a)andobservedgroupssizesofmountaincaribouinsummer(seeFielddata).

Forallmodels,weuseahandlingtimeof5daysperpreyitemandasearchrateof1km2/d,Tis30d,andthepreydensityisnumberofindividuals/1000km2.Inthesingle-preymodels,wevarytheirnumbersbetween1and300.Forthemulti-preymodels,wevarythenumbersofsecondarypreybetween1and300whilekeepingtheprimarypreystableat1000.We?rstuseatype0numericalresponse(i.e.,noresponse)becauseweareinterestedinAlleeeffectsofsmallpopulations.Toenablefurthercomparisonsandbecausewevariedtheratioofprimarytosecondarypreyconsiderablyinourmodels,wealsoincorporatedasimpletypeInumericalresponse.ThetypeInumericalresponseisbasedononepredatorper50preygroups(i.e.,alinearresponsetopreydensity;e.g.,Fuller1989).

Toinvestigateimplicationsofanimalgroupsizesbeyonddataavailablefromcaribou,weusedEq.2butvariedtheslopeandshapeoftherelationshipbetweengroupsizeandpopulationsizeofthesecondaryprey,whilekeepingthenumberofprimarypreystableat1000solitaryanimals.Tomaintainsimplicityandbecauseitwasthesuggestedrelationshipforsomespecies,wevariedtheslope(b)oftheline(groupsize¼1þbN2)tohavegroupsizesof1,2,5,and10animalswhentherewere300secondarypreybutalways1whenthelastanimalremained.

Fielddata

Mountaincaribouliveinamulti-prey–multi-predatorsysteminsoutheasternBritishColumbia,Canada,thatincludesuptosevenotherungulatespeciesthatarepreyedonbyupto?vecarnivorespecies(foradetailedmapofthestudyareaanddescriptionofthephysicalenvironment,seeWittmeretal.2005a).Mountaincaribouhavebeenstudiedusingradiotelemetrysince1984andindividualsfrom18populationshavebeenmonitored;however,fourpopulationsweresosmallandinfrequentlyseeninsummerthatinsuf?cientgroupsize

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FIG.1.Predationrates(percentageofthepopulationpreyedoneachmonth)forpreythatlivealone(dashedlines)oringroups(solidlines)for:(A)singlepreyspeciesatdifferentlevelsofabundance(1–300individuals)withatypeIIfunctionalresponseandnonumericalresponsefromthepredator;(B)singlepreyspecies(1–300individuals)withatypeIIfunctionalresponseandatypeIpredatornumericalresponse;(C)secondarypreyspecies(1–300individuals)withatypeIIfunctionalresponse,butwhenthepredator’sprimarypreypopulationisstable(1000),andwithnonumericalresponsefromthepredator;(D)secondarypreyspecies(1–300individuals)withatypeIIfunctionalresponseandatypeInumericalresponse,butwhenthepredator’sprimarypreypopulationisstable(1000).

datawereobtainedanddatafromonepopulationwerenotavailableforouranalysis.Thus,datafrom13populationswereavailabletodeterminetherelationshipbetweenpopulationsizeandgroupsize.

Collaredanimalswerelocated2–4timespermonthfroma?xed-wingaircraftandthenumberofanimalsinthegroupwasrecordedwhenevertheywereobserved.PopulationswerecensusedfromhelicoptersinMarchorearlyApril,whencaribouareinopen,high-elevationhabitats,andshortlyafternewsnowfell(Wittmeretal.2005a).Therelationshipbetweentheaveragesizeofthepopulationandmeangroupsizewasmadeforthesummerseasonwhencaribouhabitatoverlapswithalternativepreyandpredatorsandthatiswhenmostpredationoccurs(Wittmeretal.2005a).

Todetermineiftherelationshipbetweenpopulationsizeandgroupsizeislimitedtomountaincaribouand

thereforenotofbroaderutility,wealsouseddatafrommoose(Alcesalces;sampledwithinthecentralportionofthemountaincariboudistribution)andelk(Cervuselaphus;sampledinneighboringBanffNationalPark,Alberta,Canada).Forbothofthesespecies,wintercensusesfromhelicopterprovidedgroupsizesandpopulationestimatesthatvariedovertime.Wedidnotusemooseandelkdataforourmodeling,butrathertodetermineifthegroupsizerelationshipholdsbeyondcaribou.

