distance models as a tool for modelling detection

J Appl Entomol 2019143225ndash235 wileyonlinelibrarycomjournaljen emsp|emsp225copy 2018 Blackwell Verlag GmbH

Received3April2018emsp |emsp Revised13September2018emsp |emsp Accepted17October2018DOI101111jen12583

O R I G I N A L C O N T R I B U T I O N

Distance models as a tool for modelling detection probability and density of native bumblebees

Darin J McNeil12 emsp|emspClint R V Otto3 emsp|emspErin L Moser4emsp|emspKatherine R Urban‐Mead5emsp|emsp David E King6emsp|emspAmanda D Rodewald12 emsp|emspJeffery L Larkin4

1DepartmentofNaturalResourcesCornellUniversityIthacaNewYork2CornellLaboratoryofOrnithologyIthacaNewYork3USGeologicalSurveyNorthernPrairieWildlifeResearchCenterJamestownNewYork4DepartmentofBiologyIndianaUniversityofPennsylvaniaIndianaPennsylvania5DepartmentofEntomologyCornellUniversityIthacaNewYork6DepartmentofEnvironmentalConservationUniversityofMassachusettsAmherstMassachusetts

CorrespondenceDarinJMcNeilDepartmentofNaturalResourcesCornellUniversityIthacaNYEmaildjm462cornelledu

Funding informationUSDA‐NaturalResourceConservationServiceGrantAwardNumber68‐7482‐12‐502IndianaUniversityUnitedStatesDepartmentofAgricultureGrantAwardNumber68‐7482‐12‐502NaturalResourcesConservationService

AbstractEffectivemonitoringofnativebeepopulationsrequiresaccurateestimatesofpopu‐lationsizeandrelativeabundanceamonghabitatsCurrentbeesurveymethodssuchasnettingorpantrappingmaybeadequateforavarietyofstudyobjectivesbutarelimitedbyafailuretoaccountforimperfectdetectionBiasesduetoimperfectde‐tectioncouldresultininaccurateabundanceestimatesorerroneousinsightsabouttheresponseofbeestodifferentenvironmentsTogaugethepotentialbiasesofcur‐rentlyemployedsurveymethodswecomparedabundanceestimatesofbumblebees(Bombus spp)derivedfromhierarchicaldistancesamplingmodels(HDS)tobumble‐beecountscollectedfromfixed‐areanetsurveys(ldquonetcountsrdquo)andfixed‐widthtran‐sectcounts(ldquotransectcountsrdquo)at47early‐successionalforestpatchesinPennsylvaniaOurHDSmodelsindicatedthatdetectionprobabilitiesofBombussppwereimper‐fectandvariedwithsurvey‐andsite‐covariatesDespitebeingconspicuousBombus sppwerenotreliablydetectedbeyond5mHabitatassociationsofBombussppden‐sityweresimilaracrossmethodsbutthestrengthofassociationwithshrubcoverdifferedbetweenHDSandnetcountsAdditionallynetcountssuggestedsiteswithmoregrasshostedhigherBombussppdensitieswhereasHDSsuggestedthatgrasscoverwasassociatedwithhigherdetectionprobabilitybutnotBombussppdensityDensityestimatesgeneratedfromnetcountsandtransectcountswere80ndash89lowerthanestimatesgeneratedfromdistancesamplingOurfindingssuggestthatdistancemodelling provides a reliablemethod to assessBombus spp density andhabitat associationswhile accounting for imperfectdetection causedbydistancefrom observer vegetation structure and survey covariates However detectionnon‐detectiondatacollectedviapoint‐countsline‐transectsanddistancesamplingforBombussppareunlikelytoyieldspecies‐specificdensityestimatesunlessindi‐vidualscanbeidentifiedbysightwithoutcaptureOurresultswillbeusefulforin‐formingthedesignofmonitoringprogramsforBombus spp andotherpollinators

K E Y W O R D S

Bombusdetectionprobabilitydistancemodellingpollinatorssurveystransects

226emsp |emsp emspensp McNEIL Et aL

1emsp |emspINTRODUC TION

Native bees in North America are important pollinators of bothcropsandwildplants (Ashmanetal2004Garibaldiet al2013KremenWilliamsampThorp2002) Indeedbees alongwithotherpollinators are considered keystone species that facilitate sexualreproductionfor85ofangiospermsworldwide (Allen‐Wardelletal1998Kevan1990)InagriculturalportionsoftheUnitedStatespollinationservicesprovidedbynativebeesarevaluedat$3billionUSD annually (Calderone 2012) Even as the ecological and eco‐nomic importance of native bees is recognized there is amount‐ingevidence thatmanybee species aredeclining (Cameronet al2011GoulsonLyeampDarvill2008)ThesedeclinesincludenotonlymanagedspecieslikeApis melliferabutalsoNorthAmericannativetaxalikebumblebees(Bombusspp)andothers(Cameronetal2011GoulsonNichollsBotiacuteasampRotheray2015Pottsetal2010)Forexampletherustypatchedbumblebee(Bombus affinis)waslistedasFederally Endangeredunder theEndangeredSpeciesAct in 2017and several otherBombus species have been proposed for listing(JepsenEvansThorpHatfieldampBlack2013)Althoughthedriversresponsibleforpopulationdeclinesvaryamongspeciesthreatsin‐cludepesticidesnon‐nativepathogensandhabitatlossdegradation(Goulsonetal2015PerssonRundloumlfCloughampSmith2015)

