Ecology and Evolution. 2017;1–18.  | 1www.ecolevol.org

Received:25January2017  |  Revised:22April2017  |  Accepted:24April2017DOI: 10.1002/ece3.3176

O R I G I N A L R E S E A R C H

Territory surveillance and prey management: Wolves keep track of space and time

Ulrike E. Schlägel1,2  | Evelyn H. Merrill3 | Mark A. Lewis1,3

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,providedtheoriginalworkisproperlycited.©2017TheAuthors.Ecology and EvolutionpublishedbyJohnWiley&SonsLtd.

1DepartmentofMathematicalandStatisticalSciences,UniversityofAlberta,Edmonton,AB,Canada2PlantEcologyandNatureConservation,InstituteofBiochemistryandBiology,UniversityofPotsdam,Potsdam,Germany3DepartmentofBiologicalSciences,UniversityofAlberta,Edmonton,AB,Canada

CorrespondenceUlrikeE.Schlägel,PlantEcologyandNatureConservation,InstituteofBiochemistryandBiology,UniversityofPotsdam,Potsdam,Germany.Email:ulrike.schlaegel@gmail.com

Funding informationAlbertaInnovates-TechnologyFutures;NaturalSciencesandEngineeringResearchCouncilofCanada;DeutscherAkademischerAustauschdienst;CanadaResearchChairs;DeutscheForschungsgemeinschaft,Grant/AwardNumber:DFG-GRK2118/1;KillamTrusts

AbstractIdentifyingbehavioralmechanismsthatunderlieobservedmovementpatternsisdif-ficultwhenanimalsemploysophisticatedcognitive-basedstrategies.Suchstrategiesmayarisewhentimingofreturnvisitsisimportant,forinstancetoallowforresourcerenewal or territorial patrolling.We fitted spatially explicit random-walkmodels toGPSmovementdataofsixwolves(Canis lupus;Linnaeus,1758)fromAlberta,Canadatoinvestigatetheimportanceofthefollowing:(1)territorialsurveillancelikelyrelatedtorenewalofscentmarksalongterritorialedges,toreduceintraspecificriskamongpacks,and(2)delayinreturntorecentlyhuntedareas,whichmayberelatedtoanti-predatorresponsesofpreyundervaryingpreydensities.Themovementmodelsincor-porated the spatiotemporal variable “time since last visit,” which acts as a wolf’smemoryindexofitstravelhistoryandisintegratedintothemovementdecisionalongwithitspositioninrelationtoterritoryboundariesandinformationonlocalpreydensi-ties.Weusedamodelselectionframeworktotesthypothesesaboutthecombinedimportanceofthesevariables inwolfmovementstrategies.Time-dependentmove-mentforterritorysurveillancewassupportedbyallwolfmovementtracks.Wolvesgenerallyavoidedterritoryedges,butthisavoidancewasreducedastimesincelastvisitincreased.Time-dependentpreymanagementwasweakexceptinonewolf.Thiswolfselectedlocationswithlongertimesincelastvisitandlowerpreydensity,whichledtoalongerdelayinrevisitinghighpreydensitysites.Ourstudyshowsthatwecanusespatiallyexplicitrandomwalkstoidentifybehavioralstrategiesthatmergeenvi-ronmental information and explicit spatiotemporal information on pastmovements(i.e., “when”and“where”) tomakemovementdecisions.Theapproachallowsus tobetter understand cognition-basedmovement in relation to dynamic environmentsandresources.

K E Y W O R D S

animalmovement,cognition,GPSdata,landscapeoffear,movementecology,predator–prey,spatialmemory,stepselection,territoriality,timesincelastvisit

2  |     SCHLÄGEL Et aL.

1  | INTRODUCTION

Recentempiricalandtheoreticworksuggeststhatcognitionandmem-oryare important foranimals’dailymovements (Faganetal.,2013).For example, spatialmemory andmemoryof past experience allowanimalstorevisitprofitableforaginglocationsandoptimizeenergyin-take(Hopkins,2015;Merkle,Fortin,&Morales,2014;Nabe-Nielsen,Tougaard, Teilmann, Lucke, & Forchhammer, 2013; Riotte-Lambert,Benhamou,&Chamaillé-Jammes,2015;VanMoorteretal.,2009)ortotravelefficientlytocrucialresourcessuchaswaterholes(Polansky,Kilian, & Wittemyer, 2015). Cognitive abilities are associated withmetabolicneeds (e.g., largerbrainsize,maintenanceofneuralstruc-tures) andmay entail both constitutive and induced costs in termsoffecundityandotherfitnesscomponents(Burns,Foucaud,&Mery,2011). Therefore, we would expect to find cognitive-based move-ment predominantly under conditionswhere benefits can outweighcosts,thatiswhenresourcesareheterogeneousinspaceandtimebutalsopredictable (Avgar,Deardon,&Fryxell,2013;Mueller,Fagan,&Grimm,2011),andwhenresourcepatchdensityislowanddistancesbetweenpatchesarehigh(Bracis,Gurarie,VanMoorter,&Goodwin,2015;Grove,2013).Despitethegrowingeffortinaddressingcogni-tioninmovementstudiesandtheevidencethatitcanbeimportant,unravelingtheroleofcognitionandmemoryformovementisstillin-herentlydifficultbecausetheseprocessescanbe inferredonly indi-rectly,whichrequiresbothcreativeandstate-of-the-artmethodology(Faganetal.,2013).

Here,weaddresswhethergraywolves(Canis lupus)integratespa-tiotemporalaspects(i.e.,the“when”and“where”)oftheirowntravelhistory into their movement decisions. That memory of travel his-tory is important inwolfmovementdecisions isreasonablebecausewolvesexhibit littledailyoverlap inuseof their territory,especiallyinwinter,anditraisesthequestionsastotheunderlyingmechanism(Jedrzejewski,Schmidt,Theuerkauf,Jedrzejewska,&Okarma,2001).We use a novel method of modeling memory-based animal move-ments(Schlägel&Lewis,2014)toassesshypotheses(Table1)relatedtotheroleoftime-dependentterritorialandhuntingbehaviorbasedontimesincelastvisiting(TSLV)alocation.

Wolvesareknowntobeterritorialandtoscentmarktheirterri-toriestoadvertisetheirpresencetowolvesfromotherpacks(Lewis&Murray,1993;Peters&Mech,1975;Zubetal.,2003).Scentmarkscan be found across the territory, but usually territory edges aremarkedmoreheavily,especiallywhentheyborderneighboringpacks(Mech&Boitani,2006;Peters&Mech,1975;Zubetal.,2003).Iffatalencounterswithindividualsfromotherpacksoccurclosetotheterri-toryedge(Mech,1994),wewouldexpectavoidanceofterritoryedgestobeamajordrivertowolfmovement(riskavoidance;H1).However,ifscentmarksdecayandmustberenewedregularly,wewouldexpectavoidanceofterritoryedgestodeclineforlongTSLV(territorysurveil-lance;H2a,H2b)duetorenewingscentmarks.

Movementofwolvesalsomaybedrivenbystrategiesforefficientpreycapture.Forexample,selectingareasofhighpreydensity(preyselection;H3)wouldreducesearchtimetofindandpotentiallykilla

TABLE  1 Testedhypothesesregardingdriversofwolfmovement.Ourmaininterestliesintestingtime-dependentmovementstrategies(H2,H5,andH6)butweincludedtime-independentmovementbehaviorsaspossiblesimplerexplanations(H0,H1,H3,andH4).Theprobabilityofselectingalocationismodeledasalogisticweightingfunctionofthespatialattributestimesincelastvisit(TSLV),distancefromterritoryedge(edge),andpreydensity(prey)withinaspatiallyexplicitmovementmodel.Forhypothesesinvolvingtwospatialattributes,wetestedbothamodelwithadditiveterminthelinearpredictor(resultinginashiftofthelogisticweightingfunction)andamodelwithadditionalmultiplicativeinteraction(changingalsothesteepnessofthelogisticweightingfunction)

Hypothesis Behavior Spatial attributes (model)

Expected relationship with probability of selection

TSLVDistance from edgea Prey density Interaction

Nopreferences Generalmovementtendenciesonly

H0 –(null) – – – –

Riskavoidance Avoidanceofterritoryedge H1 Edge – Pos – –

Territorysurveillance

Avoidanceofedge,butreducedforlongTSLV

H2a TSLV+edge Pos Pos –

H2b TSLV+edge+TSLV×edge Posb Posb – Pos

Preyselection Preferenceforhighpreydensity

H3 Prey – – Pos –

Preyselection&riskavoidance

Preferenceforhighpreydensitybutavoidedge

H4a Edge+prey – Pos Pos –

H4b Edge+prey+edge×prey – Posb Posb Pos

Delayedreturn PreferenceforlongTSLV H5 TSLV Pos – –

Preymanagement PreferenceforlongTSLV;highpreydensityinducesearlierreturn

H6a TSLV+prey Pos – Pos –

H6b TSLV+prey+TSLV×prey Posb – Posb Pos

aApositivecoefficientforthisattributemeansthattheprobabilityofselectingalocationincreaseswithitsdistancefromtheedge,thatis,towardcentrallocations.bDominanteffectoftheattributeontheprobabilityofselection(anegativecoefficientcanbecompensatedforarangeofattributevaluesbyapositiveinteractionterm).

     |  3SCHLÄGEL Et aL.

prey(Holling,1959;McPhee,Webb,&Merrill,2012).However,ifpreyconcentrate inbufferzonesbetweenwolfterritoriesthatactasref-ugestoprey(Mech,1994),wolvesarefacedwithmakingtrade-offsinfindingpreywhileatthesametimeavoidingconspecificsfromotherpacks(preyselectionandriskavoidance;H4a,H4b).

Prey can exhibit temporary avoidance, heightened vigilance, orretreat to safer habitats in areas of recentwolf presence orwhereconspecificswere recentlykilledbywolves (Berger-Tal&Bar-David,2015;Latombe,Fortin,&Parrott,2014;Liley&Creel,2008).Contrarytopredictionsby the “riskyplaceshypothesis,”whichaccountsonlyforvaryingantipredatorbehavioracrosssiteswithdifferentlong-termpredationrisk,observationsofelkresponsestowolvessuggestthatantipredatorbehavioradjustsdynamicallytothepresenceofwolvesinlinewiththe“riskytimeshypothesis”andthe“riskallocationhypoth-esis” (Creel,Winnie,Christianson,&Liley,2008;Robinson&Merrill,2013).Thesebehavioralresponseslowerpredationsuccess,aneffectcalledbehavioraldepressionofprey(Charnov,Orians,&Hyatt,1976).Tooptimizehuntingsuccess,wolvesmaynotonlyoptimizegiving-uptimes (Brown, Laundré, &Gurung, 1999; Charnov etal., 1976), butalsoselectforlongerTSLV(delayedreturn;H5)toallowtimeforpreybehavior torecover (Latombeetal.,2014;Laundré,2010).Thisalsospreadstheriskoverallhuntingsites(Lima,2002).However,wolvesmay returnsooner toareasofhighpreydensity (preymanagement;H6a,H6b)becauseofsuccessinfindingprey(Kunkel&Pletscher,2001;McPheeetal.,2012)andgreatervariation inrecoverytimesof indi-vidualprey.

Weexaminedthesupportforthesehypothesesinamodelselec-tion frameworkusingmovementdataof sixGPS-collaredwolves inwinterwhendenningislesslikelytoinfluencemovement,andpacksare likely to be more cohesive (Metz, Vucetich, Smith, Stahler, &Peterson,2011).Wecontrastedourbehaviorallybasedmodelswithanullmodelthatassumednopreferencesforspatiotemporalbehav-iors(H0).Wefitobservedmovementtrajectoriestorandomwalksthatincludedbehavioralmechanismsvia a spatiallyexplicit anddynamicresource-selection component (Schlägel & Lewis, 2014).With this,weillustratehowtodetectaninterplayoftravelhistorywithcurrentmovementdecisionsinmovementpatternsoffree-ranginganimals.

