o‘,“ - , h"‘.¢-X‘v‘ - W t? .. w : at}. $593.. ifiwsl" w — . . -. M. ., Mira-"T “ ‘ . “‘ d - st «$.12 m H . .. + . w- QLU‘L...‘ l... M3 3‘31 “:j‘fi""1;;."~ .. L . , ~. g: m. am»: ‘3‘: 1’ :2. >931" ‘ < ' J7" _. 3h ‘ "..~ . mu- «mu: < 1.x; ‘3’.“ ‘ u ..- 1» Eta-3‘1 ‘2”. :Vh‘hfiaa- "‘ m y. “aim. *fi‘éég" a» 4/ "A {F ‘I: s: s»? '7! '3'; in "a :73: ” :mfistarm mgf‘xfiw. La?" .4, a "(Y' ’Q L — a.“ 3mm ‘ .t-Visrur’fiil'} ‘ ‘i'xu H g. 7&3 ,. V . if: a 1 ‘1‘} WWI—vy- ' ww— < — fl We“. Mm . ‘ 1’9“?" . . _ ' ’ 4'4'fa'é'14‘, ~4 my. 'nL' m vwfivisflfi' ' (WW3 3»- . g :7”): WI- ti) 1. ft .-; xi. 1,13 m “i” .L”,..‘Jl‘: mzw-m’ l t . ~ Fri?” '3 1 ,. ‘ .finnp? _. . , _, 4 a . 1,4“. .— 'N‘J A.“ ‘(11 w t‘u" " a 4:} Y :3 M :- .w ...a) .4 . _—‘. .n . "I ‘ 2.1m; ‘ a ‘f (1.4:: . V: b... .33" 7- i.- ’3 ‘7': i L . f 4 vi b a: 5 3 . ,. «~i ~ - .-.«“ ...x\r.~a‘ "4),:le 'i’x- 1»,ch 3H3; UIN IVERSITY LIBRARIES“: IIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIII III 3 1293 005921 university This is to certify that the thesis entitled An Aerial Censusing Procedure for Elk In Michigan presented by Mark R. M. Often has been accepted towards fulfillment of the requirements for M.$. degree in Fisheries and Wildlife Major professor Date November 7. I989 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before one due. DATE DUE DATE DUE DATE DUE ‘ 5‘ i i I i .‘w b r. )’—i r: l .’ MIN " -" 30 ‘3 k . V" I ) 1‘, ‘ e ' I MSU Is An AMrmetIve Action/Equal Opportunity Institution iANiAERIAIICENSUSING'ERDCEDURE FORflELKIIN MICHIGAN MarkR.M. Otten A.THESIS Sunnittedto Michigan State University in partial fulfillment of the zequiranm'rts for the degree . IMASTERLOP SCIENCE Deportnnnt of Fisheries and Wildlife 1989 be4I$WS Am ANAERIALCENSJSDBMJREMEIKINMICHIGAN BY . Mark R. M. Otter: misprojectdevelopedanaerialoensusprooedme,usingstratified randmsanpling,fortheestimatimotthemmberofelkm§ W)inuiohigan. Sanplirgmitswexedelineatedinaelkdensity stratabaoedmvisiblegramdfeatm'es. Standandflight oonditiomand seard1pmoedtneswaredetinedardusedtodetemineoptimlallooatim oteanplingetfort. Sigtrtabilityofelkwasdeteminedthmaghuseof zadio-oollaredanimls. logistic regressim analysis iniioated that, of S visibility bias mtested,mlyomiferowerarflgm1peizesignificantly (P < 0.10) affected Mobility. Sinulated census data indicated that apredictimptooemro,hasedmlymomiferoover,omsistartly producedthebestresultmaruanoptiml-sightabilitymdelwas produced. Sampling unitsweureevaluated for variance. Landensity mitsmedtobesanpledmintensivelytlnn'nedimorhighdmsity mitstodeczeasevariarneamcmtiderceirrtmalestimtescmrim futueelksurveys. MsprojeotwassupportedbytheFederalAidinWildlife mumm under Pittman-Robertsm project W-127-R, and the MidtiganDepartnantotNamralReswroes. Imfldlflcetoexpressmydeepappreciationtour.JonathanB. Haufler for acting asmymajor professor, being availablewheneverhe wasneeded,£orkiddngmewhen1mededit,andforbeingafrieni. I maldlfloetotharflcDr.SoottR.Winterstejn,mtmlyforservingmmy gndmteoamittemhrtalsoforprovidinganenormmsmmtof assistanoewiththefiorvitz-tnunpsmvariameestimtes. 