Still while evidence is fairly clear regarding bee declines forsomeregionsandorspeciesthestatusofmanybeepopulationsre‐mainsunknown(TepedinoDurhamCameronampGoodell2015)In2015theUnitedStatesPollinatorHealthTaskForceproposedthedevelopmentofnationalpollinatormonitoringprogramstoestimatepopulation trends and identify environmental stressors affectingnative bees (VilsackampMcCarthy 2015) Central to accomplishingthesegoalsistheaccurateestimationofbeepopulationsizesacrossspeciesgeneramorphospeciesandfunctionalgroupstoestablishareferencebenchmark forevaluatingpopulation trends abundanceacrossdifferenthabitatsandassessingtheoutcomesofconserva‐tioninterventions

Althoughavarietyofmethodshavebeencommonlyusedtosam‐plewildbeepopulations (eg fixed‐areaaerialnettingbeebowlsvanetraps)each is limitedby inherentmethodologicalbiasesthatmakeinferenceoftruedensitiesdifficultInparticularfewmethodsaccountforthebiascausedbyimperfectdetection(egLofflandetal2017)inthatonlybeescapturedorotherwisedetectedbyanob‐serverarecountedandsubsequentlymodelledRegardlessofsam‐plingmethodonlyafractionoftheindividualspresentatalocationwillbedetected(KeacuteryampSchmidt2008)Rawcountswhichfailtoaccountfordetectionprobabilitywillinvariablygenerateestimatesofabundancethatarebiasedlowifsomeindividualsarepresentbutnotdetected(KeacuteryampSchmidt2008MacKenzieetal20022005)Thoughsuchmethodshavemeritundermanycircumstancesac‐curateestimateofabundanceorchangesinabundanceoverspaceandtimerequiresconsiderationofmethodologicalbiaseslikethosecaused by imperfect detection (MacKenzie et al 2005) In addi‐tionfailuretoaccountforimperfectdetectioncanobfuscatehab‐itat associations particularlywhen thehabitat conditions that are

attractivetotheorganismalsomakeitmoredifficultforobserverstodetecttheorganism(MacKenzie2006)Consequentlyresearch‐ersmightbeledtobelievethatcertainhabitatconditions(associatedwithlowbeecounts)arelow‐qualityhabitatswhilebeesmayinreal‐itybeofequalgreaterabundancebutlessdetectableorviceversa(MacKenzie2006)

Herewedemonstrate theutilityofhierarchical distance sam‐pling (HDS) forestimatinghabitat‐specificdensity (ie abundanceper unit area) anddetection probability of bumblebees in decidu‐ous forest of central PennsylvaniaHierarchical distance samplingisananalyticaltechniquethatallowsresearcherstomodelhabitat‐specificabundanceandheterogeneityinspeciesdetectionwithinaunifiedframework(HedleyampBuckland2004KeacuteryampRoyle2015Royle Dawson amp Bates 2004) It builds upon standard distancesampling which is a widely used method for estimating animalabundance while for accounting imperfect detection (BucklandAnderson Burnham amp Laake 2005) However HDS differs fromstandarddistancesamplinginthatitallowsforspatialvariabilityinabundanceanddetectionacrossmultiplesitestobeexplainedasafunctionofcovariates(KeacuteryampRoyle2015)Althoughothermethodsexistforestimatingabundancewhileaccountingfordetection(egoccupancyN‐mixture etc)most requiremultiple visits with theassumptionofpopulationclosurebetweensurveys (KeacuteryampRoyle2015MacKenzieetal2005)Distancesamplingmaybeparticu‐larlyuseful for insectstudiesbecause it requiresonlyasinglesitevisittoestimatedetectionprobabilityandmanyshort‐livedinsects(likesomebeespecies)maynotemergelongenoughtoallowmul‐tiplevisitsper siteDistance samplinghasbeen routinelyusedbywildlife researchers to model abundance and detection functionsfor multiple vertebrate taxa (Hammond et al 2002 Karanth ampSunquist1995MarquesThomasFancyampBuckland2007)Toourknowledgenopreviousresearchhasdemonstratedtheuseofdis‐tancesampling toestimatebeeabundanceorhabitatassociations(BendelHovickLimbampHarmon2018)Ourgoalswereto(a)useHDStoevaluatehowBombussppdetectionprobabilityvarieswithdistancesurveytechniqueandhabitatattributes(b)compareabun‐danceanddensityestimatesgeneratedfromHDStostandardsam‐plingapproaches(fixed‐widthtransectsandfixed‐radiusnetcounts)thatdonotaccountforimperfectdetectionand(c)identifysite‐spe‐cifichabitatrelationshipsforBombussppacrosssamplingmethods