2  | MATERIALS AND METHODS

2.1 | Wolf and ungulate prey data

Datawerecollectedduring2004–2009ina25,000km2areawestofRockyMountainHouse,Alberta,Canada(52°27′N,115°45′W).TheareaispartofthecentraleastslopesoftheRockyMountains,andter-rainincludesgentlefoothillsintheeasternpartsaswellasmountains(<3,100m)towardthewest.Muchofthelandscapeiscoveredbyco-niferforest(52%),whichisinterspersedwithsmallerareasofnaturallowlands(10%),forestrycut-blocks(6%),standsofdeciduousforest(3%)withtheremainingbeinglargelypermanenticeandrock(Webb,Hebblewhite,&Merrill,2008).

During the years 2004–2006,wolveswere captured and fittedwithGPScollars(Lotek3300Swand4400S;fordetails,seeWebbetal.,

2008).Thecollarswereprogrammedtocollectlocationmeasurementsevery2hr.Thisledtoregulartimeseriesofobservedmovementsteps.Successfulfixattemptsforlocationswere90%(3300Swmodel)and82%(4400Smodel)indicatinghabitat-inducedGPSbiaswasminimal(Frairetal.,2004;Hebblewhite,Percy,&Merrill,2007).Weanalyzeddataofsixwolvesfromdifferentpackswhoseterritorieswereintheeasternpartofthestudyareawithlowelevationandnomountainval-leys.Themovementdataofthesixwolvesusedintheanalysisstartedbetween3Novemberand2Januaryandspanneduntil23Februaryand14April,dependingonindividual,spanningonaverage121days(SD23)andwithanaverageof1,458(SD289)locations/wolf.

The five major ungulate prey species for wolves were white-taileddeer(Odocoileus virginiana),muledeer(O. hemionus),elk(Cervus elaphus), moose (Alces alces), and feral horses (Equus caballus) andcomprised92–96%ofthepreybiomasswithinwolfscat(Merrill,un-published data). To obtain spatially explicit maps of densities, fecalpellet groupsdepositedoverwinterwere counted across372 tran-sects(1km×2m)aftersnowmelt.Pelletcountsfromtransectswereinterpolatedacross thestudyareausing inverse-distanceweighting.Countsofpelletgroupswereconvertedtoindividualnumbersofelkandmoose based on ratios of number of pellet groups to the esti-matednumberofindividualswithin16wildlifemanagementunitsob-tainedthroughwinteraerialsurveys.Fordeerandferalhorses,therewerenoaerialsurveyssotheratioobtainedformoosewasadjustedfordeerandhorsesbasedondifferencesinwinterdefecationratesofthespecies(McPheeetal.,2012).

To obtain a combined measure of available prey density forall four species,we calculated aweighted sumof all preynumbers,whereweightswere based on average ungulate bodymass inwin-ter(Knopff,Knopff,Kortello,&Boyce,2010;seeAppendixA1).Preydensities (number/30m2)wereaggregated toaspatial resolutionof300m×300mcells,mainlyforcomputationallimitations(seebench-marksinAppendixA3);however,wolveslikelycandetectpreywithinthisdistance(Basilleetal.,2015;Kuijperetal.,2014).Wolfmovementtrajectorieswereconsideredaccordinglyon thisspatialgridofcells,usingthecoordinatesofthecellcenters.Eachlocationofawolfwasattributedtothegridcellinwhichitfell.

2.2 | Spatial information and travel history

Relocationdatawereanalyzedusingstatisticalmovementmodelsde-velopedbySchlägelandLewis(2014).Thesemodelsarespatiallyex-plicitrandomwalksinwhichspatialinformationinfluencesmovementdecisions.Therandomwalkisperformedonadiscretegridofcellsincorrespondencetothepreydensitydata.Totestthehypothesizedex-planationsofwolfmovementbehavior(Table1),threetypesofspatialattributeswereconsidered.First,thecombinedpreydensitymeasure(prey)wasnormalizedovertheterritory(seenextparagraph)ofeachwolf.Second,foreachterritory,theminimumdistanceofeachloca-tionfromtheterritoryedge(edge)wascalculated.Distancefromedgeiszeroattheterritoryedgeandincreasesforlocationsmorecenteredwithintheterritory.Third,timesincelastvisit(TSLV)wasbasedonanindividual’sowntravelhistory.TSLVwasdefinedtospecifyateach

4  |     SCHLÄGEL Et aL.

time step, and for each location, the time (measured in time steps)sincetheanimalhadlastbeentothelocation,thatis,gridcell.TSLVisadynamicattributeofagridcellthatchangesaccordingtothein-dividual’smovement.TSLVincreasesforlocationsthattheindividualstaysawayfromandisresetto1whenevertheindividualvisitsaloca-tion.Locationswereconsideredvisitedwhentheylaywithinabufferzoneofthestraight-linepathbetweentwolocations.Thebufferzoneincludedfourgridcells,correspondingtoapproximately1,200m(seeAppendixA1foranexplanationandjustification).ToinitializeTSLV,westartedthewolfatthefirsttelemetrylocationandusedaninitialphaseof300timesteps,representing25days,whichwasexcludedfromfurtheranalysis.Before inclusion in theweighting function,allTSLVvalueswerelog-transformedbecausevalueshadawiderangeacrosstheterritory,withfewverylargevalues.Forfurtherinforma-tiononTSLV,seeAppendixA1.

AterritorywasdefinedforeachwolfbasedonaBrownianbridgekernel estimate of the individual’s utilization distribution obtainedwithRpackage“adehabitatHR”(Calenge,2006;Horne,Garton,Krone,&Lewis,2007).Forthisestimation,weusedalllocationsincludingthefirst300stepsforinitializingTSLV.Thepurposeoftheterritorywastwofold.Weused it toestimatethe“edge”oftheterritory,closetowhichthemortalityriskduetoaggressiveencounterswithotherwolfpacksmaybehigher.Wealsousedtheedgeasareflectiveboundaryin

themovementmodeltoavoidanartificialavoidanceofareaswithlongTSLVthatwerenotvisitedduringourstudyperiodforpossiblyexter-nalreasons(e.g.,otherpackactivity).Therefore,theterritoryincludedalllocationswithinthe99.9%quantileoftheestimatedutilizationdis-tribution (Figure1),whichwas the area that contained all locationspossiblyrelevantforanindividualduringthestudyperiod.

2.3 | Movement model

Inthemodels,twoaspectsaffecttheprobabilityforamovementstepbetweentimest −1andtfromlocationxt−1toxt.First,amovementkernelkdescribesgeneraltendenciesregardingspeedanddirectionalpersistence.Here,thekerneliscomposedofaWeibulldistributionforstep lengths andauniformdistribution forbearings (AppendixA1).Second,givenaprobabilitydistributionforastepbasedonthekernelk,aweightingfunctionwadjuststheseprobabilitiesbasedonprefer-encesforthethreespatialattributes,whichareencodedinthevector.Becausethemodelisspatiallyexplicit,eachlocationxhasitsownvaluesofthespatialattributes,thatist(x)= (prey(x),edge(x),TSLV(x)). Theoverallstepchoiceprobabilityisgivenby

(1)p(xt�xt−1)=k(xt;xt−1)w(t(xt))∑z∈Ω k(z;xt−1)w(t(z))

.

F I G U R E 1 Mapsofwintermovementsofsixindividualwolvesduring10–20weeks.Colorsreflectstandardizedpreydensity.Preydensityisacombinedmeasureofdensitiesofthemainungulatepreyspecies(deer,elk,moose,feralhorse).Blackcirclesarewolflocationswithblacklinesindicatingthestraight-linestepsbetweenlocations.Depictedareonly“relocating”stepsusedfortheanysisandexcludenon-relocatingstepssuchaswhenhandlingpreyandresting(numberofrelocatingstepswas177–332)

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We recall that locations representdiscrete300×300-m cells inspace.Thesuminthedenominatorisanormalizationconstantoveralarge enough area Ωaroundthecurrentlocationsuchthattheproba-bilityofsteppingoutsidethisareaisnegligible.TheradiusoftheareaΩ(ranging30–44cells,i.e.,9.0–13.2km)waschosentobelargerthanthe longeststep takenby thewolf.Stepsoutside the territoryhaveprobabilityzero.

Theweightingfunctionismodeledafteraresourceselectionprob-abilityfunction(Lele,Merrill,Keim,&Boyce,2013),givingthebinomialprobabilityofselectingalocationxbasedontheattributesoftheloca-tion,t(x).Here,weusedalogisticform,

The predictor term f(t(x),α,β,γ) contains additive and multiplica-tivecombinationsofthespatialattributes,accordingtoourhypoth-eses (Table1). For thenopreferencemodel, theweighting functionisconstantoverspace, that is,f(t(x),α,β,γ)=0, andonly thekernel

k influences movement. In the models risk avoidance, prey selec-tion, and delayed return, theweighting function includes one spa-tial attribute, and the predictor term f(t(x),α,β,γ) is simply given byα+βtslv ⋅TSLVt(x), α+βedge ⋅edge(x), or α+βprey ⋅prey(x),foreachmodel,respectively.Theparameterα is the interceptof thepredictorterm.Forasigmoidallogisticfunction,itdeterminesthepositionofthein-flection point of the curve, that is,where the function reaches thevalue 0.5. For hypotheses that involved two spatial attributes, twomodelswere considered, onewith additive termonly andonewithadditionalmultiplicativeinteraction.Forthemodelpreyselectionandrisk avoidance, the additive term is α+βedge ⋅edge(x)+βprey ⋅prey(x) (H4a,H4b)andthemultiplicativetermisγe,p ⋅edge(x) ⋅prey(x)(H4b).Themodelsterritorysurveillanceandpreymanagementwerebuiltanalo-gously,withinteractionparametersγt,e and γt,p,respectively.Thepa-rametersα,βtslv,βedge,βprey,γe,p,γt,e,γt,p determine thedirection andstrengthofpreferences.

FollowingAarts,Fieberg,andMatthiopoulos(2012),theweightingfunctionw(t(x)) is a functionof geographical space,x,via the spa-tial attributest(x) at a locationx. It can alternativelybeviewedasa weighting function over environmental space,, where attributevaluesrangeoverthethreedifferentspatialattributesTSLV,prey,andedge.This latterperspectiveallowsan interpretationof theef-fectsofspatialattributesonmovementdecisionssimilartoaclassi-calstep-selectionanalysis(Fortinetal.,2005).Whenconsideringtheweightingfunctioninenvironmentalspace,w( ),asafunctionofonevariable,forexample,w(TSLV),itisasigmoidalcurve.Additionaladdi-tivetermsoftheotherattributes(havingβcoefficients)shiftthecurve,whereasmultiplicativeterms(havingγcoefficients)additionallyinflu-encethenonlinearityorshapeofthecurve.Ashiftinthecurvemeansthat theswitch fromanavoidance (smallprobabilityofselection) toapreference(highprobabilityofselection)ofalocationhappensatadifferentvalueofthespatialattribute. If thesteepnessofthecurveincreases(decreases),theswitchhappensmore(less)abruptly.

