Ecology and Evolution 20171ndash15 emsp|emsp1wwwecolevolorg

Received3August2017emsp |emsp Revised16October2017emsp |emsp Accepted22November2017DOI101002ece33725

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

Simulations inform design of regional occupancy- based monitoring for a sparsely distributed territorial species

Quresh S Latif1 emsp|emspMartha M Ellis2emsp|emspVictoria A Saab1emsp|emspKim Mellen-McLean3

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicensewhichpermitsusedistributionandreproductioninanymediumprovidedtheoriginalworkisproperlycitedPublished2017ThisarticleisaUSGovernmentworkandisinthepublicdomainintheUSAEcology and EvolutionpublishedbyJohnWileyampSonsLtd

1RockyMountainResearchStationUSForestServiceBozemanMTUSA2MontanaStateUniversityBozemanMTUSA3Region6USForestServicePortlandORUSA

CorrespondenceQureshSLatifRockyMountainResearchStationUSForestServiceBozemanMTUSAEmailqlatiffsfedus

Funding informationRockyMountainResearchStationUSForestServiceRegion6USForestService

AbstractSparselydistributedspeciesattractconservationconcernbut insufficient informa-tion on population trends challenges conservation and funding prioritizationOccupancy-basedmonitoring is attractive for these species but appropriate sam-plingdesignandinferencedependonparticularsofthestudysystemWeemployedspatially explicit simulations to identify minimum levels of sampling effort for aregional occupancy monitoring study design using white-headed woodpeckers(Picoides albolvartus)asparselydistributedterritorialspeciesthreatenedbyhabitatdeclineanddegradationasacasestudyWecomparedtheoriginaldesignwithcom-monly proposed alternativeswith varying targets of inference (ie species rangespaceuseorabundance)andspatialextentofsamplingSamplingeffortneededtoachieveadequatepowertoobservealong-termpopulationtrend(ge80chancetoobservea2yearlydeclineover20years)with thepreviouslyused studydesignconsistedofannuallymonitoringge120transectsusingasingle-surveyapproachorge90transectssurveyedtwiceperyearusingarepeat-surveyapproachDesignsthatshifted inference toward finer-resolution trends in abundance and extended thespatial extent of sampling by shortening transects employing a single-survey ap-proachtomonitoringandincorporatingapaneldesign(33ofunitssurveyedperyear)improvedpowerandreducederrorinestimatingabundancetrendsIncontrastefforts to monitor coarse-scale trends in species range or space use with repeatsurveys provided extremely limited statistical power Synthesis and applications Samplingresolutionsthatapproximatehomerangesizespatiallyextensivesamplinganddesignsthattarget inferenceofabundancetrendsratherthanrangedynamicsareprobablybestsuitedandmostfeasibleforbroad-scaleoccupancy-basedmonitor-ingofsparselydistributedterritorialanimalspecies

K E Y W O R D S

broad-scalemonitoringdetectionprobabilityPicoides albolvartuspopulationtrendspoweranalysisspatialsimulationspeciesconservationsurveydesignwhite-headedwoodpecker

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1emsp |emspINTRODUCTION

Population monitoring informs biological conservation by revealingpopulation trends which inform conservation status and fundingpriorities (MarshampTrenham 2008) Conservationists focus on spe-ciesexperiencingsevereorconsistentdeclinesduetoanthropogenicimpacts that elevateextinction risk (MaleBeanampSchwartz2005RodriguesPilgrimLamoreuxHoffmannampBrooks2006)Speciesofuncertainstatusduetoinsufficientdataaredifficulttotargeteveniflifehistoryordeclininghabitatwarrantconcern Informationforpri-oritizing conservation is particularly limited for sparsely distributedspecies (RobertsTaylorampJoppa2016) Imperfectdetectabilityanddifficultieswithmodelingalsoimposechallengesforterritorialanimals(EffordampDawson2012LatifEllisampAmundson2016)Lowdetect-abilityandanextensiverangemaynecessitatebroadandsustainedef-forttocharacterizepopulationstatusdespitetypicallylimitedfunding(JosephFieldWilcoxampPossingham2006)

Biologistsincreasinglyuseoccupancy-basedmonitoringforthesespecies(EllisIvanampSchwartz2014Josephetal2006)Detectionndashnondetectiondatademandlessfundingthancountsormarkndashrecap-ture data allowing more spatially extensive surveys (Joseph etal2006NoonBaileySiskampMcKelvey2012)whilereplicatesamplingcan correct for imperfect detection (MacKenzie etal 2002 Tyreetal2003)Occupancyquantifiesspeciesdistributionwhichcanin-form species range at coarse scales or finer-scale changes in spaceuseorabundanceall relevant toextinction risk (ClareAndersonampMacFarland2015Josephetal2006Noonetal2012)

Studydesignformonitoringoccupancydependsondesiredinfer-enceandspeciesecologyRelatively largesamplingunitspotentiallyoccupiedbymultiple individualscanefficiently informspeciesrangeestimateswhereassmallerunitsmaybebetterfortrackingfiner-scalechangesinlocalabundance(Clareetal2015EffordampDawson2012Noonetal2012)Withsmallerunitsthetimingofreplicatesamplesusedtocorrectfordetectabilityinrelationtoterritorialmovementfur-thershapespotential inference (EffordampDawson2012Latifetal2016ValenteHutchinsonampBetts2017)Samplingcontinuouslydis-tributedpopulationsofmobileindividualswithindefinitehomerangeboundaries isespeciallychallengingsuchpopulationsare inherentlyheterogeneousinwaysnotquantifiedbycommonlyusedmodelspo-tentiallyobscuringinference(EffordampDawson2012)Morecomplexmodelsthatcorrectlyspecifythisheterogeneitytypicallyrequiremoresamplingeffortwhichmaybeinfeasibleorcompromisesamplingex-tent needed to document broad-scale trends (Welsh LindenmayerampDonnelly2013)Simulationapproachescanhelpinformdesignofoccupancy-basedmonitoringwithsuchinherentandunavoidablemis-specificationofspatialheterogeneity(Ellis IvanTuckerampSchwartz2015Ellisetal2014)

Desired inference should primarily determine monitoring ap-proach but pragmatic considerations also influence study designBiologistsmaysizesamplingunitsforstudyareacoverageortomatchthe resolution of available environmental data (Zielinski BaldwinTruex Tucker amp Flebbe 2013 eg Steenweg etal 2016 but seeLinden Fuller Royle amp Hare 2017) Additionally biologists select

statisticalmodelsthatbest leverageavailabledataForexamplede-spiteafundamentalrelationshipbetweendetectabilityandabundance(RoyleampNichols2003)analystsmayholddetectabilityconstantforparsimony(egZielinskietal2013)Samplingisoftenthendesignedtoachieveadequatestatisticalpower for trackingoccupancy trendswithoutapriori specifyingdesired targetsof inference (eg speciesrangespaceuseorabundance)Inferenceofprocesshoweverisulti-matelyneededtoinformconservation

Ourquestionsonmonitoringdesignweremotivatedbyaregionaloccupancy-basedmonitoringprogramforwhite-headedwoodpecker(Picoides albolvartus hereafterWHWOFigure1) a sparselydistrib-uted regionally endemic species with narrow habitat requirements(Garrett Raphael amp Dixon 1996 Latif Saab Mellen-Mclean ampDudley 2015)WHWOdependondrymixed conifer forests domi-natedbyponderosapine(Pinus ponderosa)andmaintainedbymixed-severity fire (cf Hessburg Agee amp Franklin 2005) Recent habitatdeclinesandevidenceoflowreproductivesuccessinsomeareashaveraisedconservationconcerns(HollenbeckSaabampFrenzel2011)butdataonpopulationtrendsarelacking(Wisdometal2002)

Tohelpfillthisinformationgapregionaloccupancy-basedmoni-toringwasestablishedtoevaluatepopulationanddistributionaltrends(Mellen-McLeanSaabBressonWalesampVanNorman2015)Repeatdetectionndashnondetection surveys along transects inpotential habitatofOregonandWashington(Figure2)informedoccupancytrendscor-rected for imperfect detection Surveyors applied a commonproto-colforbirdsofpoint-basedsurveysorientedalongtransects(seealsoRotaFletcherDorazioampBetts2009Valenteetal2017)Availablefundingwas substantial (~$800 thousand) but nevertheless limitedmonitoringto6yearsat30transectswhilealsoaccommodatingother

F IGURE 1emspPhotographofaWhite-headedWoodpecker

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objectives (Mellen-McLean etal 2015)Growing agency interest inwhite-headedwoodpeckers couldmotivate expanded andmore fo-cusedmonitoringoflong-termtrendswhichweaimedtoinform

Toaddressthequestionsraisedbythiscasestudyweusedsim-ulations to evaluate alternative approaches to regional monitoringwhile explicitly consideringpotential inference and species ecologySpatiallyexplicitsimulationscorrectlyrepresentedmodelmisspecifi-cationtypicallyinherentwithoccupancy-basedmonitoringofcontinu-ouslydistributedpopulationsimprovingestimatesofstatisticalpowerforinformingstudydesign(Ellisetal20142015)Weassessedmin-imumeffortneededfordesirablestatisticalpowergiventhehistoricalstudydesignandweexploredhowalternatesamplingallocationsin-fluencedstatisticalpowerWeconsideredsamplingallocationsalter-natelysuitedforinferringcoarse-scaledistributionalchangesorrangedynamicsversusfiner-scalechangesinabundanceorspaceuse(egValente etal 2017)Candidate designsvaried in how they favoredspatiallyextensiveversusmoreintensivesurveyallocationthevalueof which depends on population heterogeneity (Rhodes amp Jonzeacuten

2011)Alternativesconsideredhererepresentcommonlyuseddesignsforbroad-scaleoccupancy-basedstudiesthusprovidinggeneralguid-anceformonitoringsparselydistributedterritorialanimals

2emsp |emspMATERIALS AND METHODS

21emsp|emspWhite- headed Woodpecker regional monitoring

Occupancy-basedmonitoringofWHWOacross the inlandnorth-westernUnited Stateswas originally implemented in 2011ndash2016(Mellen-McLeanetal2015)Surveysoccurredalong30transectstwiceayearduringthenestingseasonMay1ndashJune30Surveyorsbroadcastrecordedcallsanddrummingtoelicitterritorialresponsesto improvedetectabilityTransectswere10 surveypoints spaced~300mapartAtransectsurveyconsistedofsurveyingeachpointalongatransectThisapproachiscommonforsurveyingbirds(com-mon approach for birds eg Amundson Royle ampHandel 2014

F IGURE 2emspNationalforestsoftheeasternCascadeMountainsOregonandWashingtonUSAWhite-headedWoodpeckerregionalmonitoringfocusedonpotentialhabitat(gray)wherelarge-conepinespecies(mainlyponderosa)dominate

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Pavlacky Blakesley White Hanni amp Lukacs 2012 Rota etal2009)andforWHWOprovidedopportunityforbroadcastingcallsfollowedbyaperiodoflistening(max5mintotal)beforeproceed-ing to the next point To conserve time surveyors immediatelyproceeded to thenextpointalonga transectwhenwhite-headedwoodpecker was first detected Thus they strictly recorded de-tectionndashnondetection data restricting the focus ofmonitoring tooccupancy

22emsp|emspPopulation and sampling simulations

Following the initial 6-year effort we simulated occupancy-basedmonitoringofwhite-headedwoodpeckerstoinformpotentialfutureeffortsRecognizingtheneedforgreatersamplingefforttomeaning-fullyquantifytrendshoweverwesimulatedsurveysofge60transectsover20years

Simulatedpopulationsexperienceddeterministictrendsbasedonanexponentialmodel

where Nt ispopulationabundanceinyeart and λN istheproportionchangeinabundanceperyear(fortheoreticalbasisseeGotelli2001)Weconsidereda rangeof trendscenariosofpotential conservationconcernλN=10098095or09thatis03364or88declineover20years Simulated trends representedeffect sizes foranalyzingpowerPositivetrends(λNgt10)werelessofaconcernforinformingprioritizationofWHWOforconservationactionandthere-forenotconsideredAlthoughrealpopulationsfluctuatestochasticallywe lacked information for simulating specific levels of stochasticityanddeterministictrendsprovidedclearereffectsizesforinterpretingpowerestimates(seealsoEllisetal2015MacKenzieampRoyle2005)We intended the range of simple deterministic trends consideredhereto informsurveillancemonitoringaimedatdocumentingunan-ticipatedchangeratherthanparticularecologicalscenarios(HuttoampBelote2013)

Wesimulatedpopulationmonitoringsoastoexplicitlyrepresentthe process of sampling discrete detectionndashnondetection data forcontinuouslydistributedpopulations(cfEffordampDawson2012Ellisetal 2014 contraMacKenzie amp Royle 2005)We conducted sim-ulations using the rSPACE package (Ellis etal 2014 2015) in R (RCoreTeam2015) Simulationsentailed (1) randomlydistributingN1 homerangesacrosssuitablehabitat(2)calculatingtheprobabilityofencounteringge1white-headedwoodpeckeratasurveypoint(3)gen-eratingdetectionndashnondetectiondatabasedontheseencounterprob-abilitiesand(4)randomlyremovingNttimes(1minusλN)individualsfromthelandscapeandrepeatingsteps2ndash3foreachremainingyeart = 2ndash20 (AppendixS1)Wecollecteddataforaregion-wide300mpointgridand laterderivedtransectmonitoringscenariosSurveyorsrarelyre-cordeddetectionsgt150maway(7of2011ndash2016detections)sowesimulated150-mfixed-radiuspointsurveys

