Counting Cats: Spatially Explicit Population Estimates of Cheetah

15 Pages·2016·1.19 MB·English

RESEARCHARTICLE
Counting Cats: Spatially Explicit Population
Acinonyx jubatus
Estimates of Cheetah ( )
Using Unstructured Sampling Data
FemkeBroekhuis1,2*,ArjunM.Gopalaswamy3,4
1 MaraCheetahProject,KenyaWildlifeTrust,Nairobi,Kenya,2 WildlifeConservationResearchUnit,
DepartmentofZoology,UniversityofOxford,Recanati-KaplanCentre,Tubney,UnitedKingdom,
3 DepartmentofZoology,UniversityofOxford,Oxford,UnitedKingdom,4 StatisticsandMathematicsUnit,
IndianStatisticalInstitute–Bangalorecentre,Bengaluru,India
*[email protected]
a11111
Abstract
Manyecologicaltheoriesandspeciesconservationprogrammesrelyonaccurateestimates
ofpopulationdensity.Accuratedensityestimation,especiallyforspeciesfacingrapid
declines,requirestheapplicationofrigorousfieldandanalyticalmethods.However,obtain-
OPENACCESS
ingaccuratedensityestimatesofcarnivorescanbechallengingascarnivoresnaturally
Citation:BroekhuisF,GopalaswamyAM(2016) existatrelativelylowdensitiesandareoftenelusiveandwide-ranging.Inthisstudy,we
CountingCats:SpatiallyExplicitPopulationEstimates
employanunstructuredspatialsamplingfielddesignalongwithaBayesiansex-specific
ofCheetah(Acinonyxjubatus)UsingUnstructured
SamplingData.PLoSONE11(5):e0153875. spatiallyexplicitcapture-recapture(SECR)analysis,toprovidethefirstrigorouspopulation
doi:10.1371/journal.pone.0153875 densityestimatesofcheetahs(Acinonyxjubatus)intheMaasaiMara,Kenya.Weestimate
Editor:MarcoFesta-Bianchet,Universitéde adultcheetahdensitytobebetween1.28±0.315and1.34±0.337individuals/100km2
Sherbrooke,CANADA acrossfourcandidatemodelsspecifiedinouranalysis.Ourspatiallyexplicitapproach
Received:January18,2016 revealed‘hotspots’ofcheetahdensity,highlightingthatcheetaharedistributedheteroge-
neouslyacrossthelandscape.TheSECRmodelsincorporatedamovementrangeparame-
Accepted:April5,2016
terwhichindicatedthatmalecheetahmovedfourtimesasmuchasfemales,possibly
Published:May2,2016
becausefemalemovementwasrestrictedbytheirreproductivestatusand/orthespatialdis-
Copyright:©2016Broekhuis,Gopalaswamy.Thisis tributionofprey.WeshowthatSECRcanbeusedforspatiallyunstructureddatatosuc-
anopenaccessarticledistributedunderthetermsof
cessfullycharacterisethespatialdistributionofalowdensityspeciesandalsoestimate
theCreativeCommonsAttributionLicense,which
permitsunrestricteduse,distribution,and populationdensitywhensamplesizeissmall.Oursamplingandmodellingframeworkwill
reproductioninanymedium,providedtheoriginal helpdeterminespatialandtemporalvariationincheetahdensities,providingafoundation
authorandsourcearecredited.
fortheirconservationandmanagement.Basedonourresultsweencourageother
DataAvailabilityStatement:Allrelevantdataare researcherstoadoptasimilarapproachinestimatingdensitiesofindividuallyrecognisable
availablefromtheDyradDigitalRepository
species.
(accessionnumberdoi:10.5061/dryad.fc324).
Funding:Thisstudywasfundedthroughvarious
privatedonorsandfoundationswhodonatedthrough
theKenyaWildlifeTrust.Thefunderhadnorolein
studydesign,datacollectionandanalysis,decisionto
Introduction
publish,orpreparationofthemanuscript.