2.4 | Statistical analysis

Movementdatawereanalyzedindividuallyforeachwolf,comparingthe fit of 10models (Table1).Wolves express different behavioralmodes,suchashandlingakill,restingawayfromakillsite,orrelocat-ingtoanewlocation(Franke,Caelli,Kuzyk,&Hudson,2006;Merrilletal.,2010).BecauseourgoalwastounderstandtheeffectofTSLVwithrespecttotheterritorysurveillanceandrevisitingareasofvary-ingpreydensities,weusedonlyrelocatingmovementstepsformodelfitting.Relocatingstepswereconsideredthosethatspannedatleastfivecells (1,500m) inourdiscretizedspace(Frankeetal.,2006;seeAppendixA1fordetails).However,non-relocatingstepswereomit-tedonlyaftercalculatingTSLVfortheentiretimeseriesensuringap-propriatevaluesofTSLVthatrepresentedthecorrecttimesbasedonthefullpath.Thefinaldatacomprised244,322,181,177,251,and276stepsforindividualsw83,w220,w230,w233,w284,andw285,respectively.

Maximum-likelihood estimates of the model parameters wereobtained by numerically optimizing the model’s likelihood function

(2)w(t(x))=1

1+e−f(t(x),α,β,γ).

TABLE  2 Parameterestimates,togetherwithstandarderrors(SE)ofthekernelkdescribinggeneralmovementtendencies(i.e.,steplength).Theparametersaretheshape(λ)andscale(σ)oftheWeibulldistributionusedtomodelsteplength.ThelastcolumngivesthemeanoftheresultingWeibulldistribution.Foreachwolf,weshowtheparameterestimatesfromthebestmodelcomparedtothenullmodel.Thenullmodelconsistentlyoverestimatesgeneraltendenciesforsteplength

λ SE (λ) σ SE (σ) Meana

w83

Null 2.45 0.12 14.39 0.42 12.76

Best 2.04 0.14 13.24 0.14 11.73

w200

Null 2.23 0.09 12.94 0.36 11.46

Best 1.82 0.10 11.41 0.10 10.14

w230

Null 2.62 0.14 10.97 0.34 9.75

Best(edge)

2.02 0.17 9.47 0.17 8.39

Best(prey)

2.04 0.17 9.50 0.17 8.41

w233

Null 2.20 0.12 13.19 0.50 11.68

Best 1.77 0.14 11.46 0.14 10.20

w284

Null 1.90 0.08 15.61 0.59 13.86

Best 1.47 0.45 13.21 0.45 11.95

w285

Null 2.21 0.09 12.52 0.38 11.09

Best 1.84 0.27 11.17 0.27 9.92

aBecause the analysis operated on 300×300m cells, the mean valuestranslateintometersviamultiplicationby300,forexample,ameanof10translatesintoameansteplengthof3km±300m.

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usingaNelder–MeadalgorithmimplementedinR(RCoreTeam2015,AppendixA1).ModelselectionwasperformedviaAkaikeinformationcriterion(AIC).WeusedthesmallsamplecriterionAICcbecauseratiosofavailablestepstonumberofparametersforthemostcomplexmodelwere≤40(Burnham&Anderson,2002).Withinnestedmodels,morecomplexmodelswereselectedwhenAICcdifferenceswerelargerthan2.WebasedthisontheruleofthumbgivenbyBurnhamandAnderson(2002)thatAICdifferencesof2orsmallerindicatesubstantialsupportforamodel.Adheringtotheprincipleofparsimony,wethereforeonlyselectedamorecomplexmodelwhenitsΔAICcwaslargerthan2com-paredtothenextsimplermodel.Parameterestimatesoftheweightingfunctionwereanalyzedfortheireffectsonmovementdecisionsusingtherepresentationoftheweightingfunctioninenvironmentalspace,w( )(Aartsetal.,2012).

3  | RESULTS

3.1 | General movement tendencies

Basedonthebest-fitmodel,meandisplacementsover2-hrtimeinter-vals(relocatingstepsonly),calculatedfromparametersoftheWeibulldistributionforstep lengths inthemovementkernelk, rangedfrom2,500to3,600m(±300mduetothespatialdiscretization)forthesixwolves(Table2).Whencomparingthiswithestimatesbasedonthenullmodel, there isaconsistent trend.Estimatesofboththeshape(λ)andscale(σ)oftheWeibulldistributionweresmallerforthebest-fitmodel,whichincludedselectionforspatialattributes,thanforthenullmodel (Table2).Thenullmodeldistributioncorrespondstothe“empirical kernel” used in classic step-selection analyses to sample“control”steps(Fortinetal.,2005).Here,thiswouldhaveconsistentlyoverestimated step length by approximately 300–570m per 2-hrstep.

3.2 | Selection for spatial attributes

For all sixwolves, the territory surveillancemodelwith interactionof TSLV and distance from territory edge (H2b) hadminimumAICc

(Table3). For one individual, w230, the same minimum AICc wasreachedbythepreymanagementmodelwithadditivetermsofTSLVandprey (H6a).Theterritorysurveillanceandpreymanagementhy-potheses are not mutually exclusive, and therefore both could besupportedbythedatawithoutcontradiction.Becausethissuggestedtheimportanceofbothterritorysurveillanceandpreymanagement,we also tested a combinedmodelwith these terms (TSLV+edge+ prey+TSLV×edge+TSLV×prey) in the weighting function. Forw230, this became the best model, and for w284 the model per-formedsimilarlywellastheterritorysurveillancemodelbutwasnei-thersignificantlybetternorparsimonious(TableA1inAppendixA2).

Parameter estimates of theweighting function for the territorysurveillancemodel (H2b)ofallwolveswereconsistentwithourpre-dictions. All multiplicative coefficients (γt,e) were positive and theirconfidenceintervalsdidnotoverlapzero,whilemostoftheadditivecoefficients(βedge, βtslv)hadconfidenceintervalsthatoverlappedzero(Table4).The overall effect ofTSLV and edge on the probability ofselection(modeledbytheweightingfunction)wasdominatedbythemultiplicative coefficientγt,e andwas thereforepositive.Theoverallselectioncoefficientforedge,givenTSLV,wasβedge+γt,e log (TSLV).AsTSLVincreased,thisbecamepositivealreadyatTSLV=2(4hr) inallcases.Similarly,theoverallselectioncoefficientforTSLV,givenedge,wasβtslv+γt,e ⋅edge.Asedge increased,startingfrom0, thisbecamepositiveatedge=1or2(correspondingtoapproximately300–900mfromtheedge)inallcases.Asaresult,therewasstrongevidenceforwolves avoiding territorial boundaries, and as TSLV increased,wolfavoidance of the edge declined (Figures2 andA2).When locationshadnotbeenvisitedformorethanapproximately7days,theweight-ing function approached a function nearly constant at one, whichmeans thatedgeandcentral locationswereselectedwith thesameprobability.

Movementpatternsofwolfw230alsosupportedthepreyman-agementmodel (H6a),where parameter estimates and the resultingweighting functiononlypartlyagreedwithourexpectations in rela-tiontothepreymanagementhypothesis(Table4).Consistentwithourprediction, the selection coefficientβtslvwaspositive, and thereforethewolfselectedforlongerTSLV,indicatingthatreturnstopreviously

ΔAICc

w83 w220 w230 w233 w284 w285

H0 Null 59.7 66.4 57.9 63.4 125.9 58.0

H1 Edge 45.2 66.6 55.6 49.7 76.6 38.2

H2a TSLV+edge 17.6 6.5 7.9 27.7 53.4 23.6

H2b TSLV + edge + TSLV×edge 0 0 0 0 0 0

H3 Prey 63.0 60.7 57.8 67.3 129.9 59.0

H4a Edge+prey 45.6 67.7 44.7 43.3 72.5 33.1

H4b Edge+prey+edge×prey 47.7 69.6 43.5 41.6 74.3 35.1

H5 TSLV 16.1 5.8 5.8 36.3 51.8 22.7

H6a TSLV+prey 18.0 5.9 0 30.2 52.7 23.2

H6b TSLV+prey+TSLV×prey 18.0 6.0 2.1 32.0 53.7 22.7

TABLE  3 Modelselectionresultsforthesixwolves.PresentedareAICc differences,ΔAICc,i=AICc,i–AICc,minforeachmodeli.Bestmodelsarehighlightedinbold.Forallindividuals,thebestmodelincludesTSLVanddistancefromterritoryedgewithmultiplicativeinteraction,supportingtheterritorysurveillancehypothesis.Forindividualw230,thefirstrankissharedwiththemodelthatincludesadditivetermsofTSLVandpreydensity,supportingthepreymanagementhypothesis

     |  7SCHLÄGEL Et aL.

visitedlocationsweredelayed(Table4,Figure3b).However,theco-efficientβedgewasnegativeandthewolfselected for locationswithlowerpreydensity(Table4,Figure3a).Asaresult,theinflectionpointofthesigmoidalcurvefromlowselectionofrecentlyvisitedsitestohigh selection of siteswith longer absencewas shifted to a highervalueofTSLV,whichledtoalongerdelayinrevisitingsiteswhenpreydensitywas high (Figure3b). Likewise, the selection for lower preydensitywasshiftedtotherightfor increasingvaluesofTSLV,whichresultedinnearlyequalselectionforallpreydensitiesafter5daysofabsence(Figure3a).

When considering the combined territory surveillance and preymanagementmodelforwolfw230,allestimatedselectioncoefficients(allβ and γcoefficients)hadlargeconfidenceintervalsthatoverlappedzero (TableA2).Whenwe plotted theweighting function based ontheseestimatesnonetheless,itwasconstantatoneovermostoftherangeofthespatialattributes,withonlytwoexceptions(FigureA3).First,abruptdeclinestozeroselectionoccurredforlocationsthathadbeenvisited during the last 2-hr-time step,which simplymay indi-catepersistentmovement.Second,theestimatespredictedadeclinetozeroselectionforthelowestpreydensityveryclosetotheedge,and this effectvanished already slightly further inside the territory.

Consideringalsothelargeandzero-overlappingconfidenceintervals,theseeffectsmaybeover-fitstospuriouseffectsatthemostextremeendsoftheattributevalues.

4  | DISCUSSION

We investigated how the time since last visiting a location influ-encedmovement decisions in relation to territory surveillance andpreymanagement.Ourmodelsarestatistical in thesensethat theydefineaprobabilitydistributionforobservedmovementsbutmecha-nistic in that they describe a behavioralmovement process. This isincontrasttoclassicresource (orstep)selectionanalysesthattreatmovementstepsasindependentdatapointsandsamplecontrolloca-tions(orsteps)beforeestimatingselectioncoefficients(Forester,Im,&Rathouz,2009;Fortinetal.,2005).Theadvantageofourmethodis that parameters of general movement tendencies and spatiallyexplicitpreferencesareestimated simultaneouslywithoutassumingthat the twoaspectsare independent (seealsoAvgar,Potts,Lewis,&Boyce,2016),whichproducesconsistentlylowerestimatesofthesteplengthdistributionthanifindependent,aprioriestimatesforstep

α βtslv βedge βprey γe,p γt,e γt,p

Territorialsurveillance:TSLV+edge+TSLV×edge

w83

Est. −2.15 −0.043a −0.014a – – 0.56 –

SE 0.86 0.20 0.091 – – 0.19 –

w220

Est. −2.41 0.47 0.039 – – 0.23 –

SE 0.53 0.15 0.042 – – 0.082 –

w230

Est. −2.97 0.49 −0.016a – – 0.82 –

SE 0.80 0.18 0.11 – – 0.31 –

w233

Est. −3.88 0.19 0.13 – – 0.33 –

SE 0.74 0.15 0.054 – – 0.10 –

w284

Est. −3.74 −0.36a 0.033 – – 0.28 –

SE 0.82 0.23 0.053 – – 0.06 –

w285

Est. −1.92 −0.045a 0.021 – – 0.58 –

SE 0.59 0.18 0.056 – – 0.22 –

Preymanagement:TSLV+prey

w230

Est. −3.96 2.66 – −1.54 – – –

SE 0.96 0.98 – 0.67 – – –

aNegativecoefficientsfortheadditivetermstillresultedinamostlypositiverelationshipduetothepositive interaction coefficient because the overall selection coefficient for TSLV, given edge, isβtslv + γt,e ⋅edge.Viceversa,theoverallselectioncoefficientforedge,givenTSLV,isβedge + γt,e ⋅TSLV.