2emsp |emspMATERIAL S AND METHODS

21emsp|emspStudy area

WesurveyedbeeswithinthePennsylvaniaWildsregionofnorth‐central Pennsylvania focusing on Centre and Clinton Counties(Figure 1) This region lies within the Appalachian Plateau of thenorthcentralAppalachianMountainsandischaracterizedbyarug‐ged series of high‐elevation ridges (300ndash600masl) punctuatedbylowvalleysalongtheAlleghenyFront(Shultz1999)Vegetationcommunities within the Pennsylvania Wilds are chiefly mature

emspensp emsp | emsp227McNEIL Et aL

deciduous‐ormixedforest (80ndash100yearspost‐harvestMcCaskilletal2009)withoak(Quercus spp)hickory(Caryaspp)andeast‐ern hemlock (Tsuga canadensis) among the most common species(WherryFoggampWahl1979)Weconcentratedoureffortswithindeciduous forests of Sproul andMoshannon State Forestswhereoak silviculture aims to restore young forest age classes throughtimber harvest and regeneration Because silvicultural practiceswithinthesetwoStateForestsaimtorestorehabitatforforestwild‐lifewefocusedoursurveyeffortswithinregeneratingoakstands0ndash9yearspost‐managementDuringsurveysavarietyoffloweringplantswereavailabletoBombussppincludinglow‐growingshrubslike hillside blueberry (Vaccinium pallidum) as well as herbaceousforbs like eastern teaberry (Gaultheria procumbens) and commoncow‐wheat(Mellampyrum linerare)MosttallwoodyplantswerenotfloweringexceptforDevilrsquoswalkingstick (Aralia spinosa)whichwedetectedonlywithinafewofoursites

22emsp|emspSite selection and survey placement

We randomly selected 47 timber stands within Sproul andMoshannon State Forests that had been recently treated withoverstory removal (basal area 23ndash92 m2ha) We attemptedto maximize the distance between sites such that our averagedistance‐to‐nearest‐site was 1110m (SE 107m range 464ndash4516m)Thisreducedthelikelihoodofindividualsbeingdetectedatmultiplesites(Redheadetal2016)Timberharvestunitsaver‐aged2314ha(SD1862harange254ndash10392ha)insizeAsin‐glesurveypointwaslocatedwithineachharvestusingarandompoint generator tool inArcGIS102 (ESRI 2011)Weattemptedtominimizeedgeeffectsbyensuringpointswererelativelycon‐sistent in their placementwith respect to timberharvest edgessamplingwas restricted to areas at least80m from theedgeoftimberharvestsandourfinalsampleofsiteswasameandistanceof11867m(SE624m)

23emsp|emspTransect surveys

Ateachpointwe sampledBombus sppusing three survey types(a) distance transects (b) transect counts and (c) aerial nettingcounts Both distance transects and fixed‐width transect countsoccurred simultaneously along 66m transects oriented north‐to‐south and centred at eachpoint locationAlong each transectobserverswalked forwardat a constant rate (~1mmin) such thattheobserverarrivedatthetransectendafter30minPriortosur‐veyseachobserver(n=2)wastrainedindistanceestimationusingdummytransectsalongwhichbeesrsquodistanceswerephysicallymeas‐uredaftereachattemptedestimateusingameasuring tapeOnceallobserverswereconsistentlyestimatingdistanceswithinplusmn025mfield surveyswere conductedwith a2m longmeasuring stick forconstantreferenceWhilewalkingalongeachsurveytransect theobserverrecordedBombussppdetectionssuchthatafinalcount()wasgeneratedforeachsurveycoupledwiththedistances(plusmn025m)betweeneachBombus sppandthetransectWedidnotattempttoidentify speciesor sex forBombus spp detected in situ thereforecountswerelikelymultiplespeciesandsexesSurveydataforeachpointincludedaBombussppcountandtheircorrespondingdetec‐tion distancesWe discerned betweenBombus spp andXylocopa virginica byabdomenpubescence(MichenerMcGinleyampDanforth1994)DistanceswererecordedastheperpendiculardistancefromthetransecttoeachbeeandnotedasthedistanceatwhichthebeewasfirstdetectedWhilewalkingalongeachtransectobserversat‐temptedtokeeptrackofpreviouslydetectedBombusspptoavoiddouble‐counting individualsthatmightbemovingamongfloralre‐sources near the transectWe anecdotally observed this methodlargely avoided double‐counting as Bombus spp are generallylarge‐bodiedconspicuousinsectsandeasilyaudibleinflightAllrawcountsanddetectiondistancesconstitutedourldquodistancetransectrdquodata(a)andrawcountswithin2mofthetransectconstitutedourldquotransectcountrdquodata(b)

F I G U R E 1 emspSurveylocationswithinthePennsylvaniaWildswhereweconductedsurveysforBombussppwithinregeneratingtimberharvests