Obtainingaccurateestimatesofdensitiesiscentraltoourunderstandingofthespatio-temporal
CompetingInterests:Theauthorshavedeclared
thatnocompetinginterestsexist. dynamicsofanimalpopulationsandprovidesthefoundationforeffectivewildlifemanagement
PLOSONE|DOI:10.1371/journal.pone.0153875 May2,2016 1/15
CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
andconservation.Thisisespeciallythecaseforlargecarnivoresasmanyspecieshaveunder-
gonedrasticdeclinesoverthelastfewdecades[1].However,obtainingaccuratedensityesti-
matesofcarnivorescanbechallengingascarnivoresnaturallyexistatrelativelylowdensities
andareoftenelusiveandwide-ranging[2].Asaresult,carnivorepopulationsarenotalways
monitoredusingrigorousmethods.Forexample,indirectmethodssuchasspoorsurveysare
commonlyusedtoestimatedensities[3,4].Tominimisecostandresources,suchsurveysare
commonlyconductedwithinarelativelysmallareaandthenextrapolatedacrossamuchlarger
areausingindex-calibrationmethods.However,thisapproachisinaccurateasthevariationsof
detectionprobabilityareleftunaccountedfor[5].Asaresult,populationestimatescouldbe
over-orunderestimated,misdirectingconservationefforts.Inlightoftheconsequencesof
theseinaccuraciesitisbeingrecognisedthatmorerobustwaysofestimatingpopulation
parametersarerequired[6].
Overthelastcoupleofdecades,photographiccapture-recapturemethods[7]havebeen
widelyusedincamera-trappingstudiestoestimatedensitiesofvariouslargefelids,including
tigers(Pantheratigris[8]),snowleopards(P.uncia[9])andjaguars(P.onca[10]).Inrecent
times,basiccapture-recapturemethods[11]havebeenreplacedbyspatiallyexplicitcapture-
recapturemethods(SECR[12,13])forestimatinganimaldensitiesof`marked’animals,
wherein,spatiallocationsofeach‘capture’areexplicitlyaccountedforinthemodelling.This
hasbeenamajoradvancementasnotonlycandensitiesbeaccuratelyestimatedacrossan
entirelandscape,butwithin-patchvariationindensitiescanbeestimatedandcanbesuitably
modelledwithcovariatesofinterest(e.g.[9]).ThepoweroftheSECRapproachhasledtoan
explosivegrowthofspatialcapture-recapturemethodologies(see[14]foravarietyofmodels
andpotentialvariants).Forexample,SECRmodelsweretraditionallythedomainofstructured
studydesignssuchascameratraparraysbutarenowadaptedtounstructuredsamplingdesigns
suchassearch-encounterdata[15,16].Thisisanimportantdevelopmentsincealthoughstruc-
turedcamera-trapstudydesignsworkwellforspeciesinforestsanddensehabitats,whereani-
malsgenerallyusewell-definedtrails,theyarenotnecessarilysuitedtospeciessuchasthe
cheetah(Acinonyxjubatus)thatresideinopenhabitatswherecamera-trappingislikelyto
yieldverylowtrappingratesleadingtopoorinferences[17].