'Ihanksalsoto Dr.Donoldo.St:aneyforfirflingtimeinhismsysd1eduletoservem mygradnateommittee. Specialtharflcstolm"elkmmter"8ender,Jim"thidcmflerstoxy" Hirsdm,andGinaBallazdforalloftheirhelpinoollectingdata,ard mkingthefieldmrkinteresting,ifmteocitim. Iwmldalsolflcetoaolowledgealloftheothergradmtesuflerrts intheDepartmentot FisheriesardWildlife for eagerlysharingtheir expertise, hwledge, experience, andfrierxiship with me. Inparticular ItmldliketotharflchmHizsdz,IouBender,JmImrd,Paul Padding,RiqueCupa,andchianforgoodtimsmarflo£fcaans. Icaruutfullyacpzessmysinoereqvpreciatimforallotthe patienthelpgivenmebyJam'mcnpsm—thamchane. ii Wittmtthehelpofmanypersaisinuiemdiigannepartmentof NaumlResamoes,thisprojectwmldhavebeenimpossibletooarrywt. Iamdeeplynuebtedtonagmitcmb, MCarlson, FrarflcBemett, Nels Johnson, Ridcmnm, andEdLangeneau fortheirparticipationinthe antimottheaerialoamts. IalsothankhelioopterpilotsSgt. Jdeennyarrngt. ImVassilakosfortheirenttmsiamardinterestin thisproject. 'marflcstour.uid1ae18am1elforprovidingmewithimportantand timlyoon'espondenoe. Iextendmywholeheartedgratimdetomytm,mybrothexs, andmy friends. Icarmotpossiblethanktrmoftenmorsinoereernaghto repaythelifetime of W, mflerstardim, wpport, andlove thattheyhavegivenne. Finally, Imuldliketharflcbiamxenmimforbeingtmstimam patierrtchrimourtimeapart, torstnringinmyfearsandmyjoys, for meittmtomditions, andforbelievinginmewl'mIdidmt believeinmyselt. iii MEOFW usror'maus ................................................ Vi LISTOF FIGJRE‘S ............................................... viii LISTOFAPPENDICES .. ................................ . ......... ix mmw............................... ....... . ............ 1 033m .................................................... 6 S'IUDYSI‘IE DESCRIPTIQI . ............. . ......................... 7 MED-DEB ....................................................... 12 Flight Cor'iditimsardCharacteristios l7 SigrrtabilityModel Data Collection ...... 18 Sigtrtabilitynodelneveloprant ..... ........ 23 OmtherSimlations 27 PopzlatimandVarianoe Estimatim 31 CensusCJosts ............. .. ..... 33 m OOOOOOIOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOO 0.0.0.... 34 mu muwm OOOOOVOOOOOOOO.0.00.00.00.000.0.0.0000...O. 34 smmbfliwmla 00.0.0000...00.0.00...OOOOOOOOOOOOOIOO 35 Ounprtersiimlatiora ..... 38 PopulatimardVarianoe Estimates ..... 4o WIm 0.0.0.0.... ........... O OOOOOOOOOOOOOOOOOOOOOOOOOOOOO 48 mnwm OOOOOOOOOOOOOOOOO0.00000...OOOOOOOOOOOOOOOO 48 SightabilityModels .............. ........... 52 Gupta-Similations 55 matimarflVariame Estimates 59 CensusOosts ...... ....................... 65 iv WICNSANDCENSUSW015......................... mm .............................................. APPENDDKI: MES ............................................ APPENDIX II: W08 ..................................... 72 7‘7 86 7. IISI‘OF‘IAELES Total area, meanarea (variance), ardelkdensities or sanpling units in low, medium, and high densitystrata fortheaerialcersusingofelk inuic'higan. Canpositiat of data sets, and independent variables includedin? logistic regression analyses forthe aerialcensusingofelkinnichigan. An"X" indicatescmirerclassesinclmedindatasets. DistribxtimothOelkgrurpswimin4omifer ooverclassesorasimlatimsdesignedtotest developedfortheaerial predictimprooedures Wotalkinuidzigan. Significant logistic regression coefficients of 7 sightability models developed for the aerial censusin; of eJJc in Michigan. mmtotalsfor4omiferooverclassesarri predicted totals for 7 sightability models built tortheaerialoensusingofeJJcinMidzigan. Bias, averagebias, range, arfimmberotpoints within 50 animals of the true populatim size fordpredictimprooedmesmflerSsinflated aerialoensusesofeJJcinMichigan. 