Weconsolidatedpointdatatorepresenttransectmonitoringsce-nariosvaryinginsamplingeffortandallocationAtransectdetectionrepresented ge1 detection at any given point along a transect on a

givendayOnehomerange(1-kmradius)couldincludemultipleneigh-boringpointssopoint-leveldetectionswithintransectswerespatiallycorrelatedwhereasge2kmtransectspacingavoidedspatialcorrelationin transectdetectionsAdditionallywith transectswewereable toexploreafundamentalissueinmonitoringdesigntherelativemeritsofsampling intensively (egmorepointspertransectorrepeatsur-veys)versusextensively(moretransects)

Weconsideredmonitoringscenariostoaccomplishtwoobjectives(1) identify levels of sampling effort capable of providing desirablepower(ge80chancetoobserveadeclinegivenλNle098) (2)com-parecommonlyconsideredsamplingallocationstrategiesrepresentingalternativetargetsofinferenceandspatialextentsofsamplingWead-dressedobjective1byvaryingsamplingeffort(ntransectge60ienpoint-surveys-per-yearge1200)withdifferenttrendsandthehistoricalsamplingallocationof10pointspertransectsurveyedtwiceeveryyearForob-jective2wefocusedonalong-termdeclinescenario(λN=098)andfixedsamplingeffort (npoint-surveys-per-year=1200)whilevaryingmoni-toringstrategiesThehistoricalallocationschemerepresentedanin-tendedinferenceofrelativelycoarse-scaletrendsAlternativeschemesincludedsurveyingshortertransects(8ndash3pointspertransect)whichtargetedinferenceoffiner-scaletrendsbysamplingsmallerareaspo-tentiallyoccupiedbyfewerindividualsWealsoconsideredsurveyingtransects only once per year representing single-survey occupancyapproacheswhoseestimatesprovidetemporalsnapshotsofpopula-tions useful for inferring changes in abundance (Hutto 2016 Latifetal2016)Finallyweconsideredsurveyinglt100oftransectsperyear (ie paneldesignsBaileyHinesNicholsampMacKenzie2007UrquhartampKincaid1999)orrepeatingsurveysatlt100oftransectseachyearHavingfixedsamplingeffort thesealternateschemesal-lowedmonitoringofmoretransectswhichextendedspatialsampling

For simplicity simulations assumed no false-negative observererror (hereafter observer error) that iswhite-headedwoodpeckerswerealwaysdetected ifpresentduringasurveyThusdetectabilitywasdeterminedexclusivelybyterritorialmovementbetweenrepeatsurveyswithinayearThisassumptionwasdefensiblebecausecall-broadcast surveys reduce observer error and standardized surveyslimit potentially confounding interannual variation in observer error(Mellen-McLeanetal2015)Additionallywecalibratedsimulationswith pilot data (Appendix S2) Encounter probabilities during a sur-vey therefore reflected the number location size and spacing ofhome ranges informedbywhite-headedwoodpeckerecologypop-ulationsizereflectedcalibrationwithpilotdataandassumedtrends(AppendicesS1andS2)

Spatialvariability indetectability (ieencounterprobabilities insimulations)emerged fromvariation innestinghabitatandrandomplacement of home rangeswithin this habitatwhich caused localabundanceandproximitytocentersofactivitytovaryamongtran-sects Reflecting likely realities detectability at occupied transectsincreasedwith increasing abundance and decreasedwith distancefromhome rangecenters (seeAppendixS1)Analyses ignored thisspatialheterogeneityandthusinformedstudydesignwhileaccount-ingforlikelyconstraintsonmodelcomplexityduetolimitedsamplingeffortWe initially considered smallerhome ranges (600m radius)

(1)Nt=N1timesλtN

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butcalibrationtopilotdatarequiredcompensatoryadjustments toinitialabundanceresultinginsimilarpatternsinstatisticalpower(QLatif unpublished data)We restricted simulations to national for-estsrepresenting77(77times106ha)ofpotentialhabitatwithintheregion(Figure2)

23emsp|emspData analysis

Forscenariosyieldingrepeat-surveydataweestimatedtrendswithtwo different occupancy models representing commonly consid-eredwaysofcorrectingfordetectability(pegLindenetal2017Steenweg etal 2016 Zielinski etal 2013) to estimate occupancyprobability (ψ Figure3ab) One model allowed detectability esti-matestovaryinterannually(hereaftertheyearly-pmodelFigure3a)whereastheotherhelddetectabilityconstant(hereafter the constant- pmodelFigure3bformodelstructuresseeAppendixS3)Becauseindividuals couldmove in or out of the surveyed areabetween re-peat surveyswithin a year thesemodels quantified the probabilityof a transect intersectingge1home rangehereafter true occupancywhichdescribesspeciesrangeorspaceuse(EffordampDawson2012MacKenzieampRoyle 2005) Theyearly-pmodel allowsdetectability

tochangewithchangingabundance(RoyleampNichols2003)tobet-terestimatetrueoccupancyTheconstant-pmodelmisspecifiestrueoccupancybutisfrequentlyconsideredandmaybeselectedforpar-simonyinappliedstudies(egZielinskietal2013)Additionallyhav-ingcontrolledforobservererror(egifnonexistentasinsimulationsorcontrolledviastandardizedsurveys)theconstant-pmodelcoercesoccupancyestimatestoreflectanyinterannualchangesshiftingthetargetofinferencetoabundance(Figure3b)

For scenarios yielding single-survey data we estimated trendsusing logistic regression (see structure inAppendix S3) Having ex-cludedobservererror insimulations logistic regressionmodelsesti-matedprobabilityofge1individualrsquosphysicalpresenceduringasurveyhereafter probability of physical presence Single-survey scenariosrepresented single-surveyoccupancyapproaches inwhich replicatesurveysoccurwithinanarrowenoughtimeframefordetectabilitytoquantifyobservererrorsothatoccupancyestimatesquantifyproba-bilityofphysicalpresence(egdouble-observerandremovaldesignsNicholsetal2008Rotaetal2009)ByomittingobservererrorfromsimulationshoweverreplicatesurveyswereunnecessarytoquantifyphysicalpresenceProbabilityofphysicalpresencerepresentsatem-poral snapshot of a population unaffected by territorial movement

F IGURE 3emspHowmodelestimatesreflectunderlyingprocessesunderalternativemonitoringapproachesRepeat-surveyoccupancyestimatesfundamentallyquantifytrueoccupancy(ab)butcanindexabundancetrendsifdetectabilityisheldconstant(bcontraA)Territorialmovementinfluencesrepeat-surveyoccupancyestimates(ab)whereassingle-surveyoccupancyestimatesrepresentpopulationsnapshotsnotinfluencedbymovement(c)False-negativeobservererrorwasnotsimulatedbutcouldinfluenceestimatesinreality

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expected to closely track abundance (Figure3c Hutto 2016 Latifetal2016)AdditionallysurveyingtransectsonlyonceallowedustomonitortwiceasmanytransectsincreasingsamplingextentInprac-ticeauxiliarysampling (eg recordingdetectiontimingordeployingmultipleobservers)wouldaccount forobservererror (Nicholsetal2008 Rota etal 2009) likely adding to uncertainty in trend esti-matesIgnoringobservererrorinbothsingle-andrepeat-surveysce-narioshowevermadetheircomparisoninformative

Wequantified occupancy trends as proportionyearly change inodds occupancy λψ =

ψt+1∕(1minusψt+1)

ψt∕(1minusψt) (MacKenzie etal 2006)We ana-

lyzeddetectionndashnondetectiondatawithfixedyeareffectsandsubse-quentlycalculatedleast-squarestrendsinyearlyoccupancyestimates(seealsoEllisetal2014)Wequantifiedstatisticalpoweraspercentsimulationswhen95Bayesiancredibleintervals(BCIs)fortheesti-matedtrendforthestudyperiod(λψ where logit(ψt)=β0+ log (λψ)times t p200MacKenzieetal2006)fellbelow1Wealsocalculatedrootmean squared error for trend estimates (RMSEN=

radic

mean(λψ minusλN) RMSEψ =

radic

mean(λψ minusλψ )) When quantifying true occupancy weconsidered occupied transects to be thosewith encounter pge05Having foundextremely limited statistical powerwithyearly-p esti-mates(seeObjective1Results)weprimarilyassessedsamplingallo-cations(Objective2)forconstant-pandlogisticregressionmodelsbutthentestedyearly-pagainwithbetterallocationFurthermoregivenlikely targets of inference we considered RMSEN most relevant toconstant- pandlogisticregressionmodelsandRMSEψ relevant to the yearly-pmodelForadditionalmethodsand rationale seeAppendixS3

3emsp |emspRESULTS

31emsp|emspOccupancy abundance and estimator behavior

Comparingtrueoccupancy(proportiontransectswithencounterpge05)andabundanceinformedunderstandingofstatisticalpowerandestima-torpropertiesTrueoccupancyrelatedpositivelywithabundancebutpla-teauedathigherabundances(Figure4ac)Trueoccupancydeclineslaggedabundancedeclines(Figure4bd)Withshortertransectstrueoccupancycorrespondedbetterbutstillimperfectlywithabundance(Figure4cd)

Occupancyestimatesremainedconstantwithnoabundancetrendand declinedwith declining abundance (Figure5) Detectability es-timates declined with declining abundance either across scenarios(constant- pestimates)orthroughtime(yearly-pestimatesFigure6)Yearly-p estimator precisionwas less than for constant-p estimatesanddeclinedwithdecliningabundance(Figures5and6)

Detectabilityestimatesfollowedthebehaviorofencounterprob-abilitiesatoccupiedtransectsbutweregenerallyhigherthatisposi-tivelybiased(Figure6)makingoccupancyestimatesnegativelybiased(Figure5)Logisticregressionestimatesdeviatedevenmorefromtrueoccupancy (Figure5cfil) reflecting thediffering targetof inference(ieprobabilityofphysicalpresenceseeSection2andAppendixS3)

32emsp|emspObjective 1 Sampling effort

Withhistoricalsurveyallocationstatisticalpowerincreasedwithin-creasingsamplingeffortandstrongerpopulationdeclines(Figure7)

F IGURE 4emspTrueoccupancy(ψ) versus abundance(N=numberofindividualsacrossall7676971haofpotentialhabitatinOregonandWashingtonnationalforestsac)andcorrespondenceof(odds)occupancy(λψ)withabundancetrends(λNbd)forsimulatedwhite-headedwoodpeckerpopulationsThirtyreplicatepopulationsmonitoredfor20yearsforeachtrendscenarioaredepictedwhensurveyedattransectsconsistingof10points(ab)orthreepoints(cd)eachInpanelsbanddtheredlineindicates11correspondence(desirableforinference)betweenoccupancyandabundancetrends

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The constant- pmodeland logistic regression (withsingle-surveyal-location) generally provided adequate power (ge80 chance of ob-servingadecline)Powerwasonlyinadequatewithasmalleffectsize(λN=098) andminimal sampling effort (j le 60 and90 transects forconstant- p and logistic regression respectively) In contrast powerwasneveradequatewith theyearly-pmodelSpurious trendswererarelyobserved(15ofsimulationsinwhichλN = 1)

With no abundance or occupancy trendsmodels estimated ac-tual trendswithminimal error and no apparent bias but error andbiasgrewwith increasingtrend (Figure8)Theconstant-pmodel in-creasingly overestimated declineswith steeper abundance declines

although abundance trendswere estimated better (RMSENle0055)than occupancy trends (RMSEψle0105) Yearly-p trend estimateswere centered between actual abundance and occupancy trends(RMSEle005) Models fitted to single-survey data estimated trueabundance trendswith the least error (RMSENle0008) and no ob-viousbias

33emsp|emspObjective 2 Sampling allocation

Monitoringstrategiesthattargetedinferenceoffiner-scaletrendsinspaceuseorabundanceandextendedsamplingspatiallygenerally

F IGURE 5emspYearlyoccupancyestimatesfromsimulatedregionalwhite-headedwoodpeckermonitoringSimulatedtrendswereλN=1(andashc)098(dndashf)095(gndashi)and09(jndashl)Repeat-surveyoccupancyestimatesassumedconstantdetectability(adgandj)orvariabledetectabilityamongyears(behandk)Single-surveyestimatesassumedperfectdetectability(cfiandl)Thirtysimulationsofmonitoringtransectsof10pointseachfor20yearsarerepresentedforeachscenario(n = 150and300transectsforrepeat-andsingle-surveyscenariosrespectively)Blackdotsandblueverticalbarsshowyearlyestimatesand95BCIsjitteredfordisplayBlacklinesconnectestimatesfromconsecutiveyearsforindividualsimulationsReddotsshowmeantrueoccupancyfor30simulationsthatisproportionofallpossibletransectsoccupied

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providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

emspensp emsp | emsp3LATIF eT AL

objectives (Mellen-McLean etal 2015)Growing agency interest inwhite-headedwoodpeckers couldmotivate expanded andmore fo-cusedmonitoringoflong-termtrendswhichweaimedtoinform

Toaddressthequestionsraisedbythiscasestudyweusedsim-ulations to evaluate alternative approaches to regional monitoringwhile explicitly consideringpotential inference and species ecologySpatiallyexplicitsimulationscorrectlyrepresentedmodelmisspecifi-cationtypicallyinherentwithoccupancy-basedmonitoringofcontinu-ouslydistributedpopulationsimprovingestimatesofstatisticalpowerforinformingstudydesign(Ellisetal20142015)Weassessedmin-imumeffortneededfordesirablestatisticalpowergiventhehistoricalstudydesignandweexploredhowalternatesamplingallocationsin-fluencedstatisticalpowerWeconsideredsamplingallocationsalter-natelysuitedforinferringcoarse-scaledistributionalchangesorrangedynamicsversusfiner-scalechangesinabundanceorspaceuse(egValente etal 2017)Candidate designsvaried in how they favoredspatiallyextensiveversusmoreintensivesurveyallocationthevalueof which depends on population heterogeneity (Rhodes amp Jonzeacuten