Ithasbeenguesstimatedthatthereareapproximately6,600adultcheetahleftontheAfrican
continentandthatthisnumberiscontinuingtodecline[18].Extinctin20countriesandoccu-
pyingonly17%oftheirhistoricrange,cheetahsarevulnerabletoextinctionandinserious
needofconservationefforts[1].Whilstaccuratedensityestimatesarecrucialforconservation
effortstobesuccessful,thesearenotalwaysavailable.Forexample,Kenyaisconsideredtobea
criticalpartoftheglobalcheetahdistributionbuttherearecurrentlynoaccuratecheetahpopu-
lationdensityestimatesinanyareainthecountry[19,20].WithinKenya,theMaasaiMara,
whichispartofalargerMara-Serengetitransboundaryregion,isbelievedtoholdoneofthe
country’smaincheetahpopulations.TheMaasaiMaraisrenownedforitsannualmigrationof
wildebeest(Connochaetestaurinus)andhighdensitiesofpredatorsbut,likemanylandscapes
aroundtheworld,itisunderincreasinganthropogenicpressure.Kenya’spopulationisnow
over41.8million,overthreetimeswhatitwasin1970[21].IntheMaasaiMara,settlements,
andthereforealsolivestock,areincreasingatarapidrate[22].Asaresult,thisareahasseen
significantdeclinesinherbivorenumbers,somespeciesdownbyathird,inthelastfewdecades
[23].WhilethereareconcernsthatthecheetahpopulationintheMaasaiMaraisfacingsimilar
declines,therearenoaccuratepopulationestimatestosupportthisortodeterminefuturepop-
ulationtrends.Inthisstudy,weaimtoprovidethefirstrigorousestimateofthecheetahpopu-
lationintheMaasaiMaraNationalReserveandthesurroundingwildlifeconservanciesusinga
sex-specificSECRmodellingapproachbasedonfieldsamplingviadirectsightingsofindivid-
ualcheetahusinganunstructuredspatialsamplingdesign.
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CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
Methods
EthicsStatement
Dataforthisstudywerecollectedusingnon-invasivemethodsandthereforeapprovalfroman
ethicscommitteewasnotrequired.PermitsforthisstudywereissuedtoFemkeBroekhuisby
theNationalCouncilforScienceandTechnology(NACOSTI),KenyaWildlifeService(KWS),
NarokCountyGovernment(NCG),theMaasaiMaraWildlifeConservanciesAssociation
(MMWCA)andtheMaraConservancy.
Studyarea
ThesurveywasconductedintheMaasaiMaralocatedintheSouth-westofKenya.Thestudy
area(centredat°1S,35°E;elevationc.1700m)coversapproximately2398km2whichincludes
theMaasaiMaraNationalReserve(MMNR),whichfallsundertheauthorityoftheNarok
CountyGovernment,andtheadjacentconservancies;MaraTriangle,MaraNorth,OlChurro,
Lemek,Olare-Motorogi,NaboishoandOlKinyeiwhicharemanagedbyprivatemanagement
companies(Fig1).TherearenophysicalbarriersbetweentheMMNRandtheconservancies
orbetweenthewildlifeareasandthesurroundingcommunityareas,allowingforfreemove-
mentofanimals.Hereafter,theMMNRandtheadjacentconservancieswillcollectivelybe
referredtoastheMaasaiMara.TothesouththeMaasaiMaraborderstheSerengetiNational
ParkinTanzania,tothenorthandwestitbordersintensiveagriculturallandandeastofthe
MaasaiMaraislargelypastoralistsettlement[24,25].
Thestudyareaexperiencesabimodalrainfallpattern,withthewetseasonspanningNovem-
ber–JuneandthedryseasonJuly–October.Thewetseasonischaracterisedbytwodistinctperiods;
theshortrains(November–December)andthelongrains(MarchtoJune)[26].Thelongrains
attractthemigratingwildebeest,Commonzebra(Equusburchelli)andThomson’sgazelle(Gazella
thomsoni)fromtheSerengeti.GenerallythemigrationreachestheNorthernSerengetiinJuly,and
thenspendsAugust,SeptemberandOctoberintheMaasaiMarabeforereturningtoTanzaniain
November[27,28].Independentofthemigration,substantialpopulationsofThomson’sgazelle—
cheetahspreferredpreyinEastAfrica[29]—areresidentyearroundasareotherpreyspeciessuch
asGrant’sgazelle(G.granti),impala(Aepycerosmelampus)andhares(Lepusspp.)[28,30].