'Iheseries maderead‘isinllatim reflectstheprcportim of elkgroups assignedto coniferclasses 1-2-3-4. Distrihrtimotelkwithinomiferageandoover classestorgmzpsseendm'inguidiiganelk popnlatim/variamehelicoptersmveys, 1989. 16 25 3O 37 39 41 43 10. Estimates of total elk pogrlation size derived from Michigan elk pcpulation/variame helicopter surveys, 1989. Estimates of varaince comments in low, medium, andhighdensity strata franMichiganelk mlatiaVvariance helicopter surveys, 1989. Costanalysisfoerethodsofoensisingelkin Michigan: a 2-4 day ocuplete air and oersus,arda4-6daystratifiedrandanaerial corms. 'Iheorertic coefficients of variability (N a 1,236, df-60) for95%ard9o%CI'sbasedmdatafrcm Michigan elk popflatia'i/Varaince helicopter surveys, 1989. Reommerfiedmmberofunitstobesurveyedineadi eJchensitystrata,whenthetotalmitstobe isknown, tortheaerialcensusingot surveyed elk innichigan. vii 44 45 47 64 66 1. 6. LIST OF Hm Locatimarflprimiplelarriownershipsofthe Midaiganelkrangeabran1973). Mean marthly tanperatures receded at Vanderbilt, Mid-ligan for the long-term period 1922-1988, and the years 1987 and 1988. Total mnthly precipitation recorded at Vanderbilt, Michigan for the lam-tom period 1922-1988, and the years 1987 and 1988. Westernsanpling units of low, medium, andhigh elkdensityoonstructedfortheaerial oermsingofelkinnichigan. Eastern sanpling units of low, medium, and high elk density cmstructed for the aerial oensusing of elk in Michigan. Anaanpleof1/4lcnirttervallmelioqarterseard1 transectsoverahypothsticalsanplingmitfor theaerialoensusimofelkinuichigan. Average biases for 4 elk population prediction prooemres under emulated aerial oensusing data for elk in Michigan. 10 14 19 .42 LIST OFAPPENDICES mm Al. Areascfsanplmgmitsccnstructedianensity strata for the aerial censusing of elk in Michigan, 1988-89 A2 . Surmrizaticn of data collected for sigtrtability modelling of elk in Michigan, 1988-89. as - GrcupSize, m-Oclmifercoveraass, c1- CmiferAge, sa-StandAge,AB-Animal Behavior, andS/lB-SeencrNotSeen. A3. amrizatimcfdataccllected forMichiganelk herdpopulatim/Variame estimatim, 1989. 6 - erpsize, (1.21--Clrzr'iifercoverClaini,cut!-I (limiter-Age, SA-StandAge, andB/C/c-mll/ Cow/Cal: ratio. A4. Correctedgrotpsizecan'itsfcrtheaerialcensusing cfelkinnichigan. Correctedccuntsarebased mthemmberofelkseenarrltheccnifercover class occupied at sighting. W 1. Sumary of mathamtical prdaability calmlatims used to predict elk mmbers in conifer class 4 for logistic regression sightability model #5 . 1“ 78 79 81 83 87 INIIDIUCI'ICN Wildlife pcleaticms have been surveyed and censused with fixed- wingaircraftandhelicqrters since at least 1935 (Cahalane 1938). nutially,mnveyflightsweremadetccamtanimlsccwpyingremote areas or areas not accessible by land vehicles (Cahalane 1938, Dice 1941). Sincethelate 1950's, however, aerialcensusing techniques havebemusedtoanveya'rtimpcpflatimswermareas,instead cfjustisolatedanimalgmups. Mcetrecently,ccnplexcensus tedmiqasanimflmtimlmdelshavebeendevelcpaitcnmdmize macarocyarfltcminimizeflighttimandmn—pwerusage(floyd et a1. 