TABLE  4 Parameterestimates(Est.)andstandarderror(SE)ofthebest-fitlogisticweightingfunctionwbasedonspatialattributesTSLV,distancefromterritoryedge(edge),andpreydensity(prey).Parametersβareselectioncoefficientsofadditiveterms(shiftingw),andparametersγdescribethemultiplicativeinteractionoftwoattributes(changingshapeofw nonlinearly).Parameterαistheinterceptofthelinearpredictoranddeterminesthepositionoftheinflectionpointofthelogisticweightingfunctionwhereitreaches0.5.Twobestmodelestimatesaregivenforwolf230becausetheyhadequalsupport.EstimatesforwhichWald-type95%confidenceintervalsdonotoverlapzeroarehighlightedinitalics

8  |     SCHLÄGEL Et aL.

length would have been used. An additional advantage to this ap-proachthatwedidnotuseinthisanalysisisincorporatingdirectionalautocorrelationofmovement in themovementkernelk (Schlägel&Lewis,2014).Inourcase,wedidnotusethisapproachbecauseourtimeseriesspannedonlyseveralweeks,andbecauseweeliminatednon-relocatingbehaviorssuchashandlingakill,restingawayfromakillsite,orrevisitingkillsites(Frankeetal.,2006;Merrilletal.,2010).Usingautocorrelatedbearingswouldhavedecreasedthenumberofstepsavailablefortheanalysisevenfurther,becausemorethantwosuccessivelocationmeasurementswouldhavebeenneededtodefinetheprobabilityofastep.

Adjustingreturnsafterpreviousvisitationisimportantwhentimeisrequiredtoreplenishhighfoodabundanceorquality(Bar-Davidetal.,2009;Davies&Houston,1981;Janmaat,Byrne,&Zuberbühler,2006;VanMoorteretal.,2009).Wefoundsupportforanadditionaltypeofresourcedepletion thatwehypothesize is related todecayof scentmarkings.First,therewasageneraltendencyofwolvestoavoidloca-tionsclosetotheterritoryedge,whichhasbeenreportedelsewhereasameanstoeludeintraspecificinterferencealongtheedgeoftheirterritories(Carbyn,1983;Mech&Harper,2002).Second,theprobabil-ityofwolvesrevisitingtheseareasincreasedintimesuggestingwolveswererespondingtoadecayinscentmarks,whichareneededforter-ritorialmaintenance (Peters&Mech, 1975;Zub etal., 2003). Scentmarkscontainpheromonesandchemicalsignalsthatelicitresponsesfromotherindividualsandcanpreventdirect,aggressiveencounters

(Mech,1994).Theyarethoughttobeaneffectivemeansofadvertise-ment because the scent remains in the environment for some timeandisreadilydetectedevenatnight (Feldhamer,Drickamer,Vessey,&Merritt, 2004).Peterson (1974) foundon IsleRoyale thatwolvesreverseddirectionof traveland retreatedwhen theyencounteredaforeignscentmarkalongtheedgeoftheirterritory.Ausband,Mitchell,Bassing,andWhite(2013)alsoreportedthatwolveswillavoidareaswhere humans place wolf scats if they are regularly maintained.Indeed,theconsistencyinterritorialsurveillanceamongallsixwolvesindicatesthereisstrongmotivationforrotationalmovementstorevisittheterritoryedgeforterritorymaintenance(Jedrzejewskietal.,2001).

In contrast, we found less support for prey density influencingwolfmovementsandformovementsbeingconsistentwithbehavioraldepressionofprey.Oneofthesixwolvesshowedsomeevidenceofitsmovementsbeing influencedbypreydensity, buteven thiswolfdidnotselectforareasofhighpreydensityaswasreportedforthisarea(McPheeetal.,2012).Thedifferencebetweenstudiesmayexistbecauseof theanalysisscale.McPheeetal. (2012) reportedthatatthelarge-scalewolvesselectedhuntpathswithhigherpreythantheoverallterritory,butatthescaleofthehuntpathlandscapefeatures

F IGURE  2 Weightingfunctionfortheterritorysurveillancemodel(H2b)basedonparameterestimatesfromindividualw220.Thismodelwasbestforallwolves.Theweightingfunctiongivestheprobabilityofselectingalocationbasedonspatialattributes,heredepictedasfunctionofdistancefromterritoryedge(edge)inenvironmentalspacewheredistancefromtheedgewasmeasuredindiscretecells(300×300m)forvaryingvaluesoftimesincelastvisit(TSLV).Theincreasingsigmoidalcurveindicatesthatlocationsclosertotheedgeareavoided.WithincreasingTSLV,thecurveisshiftedtotheleftduetothepositivecoefficient(βtslv)andbecomessteeperduetothepositiveinteractionparameter(γt,e),indicatingthattheavoidanceofedgelocationsvanishes.GraphsfortheotherindividualsshowsimilarpatternsFig.A2

0 5 10 15 20 25 30

0.0

0.2

0.4

0.6

0.8

1.0

distance from edge [cells]

wei

ghtin

g fu

nctio

n w

TSLV

1 week1 day6 hr2 hr

F I G U R E 3 Weightingfunctionforthepreymanagementmodel(H6a),withparameterestimatesfromindividualw230,forwhichthismodelsharedfirstrank.Theweightingfunctiongivestheprobabilityofselectingalocationbasedonspatialattributes,heredepictedasfunction(inenvironmentalspace)of(a)preydensityand(b)timesincelastvisit(TSLV).Preydensity(numberspercell)wasstandardizedacrosstheterritory.Whenpreydensitywashigh,theprobabilityofselectingalocationwashigherwhentimesincelastvisitwaslonger.Whenpreydensitywaslow,timesincelastvisitmatteredless

−2 −1 0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

prey density [no. per cell stand.]

wei

ghtin

g fu

nctio

n w

TSLV

2 hr6 hr1 day5 days

0 1 2 3 4 5 6 70.

00.

20.

40.

60.

81.

0log(TSLV) [log(time steps)]

wei

ghtin

g fu

nctio

n w

prey density

low (−2)mean (0)high (3)

(a)

(b)

     |  9SCHLÄGEL Et aL.

ratherthanpreydensityinfluencedmovements.Inourapproach,wefocusedonselectionalongthehuntpathandfoundthatthewolfse-lectedareasoflowratherthanhighdensity.Inaddition,weanalyzed“relocating”movementsanddidnotincludeshortsteps.Wolvespos-siblyslowdowninhighpreydensityareas,whichcouldhaveledtoaremovalofshortstepsinhighpreydensityareasinouranalysis.Themovements of thewolfwith an effect of prey density also showedevidenceofpreymanagement,whereapredatordelaysarevisittoanareabecauseavisitevokespreybehaviorsthatmakethemlessvul-nerable(Charnovetal.,1976;Jedrzejewskietal.,2001;Kotler,1992;Laporte,Muhly,Pitt,Alexander,&Musiani,2010).Wehadexpectedthat wolves would revisit sites with high density sooner becausetherecouldbehighervariationamong individualpreyrelaxingpost-encounteranti-predatorbehaviorsandpredisposingthemtowolfat-tacks;however,whenlocationshadbeenvisitedrecently,selectionbywolfw230washighestforareasoflowpreydensityperhapsbecauselowdensitiesareassociatedwithincreasedvulnerabilityifgroupsizesare small (Bergmann etal., 2006; Hebblewhite & Pletscher, 2002;Kuzyk,Kneteman,&Schmiegelow,2004).

Fromamodelingpointofview,wewereabletotesttheinfluenceoftimesincelastvisitseparatelyforterritorymaintenanceandforfor-agingbehaviors;however,anintegrationofthetwobehaviorswithinonemodelwasmoredifficult.Forwolfw230,thecombinedmodelfitbetterthantheterritorysurveillanceandthepreymanagementmodelalone.Butparameterestimatesoftheweightingfunctioninthecom-binedmodel suggestedanover-fit tospuriouseffectsof thespatialattributesattheirmostextremevalues.Apossibleexplanationisthatwolvesmakedecisions inaway thatour logisticweighting functionwasunable to represent.The logistic functioncould trackearlierorlaterreturnsto locationsbasedondistancetoedgeorpreydensity.However,wolvesmayassimilateterritorialandforagingbehaviorsinadifferentnonlinearway(Rothley,Schmitz,&Cohon,1997).Wesug-gestfurtherresearchalongthisline,possiblybymodifyingtheformofweightingfunctioninourmodelingframework.

Ourmodeldiscretizesbothspaceandtime,whichhasimplicationsforthegeneralityofourresults.Inourrandom-walkmodel,weimplic-itlyassumethattemporalscalesoftheunderlyingbehavioralprocessandourdata(2-hourly)match.Thisisacommonproblemwhenfittingdiscrete-timemovementmodelstodataforstatisticalinference,lead-ingtoparameterestimates thatare tiedto thescaleof theanalysisandthatmaynotnecessarilyagreewiththe“true”parametervaluesatthescaleofthebehavioralprocess(Schlägel&Lewis,2016).Despitethis,webelieveourresultsqualitativelyreflectthewolves’behavior,also becausewe used a logistic form of theweighting function in-steadofanexponentialform;theformerhavingperformedbetterinasimulation-basedanalysisoftherobustnessofresource-selectiontypemovementmodels(Schlägel&Lewis,2016).

Ingeneral,impactofspatialresolutionislessclearlyunderstood.Inouranalysis,weusedarelativelycoarsediscretizationof300×300mcells.Usingafinerdiscretizationwouldhaveincreasedcomputationalburdenbecause the bottleneck during likelihood function optimiza-tionwas thecomputationof thenormalizationconstant in the stepprobability(eqn1).Thisconstantrequiresmultiplicationofkerneland

weightingfunctionforalllocationswithinanareathattheindividualmay possiblymove to based on the current location (and this con-stanthastobecomputedforeverydatapointinthetimeseries).Forafinerspatialresolution,thesameareawouldconsistofmorelocations,whichwould(nonlinearly)increasetheamountofcalculationsneces-sary.Withincreasingcomputationalpower,orbyfurtherstreamliningthecode,itmaybepossibletoreducecurrentruntime(1–2daysforoursixwolvesusingmultipleCPUs).However,weconsideredthedis-cretizationsufficientbecauseofthedesignofTSLVinourmodel.ForcalculatingTSLV,weusedabufferofabout1.2kmaroundthestraightlinebetweenconsecutiveGPSfixesbecausewolfpassageaffectspreybehavior beyond the actual movement path (Latombe etal., 2014;Liley&Creel,2008).Therefore, for the sakeofTSLV, a finer spatialdiscretization would not have increased the resolution biologically.Ideally,thesizeofthebufferwouldbeintegratedasafreeparameterthatisestimatedduringmodelfitting,inwhichcaseitcouldvaryfordifferentmodels(e.g.,preymanagementandterritorysurveillance).Inouranalysis,wefixedthebuffersizetokeepmodelcomplexityatareasonablelevelgiventhelimitedtimeserieslengthofourdata.