2011)Alternativesconsideredhererepresentcommonlyuseddesignsforbroad-scaleoccupancy-basedstudiesthusprovidinggeneralguid-anceformonitoringsparselydistributedterritorialanimals

2emsp |emspMATERIALS AND METHODS

21emsp|emspWhite- headed Woodpecker regional monitoring

Occupancy-basedmonitoringofWHWOacross the inlandnorth-westernUnited Stateswas originally implemented in 2011ndash2016(Mellen-McLeanetal2015)Surveysoccurredalong30transectstwiceayearduringthenestingseasonMay1ndashJune30Surveyorsbroadcastrecordedcallsanddrummingtoelicitterritorialresponsesto improvedetectabilityTransectswere10 surveypoints spaced~300mapartAtransectsurveyconsistedofsurveyingeachpointalongatransectThisapproachiscommonforsurveyingbirds(com-mon approach for birds eg Amundson Royle ampHandel 2014

F IGURE 2emspNationalforestsoftheeasternCascadeMountainsOregonandWashingtonUSAWhite-headedWoodpeckerregionalmonitoringfocusedonpotentialhabitat(gray)wherelarge-conepinespecies(mainlyponderosa)dominate

4emsp |emsp emspensp LATIF eT AL

Pavlacky Blakesley White Hanni amp Lukacs 2012 Rota etal2009)andforWHWOprovidedopportunityforbroadcastingcallsfollowedbyaperiodoflistening(max5mintotal)beforeproceed-ing to the next point To conserve time surveyors immediatelyproceeded to thenextpointalonga transectwhenwhite-headedwoodpecker was first detected Thus they strictly recorded de-tectionndashnondetection data restricting the focus ofmonitoring tooccupancy

22emsp|emspPopulation and sampling simulations

Following the initial 6-year effort we simulated occupancy-basedmonitoringofwhite-headedwoodpeckerstoinformpotentialfutureeffortsRecognizingtheneedforgreatersamplingefforttomeaning-fullyquantifytrendshoweverwesimulatedsurveysofge60transectsover20years

Simulatedpopulationsexperienceddeterministictrendsbasedonanexponentialmodel

where Nt ispopulationabundanceinyeart and λN istheproportionchangeinabundanceperyear(fortheoreticalbasisseeGotelli2001)Weconsidereda rangeof trendscenariosofpotential conservationconcernλN=10098095or09thatis03364or88declineover20years Simulated trends representedeffect sizes foranalyzingpowerPositivetrends(λNgt10)werelessofaconcernforinformingprioritizationofWHWOforconservationactionandthere-forenotconsideredAlthoughrealpopulationsfluctuatestochasticallywe lacked information for simulating specific levels of stochasticityanddeterministictrendsprovidedclearereffectsizesforinterpretingpowerestimates(seealsoEllisetal2015MacKenzieampRoyle2005)We intended the range of simple deterministic trends consideredhereto informsurveillancemonitoringaimedatdocumentingunan-ticipatedchangeratherthanparticularecologicalscenarios(HuttoampBelote2013)

Wesimulatedpopulationmonitoringsoastoexplicitlyrepresentthe process of sampling discrete detectionndashnondetection data forcontinuouslydistributedpopulations(cfEffordampDawson2012Ellisetal 2014 contraMacKenzie amp Royle 2005)We conducted sim-ulations using the rSPACE package (Ellis etal 2014 2015) in R (RCoreTeam2015) Simulationsentailed (1) randomlydistributingN1 homerangesacrosssuitablehabitat(2)calculatingtheprobabilityofencounteringge1white-headedwoodpeckeratasurveypoint(3)gen-eratingdetectionndashnondetectiondatabasedontheseencounterprob-abilitiesand(4)randomlyremovingNttimes(1minusλN)individualsfromthelandscapeandrepeatingsteps2ndash3foreachremainingyeart = 2ndash20 (AppendixS1)Wecollecteddataforaregion-wide300mpointgridand laterderivedtransectmonitoringscenariosSurveyorsrarelyre-cordeddetectionsgt150maway(7of2011ndash2016detections)sowesimulated150-mfixed-radiuspointsurveys

Weconsolidatedpointdatatorepresenttransectmonitoringsce-nariosvaryinginsamplingeffortandallocationAtransectdetectionrepresented ge1 detection at any given point along a transect on a

givendayOnehomerange(1-kmradius)couldincludemultipleneigh-boringpointssopoint-leveldetectionswithintransectswerespatiallycorrelatedwhereasge2kmtransectspacingavoidedspatialcorrelationin transectdetectionsAdditionallywith transectswewereable toexploreafundamentalissueinmonitoringdesigntherelativemeritsofsampling intensively (egmorepointspertransectorrepeatsur-veys)versusextensively(moretransects)

Weconsideredmonitoringscenariostoaccomplishtwoobjectives(1) identify levels of sampling effort capable of providing desirablepower(ge80chancetoobserveadeclinegivenλNle098) (2)com-parecommonlyconsideredsamplingallocationstrategiesrepresentingalternativetargetsofinferenceandspatialextentsofsamplingWead-dressedobjective1byvaryingsamplingeffort(ntransectge60ienpoint-surveys-per-yearge1200)withdifferenttrendsandthehistoricalsamplingallocationof10pointspertransectsurveyedtwiceeveryyearForob-jective2wefocusedonalong-termdeclinescenario(λN=098)andfixedsamplingeffort (npoint-surveys-per-year=1200)whilevaryingmoni-toringstrategiesThehistoricalallocationschemerepresentedanin-tendedinferenceofrelativelycoarse-scaletrendsAlternativeschemesincludedsurveyingshortertransects(8ndash3pointspertransect)whichtargetedinferenceoffiner-scaletrendsbysamplingsmallerareaspo-tentiallyoccupiedbyfewerindividualsWealsoconsideredsurveyingtransects only once per year representing single-survey occupancyapproacheswhoseestimatesprovidetemporalsnapshotsofpopula-tions useful for inferring changes in abundance (Hutto 2016 Latifetal2016)Finallyweconsideredsurveyinglt100oftransectsperyear (ie paneldesignsBaileyHinesNicholsampMacKenzie2007UrquhartampKincaid1999)orrepeatingsurveysatlt100oftransectseachyearHavingfixedsamplingeffort thesealternateschemesal-lowedmonitoringofmoretransectswhichextendedspatialsampling

For simplicity simulations assumed no false-negative observererror (hereafter observer error) that iswhite-headedwoodpeckerswerealwaysdetected ifpresentduringasurveyThusdetectabilitywasdeterminedexclusivelybyterritorialmovementbetweenrepeatsurveyswithinayearThisassumptionwasdefensiblebecausecall-broadcast surveys reduce observer error and standardized surveyslimit potentially confounding interannual variation in observer error(Mellen-McLeanetal2015)Additionallywecalibratedsimulationswith pilot data (Appendix S2) Encounter probabilities during a sur-vey therefore reflected the number location size and spacing ofhome ranges informedbywhite-headedwoodpeckerecologypop-ulationsizereflectedcalibrationwithpilotdataandassumedtrends(AppendicesS1andS2)

Spatialvariability indetectability (ieencounterprobabilities insimulations)emerged fromvariation innestinghabitatandrandomplacement of home rangeswithin this habitatwhich caused localabundanceandproximitytocentersofactivitytovaryamongtran-sects Reflecting likely realities detectability at occupied transectsincreasedwith increasing abundance and decreasedwith distancefromhome rangecenters (seeAppendixS1)Analyses ignored thisspatialheterogeneityandthusinformedstudydesignwhileaccount-ingforlikelyconstraintsonmodelcomplexityduetolimitedsamplingeffortWe initially considered smallerhome ranges (600m radius)

(1)Nt=N1timesλtN

emspensp emsp | emsp5LATIF eT AL

butcalibrationtopilotdatarequiredcompensatoryadjustments toinitialabundanceresultinginsimilarpatternsinstatisticalpower(QLatif unpublished data)We restricted simulations to national for-estsrepresenting77(77times106ha)ofpotentialhabitatwithintheregion(Figure2)

23emsp|emspData analysis

Forscenariosyieldingrepeat-surveydataweestimatedtrendswithtwo different occupancy models representing commonly consid-eredwaysofcorrectingfordetectability(pegLindenetal2017Steenweg etal 2016 Zielinski etal 2013) to estimate occupancyprobability (ψ Figure3ab) One model allowed detectability esti-matestovaryinterannually(hereaftertheyearly-pmodelFigure3a)whereastheotherhelddetectabilityconstant(hereafter the constant- pmodelFigure3bformodelstructuresseeAppendixS3)Becauseindividuals couldmove in or out of the surveyed areabetween re-peat surveyswithin a year thesemodels quantified the probabilityof a transect intersectingge1home rangehereafter true occupancywhichdescribesspeciesrangeorspaceuse(EffordampDawson2012MacKenzieampRoyle 2005) Theyearly-pmodel allowsdetectability

tochangewithchangingabundance(RoyleampNichols2003)tobet-terestimatetrueoccupancyTheconstant-pmodelmisspecifiestrueoccupancybutisfrequentlyconsideredandmaybeselectedforpar-simonyinappliedstudies(egZielinskietal2013)Additionallyhav-ingcontrolledforobservererror(egifnonexistentasinsimulationsorcontrolledviastandardizedsurveys)theconstant-pmodelcoercesoccupancyestimatestoreflectanyinterannualchangesshiftingthetargetofinferencetoabundance(Figure3b)

For scenarios yielding single-survey data we estimated trendsusing logistic regression (see structure inAppendix S3) Having ex-cludedobservererror insimulations logistic regressionmodelsesti-matedprobabilityofge1individualrsquosphysicalpresenceduringasurveyhereafter probability of physical presence Single-survey scenariosrepresented single-surveyoccupancyapproaches inwhich replicatesurveysoccurwithinanarrowenoughtimeframefordetectabilitytoquantifyobservererrorsothatoccupancyestimatesquantifyproba-bilityofphysicalpresence(egdouble-observerandremovaldesignsNicholsetal2008Rotaetal2009)ByomittingobservererrorfromsimulationshoweverreplicatesurveyswereunnecessarytoquantifyphysicalpresenceProbabilityofphysicalpresencerepresentsatem-poral snapshot of a population unaffected by territorial movement

F IGURE 3emspHowmodelestimatesreflectunderlyingprocessesunderalternativemonitoringapproachesRepeat-surveyoccupancyestimatesfundamentallyquantifytrueoccupancy(ab)butcanindexabundancetrendsifdetectabilityisheldconstant(bcontraA)Territorialmovementinfluencesrepeat-surveyoccupancyestimates(ab)whereassingle-surveyoccupancyestimatesrepresentpopulationsnapshotsnotinfluencedbymovement(c)False-negativeobservererrorwasnotsimulatedbutcouldinfluenceestimatesinreality

6emsp |emsp emspensp LATIF eT AL

expected to closely track abundance (Figure3c Hutto 2016 Latifetal2016)AdditionallysurveyingtransectsonlyonceallowedustomonitortwiceasmanytransectsincreasingsamplingextentInprac-ticeauxiliarysampling (eg recordingdetectiontimingordeployingmultipleobservers)wouldaccount forobservererror (Nicholsetal2008 Rota etal 2009) likely adding to uncertainty in trend esti-matesIgnoringobservererrorinbothsingle-andrepeat-surveysce-narioshowevermadetheircomparisoninformative

Wequantified occupancy trends as proportionyearly change inodds occupancy λψ =

ψt+1∕(1minusψt+1)

ψt∕(1minusψt) (MacKenzie etal 2006)We ana-

lyzeddetectionndashnondetectiondatawithfixedyeareffectsandsubse-quentlycalculatedleast-squarestrendsinyearlyoccupancyestimates(seealsoEllisetal2014)Wequantifiedstatisticalpoweraspercentsimulationswhen95Bayesiancredibleintervals(BCIs)fortheesti-matedtrendforthestudyperiod(λψ where logit(ψt)=β0+ log (λψ)times t p200MacKenzieetal2006)fellbelow1Wealsocalculatedrootmean squared error for trend estimates (RMSEN=

radic

mean(λψ minusλN) RMSEψ =

radic

mean(λψ minusλψ )) When quantifying true occupancy weconsidered occupied transects to be thosewith encounter pge05Having foundextremely limited statistical powerwithyearly-p esti-mates(seeObjective1Results)weprimarilyassessedsamplingallo-cations(Objective2)forconstant-pandlogisticregressionmodelsbutthentestedyearly-pagainwithbetterallocationFurthermoregivenlikely targets of inference we considered RMSEN most relevant toconstant- pandlogisticregressionmodelsandRMSEψ relevant to the yearly-pmodelForadditionalmethodsand rationale seeAppendixS3

3emsp |emspRESULTS

31emsp|emspOccupancy abundance and estimator behavior

Comparingtrueoccupancy(proportiontransectswithencounterpge05)andabundanceinformedunderstandingofstatisticalpowerandestima-torpropertiesTrueoccupancyrelatedpositivelywithabundancebutpla-teauedathigherabundances(Figure4ac)Trueoccupancydeclineslaggedabundancedeclines(Figure4bd)Withshortertransectstrueoccupancycorrespondedbetterbutstillimperfectlywithabundance(Figure4cd)

Occupancyestimatesremainedconstantwithnoabundancetrendand declinedwith declining abundance (Figure5) Detectability es-timates declined with declining abundance either across scenarios(constant- pestimates)orthroughtime(yearly-pestimatesFigure6)Yearly-p estimator precisionwas less than for constant-p estimatesanddeclinedwithdecliningabundance(Figures5and6)