RESULTS

ModelingpredationrateswithpreylivingaloneInasingle-preysystem,thetypeIIfunctionalresponsemodelshowsanAlleeeffectifpreylivealoneandthepredatorhasnonumericalresponse(Fig.1A,preyalone).WhenweaddedatypeInumerical

response

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FIG.2.Relationshipbetweenthesizeofpopulationsandaveragegroupsizes.(A)Mountaincariboupopulationsizesandaveragegroupsizesobservedinsummer.(B)PopulationsizeandaveragegroupsizeofUpperColumbiamoosepopulation(errorbarsare95%CI,shownherebecauseonlythreedatapoints).(C)PopulationsizeandaveragegroupsizeofBanffeasternelkpopulation.(D)PopulationsizeandaveragegroupsizeofBanffwesternelkpopulation(adaptedfromHebblewhiteandPletscher[2002]).

tothetypeIIfunctionalresponsetheAlleeeffectdisappeared(Fig.1B,preyalone);thatis,thepredationratedeclinedasthepopulationdeclinedbecausetherewerefewerpredators.Inamulti-preysystemwithprimarypreythatarestableandabundant(1000),andararer(0–300),decliningsecondarypreyandnopredatornumericalresponsetoeitherprey,theAlleeeffectonthesecondarypreywasweakerthaninthesingle-preyscenario(Fig.1Avs.C,preyalone).Thepredationrateactuallychangedverylittleastherarepreydeclined.BecausethemagnitudeofthisAlleeeffectisproportionaltotheratioofsecondarypreytothesumofbothsecondaryandprimaryprey,itwouldhavebeenevenlessifprimarypreyweremoreabundant.IfatypeInumericalresponsewereadded(forbothprey),theweakAlleeeffectonthesecondarypreywoulddisappear(Fig.1D,preyalone).

Preylivingingroups:?elddataandmodels

ofpredationrateswithgroupsTomakemodelpredictionswithgroup-livingorgan-isms,we?rstneededtodeterminehowgroupsizechangeswithpopulationsizeandweused?elddatatoobtainthisempiricalrelationship.Between1984and2006,541caribouwereradio-collaredand2099groupswereseenduringthesummerseason,whentheaveragegroupsizewas3.8individualsand95%ofgroupshad,10members.Meangroupsizesofmountaincaribouweresigni?cantlylargerinthelargerpopulations,althoughtherelationshipwaslogarithmic(GLMcaribou:R2¼0.64,F1,11¼19.15,P¼0.001;Fig.2A).Thelargelysolitarymooseshowasimilartrend(bootstrapped95%CIsdonotoverlap;Fig.2B).Themagnitudeofchangewasstrongestforelk(Fig.2C,D;GLMEasternBanff:R2¼0.79,F1,22¼80.42,P¼0.001;GLMWesternBanff:R2¼0.59,F1,22¼31.35,P¼0.001).Mooseandelkwerenotusedinmodelscenarios,butsimplytoensurethattherelationshipisnotlimitedtocaribou.

Inallcases,thegroup-livingscenarioresultedinlowerpredationrates(Fig.1).Withasinglegroup-livingpreyandnonumericalresponse,therewasanAlleeeffectthatbecamemostpronouncedat,50animals(Fig.1A,groups).Whenweaddthenumericalresponse,theAlleeeffectagaindisappeared(Fig.1B,groups).Inthemultispeciesscenario,however,theAlleeeffect

existed

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FIG.3.Theeffectofvariouslinearrelationshipsbetweengroupsizeandpopulationsize(groupsize¼1þbN2,wherebistheslope)onthepredictedpredationrateofasecondarypreyspecieswithatypeIIfunctionalresponsebutwhenthepredator’sprimarypreypopulationisstableandmaintainedat1000animals.Predationrateisthepercentageofthepopulationpreyedoneachmonth.Thelinearrelationshipvariedfrom1animalpergroupatallpopulationsizes(solitaryspecies)towheregroupsizesincreasedfrom1to2,1to5,and1to10animalspergroupwhentherewere300individualsinthepopulation.In(A),thereisnonumericalresponse.In(B)thereisatypeIpredatornumericalresponsetothenumberofgroups.