We followed standard bee survey methods to avoid commoncausesofdetection failure (Wardetal2014)Surveyswerecon‐ductedonlyinbrightlightconditionslowwindwarmdays(ge16degC)andonlyduringlatemorningandafternoon(1000ndash1700)ThoughweattemptedtousestudydesigntoreducethepotentialimpactsofthesefactorsonBombus sppdetectabilitywealso includedthemindetectionmodellingAtthetimeofeachsurveywerecorded(a)surveyorID(b)cloudcover(c)timeofdayand(d)BeaufortWindIndex Local temperature data were downloaded from WeatherUnderground from the KUNV weather station in State CollegePennsylvania (WeatherUnderground Inc2018)Cloudcoverwasestimatedinthefieldtothenearest25(0ndash100)BeaufortWindIndexwasmeasuredonanincrementalscalefrom0to5with0rep‐resentingnowind at all (ie smokewould theoretically risewith‐outdrift)and5representinghighwindssuchthatentiretreesswayinthewind(HauampVonRenouard2006)Weavoidedsurveyinginwindindicesgt3andthusconsideredtwocategoriesofwind0ndash1ldquolowrdquo2ndash3ldquomoderaterdquoinouranalysesAllsurveystookplacefrom10to25July2017

24emsp|emspNet counts

TomeasureBombussppabundancewithinfixed‐radiusnetcountswe created 15m radius count surveys centred around each pointlocation (thecentreofeachdistancetransect)Nettedbeecountstookplaceimmediatelyupontheconclusionoftransectsurveys(de‐scribedabove)Withineachfixed‐radiusplotasingleobserverspent30minseeking‐andattemptingtocaptureallBombussppdetectedwithahandnetWechosefixed‐radiusnetsamplingbecauseitisastandardsamplingtechniquefornativebees (Perssonetal2015PottsVulliamyDafniNersquoemanampWillmer2003RoulstonSmithampBrewster2007)andwouldthereforeserveasabasisforcomparisontoourabundanceestimatesgeneratedfromHDSForeachBombus sppdetectedtheobserverattemptedtocaptureeachbeeusingahandnet(collapsible15rdquodiameternet17rdquohandleBioquipProduct7115CP)andoncecapturedallbeeswereheldcaptiveforthere‐mainderofthesurveyForeachcapturedbeethetimerwasstoppedwhiletheobserverplaced it intoaplasticzipperbagandresumedimmediately thereafter Thismethod prevented us from recaptur‐inganddouble‐countingbeeswithinthesameplotAfter30minofsurvey timehadelapsedeachBombus sppwas removed from itsbagwith forceps photographed for anotherproject and releasedunharmedInthefewoccasionswhereBombussppwereobservedbutevadedcapturetheyweretreatedasallotherBombussppcap‐turedforthepurposesofthisstudy(ieincluded)

25emsp|emspHabitat surveys

Wesurveyedregeneratingvegetationstructurewithin timberhar‐vestunitsfrom15Juneto15July2017VegetationsurveyssharedtheircentroidwithBombussppsurveysVegetationdataquantifiedhabitatstructureofwoodystemsandherbaceousunderstoryratherthan plant composition All vegetation data were collected along

three50mradialtransectseachorientedat0deg120degand240degfrompoint centreAlong each transectwe recordedplant strata at 10ldquostopsrdquo(10mapartn=30netcountlocation)Vegetationstratare‐cordedateachstopconsistedofthepresenceabsenceofsaplingshrub forbandgrasssedgeSaplingswereyoungtreeslt10cm (indiameterbreastheight)Thissamplingregimegaveusadequateres‐olutiontoassessvegetationstructure(15stopssite)whileremain‐ingof comparable scale toourbee sampling transects (33m)Wefoundvegetationstructuretobehighlycorrelatedacrossscalesaslargeas100mandthereforebelieveour50mvegetationplotsrep‐resentedsiteconditionsreasonablywellShrubswerewoodyplantswithmultipleprimarystems(incontrasttosingle‐stemmedsaplings)Forbswerebroad‐leafeddicotyledonousplants(egSolidagospp)The plant category ldquograssrdquo included any monocotyledonous plant(grassessedgesetc)Werecordedplantstratawithanoculartubesuchthatonlystratathat intersectedwithcrosshairs intheoculartube were considered present (James amp Shugart 1970) While asinglestopcouldincludemultiplestratatypeseachstratumcouldonlyberepresentedonceperstopandthuseachsitecouldhaveamaximumofn=15occurrencesforeachstratumWeanalyzedplantstrata values as percentages Prior to all analyses we calculatedSpearmanrsquosrho(ρ)forallpairsofcovariatestobemodelledBecausenonewerestronglycorrelated(Spearmanrsquosρ lt 060)nocovariateswereredundantandallweresuitableformodelling