Detectabilityestimatesfollowedthebehaviorofencounterprob-abilitiesatoccupiedtransectsbutweregenerallyhigherthatisposi-tivelybiased(Figure6)makingoccupancyestimatesnegativelybiased(Figure5)Logisticregressionestimatesdeviatedevenmorefromtrueoccupancy (Figure5cfil) reflecting thediffering targetof inference(ieprobabilityofphysicalpresenceseeSection2andAppendixS3)

32emsp|emspObjective 1 Sampling effort

Withhistoricalsurveyallocationstatisticalpowerincreasedwithin-creasingsamplingeffortandstrongerpopulationdeclines(Figure7)

F IGURE 4emspTrueoccupancy(ψ) versus abundance(N=numberofindividualsacrossall7676971haofpotentialhabitatinOregonandWashingtonnationalforestsac)andcorrespondenceof(odds)occupancy(λψ)withabundancetrends(λNbd)forsimulatedwhite-headedwoodpeckerpopulationsThirtyreplicatepopulationsmonitoredfor20yearsforeachtrendscenarioaredepictedwhensurveyedattransectsconsistingof10points(ab)orthreepoints(cd)eachInpanelsbanddtheredlineindicates11correspondence(desirableforinference)betweenoccupancyandabundancetrends

emspensp emsp | emsp7LATIF eT AL

The constant- pmodeland logistic regression (withsingle-surveyal-location) generally provided adequate power (ge80 chance of ob-servingadecline)Powerwasonlyinadequatewithasmalleffectsize(λN=098) andminimal sampling effort (j le 60 and90 transects forconstant- p and logistic regression respectively) In contrast powerwasneveradequatewith theyearly-pmodelSpurious trendswererarelyobserved(15ofsimulationsinwhichλN = 1)

With no abundance or occupancy trendsmodels estimated ac-tual trendswithminimal error and no apparent bias but error andbiasgrewwith increasingtrend (Figure8)Theconstant-pmodel in-creasingly overestimated declineswith steeper abundance declines

although abundance trendswere estimated better (RMSENle0055)than occupancy trends (RMSEψle0105) Yearly-p trend estimateswere centered between actual abundance and occupancy trends(RMSEle005) Models fitted to single-survey data estimated trueabundance trendswith the least error (RMSENle0008) and no ob-viousbias

33emsp|emspObjective 2 Sampling allocation

Monitoringstrategiesthattargetedinferenceoffiner-scaletrendsinspaceuseorabundanceandextendedsamplingspatiallygenerally

F IGURE 5emspYearlyoccupancyestimatesfromsimulatedregionalwhite-headedwoodpeckermonitoringSimulatedtrendswereλN=1(andashc)098(dndashf)095(gndashi)and09(jndashl)Repeat-surveyoccupancyestimatesassumedconstantdetectability(adgandj)orvariabledetectabilityamongyears(behandk)Single-surveyestimatesassumedperfectdetectability(cfiandl)Thirtysimulationsofmonitoringtransectsof10pointseachfor20yearsarerepresentedforeachscenario(n = 150and300transectsforrepeat-andsingle-surveyscenariosrespectively)Blackdotsandblueverticalbarsshowyearlyestimatesand95BCIsjitteredfordisplayBlacklinesconnectestimatesfromconsecutiveyearsforindividualsimulationsReddotsshowmeantrueoccupancyfor30simulationsthatisproportionofallpossibletransectsoccupied

8emsp |emsp emspensp LATIF eT AL

providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

4emsp |emsp emspensp LATIF eT AL

Pavlacky Blakesley White Hanni amp Lukacs 2012 Rota etal2009)andforWHWOprovidedopportunityforbroadcastingcallsfollowedbyaperiodoflistening(max5mintotal)beforeproceed-ing to the next point To conserve time surveyors immediatelyproceeded to thenextpointalonga transectwhenwhite-headedwoodpecker was first detected Thus they strictly recorded de-tectionndashnondetection data restricting the focus ofmonitoring tooccupancy

22emsp|emspPopulation and sampling simulations

Following the initial 6-year effort we simulated occupancy-basedmonitoringofwhite-headedwoodpeckerstoinformpotentialfutureeffortsRecognizingtheneedforgreatersamplingefforttomeaning-fullyquantifytrendshoweverwesimulatedsurveysofge60transectsover20years

Simulatedpopulationsexperienceddeterministictrendsbasedonanexponentialmodel

where Nt ispopulationabundanceinyeart and λN istheproportionchangeinabundanceperyear(fortheoreticalbasisseeGotelli2001)Weconsidereda rangeof trendscenariosofpotential conservationconcernλN=10098095or09thatis03364or88declineover20years Simulated trends representedeffect sizes foranalyzingpowerPositivetrends(λNgt10)werelessofaconcernforinformingprioritizationofWHWOforconservationactionandthere-forenotconsideredAlthoughrealpopulationsfluctuatestochasticallywe lacked information for simulating specific levels of stochasticityanddeterministictrendsprovidedclearereffectsizesforinterpretingpowerestimates(seealsoEllisetal2015MacKenzieampRoyle2005)We intended the range of simple deterministic trends consideredhereto informsurveillancemonitoringaimedatdocumentingunan-ticipatedchangeratherthanparticularecologicalscenarios(HuttoampBelote2013)

Wesimulatedpopulationmonitoringsoastoexplicitlyrepresentthe process of sampling discrete detectionndashnondetection data forcontinuouslydistributedpopulations(cfEffordampDawson2012Ellisetal 2014 contraMacKenzie amp Royle 2005)We conducted sim-ulations using the rSPACE package (Ellis etal 2014 2015) in R (RCoreTeam2015) Simulationsentailed (1) randomlydistributingN1 homerangesacrosssuitablehabitat(2)calculatingtheprobabilityofencounteringge1white-headedwoodpeckeratasurveypoint(3)gen-eratingdetectionndashnondetectiondatabasedontheseencounterprob-abilitiesand(4)randomlyremovingNttimes(1minusλN)individualsfromthelandscapeandrepeatingsteps2ndash3foreachremainingyeart = 2ndash20 (AppendixS1)Wecollecteddataforaregion-wide300mpointgridand laterderivedtransectmonitoringscenariosSurveyorsrarelyre-cordeddetectionsgt150maway(7of2011ndash2016detections)sowesimulated150-mfixed-radiuspointsurveys

Weconsolidatedpointdatatorepresenttransectmonitoringsce-nariosvaryinginsamplingeffortandallocationAtransectdetectionrepresented ge1 detection at any given point along a transect on a

givendayOnehomerange(1-kmradius)couldincludemultipleneigh-boringpointssopoint-leveldetectionswithintransectswerespatiallycorrelatedwhereasge2kmtransectspacingavoidedspatialcorrelationin transectdetectionsAdditionallywith transectswewereable toexploreafundamentalissueinmonitoringdesigntherelativemeritsofsampling intensively (egmorepointspertransectorrepeatsur-veys)versusextensively(moretransects)

Weconsideredmonitoringscenariostoaccomplishtwoobjectives(1) identify levels of sampling effort capable of providing desirablepower(ge80chancetoobserveadeclinegivenλNle098) (2)com-parecommonlyconsideredsamplingallocationstrategiesrepresentingalternativetargetsofinferenceandspatialextentsofsamplingWead-dressedobjective1byvaryingsamplingeffort(ntransectge60ienpoint-surveys-per-yearge1200)withdifferenttrendsandthehistoricalsamplingallocationof10pointspertransectsurveyedtwiceeveryyearForob-jective2wefocusedonalong-termdeclinescenario(λN=098)andfixedsamplingeffort (npoint-surveys-per-year=1200)whilevaryingmoni-toringstrategiesThehistoricalallocationschemerepresentedanin-tendedinferenceofrelativelycoarse-scaletrendsAlternativeschemesincludedsurveyingshortertransects(8ndash3pointspertransect)whichtargetedinferenceoffiner-scaletrendsbysamplingsmallerareaspo-tentiallyoccupiedbyfewerindividualsWealsoconsideredsurveyingtransects only once per year representing single-survey occupancyapproacheswhoseestimatesprovidetemporalsnapshotsofpopula-tions useful for inferring changes in abundance (Hutto 2016 Latifetal2016)Finallyweconsideredsurveyinglt100oftransectsperyear (ie paneldesignsBaileyHinesNicholsampMacKenzie2007UrquhartampKincaid1999)orrepeatingsurveysatlt100oftransectseachyearHavingfixedsamplingeffort thesealternateschemesal-lowedmonitoringofmoretransectswhichextendedspatialsampling

For simplicity simulations assumed no false-negative observererror (hereafter observer error) that iswhite-headedwoodpeckerswerealwaysdetected ifpresentduringasurveyThusdetectabilitywasdeterminedexclusivelybyterritorialmovementbetweenrepeatsurveyswithinayearThisassumptionwasdefensiblebecausecall-broadcast surveys reduce observer error and standardized surveyslimit potentially confounding interannual variation in observer error(Mellen-McLeanetal2015)Additionallywecalibratedsimulationswith pilot data (Appendix S2) Encounter probabilities during a sur-vey therefore reflected the number location size and spacing ofhome ranges informedbywhite-headedwoodpeckerecologypop-ulationsizereflectedcalibrationwithpilotdataandassumedtrends(AppendicesS1andS2)

Spatialvariability indetectability (ieencounterprobabilities insimulations)emerged fromvariation innestinghabitatandrandomplacement of home rangeswithin this habitatwhich caused localabundanceandproximitytocentersofactivitytovaryamongtran-sects Reflecting likely realities detectability at occupied transectsincreasedwith increasing abundance and decreasedwith distancefromhome rangecenters (seeAppendixS1)Analyses ignored thisspatialheterogeneityandthusinformedstudydesignwhileaccount-ingforlikelyconstraintsonmodelcomplexityduetolimitedsamplingeffortWe initially considered smallerhome ranges (600m radius)

(1)Nt=N1timesλtN

emspensp emsp | emsp5LATIF eT AL

butcalibrationtopilotdatarequiredcompensatoryadjustments toinitialabundanceresultinginsimilarpatternsinstatisticalpower(QLatif unpublished data)We restricted simulations to national for-estsrepresenting77(77times106ha)ofpotentialhabitatwithintheregion(Figure2)

23emsp|emspData analysis

Forscenariosyieldingrepeat-surveydataweestimatedtrendswithtwo different occupancy models representing commonly consid-eredwaysofcorrectingfordetectability(pegLindenetal2017Steenweg etal 2016 Zielinski etal 2013) to estimate occupancyprobability (ψ Figure3ab) One model allowed detectability esti-matestovaryinterannually(hereaftertheyearly-pmodelFigure3a)whereastheotherhelddetectabilityconstant(hereafter the constant- pmodelFigure3bformodelstructuresseeAppendixS3)Becauseindividuals couldmove in or out of the surveyed areabetween re-peat surveyswithin a year thesemodels quantified the probabilityof a transect intersectingge1home rangehereafter true occupancywhichdescribesspeciesrangeorspaceuse(EffordampDawson2012MacKenzieampRoyle 2005) Theyearly-pmodel allowsdetectability

tochangewithchangingabundance(RoyleampNichols2003)tobet-terestimatetrueoccupancyTheconstant-pmodelmisspecifiestrueoccupancybutisfrequentlyconsideredandmaybeselectedforpar-simonyinappliedstudies(egZielinskietal2013)Additionallyhav-ingcontrolledforobservererror(egifnonexistentasinsimulationsorcontrolledviastandardizedsurveys)theconstant-pmodelcoercesoccupancyestimatestoreflectanyinterannualchangesshiftingthetargetofinferencetoabundance(Figure3b)

For scenarios yielding single-survey data we estimated trendsusing logistic regression (see structure inAppendix S3) Having ex-cludedobservererror insimulations logistic regressionmodelsesti-matedprobabilityofge1individualrsquosphysicalpresenceduringasurveyhereafter probability of physical presence Single-survey scenariosrepresented single-surveyoccupancyapproaches inwhich replicatesurveysoccurwithinanarrowenoughtimeframefordetectabilitytoquantifyobservererrorsothatoccupancyestimatesquantifyproba-bilityofphysicalpresence(egdouble-observerandremovaldesignsNicholsetal2008Rotaetal2009)ByomittingobservererrorfromsimulationshoweverreplicatesurveyswereunnecessarytoquantifyphysicalpresenceProbabilityofphysicalpresencerepresentsatem-poral snapshot of a population unaffected by territorial movement

F IGURE 3emspHowmodelestimatesreflectunderlyingprocessesunderalternativemonitoringapproachesRepeat-surveyoccupancyestimatesfundamentallyquantifytrueoccupancy(ab)butcanindexabundancetrendsifdetectabilityisheldconstant(bcontraA)Territorialmovementinfluencesrepeat-surveyoccupancyestimates(ab)whereassingle-surveyoccupancyestimatesrepresentpopulationsnapshotsnotinfluencedbymovement(c)False-negativeobservererrorwasnotsimulatedbutcouldinfluenceestimatesinreality

6emsp |emsp emspensp LATIF eT AL

expected to closely track abundance (Figure3c Hutto 2016 Latifetal2016)AdditionallysurveyingtransectsonlyonceallowedustomonitortwiceasmanytransectsincreasingsamplingextentInprac-ticeauxiliarysampling (eg recordingdetectiontimingordeployingmultipleobservers)wouldaccount forobservererror (Nicholsetal2008 Rota etal 2009) likely adding to uncertainty in trend esti-matesIgnoringobservererrorinbothsingle-andrepeat-surveysce-narioshowevermadetheircomparisoninformative