Fieldmethods
Anintensivecheetahsurveywasconductedduringathree-monthperiodfrom1stAugust2014
to31stOctober2014.Basedonotherstudies,webelievethatthiswasshortenoughsonottoseri-
ouslyviolatetheassumptionofclosurebutlongenoughtocollectsufficientdata[9,17,31].The
surveyinvolvedamaximumoffivevehiclestravelingwithinthestudyareawiththeobjectiveof
adequatelycoveringtheentirestudyareaspatially.Whenevercheetahsweresighted,photographs
ofeachindividualweretakenandthenumberofindividuals,GPSlocation,dateandtimeofday
wererecorded.Inadditiontorecordingopportunisticsightingsofcheetahsduringsampling,we
alsomadeuseofinformationoncheetahlocationsprovidedbytourists,guidesandrangers,so
thatourfieldteamswoulddrivetothelocationandphoto-capturecheetahs.Samplingeffort
(GPStracks)andcheetahsightingswererecordedusinganapplicationbuiltinCybertrackerv3
[32].Toaccountforsearcheffort,GPSlocationswererecordedevery10secondsgivingadetailed
recordoftheareasthatwerecoveredinsearchofcheetahs(Fig2).Wheneverpossible,routes
travelledwerenotusedmorethanonceadaytoensurethatcheetahswerenotsightedmultiple
timespersamplingoccasion.Eachcheetahwasidentifiedaccordingtotheiruniquespotpattern
[33].Onlyindependent,adultcheetahwereusedfortheanalysisandinthecaseofmalecoali-
tionseachindividualwasconsideredtobeindependentintheanalysis.
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CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
Fig1.MapofthestudyareainSouth-westKenya(darkgrey)borderingSerengetiNationalParkinTanzania(lightgrey).
doi:10.1371/journal.pone.0153875.g001
Analyticalmethods
CheetahdensitiesintheMaasaiMarawereestimatedusingaBayesianspatiallyexplicitcap-
ture-recapturemodeladaptedtosearch-encounterdataandsexdifferencesinencounterprob-
ability[34].ThedefinitionsoftheparametersusedfortheanalysescanbefoundinTable1and
detailsontheinputvariablesaredescribedinmoredetail:
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CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
Fig2.MapoftheMaasaiMaraincludingthesamplingeffort(tracksdriven)insearchofcheetahandthestatespace.
doi:10.1371/journal.pone.0153875.g002
Statespace. ThelargestatespaceSwasdefinedasthestudyareawithabufferof40km
resultinginanareaof20,370km2(Fig2).Allhabitatswereconsideredsuitableapartfrom
intenseagriculturalareastowardsthenorthandwestofthestudyareaandlarge,denselypopu-
latedtowns[24].Unsuitablehabitataccountedfor42.58%(8673.54km2)withinthestatespace
whichwasmaskedoutfromtheanalysis[13,35].Thestatespacewasrepresentedindiscrete
650x650m(0.422km2)pixels.
Weassumedthat,duringthethree-monthsamplingperiod,nocheetahoutsidethislarge
statespacewouldbedetectedwithinthesamplingarea.Whilethemaximumdistancethatwas
coveredbyatwo-malecoalitionwas41kmwebelievethistobeareasonableassumptionasthe
calculatedMeanMaximumDistanceMovedduringthisperiodforallcheetahsightedwas
6.91km.Thiswasfurthersupportedbythefactthatphotographsreceivedofcheetahsinnearby
areas,butoutsidethisbuffer,werenotofindividualsthatwereseenwithinthedefinedsam-
plingareaoveratwoyearperiod.Withinthelargestatespacethedata-augmentedvalueof
cheetahabundanceMwassetat335(n=25andn =310;seeTable1fordefinitionsofparam-
z
eters).Thisrepresentsthemaximumnumberofcheetahspossiblewithinthestatespace,keep-
inginmindthatourexpectationforanestimateofthetruenumberofindividualsinthe
populationcomparedtothedata-augmentedpopulationM,ψ,willliewithintherange0.2–0.8
forreliableestimationofthebinomialproportion[36].