26emsp|emspHierarchical distance models

Weanalyzeddistancetransectdata(beecountsanddistances)usingHDS models implemented in the R package ldquounmarkedrdquo (Fiske ampChandler2011RCoreampTeam2018)Thepackageunmarkedfitslinearmodelsinamaximumlikelihoodframeworkandcanbecom‐bined with an Information‐Theoretic approach (Anderson 2007)forthepurposeofmodelselection(egusingAkaikersquosInformationCriterionAICBurnhamampAnderson2002)Hierarchicaldistancemodels allowed us to create and rank candidate models each ofwhich contained independent model components for detectionprobability (p) and expected animal abundance (density λ) HDSmodelsassume(a)subjectsareaccuratelyidentified(egnofalse‐presences)(b)thatallsubjectsonthetransect(distance=0m)aredetectedperfectly(p=10)(c)subjectsaredetectedattheiroriginallocation(iemovement isnot influencedbytheobserver) (d)dis‐tancesareaccuratelymeasuredand(e)detectionofeachindividualis independentofthedetectionofallotherindividuals(Thomasetal2010)Bumblebeesappeartoconstitutegoodcandidatesfordis‐tancesamplingastheycanbeeasilyidentified(togenus)inthefield(Micheneretal1994)areeasilyapproachedbyobservers(Wardetal2014)andremainrelativelystillduringpollinationsuchthataccu‐ratedistanceestimationscouldbemadeforeachworkerAlthoughdistances were measured in the field directly we binned detec‐tions as recommended by Buckland et al (2005) 0ndash1 1ndash2 2ndash33ndash4and4ndash5mMoreovertopreparedistance‐basedtransectdatawe truncated the outer 10of our data such that analyseswereconductedusingonly the closest 90ofBombus spp detections


asrecommendedfordistanceanalysesbyBucklandetal(2005)Bytruncating thedata in thiswayalldetectionswerelt5mfromtheobserver

Distance models provide robust estimates of abundance byadjusting animal counts by the probability of detection for givendistances (Buckland et al 2005) This is accomplished by fittingdetectiondistancedata to a ldquodetection functionrdquo that describes adecayindetectionprobabilityassubjectsarefurtherfromtheob‐server (Bucklandetal2005KeacuteryampRoyle2015)Toevaluateanappropriatedetectionfunctionweevaluatedmodelseachfitusingoneofthefollowingdetectionfunctions(a)exponential(b)hazardrateor(c)half‐normal(Bucklandetal2005)ThiswasdonepriortoallcovariatemodellingEachdetectionfunctionisusedtoestimatetheaverageprobabilityofdetectionwhichisthenusedtoadjustrawcountssuchthatdensitypredictionscanbemade(Bucklandetal2005)OncethemostappropriatedetectionfunctionwasselectedbasedonAICcrankitwasusedtomodeldetectionprobabilityanddensityinconsecutivemodelsWemodelleddetectionprobabilityintwotiersdetectiontier1(surveycovariatesondetection)andde‐tectiontier2(habitatcovariatesondetection)Becauseoursamplesizewasmodestweusedonlysingle‐covariatedetectionmodelstoavoidoverfittingHDSmodelsDetectiontier1includedunivariatemodels for (a) timeof day (b) surveyor (c) temperature (d) cloudcover(e)windindexand(f)anull(intercept‐only)modelDetectiontier 2 (fit independently of detection tier 1) included univariatemodelsfor(a)saplingcover(b)shrubcover(c)forbcover(d)grasscoverand(e)anullmodelWithinbothmodeltiersweusedaglobalhabitatmodel(iesapling+shrub+forb+grass)fordensitytoen‐sure thatvariation indensitywas reasonablywell explainedwhileassessingdetectionprobabilityWeconsideredcovariatestobein‐formativeiftheywerebothgt20AICclessthanthenullmodelandhadβcoefficient95confidenceintervalsthatdidnotincludezeroUsing the informative covariates fromdetection tiers1and2weconstructedasetofdensitymodels(habitatcovariatesondensity)thataccountedfor imperfectdetection (a)saplingcover (b)shrubcover (c) forbcover (d)grasscoverand (e)anullmodelThenullmodelcontainedonlyintercepttermsandtheinformativeparame‐tersfordetectionPriortomodellingallcontinuouscovariateswerestandardizedusingthescalefunctioninbaseRModelrankingwasdoneusing the ldquoaictabrdquo functionof thepackage ldquoAICcmodavgrdquoAllmodelswerefitassumingaPoissondistributioninldquogdistsamprdquoandmodelfitwasassessedbycalculatingavarianceinflationfactor(chatchatchatc)usingtheunmarkedfunctionldquofitstatsrdquo (KeacuteryampRoyle2015)Weconsideredallmodelslt20AICctobecompetingandequallysupportedbythedata(BurnhamampAnderson2002)

27emsp|emspPoisson generalized linear models

WeusedaPoissongeneralized linearmodels inR (using the ldquoglmrdquofunction)tomodelBombus sppabundancealongfixed‐radiustran‐sectsandnetcountsThisallowedustocomparehabitat‐abundancerelationshipsgeneratedfromHDSmodelstothosegeneratedfrommethodsthatdonotaccountfordetectionprobabilityAswithour