Theapproachinthispaperprovidesastepforwardintheongoingattempttoincorporatecognitionandmemoryinmovementanalyses(Avgaretal.,2015;Börger,Dalziel,&Fryxell,2008;Faganetal.,2013;Oliveira-Santos,Forester,Piovezan,Tomas,&Fernandez,2016).Ourmethodgoesbeyondpreviousapproachesthatinvestigatetraplining(Ohashi, Leslie,&Thomson,2008)orperiodicity in recursivemove-ment patterns (Bar-David etal., 2009; English etal., 2014; Giotto,Gerard,Ziv,Bouskila,&Bar-David,2015). Inourmodels, timesincelastvisittolocationsisaspatiallyexplicitfeaturethatinfluencesmove-mentdecisionsincombinationwithinformationonterritorygeometryandpreydensities.Thisallowedustoinvestigatebehaviorallycomplexmovementstrategiesinwolves,andwedemonstratedthattimesincelastvisitinfluencedfuturemovementdecisionsinrelationtoterritorysurveillance and prey management. Our approach can similarly beused tostudy theeffectof timesince lastvisit inothercontextsofresourcerenewal(e.g.,D’Souza,Patankar,Arthur,Marbà,&Alcoverro,2015;Janmaatetal.,2006).

Despite some progress in studying cognitive aspects of animalmovement, few studies have quantified the temporal and spatialscales at which individuals are aware of and respond to non-localinformation.Reported timespansduringwhichungulatesshift theirhabitatselectionafterwolfpresencerangefrom1day(Creel,Winnie,Maxwell, Hamlin, & Creel, 2005) to up to 10days (Latombe etal.,2014). In contrast,Avgar etal. (2015) found indication of nomem-orydecayinaspace-useanalysisofwoodlandcaribou.Inourstudy,wolfw230showedavaryingresponsetopreydensitywithinapprox-imately5dayssincelastvisit,afterwhichtheprobabilityofselectionleveledoffatoneforalllocations.Similarly,afterapproximately7daysofabsence,wolfmovementdecisionsbecameirrespectiveofdistancefromterritoryedge.TheseestimatesareroughlyinlinewiththescalesreportedbyLatombeetal. (2014). Inapredator–preysystemwherepredatorswin thebehavioral response race (Sih, 2005)wemay ex-pectpredators’responsetimestobelargerthantheprey’sresponse,andviceversa.Weneedmorestudiesthattrackpredatorsandprey

10  |     SCHLÄGEL Et aL.

simultaneouslyandanalyzethetemporalscalesofawarenessforbothpredators and prey to elucidate this further. Simultaneous trackingstudieshavetheadditionaladvantagethattemporalscalesofdatacanbematched.Asdiscussed above,we should expect parameter esti-matesfromresource-selectiontypeanalysestobescaledependent.Unlessweusetrulyrobustmodels,comparisonsofcognitiveaware-nessarebesttobeattemptedwhenmodelsmakethesameassump-tionsaboutthescalesofthebehavioralprocesses.

Inouranalysis,weusedafixedbuffersizeformodelingthespatialextentatwhichlocationswereconsidered“visited”forthepurposeofcalculatingTSLV.Apossibleextensionofourmodelwould treat thebuffersizeasafreeparametertobeestimatedduringmodelfitting.Withthis,itwouldbepossibletoalsogaugethespatialscaleatwhichindividualsexperiencetheirenvironmentforthisspecificpurpose.

Using information on elapsed times (“how long ago?”) can bepartof episodic-likememory in animals, a complex formofmem-ory on the what, when, and where of events, which has beendemonstrated in experiments in birds, rodents, and apes (Clayton&Dickinson,1998;Martin-Ordas,Haun,Colmenares,&Call,2010;Robertsetal.,2008).Wolvesmaystoreandretrieveinformationonelapsedtimesininternalmemory(Jacobs,Allen,Nguyen,&Fortin,2013;Lew,2011),butwolvesmayalsouseexternalizedmemoryinthe formof theirown scentmarks (Peters&Mech,1975), ashasbeen argued for neurologically simple amoebae (Reid, Beekman,Latty,&Dussutour,2013).However,whereasscentmarksneedtobeencounteredtoretrieve informationonpreviousvisits, internalmemory allowsmore efficient integrationof information for goal-orientedmovement (Asensio&Brockelman,2011;Polanskyetal.,2015).Therefore,includinggoal-orientedmovementrulesinamod-eling framework such as ourswould further elucidate the impor-tanceofinternalmemory.

ACKNOWLEDGMENTS

TheauthorsthankThomasMuellerandNathanWebbforusefulcom-mentsonthedataanalysisandtwoanonymousreviewersforvaluablecommentsonthemanuscript.UESgratefullyacknowledges fundingfrom iCORE, now part of Alberta Innovates-Technology Futures,the German Academic Exchange Service (DAAD), and the GermanResearchFoundation (DFG-GRK2118/1).MALandEHMgratefullyacknowledge Natural Sciences and Engineering Research CouncilDiscovery Grants, MAL for Accelerator grants, a Canada ResearchChair and a Killam Research Fellowship. Data collection on wolfmovements was directed by NathanWebb and HannahMcKenzieand funded by Natural Sciences Natural Sciences and EngineeringResearch Council Collaborative Research Opportunity-261091-02toEHM,AlbertaConservationAssociation,AlbertaEnvironmentandParks,AlbertaProfessionalOutfitters,FoundationforNorthAmericanWildSheep—AlbertaChapter,RockyMountainElkFoundation,RedDeer River Naturalists, Safari Club International—Northern AlbertaChapter,SundreForestProducts,andWeyerhaeuserCanada.Finally,we thank thenumerous field techniciansandvolunteerswhogath-ereddataforthisproject.

CONFLICT OF INTEREST

Nonedeclared.

DATA ACCESSIBILITY

Data available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.2j125.

ProcesseddataandRcodetoruntheanalysisforoneindividualcanbefoundonlineintheSupportingInformationforthisarticle.

REFERENCES

Aarts,G.,Fieberg,J.,&Matthiopoulos,J.(2012).Comparativeinterpreta-tionofcount,presence-absenceandpointmethodsforspeciesdistri-butionmodels.Methods in Ecology and Evolution,3,177–187.

Asensio,N.,&Brockelman,W.Y.(2011).Gibbontravelpathsaregoalori-ented.Animal Cognition,14,395–405.

Ausband,D.E.,Mitchell,M.S.,Bassing,S.B.,&White,C.(2013).Notres-passing: Using a biofence to manipulate wolf movements. Wildlife Research,40,207–216.

Avgar,T.,Baker,J.A.,Brown,G.S.,Hagens,J.S.,Kittle,A.M.,Mallon,E.E.,…Fryxell,J.M. (2015).Space-usebehaviourofwoodlandcariboubasedonacognitivemovementmodel.Journal of Animal Ecology,84,1059–1070.

Avgar,T.,Deardon,R.,&Fryxell,J.M.(2013).Anempiricallyparameterizedindividualbasedmodelofanimalmovement,perception,andmemory.Ecological Modelling,251,158–172.

Avgar,T.,Potts,J.R.,Lewis,M.A.,&Boyce,M.S. (2016). Integratedstepselectionanalysis:Bridgingthegapbetweenresourceselec-tion and animal movement.Methods in Ecology and Evolution, 7,619–630.

Bar-David, S., Bar-David, I., Cross, P. C., Ryan, S. J., Knechtel, C. U., &Getz,W.M. (2009).Methods for assessingmovement path recus-rionwithapplicationtoAfricanbuffalo inSouthAfrica.Ecology,90,2467–2479.

Basille,M.,Fortin,D.,Dussault,C.,Bastille-Rousseau,G.,Ouellet,J.P.,&Courtois,R.(2015).Plasticresponseoffearfulpreytothespatiotempo-raldynamicsofpredatordistribution.Ecology,96,2622–2631.

Berger-Tal, O., & Bar-David, S. (2015). Recursive movement patterns:Reviewandsynthesisacrossspecies.Ecosphere,6,art149.

Bergmann, E. J., Garrott, R. A., Creel, S., Borkowski, J. J., Jaffe, R., &Watson, F. G. R. (2006). Assessment of prey vulnarability throughanalysisofwolfmovementsandkillsites.Ecological Applications,16,273–284.

Börger,L.,Dalziel,B.D.,&Fryxell,J.M. (2008).Aretheregeneralmech-anismsofanimalhomerangebehaviour?Areviewandprospectsforfutureresearch.Ecology Letters,11,637–650.

Bracis,C.,Gurarie,E.,VanMoorter,B.,&Goodwin,R.A.(2015).Memoryeffects on movement behavior in animal foraging. PLoS ONE, 10,1–21.

Brown, J. S., Laundré, J.W., &Gurung,M. (1999). The ecology of fear:Optimal foraging, game theory, and trophic interactions. Journal of Mammalogy,80,385–399.

Burnham,K.P.,&Anderson,D.R. (2002).Model selection and multimodel inference: A practical information-theoretic approach,2nded.NewYork,NY:Springer.

Burns,J.G.,Foucaud,J.,&Mery,F.(2011).Costsofmemory:Lessonsfrom“mini”brains.Proceedings of the Royal Society B: Biological Sciences,278,923–929.

Calenge,C.(2006).Thepackage“adehabitat”fortheRsoftware:Atoolfortheanalysisofspaceandhabitatusebyanimals.Ecological Modelling,197,516–519.

     |  11SCHLÄGEL Et aL.

Carbyn,L.N. (1983).Wolfpredationonelk inRidingMountainNationalPark,Manitoba.The Journal of Wildlife Management,47,963–976.

Charnov,E.L.,Orians,G.H.,&Hyatt,K.(1976).Ecologialimplicationsofresourcedepression.The American Naturalist,110,247–259.

Clayton,N.S.,&Dickinson,A.(1998).Episodic-likememoryduringcacherecoverybyscrubjays.Nature,395,272–274.

Creel,S.,Winnie,J.A.,Christianson,D.,&Liley,S.(2008).Timeandspaceingeneralmodelsofantipredatorresponse:Testswithwolvesandelk.Animal Behaviour,76,1139–1146.

Creel,S.,Winnie,J.,Maxwell,B.,Hamlin,K.,&Creel,M.(2005).Elkalterhabitat selectionasanantipredator response towolves.Ecology,86,3387–3397.

Davies,N.B.,&Houston,A.I.(1981).Ownersandsatellites:Theeconom-ics of territory defence in the piedwagtail,Motacilla alba. Journal of Animal Ecology,50,157–180.

D’Souza, E., Patankar, V., Arthur, R., Marbà, N., & Alcoverro, T. (2015).Seagrassherbivorylevelssustainsite-fidelityinaremnantdugongpop-ulation.PLoS ONE,10,1–18.

English,M.,Ancrenaz,M.,Gillespie,G.,Goossens,B.,Nathan,S.,&Linklater,W.(2014).ForagingsiterecursionbyforestElephantsElephas maximus borneensis. Current Zoology,60,551–559.

Fagan,W.F.,Lewis,M.A.,Auger-Méthé,M.,Avgar,T.,Benhamou,S.,Breed,G.,…Mueller,T.(2013).Spatialmemoryandanimalmovement.Ecology Letters,16,1316–1329.

Feldhamer,G.A.,Drickamer, L. C.,Vessey, S.H.,&Merritt, J. F. (2004).Mammalogy: Adaptation, diversity, ecology, 2nd ed. New York, NY:McGraw-Hill.

Forester, J.D., Im,H. K., & Rathouz, P. J. (2009).Accounting for animalmovementinestimationofresourceselectionfunctions:Samplinganddataanalysis.Ecology,90,3554–3565.