½N jM;c(cid:2)(cid:3)Bin½M;c(cid:2)
super
Observationprocess. Thedatacollectedweresummarisedusingastandardspatialcap-
ture-recapture3-dimensionalmatrix(see[35]forafullexample)thatconsistsofindividuals
Table1. Parametersusedinthesexspecificspatiallyexplicitcapture-recaptureanalysisforcheetah
intheMaasaiMara,Kenya
Parameter Definition
n Totalnumberofcheetahsightedduringthesamplingperiod.
nz Numberofcheetahaugmentedton,sothatM=n+nzrepresentsthemaximumnumberof
cheetahsinthelargestatespaceS.
σF Rateofdeclineindetectionprobabilityasafemalecheetah’sactivitycentreincreasesasa
functionofherdistancefromthecentroidofagridcell(ortrap).
σM Rateofdeclineindetectionprobabilityasamalecheetah'sactivitycentreincreasesasa
functionofhisdistancefromthecentroidofagridcell(ortrap).
βsex Differenceinthecomplementarylog-logvalueofdetectionprobabilitybetweenamaleand
femalecheetah.
βeff Rateofchangeinthecomplementarylog-logvalueofdetectionprobability,asthelog(effort)
changesbyoneunit.Here,unitofeffortisonekilometredriven.
λ0 Basalencounterrateofacheetahwhoseactivitycentreislocatedexactlyatthecentroidofa
gridcell.
ψ Ratioofthetruenumberofindividualsinthepopulationcomparedtothedataaugmented
populationM.
ψsex Proportionofcheetahthataremale.Sexratio=1(cid:4)ccsesxexfemales:males
Nsuper TotalnumberofcheetahinthelargerstatespaceS.
W Determinestheshapeoftheestimateddetectionfunction.ThevalueofWrangesfrom0.5
(Exponential)to1(Gaussian).
D Estimateddensityofadultcheetah/100km2
doi:10.1371/journal.pone.0153875.t001
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CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
(i=1;2;3:::N),xtraplocations(j=1;2;3:::J)andxsamplingoccasions(k=1;2;3:::K).
Thisisastandardmatrixusedforspatialcapture-recapturedataforcameratrapsurveyswhich
canbeadjustedforunstructuredspatialcapture-recapturesampling[15,34].Inthiscase,the
traplocationsweredefinedby1km2pixelstorepresentanarrayof‘traps’.Thesamplingocca-
sion,or‘trapactivity’,wasbasedonwhetheragivenpixelwassurveyedonanyparticularday.
However,sinceinvestingmoreeffortincertainpixelsovertheotherscouldyieldahighernum-
berofdetectionsinhighlysampledpixels,weincorporatedanadditionalcovariateofsearch
effort(logarithmofthedistancetravelledinkilometres)perpixelpersamplingoccasion.In
addition,weincorporatedsex-specificcovariates(female=0andmale=1)asithasbeen
shownthatsexdifferencesinspatialdistributionarelikelytoinfluencetheobservationprocess
inspatialcapture-recapturemodels[10].Thisisespeciallytrueforcarnivoreswheremalesand
femalestendtohavedifferenthomerangesizes[37,38].
Spatialcapture-recapturemodelsemployavarietyofdetectionfunctionmodels[16,39]to
definethemechanismofthedeclineindetectionprobabilityasthedistancebetweentheactiv-
itycentreofananimalfromatraplocation(inourcase,thecentroidofapixel)increases.