HDSmodels Poisson regressionmodels allowed us tomodel beecountsasafunctionofhabitatcovariates(a)saplingcover(b)shrubcover (c) forbcover (d)grasscover and (e) anull (intercept‐only)modelWemodelled our fixed‐radius transect counts by truncat‐ing allHDS‐transect databy2mof the transect line and treatingthedataasarawcount(HanleyAwbiampFranco2014Scheperetal 2015) which is a standard technique when conducting visualencounter surveys Net count data were modelled in a compara‐blemanner such that raw countsweremodelled as a function ofhabitat covariatesWedid not account for imperfect detection ineither of these models but rather modelled Bombus spp countarea interpretedasadensityWeagainusedan information‐theo‐reticapproach(Anderson2007)withmodelrankingbasedonAICc consideringmodelslt20AICctobeequallysupportedbythedata(BurnhamampAnderson2002)Wealsousedsingle‐covariatemodelstoavoidoverlycomplexmodelsandtheinclusionofuninformativeparameterswithintopmodels(Arnold2010)

3emsp |emspRESULTS

Wedetected194individualBombus sppwithin5mofwhich136werewithin2mof the transect lineDuringaerialnetcountswecapturedn = 201 BombussppworkersOfthebeescapturedduringaerial net countsover50wereB impatienswith the remainderbeingamixedcommunityoflesscommonspecieslikeB bimaculatus and B vagans

31emsp|emspDetection probability

Ofthreedetectionfunctionmodelsweranthebest‐rankedmodelincludedanexponentialdetectionfunctionwheredetectionprob‐abilitygt5mfromthetransectwasasymp0(Figure2)Usinganexponen‐tialdetection functionwe foundthatdetectionprobabilityvariedas a functionof time since1000 (theearliestpossible start time)

F I G U R E 2 emspFrequencyofdetections(greybarsrightaxis)forBombussppwithinregeneratingtimberharvestsDetectionprobability(leftaxis)declinedasafunctionofdistancefromtransectandwasfittoanexponentialdetectionfunction(blackline)Bombussppwereonlyrarelydetectedfurtherthan5mfromthetransectline


andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero

32emsp|emspHabitat modelling

Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter

95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)

33emsp|emspDensity estimation

Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp

Model name K AICc ΔAICc AICc Wt β estimate (95CI)

Surveycovariatesondetectionprobability

p(observer) 7 34893 000 078 058(021to095)

p(time) 7 35156 264 021 minus023(minus038tominus008)

p () 6 35829 936 001 ‐

p(wind) 7 35987 1094 000 minus016(minus044to013)

p(temp) 7 36064 1172 000 minus005(minus019to009)

Sitecovariatesondetectionprobability

p(grass) 7 35267 000 085 035(007to063)

p(forb) 7 35827 561 005 017(minus004to037)

p() 6 35829 562 005 ‐

p(shrub) 7 35965 699 003 minus013(minus035to009)

p (sapling) 7 36048 782 002 010(minus016to036)

NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)

TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)

F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)


forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)

4emsp |emspDISCUSSION

Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance

samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework

Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity


Hierarchicaldistancesampling

λ(sapling) 6 33769 000 098 minus030(minus045tominus014)

λ(shrub) 6 34583 813 002 021(005to037)

λ() 5 3502 1251 000 ndash

λ(grass) 6 35041 1271 000 minus017(minus038to005)

λ(forb) 6 35282 1513 000 minus001(minus016to014)

Transectcounts


λ(shrub) 2 28448 685 003 085(025to144)


λ() 1 29007 1244 000 ‐

λ(forb) 2 29216 1454 000 0133(minus074to101)

Netcounts


λ(grass) 2 38438 2367 000 085(003to167)

λ(shrub) 2 38565 2494 000 041(minus009to090)

λ() 1 38608 2537 000 ndash

λ(forb) 2 38709 2638 000 039(minus031to109)

NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)

TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution


DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade

Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees

ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod

F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)

F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts


SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems

Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity

Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling

Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals

mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)

Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly

ACKNOWLEDG EMENTS

Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions


of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment

AUTHORSrsquo CONTRIBUTIONS

DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript

ORCID

Darin J McNeil httporcidorg0000‐0003‐4595‐8354

Clint R V Otto httporcidorg0000‐0002‐7582‐3525

Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306

R E FE R E N C E S

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AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia

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BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9

BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030

BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd

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HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006

Hau E amp Von Renouard H (2006) The wind resource London UKElsevier

Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578

JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736

Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf

Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110

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KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress

KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210

Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)

Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599


LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280

MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2

MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2

MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier

Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17

Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2

McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation

MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress

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Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136

PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353

Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546

Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2

Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127

Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level

floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479

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SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518

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Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x

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VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce

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How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583