1979, Meld et al. 1980, Crete et a1. 1986, Huston at al. 1986, Sanneletal. 1987). A Aerialcensusingisprcbablythecnlyfeasiblearrieccrmicalway to census manybiggame species (Anderson et a1. 1980:294). To date, partialcrccupleteaerialsurveyshavebeenusedtccamtmcsemg M) (Gasawayetal. 1985),Alaskanbrwnbear(LMM) (EridcscnandSiniff 1963), bison (2mm) (WolfeandKinball 1989), caribou/reindeer Wm) (Kleinarximzyakinl982), mmm) (Bledtnere‘tal. 1951,9obe11950),pmaghom antelope WM) (Sprites: 1950), mm’cainqoat (MW) Wad-1986bmledeermnes W) (Mold et a1. 1980), admits-tailed deer W 1 2 W) (Petrides 1953,1ecneta1. 1987). cmditionsmderwhich successfulaerialcensusesstmldtakeplace,honever,canbevery rigorous (DavisandWinstead 1980:225). Surveyflightsmustbetimedto cptimizetheprcbabilityofsightingthelargestmmbercfanimals. As such, base-line informaticn on species behavior, range, habitat usage, ardrespmsetoweathermstbestrcnglyccnsidered. Aerial surveys, designedtcprcducemeasures of population size or density, will consistently underestimte true population size (Caughley 1974),particularlyvmenanimalsccc1mindensecover(8easan1979). Ecutledge (1981) cautia'nedthattctal comtsbasedsclelycma series of incapletecrpartialaerdalmrveysczmntprcdwereliablepcptflatim estimates. Wimtimsareprimarilythereezltcftheimmplete visibilitycfanimlsfrantheair. mmmdercptimlcaflitiaaard mflerstringentlyplamadarfiexewtedprccedmes,aerialcamtshave missedll-7l% cftheanimalsknctmtcbepresentWatthey 1977:34). In general,thevisibilitycfananimal,crgmip,willdecreasewith decreasesingrcupsize,animalbcdysize,movanentcractivitylevel, andcbservereaqaeriercerarflwimircreasesinvegetativecover,seard1 speedardaltiuade,ardtinespentcbsewing(smrpearri3easanl987). Aerialsurveyprccedurescanalscbeprcblenaticduetcacceptable weather ccnditims, short maxinm flight times (fuel loading limits), andresu'ictims associatedwithanimldistrihrtimandterrain. InprovanentsinaerialcersusingtedmiqueshavetakmS form: refinerients in survey methodology, calculation and application of correction factors, and a canbinaticn of both of these. Refinanents in amreytedmiqueincreasecensasefficiencytcsmedegree,butare 3 mrmallyetplcyedtcmadmizetheprcbabilitycfsightirgananinal(cr animlgrcup). Manyfcmscftectnfiquemcdificatimhavebeen inplanented,withvaryingdegreesofsuccess. Before1964,mstcensus tedmiquerefinanmtswerebasedmdlangesinnightdraracteristics, mileflleactualmethcdolcgyrenainedrelativelymdianged. 'lhese studiesinvariablyusedsanefcrmcfline-transectflightsdtaneinan attapttoccverthemtirestudyareaandtcccmtallanimlspresent (Cahalane1938,saugstad1942, Ricrdanl948,&1edmeretal. 1951). Wtcthisnethcdclcgyhaveimludedtheusecfstratified randan sapling with @timl allocatim (Siniff and Skccg 1964), stratifiedrardonsanplirgwithprcpcrtimalallccatimmvansetal. 1966), simultanecm use of fixed-wing aircraft andheliccpters (lovaas et a1. 1966), increasing search intensity (leResche andRansch 1974), vimalrecapturecfmarksdanimalsmiceandI-Iarder1977), stratificatimcfthesttxiyareabasedmanimldensitywloydetal. 