Ratherthanexplicitlytestingvariousdetectionfunctionmodels,weconsideraninfinitenum-
berofpossibilitiesbetweenaperfectnegativeexponentialdetectionfunctiontoaperfect
Gaussiandetectionfunction[13]byexplicitlyestimatingtheparameterϑ.Avalueofϑ=0.5
specifiesaperfectnegativeexponentialfunctionwhichwouldindicatethatananimal’sactivity
isconcentratedarounditsactivitycentrewhichisindicativeofincreasedfidelitytotheactivity
centre.Avalueofϑ=1specifiesaperfectGaussianfunctionwhichwouldindicatethatanani-
mal’sactivityismorewidespreadandlessconcentratedinaparticularareawhichmaybechar-
acteristicofanimalsthathavehome-rangeswithalesserdegreeoffidelitytotheactivitycentre.
Thus,theparameterϑdefinestheshapeofthedetectionfunction,andisindicativeofthe
resourceutilisationmechanismofcheetahsinourexample.Hence,theprobabilityofdetecting
acheetahi,insamplingoccasionkatpixelj,π ,isdefinedbyacomplementarylog-logfunc-
ijk
tionofcovariates.Basedonthis,thefullmodelis:cloglog(π )=logλ +β [log(EFFORT )]+
ijk 0 eff jk
β (SEX)-f[dist(i,j|ϑ,σ )]
sex sex
Bayesianmodels. Thefollowingfourapriorimodelsweredefined:
Model1:Fullmodelthatassumesdetectionprobabilityissex-specificandthedetection
functionshapeisestimated(definedbyϑ).
½b ;Wð:Þ(cid:2)
sex
Model2:Assumesdetectionprobabilityisnotafunctionofsex.However,rateofdeclinein
detectionprobabilityσremainssex-specific,sincethisparameterisalsorelatedtoanimal
movement.
½b ¼0ðfixedÞ;Wð:Þ(cid:2)
sex
Model3:Detectionprobabilitydoesnotvarybetweensexanddetectionfunctionshape,
definedbyϑ,isfixedatacertainvalue(implyingafixedhybridmodelbetweenaGaussianand
anegativeexponentialdetectionfunction).
½b ¼0ðfixedÞ;W¼0:75ðfixedÞ(cid:2)
sex
Model4:Detectionprobabilityissex-specificbuttheshapeofthedetectionfunctionisfixed.
½b ;W¼0:75(cid:2)
sex
ThesefouraprioriBayesianSECRmodelswereimplementedusinganadaptationofthe
packageSCRbayes(https://github.com/jaroyle/SCRbayes)intheprogrammingenvironmentR
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CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
[40].ThemodelswereimplementedusingtheBayesianMarkovChainMonteCarle(MCMC)
simulationusingtheMetropolis-Hastingsalgorithm[41].TheMCMCchainconvergenceforall
themodelswasassessedusingtheGelman-Rubindiagnostic[42].Eachmodelwassetfor11,000
iterationswithaburn-inperiodof1,000iterations.Theburn-inperiodwasrefinedduringlater
stagesofananalysisiftherewasevidencefromthediagnosticsthatthemodelhadnotarrivedat
astationarydistributionbythen.Asaresulttherewere4000–5000posteriorsamplesforeach
chain.Atotalofeightchainswererunforeachmodel.Foreachmodel,aBeta(1,1)priorwas
usedforψ.Thispriorisintendedtobeuninformative,whichiswhywemadesurethatMwas
largeenoughsothattheestimateofψwasmuchlessthan1.Wethereforebelievethattheprob-
lemofapotentiallytruncatedposterior,asobservedinLink[43],doesnotapplyinourcase.In
addition,allthecoefficientsinthelinearpredictorhadimproperflatpriorson[-1;1]fora
suitabletransformationoftheparameter.Theinterceptwasln(λ ),whereλ wastheexpected
0 0
numberofcapturesofasingleanimalinasingletraponasinglecaptureoccasion,whenthedis-
tancebetweenthetrapandthecentreoftheanimal'shomerangeiszero.Thistranslated,there-
fore,intoimpliedscalepriorsforλ andβ .TheϑhadaUniform(0.5,1)priortofacilitatethe
0 effort
shapeoftheresourceselectionfunctiontohaveanequalprobabilitytobeanyformbetweena
half-normalandanegativeexponentialdetectionfunction.AflatUniform[0,1]priorwasused
forσandactivitycentreshaduniformpriors,sothatallpixels(potentialhome-rangecentres)
withsuitablehabitathadanequalprobabilityofhostingahome-rangecentrewhereaspixelswith
unsuitablehabitathadzeroprobabilityofhostingahome-rangecentre.Eachmodelwassubse-
quentlycheckedforadequacyutilisingtheBayesianp-valueassessmentusingateststatistic
basedonindividualencountersasimplementedinRoyleetal.[13].Parameterestimatesare
reportedtogetherwiththeposteriorstandarddeviations.