1emsp |emspINTRODUC TION

Native bees in North America are important pollinators of bothcropsandwildplants (Ashmanetal2004Garibaldiet al2013KremenWilliamsampThorp2002) Indeedbees alongwithotherpollinators are considered keystone species that facilitate sexualreproductionfor85ofangiospermsworldwide (Allen‐Wardelletal1998Kevan1990)InagriculturalportionsoftheUnitedStatespollinationservicesprovidedbynativebeesarevaluedat$3billionUSD annually (Calderone 2012) Even as the ecological and eco‐nomic importance of native bees is recognized there is amount‐ingevidence thatmanybee species aredeclining (Cameronet al2011GoulsonLyeampDarvill2008)ThesedeclinesincludenotonlymanagedspecieslikeApis melliferabutalsoNorthAmericannativetaxalikebumblebees(Bombusspp)andothers(Cameronetal2011GoulsonNichollsBotiacuteasampRotheray2015Pottsetal2010)Forexampletherustypatchedbumblebee(Bombus affinis)waslistedasFederally Endangeredunder theEndangeredSpeciesAct in 2017and several otherBombus species have been proposed for listing(JepsenEvansThorpHatfieldampBlack2013)Althoughthedriversresponsibleforpopulationdeclinesvaryamongspeciesthreatsin‐cludepesticidesnon‐nativepathogensandhabitatlossdegradation(Goulsonetal2015PerssonRundloumlfCloughampSmith2015)

Still while evidence is fairly clear regarding bee declines forsomeregionsandorspeciesthestatusofmanybeepopulationsre‐mainsunknown(TepedinoDurhamCameronampGoodell2015)In2015theUnitedStatesPollinatorHealthTaskForceproposedthedevelopmentofnationalpollinatormonitoringprogramstoestimatepopulation trends and identify environmental stressors affectingnative bees (VilsackampMcCarthy 2015) Central to accomplishingthesegoalsistheaccurateestimationofbeepopulationsizesacrossspeciesgeneramorphospeciesandfunctionalgroupstoestablishareferencebenchmark forevaluatingpopulation trends abundanceacrossdifferenthabitatsandassessingtheoutcomesofconserva‐tioninterventions

Althoughavarietyofmethodshavebeencommonlyusedtosam‐plewildbeepopulations (eg fixed‐areaaerialnettingbeebowlsvanetraps)each is limitedby inherentmethodologicalbiasesthatmakeinferenceoftruedensitiesdifficultInparticularfewmethodsaccountforthebiascausedbyimperfectdetection(egLofflandetal2017)inthatonlybeescapturedorotherwisedetectedbyanob‐serverarecountedandsubsequentlymodelledRegardlessofsam‐plingmethodonlyafractionoftheindividualspresentatalocationwillbedetected(KeacuteryampSchmidt2008)Rawcountswhichfailtoaccountfordetectionprobabilitywillinvariablygenerateestimatesofabundancethatarebiasedlowifsomeindividualsarepresentbutnotdetected(KeacuteryampSchmidt2008MacKenzieetal20022005)Thoughsuchmethodshavemeritundermanycircumstancesac‐curateestimateofabundanceorchangesinabundanceoverspaceandtimerequiresconsiderationofmethodologicalbiaseslikethosecaused by imperfect detection (MacKenzie et al 2005) In addi‐tionfailuretoaccountforimperfectdetectioncanobfuscatehab‐itat associations particularlywhen thehabitat conditions that are

attractivetotheorganismalsomakeitmoredifficultforobserverstodetecttheorganism(MacKenzie2006)Consequentlyresearch‐ersmightbeledtobelievethatcertainhabitatconditions(associatedwithlowbeecounts)arelow‐qualityhabitatswhilebeesmayinreal‐itybeofequalgreaterabundancebutlessdetectableorviceversa(MacKenzie2006)

Herewedemonstrate theutilityofhierarchical distance sam‐pling (HDS) forestimatinghabitat‐specificdensity (ie abundanceper unit area) anddetection probability of bumblebees in decidu‐ous forest of central PennsylvaniaHierarchical distance samplingisananalyticaltechniquethatallowsresearcherstomodelhabitat‐specificabundanceandheterogeneityinspeciesdetectionwithinaunifiedframework(HedleyampBuckland2004KeacuteryampRoyle2015Royle Dawson amp Bates 2004) It builds upon standard distancesampling which is a widely used method for estimating animalabundance while for accounting imperfect detection (BucklandAnderson Burnham amp Laake 2005) However HDS differs fromstandarddistancesamplinginthatitallowsforspatialvariabilityinabundanceanddetectionacrossmultiplesitestobeexplainedasafunctionofcovariates(KeacuteryampRoyle2015)Althoughothermethodsexistforestimatingabundancewhileaccountingfordetection(egoccupancyN‐mixture etc)most requiremultiple visits with theassumptionofpopulationclosurebetweensurveys (KeacuteryampRoyle2015MacKenzieetal2005)Distancesamplingmaybeparticu‐larlyuseful for insectstudiesbecause it requiresonlyasinglesitevisittoestimatedetectionprobabilityandmanyshort‐livedinsects(likesomebeespecies)maynotemergelongenoughtoallowmul‐tiplevisitsper siteDistance samplinghasbeen routinelyusedbywildlife researchers to model abundance and detection functionsfor multiple vertebrate taxa (Hammond et al 2002 Karanth ampSunquist1995MarquesThomasFancyampBuckland2007)Toourknowledgenopreviousresearchhasdemonstratedtheuseofdis‐tancesampling toestimatebeeabundanceorhabitatassociations(BendelHovickLimbampHarmon2018)Ourgoalswereto(a)useHDStoevaluatehowBombussppdetectionprobabilityvarieswithdistancesurveytechniqueandhabitatattributes(b)compareabun‐danceanddensityestimatesgeneratedfromHDStostandardsam‐plingapproaches(fixed‐widthtransectsandfixed‐radiusnetcounts)thatdonotaccountforimperfectdetectionand(c)identifysite‐spe‐cifichabitatrelationshipsforBombussppacrosssamplingmethods