1979, Meldetal. 1980,1-Icustcnetal. 1986),theuseof belt tramects(DeYomgl985),ardtheusecfaerialphotcgrafiIyOtyersard Bowenl989). Alttnaghtheseandotherstudiesutilizedmethcdsbest suitedtcmeetspecificcbjectives,mcretraditicnaltedmiquesmay stillbeamrcpriatefcrsaneresearda. arrrmtsuidies,fcrinstance, often relycnstratified quadrat sampling, butBeasanetal. (1986) and miteetal.(1989)cmterflthatinnanycaseslire-transectsmystill be the most efficient and effective method available. 4 In recent years, attaupts at minimizing visibility biases have focused mre on the development and application of correction factors flaanmfurtherrefinemerrtsintedmique. Correctimfactcrsare derived tron sightability fmnticns obtained through gromd-fiuthing procedures. Sightability functions are mathenatical probabilities calallatedtcacccuntfor individualsmissedmringcensus fly-overs (Caughley 1974). Sighting probabilities can be' developed in a variety ofways, andareusuallyspecific foraparticularanimalspecies inan identified area. Gaughley (1974) saggested calculating the partial regression of variables affecting sightability in defined density strata. Cock and Jacobson (1979) developed a method of estimating visibilitybiasbycmparingtheirdependentcctmtsof2 observers. Sandal and Pollock (1981) developed ccrrectim factors specifically for animlsthatccaxringrwpsbyestimatingsightabilitythroughthe extrapolatim of an asymptotic regression function. Crete et a1. (1986) corrected helicopter quadrat counts of noose by simltaneously cmdnctingafixed—wingccmit (assumedtcbeaccurate) ofthesampled quadrats. thastcnetal. (1986) corrected formissedanimalsby applyihgafixedsightingprcbabilityovertheentiresuldyarea, using Cmaghley's (1977:47) WMatim-index technique. Samuel et a1. (1987) used a logistic regression procedure, based on factors significantly affecting sightability, to build sighting probabilities and produce a prediction equation. Visibility. bias can be a severe problen, aruanyaccurateaerialcensusingprocedm'emstinclude correction factorstcacccm‘ttfcrmissaianimls (PollockandKendall 1987) . 5 'menativeuidziganentherdwasextirpatedfranthelmer peninsulaby1877 (mlrie1951:28). Inl918,7elkwere released along the SturgecnRiver 6.4 km south of Wolverine (Stephenson 1942), became established,andeventuallygaverisetcthepresentelkherdin Midiigan'sncrthernlwerpeninsula. Since it's establistnnent,theelk herdhasexperiencedpericdsofrapidgrwtharflpericdscfsevere declineabran1973,Beyerl987). 'meMidliganDepartmentchatural ResamcesGDtR)hasusedacmbiredairandgmmdcensusinanatteipt tccotmteveryelkwithintherange(T.Carlsm,pers.ccumm.). 'Ihis teclmiquewasfirstusedinl975,prcducingaherdestimtecf200 aniinalsmm11984). mmlghinplmentatimcfthemknanagenentplan OM1984)theetherdhasincreasedsteadilyfrmBSOinl984tc94o in 1985, 950 in 1986, 1000 in 1987 (Beyer 1987:123), and 1020 in 1988 (E. E. Iarqeneau, pers. cammm.). 'mecensusnethcdusedbytheMmercvidedanarprmdmticncfelk mmbersmdcmstiurtedaccnsiderableinvesmerrtcftime,w'eyand mnpcwer. mispaperdescribesarmcermsirgtedmiquethatwas develcpedtoinzreaseacwracyandreduceexperflimrescfflmmeelk surveys. 