Results
Theresultsofthefourmodelspredictthatthedensityforcheetahsinsuitablehabitatwithin
theMaasaiMaralandscapeliesbetween1.28±0.315and1.34±0.337adults/100km2.These
resultsarebasedon59sightingsof25individuals(ninemalesweresightedon25occasions
and16femalesweresightedon34occasions)thatweresightedoveraninvestedsampling
effortof8397kmduringathree-monthperiod.Thenumberofsightingsperindividualranged
fromonetosevenandthebasalencounterrate(λ ),implyingthattheprobabilityofsightinga
0
cheetahperkilometredriven=1-exp(-λ ),was0.004.
0
Theanalysisprovidesestimatesforvariousotherparameters,includingasexratioof
approximatelyfivefemalestoeveryonemale.Therewashoweverahighsamplingcovariance
betweendensity(D)andthesexratio(ψ )asevidentfrompairwisecovarianceplotsof
sex
parametersfromtheMCMCoutput.Theestimateddetectionfunction(ϑ)wascloserto1than
to0.5indicatingthattheshapewasclosertoGaussianratherthananegativeexponential.Fig3
depictstheexpectedpixel-specificposteriordensitiesandshowstheheterogeneousdistribution
ofcheetahwithinthelandscape.Theexpectednumberofcheetah/km2perpixelrangedfrom
0.001to0.037showingclear‘hotspot’areasforcheetah.
Theposteriormeanestimatesalongwithposteriorstandarddeviationsoftheseestimatesof
theparametersforModels1–4andtheGelman-RubinstatisticarereportedinTable2.The
Bayesianp-valueestimatesforallthemodelsarebetween0.67–0.69indicatingthatallthemod-
elswereadequate,asthevaluesliewellwithintheextremities(0.15–0.85).
Discussion
Theresultsindicatethatsex-specificSECRmodelsforunstructuredspatialsamplingcanbe
usedsuccessfullytoestimatepopulationparametersforlowdensityspeciesthatresideinopen
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CountingCats:SpatiallyExplicitPopulationEstimateofCheetah
Fig3.MapoftheestimatedposteriordensityofcheetahintheMaasaiMara,Kenyaforeach0.422km2pixelfortheperiodbetween1stAugustand
31stOctober2014.Thecheetahdensity/km2perpixelrangedfrom0.001(darkblue)to0.037(red).