Wequantified occupancy trends as proportionyearly change inodds occupancy λψ =

ψt+1∕(1minusψt+1)

ψt∕(1minusψt) (MacKenzie etal 2006)We ana-

lyzeddetectionndashnondetectiondatawithfixedyeareffectsandsubse-quentlycalculatedleast-squarestrendsinyearlyoccupancyestimates(seealsoEllisetal2014)Wequantifiedstatisticalpoweraspercentsimulationswhen95Bayesiancredibleintervals(BCIs)fortheesti-matedtrendforthestudyperiod(λψ where logit(ψt)=β0+ log (λψ)times t p200MacKenzieetal2006)fellbelow1Wealsocalculatedrootmean squared error for trend estimates (RMSEN=

radic

mean(λψ minusλN) RMSEψ =

radic

mean(λψ minusλψ )) When quantifying true occupancy weconsidered occupied transects to be thosewith encounter pge05Having foundextremely limited statistical powerwithyearly-p esti-mates(seeObjective1Results)weprimarilyassessedsamplingallo-cations(Objective2)forconstant-pandlogisticregressionmodelsbutthentestedyearly-pagainwithbetterallocationFurthermoregivenlikely targets of inference we considered RMSEN most relevant toconstant- pandlogisticregressionmodelsandRMSEψ relevant to the yearly-pmodelForadditionalmethodsand rationale seeAppendixS3

3emsp |emspRESULTS

31emsp|emspOccupancy abundance and estimator behavior

Comparingtrueoccupancy(proportiontransectswithencounterpge05)andabundanceinformedunderstandingofstatisticalpowerandestima-torpropertiesTrueoccupancyrelatedpositivelywithabundancebutpla-teauedathigherabundances(Figure4ac)Trueoccupancydeclineslaggedabundancedeclines(Figure4bd)Withshortertransectstrueoccupancycorrespondedbetterbutstillimperfectlywithabundance(Figure4cd)

Occupancyestimatesremainedconstantwithnoabundancetrendand declinedwith declining abundance (Figure5) Detectability es-timates declined with declining abundance either across scenarios(constant- pestimates)orthroughtime(yearly-pestimatesFigure6)Yearly-p estimator precisionwas less than for constant-p estimatesanddeclinedwithdecliningabundance(Figures5and6)

Detectabilityestimatesfollowedthebehaviorofencounterprob-abilitiesatoccupiedtransectsbutweregenerallyhigherthatisposi-tivelybiased(Figure6)makingoccupancyestimatesnegativelybiased(Figure5)Logisticregressionestimatesdeviatedevenmorefromtrueoccupancy (Figure5cfil) reflecting thediffering targetof inference(ieprobabilityofphysicalpresenceseeSection2andAppendixS3)

32emsp|emspObjective 1 Sampling effort

Withhistoricalsurveyallocationstatisticalpowerincreasedwithin-creasingsamplingeffortandstrongerpopulationdeclines(Figure7)

F IGURE 4emspTrueoccupancy(ψ) versus abundance(N=numberofindividualsacrossall7676971haofpotentialhabitatinOregonandWashingtonnationalforestsac)andcorrespondenceof(odds)occupancy(λψ)withabundancetrends(λNbd)forsimulatedwhite-headedwoodpeckerpopulationsThirtyreplicatepopulationsmonitoredfor20yearsforeachtrendscenarioaredepictedwhensurveyedattransectsconsistingof10points(ab)orthreepoints(cd)eachInpanelsbanddtheredlineindicates11correspondence(desirableforinference)betweenoccupancyandabundancetrends

emspensp emsp | emsp7LATIF eT AL

The constant- pmodeland logistic regression (withsingle-surveyal-location) generally provided adequate power (ge80 chance of ob-servingadecline)Powerwasonlyinadequatewithasmalleffectsize(λN=098) andminimal sampling effort (j le 60 and90 transects forconstant- p and logistic regression respectively) In contrast powerwasneveradequatewith theyearly-pmodelSpurious trendswererarelyobserved(15ofsimulationsinwhichλN = 1)

With no abundance or occupancy trendsmodels estimated ac-tual trendswithminimal error and no apparent bias but error andbiasgrewwith increasingtrend (Figure8)Theconstant-pmodel in-creasingly overestimated declineswith steeper abundance declines

although abundance trendswere estimated better (RMSENle0055)than occupancy trends (RMSEψle0105) Yearly-p trend estimateswere centered between actual abundance and occupancy trends(RMSEle005) Models fitted to single-survey data estimated trueabundance trendswith the least error (RMSENle0008) and no ob-viousbias

33emsp|emspObjective 2 Sampling allocation

Monitoringstrategiesthattargetedinferenceoffiner-scaletrendsinspaceuseorabundanceandextendedsamplingspatiallygenerally

F IGURE 5emspYearlyoccupancyestimatesfromsimulatedregionalwhite-headedwoodpeckermonitoringSimulatedtrendswereλN=1(andashc)098(dndashf)095(gndashi)and09(jndashl)Repeat-surveyoccupancyestimatesassumedconstantdetectability(adgandj)orvariabledetectabilityamongyears(behandk)Single-surveyestimatesassumedperfectdetectability(cfiandl)Thirtysimulationsofmonitoringtransectsof10pointseachfor20yearsarerepresentedforeachscenario(n = 150and300transectsforrepeat-andsingle-surveyscenariosrespectively)Blackdotsandblueverticalbarsshowyearlyestimatesand95BCIsjitteredfordisplayBlacklinesconnectestimatesfromconsecutiveyearsforindividualsimulationsReddotsshowmeantrueoccupancyfor30simulationsthatisproportionofallpossibletransectsoccupied

8emsp |emsp emspensp LATIF eT AL

providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

emspensp emsp | emsp5LATIF eT AL

butcalibrationtopilotdatarequiredcompensatoryadjustments toinitialabundanceresultinginsimilarpatternsinstatisticalpower(QLatif unpublished data)We restricted simulations to national for-estsrepresenting77(77times106ha)ofpotentialhabitatwithintheregion(Figure2)

23emsp|emspData analysis

Forscenariosyieldingrepeat-surveydataweestimatedtrendswithtwo different occupancy models representing commonly consid-eredwaysofcorrectingfordetectability(pegLindenetal2017Steenweg etal 2016 Zielinski etal 2013) to estimate occupancyprobability (ψ Figure3ab) One model allowed detectability esti-matestovaryinterannually(hereaftertheyearly-pmodelFigure3a)whereastheotherhelddetectabilityconstant(hereafter the constant- pmodelFigure3bformodelstructuresseeAppendixS3)Becauseindividuals couldmove in or out of the surveyed areabetween re-peat surveyswithin a year thesemodels quantified the probabilityof a transect intersectingge1home rangehereafter true occupancywhichdescribesspeciesrangeorspaceuse(EffordampDawson2012MacKenzieampRoyle 2005) Theyearly-pmodel allowsdetectability

tochangewithchangingabundance(RoyleampNichols2003)tobet-terestimatetrueoccupancyTheconstant-pmodelmisspecifiestrueoccupancybutisfrequentlyconsideredandmaybeselectedforpar-simonyinappliedstudies(egZielinskietal2013)Additionallyhav-ingcontrolledforobservererror(egifnonexistentasinsimulationsorcontrolledviastandardizedsurveys)theconstant-pmodelcoercesoccupancyestimatestoreflectanyinterannualchangesshiftingthetargetofinferencetoabundance(Figure3b)

For scenarios yielding single-survey data we estimated trendsusing logistic regression (see structure inAppendix S3) Having ex-cludedobservererror insimulations logistic regressionmodelsesti-matedprobabilityofge1individualrsquosphysicalpresenceduringasurveyhereafter probability of physical presence Single-survey scenariosrepresented single-surveyoccupancyapproaches inwhich replicatesurveysoccurwithinanarrowenoughtimeframefordetectabilitytoquantifyobservererrorsothatoccupancyestimatesquantifyproba-bilityofphysicalpresence(egdouble-observerandremovaldesignsNicholsetal2008Rotaetal2009)ByomittingobservererrorfromsimulationshoweverreplicatesurveyswereunnecessarytoquantifyphysicalpresenceProbabilityofphysicalpresencerepresentsatem-poral snapshot of a population unaffected by territorial movement

F IGURE 3emspHowmodelestimatesreflectunderlyingprocessesunderalternativemonitoringapproachesRepeat-surveyoccupancyestimatesfundamentallyquantifytrueoccupancy(ab)butcanindexabundancetrendsifdetectabilityisheldconstant(bcontraA)Territorialmovementinfluencesrepeat-surveyoccupancyestimates(ab)whereassingle-surveyoccupancyestimatesrepresentpopulationsnapshotsnotinfluencedbymovement(c)False-negativeobservererrorwasnotsimulatedbutcouldinfluenceestimatesinreality

6emsp |emsp emspensp LATIF eT AL

expected to closely track abundance (Figure3c Hutto 2016 Latifetal2016)AdditionallysurveyingtransectsonlyonceallowedustomonitortwiceasmanytransectsincreasingsamplingextentInprac-ticeauxiliarysampling (eg recordingdetectiontimingordeployingmultipleobservers)wouldaccount forobservererror (Nicholsetal2008 Rota etal 2009) likely adding to uncertainty in trend esti-matesIgnoringobservererrorinbothsingle-andrepeat-surveysce-narioshowevermadetheircomparisoninformative

Wequantified occupancy trends as proportionyearly change inodds occupancy λψ =

ψt+1∕(1minusψt+1)

ψt∕(1minusψt) (MacKenzie etal 2006)We ana-

lyzeddetectionndashnondetectiondatawithfixedyeareffectsandsubse-quentlycalculatedleast-squarestrendsinyearlyoccupancyestimates(seealsoEllisetal2014)Wequantifiedstatisticalpoweraspercentsimulationswhen95Bayesiancredibleintervals(BCIs)fortheesti-matedtrendforthestudyperiod(λψ where logit(ψt)=β0+ log (λψ)times t p200MacKenzieetal2006)fellbelow1Wealsocalculatedrootmean squared error for trend estimates (RMSEN=

radic

mean(λψ minusλN) RMSEψ =

radic

mean(λψ minusλψ )) When quantifying true occupancy weconsidered occupied transects to be thosewith encounter pge05Having foundextremely limited statistical powerwithyearly-p esti-mates(seeObjective1Results)weprimarilyassessedsamplingallo-cations(Objective2)forconstant-pandlogisticregressionmodelsbutthentestedyearly-pagainwithbetterallocationFurthermoregivenlikely targets of inference we considered RMSEN most relevant toconstant- pandlogisticregressionmodelsandRMSEψ relevant to the yearly-pmodelForadditionalmethodsand rationale seeAppendixS3

3emsp |emspRESULTS

31emsp|emspOccupancy abundance and estimator behavior

Comparingtrueoccupancy(proportiontransectswithencounterpge05)andabundanceinformedunderstandingofstatisticalpowerandestima-torpropertiesTrueoccupancyrelatedpositivelywithabundancebutpla-teauedathigherabundances(Figure4ac)Trueoccupancydeclineslaggedabundancedeclines(Figure4bd)Withshortertransectstrueoccupancycorrespondedbetterbutstillimperfectlywithabundance(Figure4cd)

Occupancyestimatesremainedconstantwithnoabundancetrendand declinedwith declining abundance (Figure5) Detectability es-timates declined with declining abundance either across scenarios(constant- pestimates)orthroughtime(yearly-pestimatesFigure6)Yearly-p estimator precisionwas less than for constant-p estimatesanddeclinedwithdecliningabundance(Figures5and6)

Detectabilityestimatesfollowedthebehaviorofencounterprob-abilitiesatoccupiedtransectsbutweregenerallyhigherthatisposi-tivelybiased(Figure6)makingoccupancyestimatesnegativelybiased(Figure5)Logisticregressionestimatesdeviatedevenmorefromtrueoccupancy (Figure5cfil) reflecting thediffering targetof inference(ieprobabilityofphysicalpresenceseeSection2andAppendixS3)

32emsp|emspObjective 1 Sampling effort

Withhistoricalsurveyallocationstatisticalpowerincreasedwithin-creasingsamplingeffortandstrongerpopulationdeclines(Figure7)

F IGURE 4emspTrueoccupancy(ψ) versus abundance(N=numberofindividualsacrossall7676971haofpotentialhabitatinOregonandWashingtonnationalforestsac)andcorrespondenceof(odds)occupancy(λψ)withabundancetrends(λNbd)forsimulatedwhite-headedwoodpeckerpopulationsThirtyreplicatepopulationsmonitoredfor20yearsforeachtrendscenarioaredepictedwhensurveyedattransectsconsistingof10points(ab)orthreepoints(cd)eachInpanelsbanddtheredlineindicates11correspondence(desirableforinference)betweenoccupancyandabundancetrends

emspensp emsp | emsp7LATIF eT AL

The constant- pmodeland logistic regression (withsingle-surveyal-location) generally provided adequate power (ge80 chance of ob-servingadecline)Powerwasonlyinadequatewithasmalleffectsize(λN=098) andminimal sampling effort (j le 60 and90 transects forconstant- p and logistic regression respectively) In contrast powerwasneveradequatewith theyearly-pmodelSpurious trendswererarelyobserved(15ofsimulationsinwhichλN = 1)

With no abundance or occupancy trendsmodels estimated ac-tual trendswithminimal error and no apparent bias but error andbiasgrewwith increasingtrend (Figure8)Theconstant-pmodel in-creasingly overestimated declineswith steeper abundance declines

although abundance trendswere estimated better (RMSENle0055)than occupancy trends (RMSEψle0105) Yearly-p trend estimateswere centered between actual abundance and occupancy trends(RMSEle005) Models fitted to single-survey data estimated trueabundance trendswith the least error (RMSENle0008) and no ob-viousbias