'misnethcdclcgyutilizesstarxiardseardiprocedtmesarfi sightability correction factors to prcciuce a statistically-based herd estimate (with confidence intervals) solely frun helicopter comts. mistedmiquewfllallowmmaragerstcacwratelymeytheentire elkherdinamoreefficientmamer. DETECTIVE meprineryobjectivecfthissuldywastcdevelopanacwrate, stratified randon, aerial censusing tedmique that world provide a statisticallybasedestimatecfthesizecftheuichiganelkherd. In addition, several other dajectives were identified. 1. 'I'ciderrtifythcsefactcrs that significantly (P.aspea(musspp-),mtepim(2mmis).aearmaple mm}.mfirfipheMM) (14912111973)- Iransitimalareasaredaninatedbywillommspp.),pccrquality redmple. poorquality aspens. andwhite birch (2111192923134) (Mcr'anl973). tbran(l973:7)broluethephysicgra§1ycftheelkrange into 6 general classes: sardyoutwashplains, mueshplain-mcrainic eccta'ies, steepmcrainic slopes, morainic uplands, riveldaanks and bottanlarris,andcmifermsswanps. 10 .82 Be 52 memo» 65 you 98 68782 scion gig." on» you omega: 539895, no @0383 333%» 35:05 and: EEZOE con >cz soc .Eom Mai .23. 0:3. .32 3.2: £0.32 norm :2. _ _ p _ e _ _ _ 0" 051“.“ I) o HHHLVHEIcIWEIL 11 ova >oZ goo soon .89 one 83 88» ofi you 93 68739 88% .euoplmcca.oou_nou.cnmaouazi.uawonoocm>;uo.ooogooeu ccaunuenfiomsn_adoecoe Hosea .n .mam m=< _ $9202 .33. 0:3. _ . .32 _ at: not: see :3. wwafi ham“ wwaalmmau . »'I’ll:|ov' IT IIIIII Ill GQI‘QOVG’JN—i W3 NI NOIlVlIdIOHHd , IO ‘— Winfinaerialcensusimofelkinuichigan involved bothaninprovenentinsurveytectmique, andtheuseofccrr'ecticn factors to account for visibility bias. Technique inprovanents included a standardization of flight/Weather ccnditims , a standardization of helicopter flight characteristics, the cmstr'uctim of sanpling mit bonfiariestcfacilitatethestratificatimofthemeyarea, andthe calculaticn of variance estimates for the optimal allocation of sanpling effort. Correctim factors, designed to account for animals missed during censusing, were developed through sightability modelling procedures, and judged for accuracy through miter simlations. '9m11mihiiM mepresentelkrargeencmpassesalargeareainmmigan's northernlowerpeninsula, mimportiasofcieboygan,mltnorency, Otsego, andPresqueIslecounties. Sinceanareathissizecculdnotbe totallysurveyedinarelativelyshortpericdcftime, itwasnecessary toexcluieportimsoftherangewifilcccasimalccwrrencesofsmall mmbersofelk, stratifytheremainingarea,arficcrstructsanpling mitswithineachstrattm. Iocatimsofelkgroupssightedduringthe previous SMIINRechcunts (1984 to1988) wereplcttedona l:84,480map todetermineelkdistributiasanddensitiesthmlgtmtulerange. 12 13 Areaswheredersitywasbelowlelkperlomzwereexcludedfrdn sanplirgardflightccmiderations. Asaresult,theareatobe simveyedencaipassedl,015.5]mzoftheprineryeucrargelyingeastof U.S. Interstate 75,northoftheWilJ 3 finale 3 .33 53583233308330 mouse? axes—4 .cnogazfifiucgggofiuou 33588.83 039a >5 coo—#05 swag; one .38 sumo no 8380980 .N 0.33. 