doi:10.1371/journal.pone.0153875.g003
habitats.Thisisespeciallythecasewhencoveringalargeareainashortperiodoftimesoasto
minimiseviolatingtheassumptionofaclosedsystem.Whiletheposteriorvariancesofthe
expecteddensityestimatesarerelativelyhigh,thisisaninherentproblemwhensamplesizes
aresmall.Inthepast,cheetahdensitieshavebeenestimatedusingbothindirectsurvey
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Table2. PosteriorestimatesofparametersforModels1–4includingtheposteriorstandarddeviation(PSD). Density(D)isgivenasnumberofadult
cheetah/100km2
Model Model1[βsex,θ(.)] Model2[βsex=0(fixed), Model3[βsex=0(fixed), Model4[βsex,θ=0.75
θ(.)] θ=0.75(fixed)] (fixed)]
Numberofposteriorsamplesused 4000 5000 5000 5000
Maximumvalueofpotentialreduction 1.18 1.12 1.11 1.13
factor
BayesianP-value 0.6729 0.6838 0.6767 0.6732
Parameter Posterior PSD Posterior PSD Posterior PSD Posterior PSD
mean mean mean mean
σF 3.660 1.272 3.300 1.241 2.740 0.331 2.690 0.303
σM 8.130 3.589 7.460 3.814 5.330 0.748 5.810 1.337
βsex -0.120 0.531 - - - - -0.140 0.596
βeff -0.009 0.012 -0.009 0.012 -0.009 0.012 -0.009 0.013
λ0 0.004 0.002 0.004 0.002 0.004 0.001 0.004 0.002
ψ 0.450 0.112 0.460 0.116 0.450 0.111 0.469 0.120
ψsex 0.162 0.073 0.146 0.068 0.159 0.071 0.146 0.700
Nsuper 149.800 36.780 153.100 37.960 151.14 36.352 157.160 39.390
ϑ 0.831 0.127 0.792 0.134 - - - -
D 1.28 0.315 1.33 0.326 1.29 0.311 1.34 0.337
doi:10.1371/journal.pone.0153875.t002
methodssuchasinterviews[44]andspoorsurveys[3]butthesetechniqueshavetheirlimita-
tions.Withbothmethodsthereistheuncertaintyassociatedwiththemisidentificationofchee-
tahandtheirspoor,especiallyastheyareoftenconfusedwithleopard(P.pardus)and
thereforeestimatesbasedonindirectmethodsmightbemisrepresentative.Evenwithoutmis-
identificationerrorstheseapproachescanbehighlyinaccurate,especiallywhendetectionprob-
abilitiesarelowandvaryingduetoahighamountofoverdispersion[5].Asaresult,changesin
populationestimatescannotbeaccuratelyestimated,consequentlymisdirectingconservation
decisions.Inlightoftheseinaccuraciesitisincreasinglyrecognisedthatecologistsmust
embraceuniversallyrobustmethodsthatexplicitlyrecognisetheimportanceofestimating
detectionprobabilities[6].
Capture-recapturemodelsthattakeintoaccountdetectionprobability,havebeenusedin
camera-trapstudiestoestimatecheetahdensitiesinAlgeria[45],Namibia[46],SouthAfrica
[47]andBotswana[17,48].Cheetah,however,occuratlowdensitiesandtraverselargeareas
soinareaswithopenhabitats,cameratrappingmethodsarelikelytoyieldverylowtrapping
ratesandtheresultingestimatesofparametersarelikelytohavehighsamplingvariancesand
covariances.Furthermore,whilecamera-trapstudiesarefeasibleforsmallareaslikethosein
Botswana(240km2[17]),Namibia(277km2[46])andSouthAfrica(300km2[47]),largerareas
arelogisticallydifficulttomaintain,costlyand,iftheadjacentblockmethodisused,arelikely
tobeconfoundedbyspatialandtemporalvariation[49].Inaddition,thementionedstudies
usedbasiccapture-recapturemodelsthatdonotaccountforvariabletrapeffort(inevitablein
fieldsampling)orforthespatialarrangementofindividuals[13],whichoftenleadstoan
upwardsbiasindensityestimates(see[9,14]).
Generallyinlargecarnivores,malesandfemalesdifferinrangingbehaviourandhence
detectionrateislikelytodifferbetweensexes[37].Insuchcircumstancesestimatescanbe
improvedbyaccountingforsex[10].Moreover,byincludingsexasaparameter,thesexratio
andsex-specificmovementparametersofthepopulationcanbedetermined.Forcheetahthe
sexratioatbirthtendstobeequal[50]butadultfemaleshaveahigherchanceofsurvivalthan
malesandintheSerengetiNationalParkinTanzaniatheadultsexratiowasfoundtobe0.8
PLOSONE|DOI:10.1371/journal.pone.0153875 May2,2016 10/15