33emsp|emspObjective 2 Sampling allocation

Monitoringstrategiesthattargetedinferenceoffiner-scaletrendsinspaceuseorabundanceandextendedsamplingspatiallygenerally

F IGURE 5emspYearlyoccupancyestimatesfromsimulatedregionalwhite-headedwoodpeckermonitoringSimulatedtrendswereλN=1(andashc)098(dndashf)095(gndashi)and09(jndashl)Repeat-surveyoccupancyestimatesassumedconstantdetectability(adgandj)orvariabledetectabilityamongyears(behandk)Single-surveyestimatesassumedperfectdetectability(cfiandl)Thirtysimulationsofmonitoringtransectsof10pointseachfor20yearsarerepresentedforeachscenario(n = 150and300transectsforrepeat-andsingle-surveyscenariosrespectively)Blackdotsandblueverticalbarsshowyearlyestimatesand95BCIsjitteredfordisplayBlacklinesconnectestimatesfromconsecutiveyearsforindividualsimulationsReddotsshowmeantrueoccupancyfor30simulationsthatisproportionofallpossibletransectsoccupied

8emsp |emsp emspensp LATIF eT AL

providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

6emsp |emsp emspensp LATIF eT AL

expected to closely track abundance (Figure3c Hutto 2016 Latifetal2016)AdditionallysurveyingtransectsonlyonceallowedustomonitortwiceasmanytransectsincreasingsamplingextentInprac-ticeauxiliarysampling (eg recordingdetectiontimingordeployingmultipleobservers)wouldaccount forobservererror (Nicholsetal2008 Rota etal 2009) likely adding to uncertainty in trend esti-matesIgnoringobservererrorinbothsingle-andrepeat-surveysce-narioshowevermadetheircomparisoninformative

Wequantified occupancy trends as proportionyearly change inodds occupancy λψ =

ψt+1∕(1minusψt+1)

ψt∕(1minusψt) (MacKenzie etal 2006)We ana-

lyzeddetectionndashnondetectiondatawithfixedyeareffectsandsubse-quentlycalculatedleast-squarestrendsinyearlyoccupancyestimates(seealsoEllisetal2014)Wequantifiedstatisticalpoweraspercentsimulationswhen95Bayesiancredibleintervals(BCIs)fortheesti-matedtrendforthestudyperiod(λψ where logit(ψt)=β0+ log (λψ)times t p200MacKenzieetal2006)fellbelow1Wealsocalculatedrootmean squared error for trend estimates (RMSEN=

radic

mean(λψ minusλN) RMSEψ =

radic

mean(λψ minusλψ )) When quantifying true occupancy weconsidered occupied transects to be thosewith encounter pge05Having foundextremely limited statistical powerwithyearly-p esti-mates(seeObjective1Results)weprimarilyassessedsamplingallo-cations(Objective2)forconstant-pandlogisticregressionmodelsbutthentestedyearly-pagainwithbetterallocationFurthermoregivenlikely targets of inference we considered RMSEN most relevant toconstant- pandlogisticregressionmodelsandRMSEψ relevant to the yearly-pmodelForadditionalmethodsand rationale seeAppendixS3

3emsp |emspRESULTS

31emsp|emspOccupancy abundance and estimator behavior

Comparingtrueoccupancy(proportiontransectswithencounterpge05)andabundanceinformedunderstandingofstatisticalpowerandestima-torpropertiesTrueoccupancyrelatedpositivelywithabundancebutpla-teauedathigherabundances(Figure4ac)Trueoccupancydeclineslaggedabundancedeclines(Figure4bd)Withshortertransectstrueoccupancycorrespondedbetterbutstillimperfectlywithabundance(Figure4cd)

Occupancyestimatesremainedconstantwithnoabundancetrendand declinedwith declining abundance (Figure5) Detectability es-timates declined with declining abundance either across scenarios(constant- pestimates)orthroughtime(yearly-pestimatesFigure6)Yearly-p estimator precisionwas less than for constant-p estimatesanddeclinedwithdecliningabundance(Figures5and6)

Detectabilityestimatesfollowedthebehaviorofencounterprob-abilitiesatoccupiedtransectsbutweregenerallyhigherthatisposi-tivelybiased(Figure6)makingoccupancyestimatesnegativelybiased(Figure5)Logisticregressionestimatesdeviatedevenmorefromtrueoccupancy (Figure5cfil) reflecting thediffering targetof inference(ieprobabilityofphysicalpresenceseeSection2andAppendixS3)

32emsp|emspObjective 1 Sampling effort

Withhistoricalsurveyallocationstatisticalpowerincreasedwithin-creasingsamplingeffortandstrongerpopulationdeclines(Figure7)

F IGURE 4emspTrueoccupancy(ψ) versus abundance(N=numberofindividualsacrossall7676971haofpotentialhabitatinOregonandWashingtonnationalforestsac)andcorrespondenceof(odds)occupancy(λψ)withabundancetrends(λNbd)forsimulatedwhite-headedwoodpeckerpopulationsThirtyreplicatepopulationsmonitoredfor20yearsforeachtrendscenarioaredepictedwhensurveyedattransectsconsistingof10points(ab)orthreepoints(cd)eachInpanelsbanddtheredlineindicates11correspondence(desirableforinference)betweenoccupancyandabundancetrends

emspensp emsp | emsp7LATIF eT AL

The constant- pmodeland logistic regression (withsingle-surveyal-location) generally provided adequate power (ge80 chance of ob-servingadecline)Powerwasonlyinadequatewithasmalleffectsize(λN=098) andminimal sampling effort (j le 60 and90 transects forconstant- p and logistic regression respectively) In contrast powerwasneveradequatewith theyearly-pmodelSpurious trendswererarelyobserved(15ofsimulationsinwhichλN = 1)

With no abundance or occupancy trendsmodels estimated ac-tual trendswithminimal error and no apparent bias but error andbiasgrewwith increasingtrend (Figure8)Theconstant-pmodel in-creasingly overestimated declineswith steeper abundance declines

although abundance trendswere estimated better (RMSENle0055)than occupancy trends (RMSEψle0105) Yearly-p trend estimateswere centered between actual abundance and occupancy trends(RMSEle005) Models fitted to single-survey data estimated trueabundance trendswith the least error (RMSENle0008) and no ob-viousbias

33emsp|emspObjective 2 Sampling allocation

Monitoringstrategiesthattargetedinferenceoffiner-scaletrendsinspaceuseorabundanceandextendedsamplingspatiallygenerally

F IGURE 5emspYearlyoccupancyestimatesfromsimulatedregionalwhite-headedwoodpeckermonitoringSimulatedtrendswereλN=1(andashc)098(dndashf)095(gndashi)and09(jndashl)Repeat-surveyoccupancyestimatesassumedconstantdetectability(adgandj)orvariabledetectabilityamongyears(behandk)Single-surveyestimatesassumedperfectdetectability(cfiandl)Thirtysimulationsofmonitoringtransectsof10pointseachfor20yearsarerepresentedforeachscenario(n = 150and300transectsforrepeat-andsingle-surveyscenariosrespectively)Blackdotsandblueverticalbarsshowyearlyestimatesand95BCIsjitteredfordisplayBlacklinesconnectestimatesfromconsecutiveyearsforindividualsimulationsReddotsshowmeantrueoccupancyfor30simulationsthatisproportionofallpossibletransectsoccupied

8emsp |emsp emspensp LATIF eT AL

providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

emspensp emsp | emsp7LATIF eT AL

The constant- pmodeland logistic regression (withsingle-surveyal-location) generally provided adequate power (ge80 chance of ob-servingadecline)Powerwasonlyinadequatewithasmalleffectsize(λN=098) andminimal sampling effort (j le 60 and90 transects forconstant- p and logistic regression respectively) In contrast powerwasneveradequatewith theyearly-pmodelSpurious trendswererarelyobserved(15ofsimulationsinwhichλN = 1)

With no abundance or occupancy trendsmodels estimated ac-tual trendswithminimal error and no apparent bias but error andbiasgrewwith increasingtrend (Figure8)Theconstant-pmodel in-creasingly overestimated declineswith steeper abundance declines

although abundance trendswere estimated better (RMSENle0055)than occupancy trends (RMSEψle0105) Yearly-p trend estimateswere centered between actual abundance and occupancy trends(RMSEle005) Models fitted to single-survey data estimated trueabundance trendswith the least error (RMSENle0008) and no ob-viousbias

33emsp|emspObjective 2 Sampling allocation

Monitoringstrategiesthattargetedinferenceoffiner-scaletrendsinspaceuseorabundanceandextendedsamplingspatiallygenerally

F IGURE 5emspYearlyoccupancyestimatesfromsimulatedregionalwhite-headedwoodpeckermonitoringSimulatedtrendswereλN=1(andashc)098(dndashf)095(gndashi)and09(jndashl)Repeat-surveyoccupancyestimatesassumedconstantdetectability(adgandj)orvariabledetectabilityamongyears(behandk)Single-surveyestimatesassumedperfectdetectability(cfiandl)Thirtysimulationsofmonitoringtransectsof10pointseachfor20yearsarerepresentedforeachscenario(n = 150and300transectsforrepeat-andsingle-surveyscenariosrespectively)Blackdotsandblueverticalbarsshowyearlyestimatesand95BCIsjitteredfordisplayBlacklinesconnectestimatesfromconsecutiveyearsforindividualsimulationsReddotsshowmeantrueoccupancyfor30simulationsthatisproportionofallpossibletransectsoccupied

8emsp |emsp emspensp LATIF eT AL

providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

8emsp |emsp emspensp LATIF eT AL

providedmorepowerandlessestimationerrorthanthehistoricalstrategy Power improved and estimation error decreased whenmonitoring shorter butmore transects (Figures9 and 10) Powerwasgreatestanderror(RMSEN)leastwhenmonitoringtheprobabil-ityofphysicalpresencewithsingle-surveydata(Figures8cand10)Incontrastwefoundthe leastpowerandgreatesterror (RMSEψ) whenattemptingtomonitortrueoccupancywithrepeatsurveysandthe yearly-pmodel (Figure8b) Interestingly despitemoreexplic-itlytargetinginferenceofoccupancyyearly-ptrendsestimatesdidnotestimateoccupancytrendswithanylesserror(RMSEψle0105)thanlogisticregression(RMSEψle0055)Althoughitprovidedad-equatepower inmanyscenarios theconstant-pmodel tended tooverestimatebothoccupancyandabundancedeclines (Figures8aand9)

Paneldesignswith relativelysmallpanels (33of transectssur-veyed eachyear) also improved power and reduced error althoughlargerpanels (50of transectssurveyedeachyear)didnotprovidenotablegainsConductingfewerrepeatsurveysinexchangeformoretransects also did not substantively affect power and tended to in-creaseestimationerror(Figure11)

Thedesignthatmaximizedpowerandminimizederrorwithcon-stant- pand logistic regressionmodelswasa33paneldesignwith3 points per transects Even with this design the yearly-p modelprovided inadequate power (13) although trend estimation errorwas lessthanwiththehistoricaldesign (RMSEψ=0009nsim = 100 ntransect=600over20yearscomparewithFigure7b)

4emsp |emspDISCUSSION

Oursimulationssuggestedminimumlevelsofsamplingeffortneededtoprovideadequatepowerwhilealsoinformingstudydesignformon-itoringWHWOwithexplicittargetsofinferenceWiththehistoricaldesignofsurveyingtransectswith10pointseachtwiceayeartotar-getcoarse-scaletrendsintrueoccupancy(speciesrangeorspaceuse)we found 60ndash90 transects could be sufficient for desirable powerThisdesignwouldrequireholdingdetectabilityconstantacrossyearshoweverwhichwouldforceoccupancyestimatestoindexabundance(constant- pmodel)andcloudpotential inferenceSurveyingshortertransects (ie closer to the span of one home range) using a 33

F IGURE 6emspDetectionprobability(p black=medianblue=95BCIs)estimatesfromrepeat-surveyoccupancymodelsandencounterprobabilities(redietruedetectability)forsimulatedwhite-headedWoodpeckerregionalmonitoringScenariosentailedmonitoring150transectsof10pointseachsurveyedtwiceyearlyfor20yearsEstimatesassumeconstantdetectability(a)orvariabledetectabilityamongyears(bndashejitteredhorizontallyfordisplay)Encounterprobabilitiesaremedianvaluesforoccupiedtransects(iewithencounter pge05)SimulatedtrendswereλN=10(ab)098(ac)095(ad)or09(ae)(n = 30simulationsperscenario)

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

emspensp emsp | emsp9LATIF eT AL

paneldesigncouldallowstrongerandclearerinferenceofabundancetrendsextendsamplingspatiallyandimprovepowerForfurtherim-provementstopowerandinferencewecouldsurveytransectsonlyonceperyeartomonitortheprobabilityofphysicalpresencewhileaccountingforobservererrorIncontrastsamplingdesignedtodocu-mentchangesintrueoccupancydidnotappearfeasibleatsamplinglevels considered here

41emsp|emspSampling resolution and scale of inference

Ourresultsfurtheremphasizethebenefitsofsamplingatresolutions(ie unit size grid cell size) approximating the size of an individualhomerangedocumentedbyothers(EffordampDawson2012Lindenetal2017)FinerresolutionsamplinggeneratesoccupancyestimatesthatmorecloselytrackabundanceThisestimatorpropertyshouldbedesirable for practitionerswhomonitor occupancy in lieu of abun-danceprimarilyonpragmaticgrounds