26 'nlscmitercwerclasscoefficientisanegativemmbersimeinczeases in vegetative cover decrease sight-ability (Cook and Jacobson 1979) . Conversely, the group size coefficient is positive since an increase in animal group size increases the probability of sighting that gmlp firm the air (Sannel et al. 1987) If the logistic regression procedure detemmedthatstarfiageclassalsohadasignificant influenoeon sigtrtability, the model would take the tom: u - C + 0g(gm1p size) - Commuter cover class) - Cs(stand age class). where, u,c,Cg,andccaredetinedasabove Cs-tharegressimcoeflicientforstaxflageclass Herethestarxiageclasscoefficierttisalsonegativesincean irureaseinthsageofthedmimntvegetatimdecreasesthesighting probability (Caughley 1974). the sigl‘rtability value (u) is determined byinsertingobsenredgmxpsize,cmifercoverclass,andstandage classintotheirrespectiveplacesardcanyingcutthearitlmetic. In addition, tilederivedmdel cwldbeexpardedto inchrle visibility differencescausedbycmiferage. Forfllisvariable,thsresultant regression coefficient would also be negative since increases in vegetation age decrease animal visibility. ‘ 27 Conversion or all 7 elk sightability models to correction factors was acouplishedusingtheproceduregivenbySamiel etal. (1987). In each case, a sighting prdoability function was first derived through the fonmla: expu y: l+expu y- the sighting probability u - the sightability value Franthesefunctimsthen, correctimtactorswerecalculatedby invertingeadisighting probability (l/y). Correction factorswerethen appliedtoactmllvisualcumtstoarriveatanestimatimofelk abmflanceinthsmitssampled. mm Jiflgementofmdels,basedmaccuracyandstability,was accomplished through prediction calculations and through canputer simlatim. Initially, models were jtidged based solely on how accuratelythsypredictedthetotalmnnberofencineadiofthe4 conifercoverclasses. Predictedelkmmaersm'ecalculatedby applyingcorrectimfactors,determinedforall7mdels,toco\mtsof elkgrwpsactuallyseenbyhelicoptercrews. Sincethedatasetused tobuildmdelSanittedeJJcobsenratiorisinconiferclassma nathematical probability calculation was used to predict elk mmbers in thatclassmpperdixn). Eachpredictimwasthenccnparedtothe toralmmberofelkingralpsweenarflmtseemcmrtainingaconared 28 animal, foreadioftlle4cmifercovechess. Inthismamier,models that mtelyanica'sistentlypredictedkrmelktotalsfrcm observedelktctals, calldbeseparatedfimfliosemdelsthatdidmt. Aoalrateardconsisterrtmdels,mdelparts, andnathenatical probability calwlationswereusedtoconstruct4 elkpredictim prooeduresofvazyingccuplexity. ProcedureIutilizedasinglemodel topmedictelkmmbers,pzoceduresIIIalfl'IVutilizedpartsof2models topredicteJJcmnnbers,whileproceduresIIutilizedpartsof3models toptredictelkmmbers, asdescribedbelcw. ProcedureI: Allcoverclassespredictedwithmdell. ProcednreII: Coverclassesl, 2, and3predictedwithmode15: ccverclass IVpredicted mthematically (Appendix II). ProcedureIII: coverclasslpredictedwithmodelll;coverclasses2 ardBpredictedwithmodeléscoverclassllpredicted mathenatically. ProcedureIV: GoverclasslpredictedwithmodelMcoverclassesZ andapredictedwithmode13(inthisprocedureccver class4iscanbinedwithclass3). Allprocedureswerethentestedforacwracyandcmsistencywith simlatedelkcalsusingdata. 