2emsp |emspMATERIAL S AND METHODS

21emsp|emspStudy area

WesurveyedbeeswithinthePennsylvaniaWildsregionofnorth‐central Pennsylvania focusing on Centre and Clinton Counties(Figure 1) This region lies within the Appalachian Plateau of thenorthcentralAppalachianMountainsandischaracterizedbyarug‐ged series of high‐elevation ridges (300ndash600masl) punctuatedbylowvalleysalongtheAlleghenyFront(Shultz1999)Vegetationcommunities within the Pennsylvania Wilds are chiefly mature























3emsp |emspRESULTS














p(observer) 7 34893 000 078 058(021to095)


p () 6 35829 936 001 ‐




p(grass) 7 35267 000 085 035(007to063)

p(forb) 7 35827 561 005 017(minus004to037)

p() 6 35829 562 005 ‐















λ(shrub) 6 34583 813 002 021(005to037)

λ() 5 3502 1251 000 ndash



Transectcounts


λ(shrub) 2 28448 685 003 085(025to144)


λ() 1 29007 1244 000 ‐

λ(forb) 2 29216 1454 000 0133(minus074to101)

Netcounts


λ(grass) 2 38438 2367 000 085(003to167)

λ(shrub) 2 38565 2494 000 041(minus009to090)

λ() 1 38608 2537 000 ndash

λ(forb) 2 38709 2638 000 039(minus031to109)
















ACKNOWLEDG EMENTS






ORCID




R E FE R E N C E S























































































3emsp |emspRESULTS














p(observer) 7 34893 000 078 058(021to095)


p () 6 35829 936 001 ‐




p(grass) 7 35267 000 085 035(007to063)

p(forb) 7 35827 561 005 017(minus004to037)

p() 6 35829 562 005 ‐















λ(shrub) 6 34583 813 002 021(005to037)

λ() 5 3502 1251 000 ndash



Transectcounts


λ(shrub) 2 28448 685 003 085(025to144)


λ() 1 29007 1244 000 ‐

λ(forb) 2 29216 1454 000 0133(minus074to101)

Netcounts


λ(grass) 2 38438 2367 000 085(003to167)

λ(shrub) 2 38565 2494 000 041(minus009to090)

λ() 1 38608 2537 000 ndash

λ(forb) 2 38709 2638 000 039(minus031to109)
















ACKNOWLEDG EMENTS






ORCID




R E FE R E N C E S










































































p(observer) 7 34893 000 078 058(021to095)


p () 6 35829 936 001 ‐




p(grass) 7 35267 000 085 035(007to063)

p(forb) 7 35827 561 005 017(minus004to037)

p() 6 35829 562 005 ‐















λ(shrub) 6 34583 813 002 021(005to037)

λ() 5 3502 1251 000 ndash



Transectcounts


λ(shrub) 2 28448 685 003 085(025to144)


λ() 1 29007 1244 000 ‐

λ(forb) 2 29216 1454 000 0133(minus074to101)

Netcounts


λ(grass) 2 38438 2367 000 085(003to167)

λ(shrub) 2 38565 2494 000 041(minus009to090)

λ() 1 38608 2537 000 ndash

λ(forb) 2 38709 2638 000 039(minus031to109)
















ACKNOWLEDG EMENTS






ORCID




R E FE R E N C E S










































































λ(shrub) 6 34583 813 002 021(005to037)

λ() 5 3502 1251 000 ndash



Transectcounts


λ(shrub) 2 28448 685 003 085(025to144)


λ() 1 29007 1244 000 ‐

λ(forb) 2 29216 1454 000 0133(minus074to101)

Netcounts


λ(grass) 2 38438 2367 000 085(003to167)

λ(shrub) 2 38565 2494 000 041(minus009to090)

λ() 1 38608 2537 000 ndash

λ(forb) 2 38709 2638 000 039(minus031to109)
















ACKNOWLEDG EMENTS






ORCID




R E FE R E N C E S














































































ACKNOWLEDG EMENTS






ORCID




R E FE R E N C E S





































































ORCID




R E FE R E N C E S

































































distance models as a tool for modelling detection

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