Fortin,D.,Beyer,H.L.,Boyce,M.S.,Smith,D.W.,Duchesne,T.,&Mao,J.S.(2005).Wolvesinfluenceelkmovements:BehaviorshapesatrophiccascadeinYellowstoneNationalPark.Ecology,86,1320–1330.

Frair,J.L.,Nielsen,S.E.,Merrill,E.H.,Lele,S.R.,Boyce,M.S.,Munro,R.H.M.,…Beyer,H.L.(2004).RemovingGPScollarbiasinhabitatselectionstudies.Journal of Applied Ecology,41,201–212.

Franke,A.,Caelli,T.,Kuzyk,G.,&Hudson,R.J.(2006).Predictionofwolf(Canis lupus)kill-sitesusinghiddenMarkovmodels.Ecological Modelling,197,237–246.

Giotto,N.,Gerard,J.F.,Ziv,A.,Bouskila,A.,&Bar-David,S.(2015).Space-usepatternsoftheAsiaticwildass(Equus hemionus):Complementaryinsightsfromdisplacement,recursionmovementandhabitatselectionanalyses.PLoS ONE,10,1–21.

Grove, M. (2013). The evolution of spatial memory. Mathematical Biosciences,242,25–32.

Hebblewhite,M., Percy,M., &Merrill, E. H. (2007).Are all global posi-tioningsystemcollarscreatedequal?Correctinghabitat-inducedbiasusingthreebrandsintheCentralCanadianRockies.Journal of Wildlife Management,71,2026–2033.

Hebblewhite,M.,&Pletscher,D.H. (2002).Effectsofelkgroup sizeonpredationbywolves.Canadian Journal of Zoology,80,800–809.

Holling,C.S.(1959).Thecomponentsofpredationasrevealedbyastudyofsmall-mammalpredationoftheEuropeanpinesawfly.The Canadian Entomologist,91,293–320.

Hopkins,M.E.(2015).Mantledhowlermonkeyspatialforagingdecisionsreflect spatial and temporal knowledge of resource distributions.Animal Cognition,19,1–17.

Horne,J.S.,Garton,E.O.,Krone,S.M.,&Lewis,J.S. (2007).AnalyzinganimalmovementsusingBrownianbridges.Ecology,88,2354–2363.

Jacobs,N.S.,Allen,T.A.,Nguyen,N.,&Fortin,N.J. (2013).Critical roleof the hippocampus in memory for elapsed time. The Journal of Neuroscience,33,13888–13893.

Janmaat,K.R.L.,Byrne,R.W.,&Zuberbühler,K. (2006).Evidenceforaspatialmemoryoffruitingstatesofrainforesttreesinwildmangabeys.Animal Behaviour,72,797–807.

Jedrzejewski,W.,Schmidt,K.,Theuerkauf,J.,Jedrzejewska,B.,&Okarma,H.(2001).Dailymovementsandterritoryusebyradio-collaredwolves(Canis lupus)inBialowiezaPrimevalForestinPoland.Canadian Journal of Zoology,79,1993–2004.

Knopff, K.H., Knopff,A.A., Kortello,A.,&Boyce,M. S. (2010).Cougarkillrateandpreycompositioninamultipreysystem.Journal of Wildlife Management,74,1435–1447.

Kotler,B.P.(1992).Behavioralresourcedepressionanddecayingperceivedriskofpredationintwospeciesofcoexistinggerbils.Behavioral Ecology and Sociobiology,30,239–244.

Kuijper,D.P.J.,Verwijmeren,M.,Churski,M.,Zbyryt,A.,Schmidt,K.,Jedrzejewska, B., & Smit, C. (2014).What cues do ungulates usetoassesspredation risk indense temperate forests?PLoS ONE,9,1–12.

Kunkel,K.,&Pletscher,D.H. (2001).Winterhuntingpatternsofwolvesin and near Glacier National Park, Montana. The Journal of Wildlife Management,65,520–530.

Kuzyk,G.W.,Kneteman,J.,&Schmiegelow,F.K.A.(2004).Winterhabitatusebywolves,Canis lupus, in relation to forestharvesting inWest-centralAlberta.The Canadian Field- Naturalist,118,368–375.

Laporte, I.,Muhly,T.B., Pitt, J.A.,Alexander,M.,&Musiani,M. (2010).Effectsofwolvesonelkandcattlebehaviors:Implicationsforlivestockproductionandwolfconservation.PLoS ONE,5,e11954.

Latombe,G.,Fortin,D.,&Parrott,L.(2014).Spatio-temporaldynamicsintheresponseofwoodlandcaribouandmoosetothepassageofgreywolf.Journal of Animal Ecology,83,185–198.

Laundré, J. W. (2010). Behavioral response races, predator-prey shellgames,ecologyoffear,andpatchuseofpumasandtheirungulateprey.Ecology,91,2995–3007.

Lele, S.R.,Merrill, E.H.,Keim,J.,&Boyce,M. S. (2013). Selection, use,choiceandoccupancy:Clarifyingconceptsinresourceselectionstud-ies.Journal of Animal Ecology,82,1183–1191.

Lew,A.R.(2011).Lookingbeyondtheboundaries:Timetoputlandmarksbackonthecognitivemap?Psychological Bulletin,137,484–507.

Lewis,M.A.,&Murray,J.D.(1993).Modellingterritorialityandwolf-deerinteractions.Nature,366,738–740.

Liley, S., & Creel, S. (2008). What best explains vigilance in elk:Characteristics of prey, predators, or the environment? Behavioral Ecology,19,245–254.

Lima, S. L. (2002). Puttingpredators back intobehavioral predator–preyinteractions.Trends in Ecology & Evolution,17,70–75.

Martin-Ordas, G., Haun, D., Colmenares, F., & Call, J. (2010). Keepingtrackoftime:Evidenceforepisodic-likememoryingreatapes.Animal Cognition,13,331–340.

McPhee,H.M.,Webb,N.F.,&Merrill,E.H.(2012).Hierarchialpredation:Wolf(Canis lupus)selectionalonghuntpathsandatkillsites.Canadian Journal of Zoology,90,555–563.

Mech,L.D.(1994).Bufferzonesofterritoriesofgraywolvesasregionsofintraspecificstrife.Journal of Mammology,75,199–202.

Mech,L.D.,&Boitani,L.(Eds.)(2006).Wolves: Behaviour, ecology, and con-servation.Chicago,IL:UniversityofChicagoPress.

Mech,L.D.,&Harper,E.K.(2002).Differentialuseofawolf,Canis lupus,pack territory edge and core. The Canadian Field- Naturalist, 116,315–316.

Merkle,J.A.,Fortin,D.,&Morales,J.M.(2014).Amemory-basedforagingtacticrevealsanadaptivemechanismforrestrictedspaceuse.Ecology Letters,17,924–931.

Merrill,E.,Sand,H.,Zimmermann,B.,McPhee,H.,Webb,N.,Hebblewhite,M.,…Frair,J.L.(2010).Buildingamechanisticunderstandingofpreda-tionwithGPS-basedmovementdata.Philosophical transactions of the Royal Society B, Biological sciences,365,2279–2288.

Metz,M.C.,Vucetich,J.A.,Smith,D.W.,Stahler,D.R.,&Peterson,R.O.(2011).Effectofsocialityandseasonongraywolf(Canis lupus)forag-ingbehavior: Implications forestimatingsummerkill rate.PLoS ONE,6,1–10.

12  |     SCHLÄGEL Et aL.

APPENDIX A1

COMBINED PREY DATA

To calculate the combined prey density measure, we calculated aweightedsumofpreynumbersofallfourspecies.Thatis,ourmeasureofpreydensitywas

where Nisthenumberofindividualsofthepreyspeciesindicatedinthesubscript,andwisaweightbetween0and1toadjustforthesizeoftheprey.Theweightswerebasedonungulatebodymassinwinter(Knopffet al.2010),forsimplicityaveragedoverfemaleandmales,

Tomake theweightsunitless,weconverted themtoanumberbe-tween0and1bydividingthevalueofeachspeciesbythesumofall,

TIME SINCE LAST VISIT

WedefinedthevariableTSLVtospecifyateachtimestept,andforeachlocationx,thetime,measuredintimesteps,sincetheanimalhadlastbeentothelocation,denotedbymt(x).Forexample, ifbetweentimest−1andttheanimalmovedfromlocationxt−1toxt,weconsid-eredalllocationsonthepathfromxt−1toxtasmostrecentlyvisitedandandsettheirvalueofTSLVattimettobe1.Thatis,wedefinedmt(z)=1foralllocationszthatlieonthepathbetweenxt−1 and xt.ForthecalculationofTSLV,wedefined thepath tobe thestraight linebetweentwolocations.Becauseitisunlikelythatanindividualmovesinastraightline,wealsoconsideredlocationswithinacertaindistanceofthelineasvisited(forthepurposeofcalculatingTSLV).Fortheselocations,TSLVwasalsosetto1.Becauseweaimedtounderstandtheinfluenceofthetravelhistoryinrelationtoprey,wetookintoac-count at which distances wolf presence influences prey behavior.Studiesonelk–wolfrelationshipsfoundthatwolfpresencecanaffectelk behavior, such as group size, vigilance, andmovement rates, atdistancesof1–5km(Liley&Creel2008;Proffittet al.2009).Here,weuseddiscretizedspacewithlandscapecellsofsize300×300m.We

Nprey=wdeer×Ndeer+welk×Nelk+wmoose×Nmoose+whorse×Nhorse

bdeer= 82.5, belk= 275, bmoose= 434, bhorse= 420

wspecies=bspecies

bdeer+belk+bmoose+bhorse.

Mueller,T.,Fagan,W.F.,&Grimm,V.(2011).Integratingindividualsearchandnavigationbehaviorsinmechanisticmovementmodels.Theoretical Ecology,4,341–355.

Nabe-Nielsen,J.,Tougaard,J.,Teilmann,J., Lucke,K.,&Forchhammer,M. C. (2013). How a simple adaptive foraging strategy can leadto emergent home ranges and increased food intake.Oikos, 122,1307–1316.

Ohashi,K.,Leslie,A.,&Thomson,J.D.(2008).Traplineforagingbybumblebees:V.Effectsofexperienceandpriorityoncompetitiveperformance.Behavioral Ecology,19,936–948.

Oliveira-Santos, L. G. R., Forester, J. D., Piovezan, U., Tomas,W. M., &Fernandez,F.A.S.(2016).Incorporatinganimalspatialmemoryinstepselectionfunctions.Journal of Animal Ecology,85,516–524.

Peters, R. P., & Mech, L. D. (1975). Scent-marking in wolves. American Scientist,63,628–637.

Peterson,R.O.(1974).WolfecologyandpreyrelationshipsonIsleRoyale.United States National Park Service Scientific Monograph Series, 11,1–210.

Polansky, L., Kilian,W., &Wittemyer, G. (2015). Elucidating the signifi-canceofspatialmemoryonmovementdecisionsbyAfricansavannahelephantsusingstate-spacemodels.Proceedings of the Royal Society B: Biological Sciences,282,20143042–20143042.

RCoreTeam.(2015).R: A language and environment for statistical computing. RFoundation forStatisticalComputing,Vienna,Austria.URLhttps://www.R-project.org/.

Reid,C.R.,Beekman,M.,Latty,T.,&Dussutour,A.(2013).Amoeboidor-ganismusesextracellularsecretionstomakesmartforagingdecisions.Behavioral Ecology,24,812–818.

Riotte-Lambert, L., Benhamou, S., & Chamaillé-Jammes, S. (2015). Howmemory-basedmovement leads tononterritorial spatial segregation.The American Naturalist,185,E103–E116.

Roberts,W.A.,Feeney,M.C.,Macpherson,K.,Petter,M.,Mcmillan,N.,&Musolino,E.(2008).Episodic-likememoryinrats:Isitbasedonwhenorhowlongago?Science,320,113–115.