Single-survey sampling can similarly benefit monitoring of ter-ritorial animals by providing temporal snapshots of populations un-affected by movement and therefore closely related to abundance(Hutto2016Latifetal2016)Wesimulatedanidealworldwithnoobservererrorwhereinsingle-surveyestimateswerereadilyinterpre-tableastheprobabilityofphysicalpresenceInrealitysomeobservererrorislikelyrequiringauxiliarysamplingtoestimateasnapshotprob-abilityofphysicalpresenceAuxiliarymeasurementsofdetectiontim-ingorcovariatesofobservererrorcould informbiascorrectionwithminimaladditionalsurveyeffort(LeleMorenoampBayne2012Rotaetal2009)Formonitoringwhite-headedwoodpeckersanalysisofdetection timings recorded historically (Mellen-McLean etal 2015)

combinedwithpublishedguidelines(MacKenzieampRoyle2005)couldinformoptimalsurveylengthforsinglesurveysOtherapproachesaredescribed butwould requiremore effort or are designed to informabundanceratherthanoccupancyestimates(egmultipleobserversreplicated camera or track stations distance sampling Amundsonetal2014Nicholsetal2008)Lackingdataonobservererrornaiumlveoccupancy could usefully index abundance ifwe are confident thatobservererrordoesnotvaryinterannuallyandthereforecannotcon-found trendestimation (egwith standardizingbird surveysHutto2016)

Observer error canvarywith local abundance (RoyleampNichols2003) potentially introducing noise not represented in our simula-tionsLargersamplingunitspotentiallyoccupiedbymultiple individ-uals would be most prone to such variability so aligning samplingresolutionwithhomerangesizewouldbedesirableevenwithasingle-surveydesign

A single-survey design would require consistently conductingsurveyswhen individuals are readily detectableWith sensitivity ofnestsurvivaltotemperature(Hollenbecketal2011)climatechangemay alter nesting phenology potentially influencing responsivenesstocallbroadcastsSuchchangescouldnecessitateadjustingthetim-ingofsurveyswhichcouldbe informedbytargetedrepeatsurveysas are commonly implemented for birds (Latif Fleming Barrows ampRotenberry2012Rotaetal2009)

Ourresultsindicatechallengesformonitoringtoinferchangesinspeciesrange(coarse-scale)orspaceuse(finerscale)asinyearly-p scenarioshereBydefinitionoccupancyonlydeclineswhenabun-dancedeclinesenoughtoresult in localextirpationso trueoccu-pancydeclines could indicate strongneed for conservationMore

F IGURE 7emspSimulation-basedpowertoobservewhite-headedwoodpeckerregionaloccupancytrends(percentsimulationswith95BCIlt1)Scenariosvariedinnumberoftransectsmonitoringapproach(constant-poryearly-p occupancymodelsorlogisticregression)and trend (λN=exponentialchangeinabundance)Forallscenariostransectsconsistedof10surveypointssurveyedtwice(occupancymodels)oronce(logisticregression)peryearConstant-passumedconstantdetectabilitywhereasyearly-p allowedvariabledetectabilityamongyearsLogisticregressionalloweddoublethenumberoftransectsbyanalyzingsingle-surveydata

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

10emsp |emsp emspensp LATIF eT AL

intensivesamplinginareasoryearswithlowabundancehowevermay be needed to correctly identify occupancy declinesAt finerscalesspatialheterogeneityindetectabilityarisingfromvariabilityinlocalabundanceandhomerangesthatlackdefinitiveboundariescanlimitaccurateestimationofspaceuse(EffordampDawson2012)Biasesinoccupancyanddetectabilityestimatesobservedherelikelyprimarily reflect theseeffects Includinghabitat relationshipswithoccupancy in analytical models (omitted from simulations) mighthelpbyaccountingsomewhatforspatialheterogeneityinthedatabuteffectsondetectabilityofvaryinglocalabundanceandproxim-itytohomerangesatoccupiedtransectswouldremainEffectivelyestimating species distribution at any scale may require substan-tial spatial or temporal replicationwithin samplingunits (Pavlackyetal2012Valenteetal2017)Givenlikelydemandsonfundingsuch approaches may be feasibly implemented only infrequently(egCruickshankOzgulZumbachampSchmidt2016)Alternativelypredictivemodels (eg Hollenbeck etal 2011 Latif etal 2015WightmanSaabForristalMellen-McLeanampMarkus2010)couldsupplementtrendmonitoringbyidentifyingchangesinhabitat

Nestedsurveys (egpointsalongtransects)can informhierar-chicallystructuredmodelscapableofestimatingpatternsortrendsatmultiplescales(Pavlackyetal2012Rotaetal2009RoyleampKeacutery2007)Multiscaleinferencewouldrequiresufficientsamplingatall scalesof interesthoweverwhichmaybebeyond resources

availableformanymonitoringprograms(Valenteetal2017)Ourinitial attempts found inadequate sampling for meaningful multi-scaleinference(QLatifunpublisheddata)soweabandonedsuchapproacheshere

42emsp|emspSampling extent

Spatiallyextensivesamplingistheoreticallyadvantageouswhenmon-itoringspatiallyheterogeneouspopulations(RhodesampJonzeacuten2011)Inour simulations spatial heterogeneity emerged fromunevendis-tributionofhabitatandrandomvariation in localabundanceamongoccupiedtransectsThebenefitsobservedherewithshortertransectsandsinglesurveyscouldreflectadvantagesofspatiallyextendedsam-pling Panel designs however didnot inherently change the targetofinferenceandsotheirresultsmoredefinitivelydemonstratedpo-tential advantageswith spatially extended sampling In contrast ig-noring heterogeneity inherent in continuously distributed territorialspeciesmayobscureadvantagesofpaneldesigns(Baileyetal2007UrquhartampKincaid1999)

Notall spatialextensions tosamplingwerebeneficialGivenarepeat-surveydesignwegainednothingbyreducingrepeatsurveystomonitormoretransectsSuchstrategiesrequirehighdetectability(MacKenzieampRoyle 2005) likely uncharacteristic of sparsely andcontinuously distributed territorial species (see above) The lack

F IGURE 8emspCorrespondenceofestimatedoccupancytrends(λψ) with true abundance(λN)andoccupancy(λψ) trends Trendswereestimatedwithrepeat-surveyconstant- p(a)andyearly-p(b)occupancymodelsandlogisticregressionanalyzingsingle-surveydata(c)RedandbluedotsmarkperfectcorrespondencewithactualabundanceandoccupancytrendsrespectivelyRootmeansquarederrorquantifiestheoverallestimationerrorwithrespecttoabundance(RMSEN) and occupancy(RMSEψ) trends

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

emspensp emsp | emsp11LATIF eT AL

ofbenefitwith50panelsmayreflectsitefidelity fixedat100inoursimulationsBymonitoringdifferent transects insuccessiveyears the number and distribution of individuals along surveyedtransectsvariedinterannuallypotentiallyobscuringtrendsWhite-headed woodpecker do exhibit site fidelity (Garrett etal 1996)sopaneldesignbenefitscouldtrade-offwithbenefitsofsamplingthesamesetsofindividualsinsuccessiveyearsInrealityhoweverpopulation processes (eg dispersal and turnover) could also ob-scuretrendsTheextentofpanelingneededtobenefitpowerwouldthereforedependonlevelsofspatialversustemporalheterogeneityinpopulation trends (RhodesampJonzeacuten2011) the latterofwhichwas omitted from simulations here Additionally panel designscould limitstudyofprocessesunderlyingoccupancydynamicsforexamplecolonizationandpersistence(Baileyetal2007)

43emsp|emspStudy limitations

Our simulations did not include spatial or temporal stochasticity inpopulationdynamicsindividualmovementbetweenyearsorbehav-ioralinteractionsbetweenneighborsallofwhichcouldmodulateoc-cupancyestimatesortrends(ReynoldsWiensJoyampSalafsky2005SauerFallonampJohnson2003WarrenVeechWeckerlyOrsquoDonnellampOtt2013)Bynotaccountingfortheserealitiespowerestimatesmaybe liberal and thereforeprobablybestused to informa lowerboundforsamplesizeAccordinglywerecommendge120orge90tran-sectswithsingle-surveyorrepeat-surveymonitoringrespectivelyofwhite-headedwoodpeckersacrossourstudyregion

Our treatmentofsite fidelityhowever isconservativeForsim-plicitywesimulatedpopulationswith100sitefidelityandzeroim-migrationorrecruitmentandtoavoidartifactsoftheseassumptionsanalysis models assumed occupancy varied independently amongyears Inrealitymodelscorrectlyspecifyinguncertaintyarisingfromadditionalpopulationprocesses (egRoyleampKeacutery2007)could im-prove power to observe trends (althoughwith likely increased datademands)Modelsthatcorrectlyspecifyhabitatrelationshipswithoc-cupancycouldalsohelpGiventhepotentiallycounteractingfeaturesofsimulationsweexpectpowerestimatesweresufficientlyinforma-tivetocomparealternativestudydesigns

Simulations ignoredspatialvariationinhomerangesizewhichcan confound interpretation of occupancy estimates and trendsdrawnfromrepeatsurveys(EffordampDawson2012)Simulationsin-cludingsuchrealitiescouldfurtherinformrepeat-surveymonitoringAlternativelysingle-surveymonitoringwouldavoidthis issueandcouldbecomplementedwithfocusedstudyofspaceusedynamics

Ourtreatmentofsurveycostdidnotfullyaccountfortraveltimeamong transectsWe expect little difference in cost of repeating asurvey versus surveying a new transect but travel time could limittransectnumbermore than lengthTo fully informstudydesignbi-ologistswouldneed toattachcosts to scenariosexploredhereForwhite-headedwoodpeckersclusteringtransectswithsufficientspac-ingforstatistical independence(eg2ndash5kmassuminghomerangesle1kmradius)couldreducetraveltimealthoughpotentiallyraisingtheneedtoaccountforspatialheterogeneityatcoarserscales(egamongsub-regions)

F IGURE 9emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-poccupancymodelunderalternativesamplingallocationstrategies Error is calculated relative to theactualabundancetrendλN=098(RMSE=RMSEN)Strategiesdepictedinvolvemonitoringrotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransectsParentheticvaluesindicatethetotalnumberoftransectsmonitoredoverthe20-yearstudyperiod

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

12emsp |emsp emspensp LATIF eT AL

F IGURE 10emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)forthesingle-surveylogisticregressionunderalternativesamplingallocationstrategiesErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Strategiesdepictedinvolvemonitoringarotatingsubsetsoftransectseachyear(barcolor)orfewerpointspertransect(x-axis)inexchangeformonitoringmoretransects Parenthetic values indicate the totalnumberoftransectsmonitoredoverthe20-yearstudyperiod

F IGURE 11emspStatisticalpower(percentsimulationswith95BCIlt1)andtrendestimationerror(RMSE)fortherepeat-surveyconstant-pmodelforscenariosthatvarytheproportionoftransectssurveyedasecondtimeeachyearinexchangeformonitoringmoretransectsErroriscalculatedrelativetotheactualabundancetrendλN=098(RMSE=RMSEN) Parenthetic values indicate the total numberoftransectsmonitoredoverthe20-yearstudyperiod

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

emspensp emsp | emsp13LATIF eT AL

44emsp|emspAdditional considerations and broader implications

Agencybiologistsoftenconduct repeatsurveys toestimatedetect-abilityandtherebyimprovecredibilityoftrendestimatesThisstrat-egy potentially implies an overly rigid allocation of effort betweensamplingtoinformoccupancyversusdetectabilityRepeatsurveysofmobilespeciesmayunwittinglyfocusefforttowardtrackingdistribu-tionalshiftswhichcanbehardertoobserveandnotnecessarilymorerelevant to conservation than changes in abundance Additionallypractitionersoftendiscountthepotentialfordetectabilitytochangewithchangingabundance(egAhumadaHurtadoampLizcano2013vanStrienvanSwaayampTermaat2013Zielinskietal2013)whichmaylimitexplicitinferenceofabundancetrendsversusrangedynam-icsfromoccupancy-basedtrendestimatesEstimatingdetectabilityisonlyuseful ifdoingso improves inferenceofunderlyingpopulationprocesses or accounts for interannual variability in observer errorTheformerrequiresconsideringwhichprocessescanbemorereadilyinferred by accounting for detectability at the scale it ismeasuredIf instead biologists are solely concernedwith controlling observererrormonitoring of population indicesmay bemore cost-effectivewhileprovidingequivalentorstrongerinferenceofpopulationchange(Hutto2016Johnson2008Welshetal2013)

Despite growing sophistication of occupancy models (BaileyMacKenzieampNichols2014)heterogeneityarisingfromlocallyvary-ingabundanceandpoorlydefinedhomerangeboundaries(EffordampDawson 2012)will continue to challengemonitoring efforts espe-ciallywhere fundingconstrainsdataandconsequentlymodelcom-plexitySimulationscanhelpexploreourcapacityfor inferencewithmodels necessarilymisspecifieddue to limiteddataGeneral powerformulasavailableforoccupancymodelsignorespatialheterogeneity(Guillera-ArroitaampLahoz-Monfort2012MacKenzieampRoyle2005)Spatiallyexplicitsimulationsthereforecomplementthesetoolsfortai-loringsamplingdesignstoparticularstudysystems

Information on regional trends should be combined with in-formation on various population parameters measured at differ-ent scales to fully inform species conservation status (Nichols ampWilliams 2006) For example other studies currently underwayexamine forestmanagement effects onwhite-headedwoodpeckernestdensitiesnestsurvivalandhabitatuse(Mellen-McLeanetal2015)Statisticalmodelscannowintegratemultiplesourcesofdatatobetterinformparameterestimation(Dorazio2014Nicholsetal2008)Simulationsthatexplicitlyanddistinctlydescribepopulationfromobservationprocessescouldinformsamplingdesigntosupporttheseapproaches