regardlessofwhetherthepredatordidordidnotshowanumericalresponse(Fig.1C,D,groups).ThestrengthoftheAlleeeffectincreasedthemorethegroupsizedeclinedwithdecliningpopulationsize(Fig.3).

DISCUSSION

Itisnowcommonto?ndsituationsinwhichdeclining,rarepreyspeciesaresubjecttoelevatedpredationratesbecausepredatorsaresustainedbyotherprimaryprey(e.g.,Seip1992,HoltandLawton1994,Sweitzeretal.1997,Sinclairetal.1998,Norbury2001,Robinsonetal.2002).Insomeinstances,thedecliningpreyappearstobesubjecttoanAlleeeffect(Sinclairetal.1998,Wittmeretal.2005b).Previoustheoreticalmodelingofpredator-mediatedAlleeeffectsconsideredonlytherare,secondarypreyspeciesinthefunctionalresponseofthepredator.Withasinglepreyspeciesandnonumericalresponsetothenumberofprey,ourresults,likethoseofGascoigneandLipcius(2004),predictastrongAlleeeffect.However,conditionsforthisscenariowouldberareandmaybelimitedtosituationssuchaswhereexoticpredatorsarepreyingonaspeciesthathasnotevolvedapredatoravoidancestrategy.Underthisscenario,apredatormaykillallindividualsofthespeciesquicklywithoutswitchingtootherpreyspecies.Itisprobablymorecommon,however,thattherarepreyarebutoneofseveralpreyspecies,anditisherethatpredictionsofourfunctionalresponsemodeldifferfromthoseofMessier(1995),Sinclairetal.(1998),andGascoigneandLipcius(2004).

MultiplepreyspeciesinthefunctionalresponseGiventhatthebasisofthediscequationisthechangeintimethatapredatorspendshandlingandsearchingforpreyatdifferentpreydensities(Holling1959b),allpreyspeciesshouldbeincluded.LimitingthefunctionalresponsetojusttherarespeciesthatissufferinganAlleeeffectassumesthatpredatorsarespendingenoughtimehandlingthisspeciestoaffectpredationratestoasigni?cantdegree.Italsoassumesthatachangeinthenumberofprimarypreywillnotaffectthenumberofthesecondaryspeciesthatanindividualpredatorwillkill.Thisisclearlynottrue.Ifthenumberofprimarypreygreatlyincreases,theneachpredatorwillspendlesstimesearchingandmoretimehandlingprimarypreythanbefore.Conversely,ifthenumberofprimarypreydeclines,http://wendang.chazidian.combiningallpreyspeciesintothediscequationcausesthemorecommonpreytodominatethefunctionalresponse,ortheamountoftimeapredatorspendshandlingandsearchingforprey.Thismodi?cationonlyrequiredsummingvaluesofbothpreyspeciesforthedensityandhandlingtimeexpressedinHolling’s(1959b)discequation.

Whenwemodi?edthefunctionalresponsetoincludeanabundantbutstableprimaryprey,ourmodelpredictedaveryweakAlleeeffectwhenthereisnonumericalresponseandnoAlleeeffectwithatypeInumericalresponse.Inbothcases,ifthereisanabundanceofprimaryprey,thepredationrateonthesecondarypreyisessentiallydensityindependent(i.e.,‘‘bycatch’’).Inotherwords,changesindensityofthesecondarypreyspecieshavelittleeffectonthepredationratethatitexperiences.ThisresultdiffersfromthoseofMessier(1995:Fig.4b),GascoigneandLipcius(2004),andSinclairetal.(1998),whousedonlyonespeciesinthefunctionalresponseandavarietyofwaysto

account