Robinson,B.G.,&Merrill,E.H.(2013).Foraging-vigilancetrade-offsinapartiallymigratorypopulation:Comparingmigrantsandresidentsonasympatricrange.Animal Behaviour,85,849–856.

Rothley,K.D.,Schmitz,O.J.,&Cohon,J. L. (1997).Foraging tobalanceconflictingdemands:Novel insights fromgrasshoppersunderpreda-tionrisk.Behavioral Ecology,8,551–559.

Rowcliffe, J. M., Carbone, C., Kays, R., Kranstauber, B., & Jansen, P. A.(2012).Biasinestimatinganimaltraveldistance:Theeffectofsamplingfrequency.Methods in Ecology and Evolution,3,653–662.

Schlägel,U.E.,&Lewis,M.A.(2014).Detectingeffectsofspatialmemoryanddynamic informationonanimalmovementdecisions.Methods in Ecology and Evolution,5,1236–1246.

Schlägel,U.E.,&Lewis,M.A.(2016).Robustnessofmovementmodels:Canmodelsbridgethegapbetweentemporalscalesofdatasetsandbe-haviouralprocesses?Journal of Mathematical Biology,73,1691–1726.

Sih,A.(2005).Predator-preyspaceuseasanemergentoutcomeofabe-havioralresponserace.Ecology of Predator- Prey Interactions,240–255.

VanMoorter, B.,Visscher,D., Benhamou, S., Börger, L., Boyce,M. S., &Gaillard,J.M.(2009).Memorykeepsyouathome:Amechanisticmodelforhomerangeemergence.Oikos,118,641–652.

Webb,N.,Hebblewhite,M., &Merrill, E. (2008). Statisticalmethods foridentifying wolf kill sites using global positioning system locations.Journal of Wildlife Management,72,798–807.

Zub,K.,Theuerkauf,J.,Jedrzejewski,W.J.,Jedrzejewska,B.J.,Schmidt,K.,&Kowalczyk,R.(2003).WolfpackterritorymarkingintheBialowiezaPrimevalForest(Poland).Behaviour,140,635–648.

SUPPORTING INFORMATION

Additional Supporting Information may be found online in thesupportinginformationtabforthisarticle.

How to cite this article:SchlägelUE,MerrillEH,LewisMA.Territorysurveillanceandpreymanagement:Wolveskeeptrackofspaceandtime.Ecol Evol. 2017;00:1–18. https://doi.org/10.1002/ece3.3176

     |  13SCHLÄGEL Et aL.

definedabufferaroundacellusingtherectilineardistancemeasure(morecolloquiallyalsoreferredtoasManhattandistance)

where x and yaretwolocationsonthegridwitheasting(x-axis)andnorthing (y-axis)coordinatesxeast,yeast and xnorth,ynorth, respectively.The coordinateswere taken from the centerof each cell.With thisdistancemeasure,thebufferbecomesadiamond-shapedareaaroundthecentercell.Ifwedefineabufferofsizeδaroundthelocationx,thecornersofthebufferareaarethosecellsthatareδcellsawayfromxinexactnorthern,eastern,southern,andwesterndirections.Forthecal-culationofTSLV,weusedabufferofsizeoffourcells.Wecalculatedthebufferforeachcellthatisintersectedbythestraightlineofastep(Fig.A1,a).Adistanceoffourcellsinthediscretizedspacecorrespondsto1.2kmincontinuousspace.Usingabufferaroundthestraightlinebetween two locationswasa simplewayofaccounting for the factthatwedidnotobservealllocationsthatananimalvisitedonitspath.Amoresophisticatedapproachwouldbetoimplement,forexample,aBrownianbridgefortheestimatedpathbetweentwosuccessiveloca-tions (Horne et al. 2007).One could even go further and expand aBrownian bridge model to include the more complex movementmechanismsstudiedhere.Forallother locations thatwerenotconsideredvisited,TSLV in-

creasedby1ateverytimestep.Thatis,wesetmt(z)=mt−1(z)+1forlocationsznotvisitedduringtimest−1andt.Thisledtoamapwithvalues ofTSLV similar to amapwith environmental attributes, butwhichchangedatevery timestep.TSLV increased inareas that theindividual stayed away from and was reset to 1 whenever an

individualvisitedalocation,thatis,whenitcamesufficientlyclosetothelocation(Fig.A1,b).Thedynamicmapwasupdatedattheendofeachmovementstep,andtherefore,theweightingfunctionwattimetwasbasedonTSLVattimet−1.GivenTSLVforsomepointintime,itisstraightforwardtoupdateit

forallfollowingtimestepsbasedontheanimal’smovementpath.ToobtainaninitialmapofTSLV,weseparatedmovementtrajectoriesintotwo segments.We used the first 300movement steps to initializeTSLVandusedtherestofthetrajectoryforstatisticalinference.Thetimethatcorrespondedtothebeginningofthesecondpartofthetra-jectorywassettobet =1.WecalculatedTSLVatt =1foralllocationsthat were visited during the initialization phase. For locations thatwerenotvisited,wesetTSLVtothelengthoftheinitializationphase.Thetrajectoriescontainedmissedobservations.Ifatatimestept

thecorrespondinglocationwasmissing,weupdatedTSLVbyincreas-ing TSLVforalllocationsby1.Wedidnotresetanyvalueto1becausetherewasnocurrentpathavailable.However,weaccountedforthislateratthenextavailabletimestep.Atthattime,weresetTSLVto1fortheentirepathsincethelastavailablelocation.Becauseat leasttwotimeintervalshadpassedsincethelastlocation,weincreasedthebuffersizefortheselongerstepsby2.

MOVEMENT KERNEL

Thegeneralmovementkernelk isthedensityfunctionofarandomwalk in discretized two-dimensional space. For this, we sampled acontinuous-spacedensityatdiscretepoints(representingthecenter

d (x,y)= ||xeast−ynorth||+ ||xnorth− ynorth

|| ,

F I G . A 1 DepictionofthedynamicmapTSLV.(a)TSLVisresetto1forlocationswithinabufferarea(blue)aroundthestraight-linepath(blackline)betweencurrentandpreviouslocation(blackcells).(b)ExampleforthedynamicmapTSLVatoneparticulartimestep,heredepictedforwolfw220.Thecurrentlocationismarkedwithablacktriangle,andthelast20timestepsaredepictedbyblackdotsandblacklines.TherecentpathofthewolfhaslowvaluesofTSLV(whitetolightyellow),andareaswithlongabsencehavehighvaluesofTSLV(red).(c)Allsteps(markedbycrosses)thatarepossibleas“relocating”steps,whenrelocatingstepsarechosentohavesteplength≥5cells(~1500m).Theredcirclerepresentslocationsthatarewithin1000mofthecurrentlocation.Stepsofthislength(orshorter)wouldnaturallyendatalocationwithTSLV=1.

5 10 15 20 255

1015

20Easting [cells]

Nor

thin

g [c

ells

]

(a)

(c)

(b)

0 5 10 15 20 25 30

1015

2025

Easting [cells]

Nor

thin

g [c

ells

]

580,000 585,000 590,000 595,000 600,000 605,000

5,79

0,00

05,

800,

000

5,81

0,00

0

Easting [m]

Nor

thin

g [m

]

0 100 200 300 400

TSLV

14  |     SCHLÄGEL Et aL.

locationofeachcellinthelandscape).Thenormalizationconstantinthestepprobabilitygiveninthemanuscriptassuresthatstepproba-bilitiesareproperlynormalizedoverthediscretizedspace.WeusedaWeibulldistributionforsteplengthsandassumedauniformdistribu-tionforbearings.Amajorreasonforusingsimplyauniformdistribu-tionforbearingswastoretainasmanystepsaspossible.Inacorrelatedrandomwalk,bearingsareautocorrelated,andtherefore,threesuc-cessive locationmeasurementsareneededtodefinetheprobabilityforonemovementstep.Withmissingmeasurementsinthetimese-ries,thiswoulddecreasethenumberofavailablesteps.Forexample,forwolfw233with177stepsavailableforanalysis,thiswouldremove21of those steps,despitea reasonable fix rateof84%.Given thatusingautocorrelatedbearingswouldalsoaddaparameter,thiswouldreducetheratioofavailabledatapointsandnumberofparametersto17(from22).Thus,thekernelisgivenby

where λ and σaretheshapeandscaleparameteroftheWeibulldistribution,respectively.Thefactor1/||x−y||isduetoachangefrompolarcoordinates(usingsteplengthsandbearingstodefineastep)toEuclideanspatialcoordinates.

RELOCATING STEPS

Weonlyanalyzedstepswithaminimumlength.Frankeetal. (2006)usedahiddenMarkovmodeltoidentifythethreemajormodes“bed-ding,”“localizedactivity,”and“relocating”inwolfbehavior.Theyfoundthattherelocatingmodewascharacterizedbystepswithlengthabove200m,with themajorityof stepsbetween500and2500m.Thesedistanceswere obtained usingmovement datawith hourly locationmeasurements and thereforewere not immediately transferrable toour studywith2-hourlymovementdata.Roughly, stepsata rateof500mperhourmaybeconvertedto1000mper2hralthough it isknownthatmeasurementsof traveldistanceare influencedbysam-plingrate,andthelongerthetimeintervalbetweenlocationmeasure-mentsthelargertheriskofunderestimatingtruetraveldistance(Pépinet al. 2004; Rowcliffe et al. 2012). Still,with these considerations, itseemedappropriatetosetthethresholdfordefiningrelocatingstepsat about 1000m. If movementwas straight in east-west or north-southdirection,1000mcorrespondedtoaboutthreecellsinthedis-cretizedspace.AnotherpointtoconsiderforthethresholdwastheuseofthebufferforTSLV.Ifastepwaswithinthebuffersizeofthelastvisited location, thestepnaturallyendedata locationwithTSLV =1(Fig.A1,c).Incontrast,ifastepwaslargerthanthebuffersize,whichwasfourcells(~1200m),itcouldendatalocationwithTSLV =1,espe-ciallywhentheanimalbacktracked.However,therewasalsoachancethat thestepended ina locationoutside thebufferof thepreviousstepwithTSLV>1.ToavoidanartificialbiastowardsmallervaluesofTSLVforsmallsteps,wedefinedtheminimumsteplengthtobefivecells,correspondingroughlyto1,500mincontinuousspace(Fig.A1,c).

Usingonlystepswithaminimumlength,strictlyspeakingwewouldhavetoadjustthemovementkernelkbytruncatingtheWeibulldistri-butionattheminimumsteplength.Thiswouldleadtoaslightlylowerestimatedmeansteplengthforallmodels.Giventhefairlylargemeansteplengths,wedidnotconsiderthisproblematic.Inaddition,wedidnotimplementthetruncatedWeibullbecauseouraimwastorestricttheanalysistostepsthatcanbeattributedtoa“relocating”behavioralmode.Ideally,adistinctionofbehavioralmodesisperformedbyothermeans,forexample,usingahiddenMarkovmodel(McClintocket al. 2012), inwhichcase“relocating”stepscouldhavealsosmallersteplength.Wedidnot embedourmodel into a hiddenMarkovmodel,becausebasedonourrestrictedtimeserieslength,wecouldnotin-crease model complexity arbitrarily. However, for data sets withlongertimeserieslength,forexample,duetohighertemporalresolu-tion, we recommend more sophisticated approaches to datasegmentation.