ACKNOWLEDGMENTS

Region6oftheUSForestServiceprimarilyfundedtheinitialregionalmonitoring effort including this study Rocky Mountain ResearchStation andMontana State University also supported this work JDudleyhelpedwithsomedatamanagementWethank fieldcrewsspecifically crew leaders E Johnson S Mellmann-Brown and A

WoodrowWethankBBirdJTuckerCAmundsonJHinesandtwoanonymousreviewersforfeedbackoninitialdraftsTKogutpro-videdtheFigure1photo

CONFLICT OF INTEREST

Nonedeclared

AUTHOR CONTRIBUTIONS

QLatif implementedsimulationsanddataanalysisanddraftedthemanuscriptMEllisVSaabandKMellen-McLeanprovidedsubstan-tivefeedbackduringconceptualframingsimulationdesignandimple-mentationandmanuscriptpreparation

DATA ACCESSIBILITY

R scripts for initiating simulations using the rSPACE package andBUGS code defining data analysismodels are provided online sup-portinginformation

ORCID

Quresh S Latif httporcidorg0000-0003-2925-5042

REFERENCES

AhumadaJAHurtadoJamp LizcanoD (2013)Monitoring the statusand trendsof tropical forest terrestrialvertebrate communities fromcameratrapdataAtoolforconservationPLoS One8e73707httpsdoiorg101371journalpone0073707

AmundsonCLRoyleJAampHandelCM(2014)AhierarchicalmodelcombiningdistancesamplingandtimeremovaltoestimatedetectionprobabilityduringavianpointcountsAuk131476ndash494httpsdoiorg101642AUK-14-111

BaileyLLHinesJENicholsJDampMacKenzieDI(2007)Samplingdesign trade-offs in occupancy studies with imperfect detectionExamplesandsoftwareEcological Applications17281ndash290httpsdoiorg1018901051-0761(2007)017[0281SDTIOS]20CO2

Bailey L LMacKenzieD IampNicholsJD (2014)Advancesandap-plications of occupancymodelsMethods in Ecology and Evolution51269ndash1279httpsdoiorg1011112041-210X12100

ClareJDJAndersonEMampMacFarlandDM(2015)Predictingbob-catabundanceatalandscapescaleandevaluatingoccupancyasaden-sityindexincentralWisconsinThe Journal of Wildlife Management79469ndash480httpsdoiorg101002jwmg844

Cruickshank S S Ozgul A Zumbach S amp Schmidt B R (2016)Quantifying population declines based on presence-only records forred-listassessmentsConservation Biology301112ndash1121httpsdoiorg101111cobi12688

Dorazio R M (2014) Accounting for imperfect detection and surveybias in statistical analysis of presence-only dataGlobal Ecology and Biogeography231472ndash1484httpsdoiorg101111geb12216

EffordMGampDawsonDK (2012)OccupancyincontinuoushabitatEcosphere31ndash15article32

EllisMM IvanJSampSchwartzMK (2014)Spatiallyexplicitpoweranalyses for occupancy-based monitoring of wolverine in the USRocky Mountains Conservation Biology 28 52ndash62 httpsdoiorg101111cobi12139

14emsp |emsp emspensp LATIF eT AL

EllisMMIvanJSTuckerJMampSchwartzMK(2015)rSPACESpatiallybasedpoweranalysisforconservationandecologyMethods in Ecology and Evolution6621ndash625httpsdoiorg1011112041-210X12369

GarrettKLRaphaelMGampDixonRD(1996)White-headed wood-pecker (Picoides albolarvatus) Birds of North America Cornell Lab ofOrnithologyIssue252

GotelliNJ(2001)A primer of ecologySunderlandMASinauerAssociatesInc

Guillera-ArroitaGampLahoz-MonfortJJ(2012)Designingstudiestode-tectdifferencesinspeciesoccupancyPoweranalysisunderimperfectdetection Methods in Ecology and Evolution3 860ndash869 httpsdoiorg101111j2041-210X201200225x

HessburgPFAgeeJKampFranklinJF(2005)Dryforestsandwildlandfiresofthe inlandNorthwestUSAContrasting landscapeecologyofthepre-settlementandmodernerasForest Ecology and Management211117ndash139httpsdoiorg101016jforeco200502016

HollenbeckJ P SaabVAampFrenzelRW (2011)Habitat suitabilityandnestsurvivalofWhite-headedWoodpeckersinunburnedforestsofOregonJournal of Wildlife Management751061ndash1071httpsdoiorg101002jwmg146

HuttoRL(2016)Shouldscientistsberequiredtouseamodel-basedsolu-tiontoadjustforpossibledistance-baseddetectabilitybiasEcological Applications261287ndash1294httpsdoiorg101002eap1385

HuttoRLampBeloteRT(2013)DistinguishingfourtypesofmonitoringbasedonthequestionstheyaddressForest Ecology and Management289183ndash189httpsdoiorg101016jforeco201210005

Johnson D H (2008) In defense of indices The case of bird surveysJournal of Wildlife Management72857ndash868

Joseph L N Field S A Wilcox C amp Possingham H P (2006)Presence-absence versus abundance data for monitoring threat-ened species Conservation Biology 20 1679ndash1687 httpsdoiorg101111j1523-1739200600529x

LatifQ S EllisMMampAmundsonC L (2016)Abroader definitionofoccupancyCommentonHayesandMonfilsThe Journal of Wildlife Management80192ndash194httpsdoiorg101002jwmg1022

LatifQSFlemingKDBarrowsCampRotenberryJT(2012)ModelingseasonaldetectionpatternsforburrowingowlsurveysWildlife Society Bulletin36155ndash160httpsdoiorg101002wsb97

LatifQSSaabVAMellen-McleanKampDudleyJG(2015)Evaluatinghabitat suitability models for nestingwhite-headedwoodpeckers inunburned forest The Journal of Wildlife Management 79 263ndash273httpsdoiorg101002jwmg842

LeleSRMorenoMampBayneE(2012)DealingwithdetectionerrorinsiteoccupancysurveysWhatcanwedowithasinglesurveyJournal of Plant Ecology522ndash31httpsdoiorg101093jpertr042

LindenDWFullerAKRoyleJAampHareMP(2017)Examiningtheoccupancy-densityrelationshipforalowdensitycarnivoreJournal of Applied Ecology542043ndash2052

MacKenzieDINicholsJDLachmanGBDroegeSRoyleJAampLangtimmCA(2002)Estimatingsiteoccupancyrateswhendetec-tionprobabilitiesare less thanoneEcology832248ndash2255httpsdoiorg1018900012-9658(2002)083[2248ESORWD]20CO2

MacKenzieD INicholsJDRoyleJAPollockKHBaily L LampHinesJE(2006)Occupancy estimation and modelingSydneyNSWElsevierInc

MacKenzie D I amp Royle J A (2005) Designing occupancy studiesGeneraladviceandallocatingsurveyeffortJournal of Applied Ecology421105ndash1114httpsdoiorg101111j1365-2664200501098x

MaleTDBeanMJampSchwartzM(2005)MeasuringprogressinUSendangeredspeciesconservationEcology Letters8986ndash992httpsdoiorg101111j1461-0248200500806x

MarshDMampTrenhamPC(2008)CurrenttrendsinplantandanimalpopulationmonitoringConservation Biology22647ndash655httpsdoiorg101111j1523-1739200800927x

Mellen-McLean K Saab V Bresson B Wales A amp VanNorman K(2015) White-headed woodpecker monitoring strategy and protocols for the Pacific Northwest Region (34 pp) v13 PortlandORUS ForestServicePacificNorthwestRegion

Nichols J D Bailey L L OrsquoConnellA F Jr Talancy NW CampbellGrant E H Gilbert A T hellip Hines J E (2008) Multi-scale occu-pancy estimation and modelling using multiple detection meth-ods Journal of Applied Ecology 45 1321ndash1329 httpsdoiorg101111j1365-2664200801509x

Nichols J D amp Williams B K (2006) Monitoring for conservationTrends in Ecology amp Evolution21668ndash673httpsdoiorg101016jtree200608007

Noon B R Bailey L L SiskTD ampMcKelvey K S (2012) Efficientspecies-levelmonitoringatthe landscapescaleConservation Biology26432ndash441httpsdoiorg101111j1523-1739201201855x

PavlackyDCBlakesleyJAWhiteGCHanniDJampLukacsPM(2012)Hierarchicalmulti-scaleoccupancyestimation formonitoringwildlifepopulationsThe Journal of Wildlife Management76154ndash162httpsdoiorg101002jwmg245

RCoreTeam(2015)R A language and environment for statistical comput-ingViennaAustriaRFoundationforStatisticalComputingRetrievedfromhttpswwwR-projectorg

ReynoldsRTWiensJDJoySMampSalafskySR(2005)Samplingconsiderations fordemographicandhabitat studiesofnortherngos-hawksJournal of Raptor Research39274

Rhodes J R amp Jonzeacuten N (2011) Monitoring temporal trends in spa-tiallystructuredpopulationsHowshouldsamplingeffortbeallocatedbetween space and time Ecography 34 1040ndash1048 httpsdoiorg101111j1600-0587201106370x

RobertsDLTaylorLampJoppaLN(2016)ThreatenedordatadeficientAssessing theconservationstatusofpoorlyknownspeciesDiversity and Distributions22558ndash565httpsdoiorg101111ddi12418

RodriguesASLPilgrimJDLamoreuxJFHoffmannMampBrooksT M (2006) The value of the IUCN Red List for conservationTrends in Ecology amp Evolution 21 71ndash76 httpsdoiorg101016jtree200510010

RotaCTFletcherRJJrDorazioRMampBettsMG(2009)OccupancyestimationandtheclosureassumptionJournal of Applied Ecology461173ndash1181

Royle J A amp Keacutery M (2007) A Bayesian state-space formulation ofdynamic occupancy models Ecology 88 1813ndash1823 httpsdoiorg10189006-06691

RoyleJAampNicholsJD(2003)Estimatingabundancefromrepeatedpresence-absencedataorpointcountsEcology84777ndash790httpsdoiorg1018900012-9658(2003)084[0777EAFRPA]20CO2

Sauer J R Fallon J E amp Johnson R (2003) Use of NorthAmericanBreedingBirdSurveydatatoestimatepopulationchangeforbirdcon-servation regions The Journal of Wildlife Management 67 372ndash389httpsdoiorg1023073802778

SteenwegRWhittingtonJHebblewhiteMForshnerAJohnstonBPetersenDhellipLukacsPM(2016)Camera-basedoccupancymoni-toringatlargescalesPowertodetecttrendsingrizzlybearsacrosstheCanadianRockiesBiological Conservation201 192ndash200httpsdoiorg101016jbiocon201606020

vanStrienAJvanSwaayCAMampTermaatT(2013)Opportunisticcitizensciencedataofanimalspeciesproducereliableestimatesofdis-tributiontrendsifanalysedwithoccupancymodelsJournal of Applied Ecology501450ndash1458httpsdoiorg1011111365-266412158

TyreAJTenhumbergBFieldSANiejalkeDParrisKampPossinghamHP (2003) Improvingprecisionand reducingbias inbiological sur-veysEstimatingfalse-negativeerrorratesEcological Applications131790ndash1801httpsdoiorg10189002-5078

Urquhart N S amp Kincaid T M (1999) Designs for detecting trendfromrepeatedsurveysofecological resourcesJournal of Agricultural

emspensp emsp | emsp15LATIF eT AL

Biological and Environmental Statistics 4 404ndash414 httpsdoiorg1023071400498

ValenteJJHutchinsonRAampBettsMG(2017)Distinguishingdistri-butiondynamicsfromtemporaryemigrationusingdynamicoccupancymodelsMethods in Ecology and Evolution81707ndash1716

WarrenCCVeechJAWeckerlyFWOrsquoDonnellLampOttJR(2013)Detectionheterogeneityandabundanceestimationinpopulationsofgolden-cheekedwarblers(Setophaga chrysoparia) The Auk130677ndash688httpsdoiorg101525auk201313022

Welsh A H Lindenmayer D B amp Donnelly C F (2013) Fitting andinterpreting occupancy models PLoS One 8 e52015 httpsdoiorg101371journalpone0052015

WightmanCSSaabVAForristalCMellen-McLeanKampMarkusA (2010) White-headed Woodpecker nesting ecology after wild-fire Journal of Wildlife Management 74 1098ndash1106 httpsdoiorg1021932009-174

WisdomMJHolthausenRSWalesBCHargisCDSaabVALeeDChellipEamesMR(2002)Source habitats for terrestrial vertebrates of focus in the interior Columbia basin Broadscale trends and manage-ment implicationsmdashVolume 1 overviewGenTechRepPNW-GTR-485PortlandORUSDepartmentofAgricultureForestServicePacific

Northwest Research Station 3 vol (Quigley ThomasM tech edInterior Columbia Basin Ecosystem Management Project scientificassessment)

ZielinskiW J Baldwin JATruex R LTucker JMamp Flebbe PA(2013) Estimating trend in occupancy for the southern Sierra fisherMartes pennantipopulationJournal of Fish and Wildlife Management43ndash19httpsdoiorg103996012012-JFWM-002

SUPPORTING INFORMATION

Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle

How to cite this articleLatifQSEllisMMSaabVAMellen-McLeanKSimulationsinformdesignofregionaloccupancy-basedmonitoringforasparselydistributedterritorialspeciesEcol Evol 2017001ndash15 httpsdoiorg101002ece33725