LIKELIHOOD FUNCTION AND OPTIMIZATION

Thelikelihoodfunctionofthemodelis

forallavailablestepsfromxti−1toxtiwith∥xti−1 −xti ∥≥5.Duringmodelfitting,weconditionedthelikelihoodonthefirstlocationofeachseg-mentofsuccessivelyavailablelocations.NotethatnonrelocatingstepswereomittedaftercalculatingTSLV

fortheentiretimeseries.Therefore,stepsusedforthefinalanalysishadappropriatevaluesofTSLV,representingcorrecttimesbasedonthefullpath.Weoptimizedthe likelihoodfunctionusingaNelder–Meadalgo-

rithmimplementedinR(RCoreTeam2015).Tofindthefindglobalmaximum, we optimized the likelihood function starting at variouspointsinparameterspace.Fromtheseresults,wechosetheparame-terwiththehighestlikelihoodvalueandusedthemasstartingpointforthefinaloptimization.WeusedanestimateoftheHessianmatrixofthelog-likelihoodattheoptimalparametervaluestoobtainstand-arderrorsofthemaximum-likelihoodestimates.

REFERENCES

Franke,A.,Caelli,T.,Kuzyk,G.,&Hudson,R.J.(2006).Predictionofwolf(Canis lupus)kill-sitesusinghiddenMarkovmodels.Ecological Modelling,197,237–246.

Knopff, K.H., Knopff,A.A., Kortello,A.,&Boyce,M. S. (2010).Cougarkillrateandpreycompositioninamultipreysystem.Journal of Wildlife Management,74,1435–1447.

Liley, S., & Creel, S. (2008). What best explains vigilance in elk:Characteristics of prey, predators, or the environment? Behavioral Ecology,19,245–254.

McClintock,B.T.,King,R.,Matthiopoulos,J.,Mcconnell,B.J.,&Morales,J.M. (2012).Ageneraldiscrete-timemodelingframeworkforanimalmovementusingmultistaterandomwalks.Ecological Monographs,82,335–349.

k (x;y)=1

2� ∥x−y∥

λ

σ

(∥x−y∥

σ

)λ−1

exp

(−

(∥x−y∥

σ

)λ),

L (λ,σ,α,β,γ)=

N∏

i

p(xti |xti−1 ,λ,σ,α,β,γ)

     |  15SCHLÄGEL Et aL.

Pépin,D.,Adrados,C.,Mann,C.,&Janeau,G.(2004).AssessingrealdailydistancetravelledbyungulatesusingdifferentialGPSlocations.Journal of Mammalogy,85,774–780.

Proffitt,K.,Grigg,J.,Hamlin,K.,&Garrott,R.(2009).Contrastingeffectsofwolvesandhumanhuntersonelkbehavioral responsestopredationrisk.Journal of Wildlife Management,73,345–356.

RCoreTeam(2015).R: A language and environment for statistical computing. Vienna,Austria: R Foundation for StatisticalComputing. https://ww-w.R-project.org/

Rowcliffe, J. M., Carbone, C., Kays, R., Kranstauber, B., & Jansen, P. A.(2012).Biasinestimatinganimaltraveldistance:Theeffectofsamplingfrequency.Methods in Ecology and Evolution,3,653–662.

APPENDIX A2

T A B L E A 1 . Modelselectionresultswhenthemodelswithtime-dependenteffectforbothdistancefromedgeandpreydensity(lasttworows)wereincluded.PresentedareAICcdifferences,ΔAICc,i=AICc,i−AICc,minforeachmodeli.Bestmodelsarehighlightedinbold.Forindividualw230themostcomplexmodelbecomesbest,howeverparameterestimatessuggestthatthemodelisanover-fittospuriouseffectsofextremevaluesofthespatialattributes(TableA2,Fig.A3).

ΔAICc

w83 w220 w230 w233 w284 w285

null 59.7 66.4 60.3 63.4 126.3 58.0

edge 45.2 66.6 58.0 49.7 77.0 38.2

TSLV+edge 17.6 6.5 10.3 27.7 53.8 23.6

TSLV+edge+TSLV*edge 0 0 2.4 0 0.4 0

prey 63.0 60.7 60.2 67.3 130.4 59.0

edge+prey 45.6 67.7 47.1 43.3 72.9 33.1

edge+prey+edge*prey 47.7 69.6 45.9 41.6 74.7 35.1

TSLV 16.1 5.8 8.2 36.3 52.2 22.7

TSLV+prey 18.0 5.9 2.4 30.2 53.1 23.2

TSLV+prey+TSLV*prey 18.0 6.0 4.5 32.0 54.1 22.7

TSLV+edge+prey 19.6 7.3 4.4 29.1 54.0 24.1

TSLV+edge+prey+ TSLV*edge+TSLV*prey

2.1 2.1 0 1.9 0 0.9

T A B L E A 2 . ParameterestimatesforthemodelwithinteractionofbothdistancefromedgeandpreydensitywithTSLV.Standarderrorsfortheselectionandinteractioncoefficientsarealllargerthantheestimatesthemselves,leadingtolargeWald-typeconfidenceintervalsthatoverlapzero,indicatinghighuncertaintyintheestimates.

α βtslv βedge βprey γedge γprey

w230

Est. −3.57 2.49 −0.07 −1.3 1.64 3.43

SE 1.73 2.93 0.13 1.56 2.44 5.22

16  |     SCHLÄGEL Et aL.

F I G . A 2 Weightingfunctionfortheterritorysurveillancemodel(H2b)withminimumAICcusingtheestimatedparameters.Panelscorrespondtoindividualwolves.Theweightingfunctiongivestheprobabilityofselectingalocationbasedonspatialattributes,heredepictedasfunctionofdistancefromterritoryedge(inenvironmentalspace).Distancefromtheedgeismeasuredindiscretecells(300×300m).Forallwolves,theincreasingdirectionofthesigmoidalcurveindicatesthatlocationsclosertotheedgeareavoided.Withincreasingtimesincelastvisit(TSLV),thecurveisshiftedtotheleftduetothepositivecoefficient(βtslv)andbecomessteeperduetothepositiveinteractionparameter(γt,e),indicatingthattheavoidanceofedgelocationsdecreases.Theweightingfunctionsforthedifferentwolvesshowthesamegeneralpatternandonlyvaryslightly.Thisvariationislikelyduetoindividualvariationofthewolves’behaviorandterritories(seealsoFig.1).

10 15 200.

.40.

8

distance from edge [cells]

wei

ghtin

g fu

nctio

n w

(edg

e)

w83

10 15 20 25 30

0..4

0.8

distance from edge [cells]

wei

ghtin

g fu

nctio

n w

(edg

e)

w220

10 15 20

0..4

0.8

distance from edge [cells]

wei

ghtin

g fu

nctio

n w

(edg

e)

w230

10 15 20 25

0..4

0.8

distance from edge [cells]w

eigh

ting

func

tion

w(e

dge)

w233

10 15 20 25 30

0..4

0.8

distance from edge [cells]

wei

ghtin

g fu

nctio

n w

(edg

e)

w284

10 15 20

0.

0 50

00 5

00

0 5

00

0 5

00

0 5

00

0 5

00.

40.

8

distance from edge [cells]

wei

ghtin

g fu

nctio

n w

(edg

e)

w285

TSLV = 84 (1 week)TSLV = 12 (1 day)TSLV = 3 (6 hr)TSLV = 1 (2 hr)

     |  17SCHLÄGEL Et aL.

F I G . A 3 WeightingfunctionforthejointmodelTSLV+edge+prey+TSLV×edge+TSLV×preywithparameterestimatesfromindividualw230.Theweightingfunctiongivestheprobabilityofselectingalocationbasedonspatialattributes,heredepictedasfunctioninenvironmentalspaceofthethreespatialattributestimesincelastvisit(TSLV)(aandb),preydensity(candd),anddistancefromterritoryedge(eandf).TSLVismeasuredintimesteps;preydensity(numberpercell)isstandardizedovertheterritory;distancefromedgeismeasuredincells(300×300m).aandc:Distancefromedgeisfixedat2(approx.600–900mfromedge).bandd:Distanceisfixedat5(approx.1.8–2.1kmfromedge).eandf:Preydensityisfixedat−1(belowaverage)and1(aboveaverage),respectively.Theweightingfunctionwasnearlyconstantat1acrossmostoftherangesofspatialattributes,withonlytwonotableexceptions.First,abruptdeclinestozeroselectionoccurredforlocationsthathadbeenvisitedduringthelast2-h-timestep(allpanels),whichsimplymayindicatepersistentmovement.Second,theestimatespredictadeclinetozeroselectionforverylowpreydensityclosetotheedge(aandc),butthiseffectvanishedalreadyslightlyfurtherinsidetheterritory(bandd).Thus,effectswerepredictedonlyatthemostextremeendsoftheattributevalues.Furthermore,standarderrorsofparameterestimateswerelargesuchthatWald-typeconfidenceintervalsoftheparameterswouldoverlapzero(TableA2).

0.0

0.2

0.4

0.6

0.8

1.0

log(TSLV)

wei

ghtin

g fu

nctio

n w

(log(

TS

LV))

(a)

0.0

0.2

0.4

0.6

0.8

1.0

log(TSLV)

wei

ghtin

g fu

nctio

n w

(log(

TS

LV))

(b)

prey density

low (−2)mean (0)high (2)

−2 −1 4

0.0

0.2

0.4

0.6

0.8

1.0

prey density

wei

ghtin

g fu

nctio

n w

(pre

y)

(c)

−2 −1

0.0

0.2

0.4

0.6

0.8

1.0

prey densityw

eigh

ting

func

tion

w(p

rey)

(d)

TSLV

2 hours4 hours1 day5 days

10 20

0.0

0.2

0.4

0.6

0.8

1.0

distance to territory edge

wei

ghtin

g fu

nctio

n w

(edg

e)

(e)

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

0 1 2 3 0 1 2 3 4

0 5 15 0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

distance to territory edge

wei

ghtin

g fu

nctio

n w

(edg

e)

(f)

TSLV

2 hours4 hours1 day5 days

18  |     SCHLÄGEL Et aL.

APPENDIX A3

Runtime benchmarks

Here,weprovideanoverviewofthecomputationalloadofthemodelfitting.ThemeasurementsprovidedhereresultfromtestrunsonaPCwithIntelCorei52.3GHzprocessor.Weuseddataofwolf220.Modelfittingrequiredoptimizationofthelikelihoodfunctionoveramultidi-mensionalparameterspace.Forthenullmodel,therewereonlytwoparameters to estimate, while the most complex model containedeightparameters(thosepresentedinTableA2,plusσ and λ).Oneeval-uationofthelikelihoodfunctionrequiredapproximately0.54seconds.Mostofthisruntimecanbeattributedtocomputationofthenormali-zationconstant(denominator)ineqn1.Duringtheoptimizationrou-tine, the likelihood function has to be evaluated many times. Theamount of calls to the likelihood function necessary until the

optimization routing convergesvaries dependingonwhichmodel isfitted.Duringourtestruns,thenullmodelrequiredupto93callstothe function; the territory surveillance model (H2b) required up to1147calls;themostcomplexmodelrequiredupto2000calls(whichwehadsetasmaximumnumberofiterationsintheoptimfunctioninR).Tofindaglobalmaximuminmultidimensionalparameterspace,itiscustomary to perform the optimization multiple timeswith varyingstartingvalues.Weused20startingvaluesandusedtheresultingop-timumforthefinaloptimization.Thus,ifweuse1000iterationsuntilconvergence as a baseline, one model fit requires approximately190minutes.Wehad10models(Table1),notcountingtheadditionalrunswiththemostcomplexmodel(TableA1),andsixwolves,resultingin an approximate runtime of 8days.Note that the actual runtime,however,canbeshortenedbyrunningtheanalysissimultaneouslyonmultipleCPUs.