'nlepmposeofthesesimlationsms threefold: todeteminemidlprooedurewasmostaccurateardmbiased, todetemimmethersmglemdelormltiplemdelpmoedureshardled elkcensusdatabetter, andtoassesstheeasewithmichcmplex prooedurescouldbeused. All sinulations were performed with the lotus 1-2-3 personal cmprtersoftware package, version 2.0 (IeBlcmdaniOobb 1985). One muredgroupsofencwereplacedwithinallconiferclasses, usings 29 ratiosdianescrableB). mismsdonetotestmodelperfomancemder varimselkgrmlpdistribxiaathatwereeitherdasexvedmthefield, juhedprobabletoocalr',judgedpossibletoocam,judgedtooextrsne tooccir,orjudgedtootmiformtoocalr('rable3). Elkgrcupsizes wererandanly generated, within specified ban'daries, foreadlconifer coverclass. Omiferccverclassl(O-25%cmifer)cmtainedgrcups franlto 50 animals insize, coverclass 2 (26-50% conifer) contained gm1pslto30animlsin-size,coverclass3(51-75%cmifer)com:ained groupsfranltoZOanimalsinsize,ardcoverclass4(>75%conifer) cartsinedgmzpsfrmltolSanimalsinsize. Q‘icethernmberardsize ofgmlpspresentineadlcmifercoverclassmredetemined,eadi gmupmsrarxianly designatedas"seen"or"not seen". Sinulationswere castructedsudlthatfrmm-Qfiofgrnlpsincoverclasslwere "seen",fran65-90% ofgrqmsincoverclassZwere"seen",fran30-60% ofgrmpsincoverclasstere"sem",ardfran0—20%ofgmzpsin coverclass4were"seen". 'meserangesreflectthepercentageof gralpsaculallyseendurirgdataconectim,ardagreewithrangesgiven by'r. Carlson (pets. cammn.). ProceduresI-IVwerethenusedto predictelkmmbersineachcmifercoverclasssolelyfrmthesizesof elkgrmpsdesignatedas"seen". 'I‘ctalelkpredictedbyeadiprooedm'e forthedconifercoverclasseswasthmcmparedtothetotalmmberof elklowntobepresentineadlclass. 'memmberofelkpredictedin allclassesbyeadiprocedureardthemmbercfslklmcwntobepresent inallclasseswasalsocaupared. 30 'I‘able3. Distrihltimof 100elkgrcupswithin4cmifercoverclasses of 8 simlations designed to test prediction developedfortheaerialcensusingofelkihnidligan. W Sinulation 1 (0-252) 2 (26-50%) 3 (51-75%) 4 (752+) (Distribution) Sinulation 1 (Entree) 31 32 32 5 Simulation 2 (Even) 25 25 25 25 Simlatim 3 (Cbserved) 46 20 14 20 SinJaltim 4 (Probable) so 18 18 14 Sinulaticn 5 (Possible) 6o 14 13 13 Sinulaticn 6 (Extrane) 61 25 10 4 Simflatim 7 (Even) 31 23 23 23 Simulation 8 (Possible) 4o 20 20 20 31 Results of cmputer simlatiom were analyzed to evaluate the perfomneofmprocemnesbasedonaveragebias,mmberofestinetes withinSOoftheknomtotal, rangeofestinates (distanoebetweenthe mininmardmaximmestimate), andoverallbias. Achi-squaretestof signirioamewaspertormedtotestmemermdelswerehiasedmdereadi sinulatim. Biasterdenciesweregiventhenostcmsideratimwlen judging predictim procedures, followed by average bias, and range. mmmm wringflightsmadebeoaemZBFebmalyardzmrdi,1989,1mitsof 1w,nedim,ardhighelkdensitiesweres\mveyedtoestimtevariames for the optimal allocatim of sanpling effort, and to estimate Michigan elkherd'size. Imitstobesurveyedmrechosen,bystrata,usinga randan mnuber generator. Ten low density, 14 medium density, and 14 highdensitymitswereanveyedusimthestaniardizedseardl pmocedmesdsscribedabove. AMichiganINRobservenarria pilot/observercmmtedardrecordedallanimalsseendurmghelicwter flyovels. Elkcountswerenotcorrectedforvisibilitybiasmltilall mitshadbeensurveyed. Anestimatecfthetotalelkpopllatimwasmadetrcmthedata collectedfranZBFebruarythrmghzm,1989. Sinoethesanpling mitsusedinthiscensuswereofmiequalsize,theexpardedpopalatim estimtewasbasedmtheratioofareasanpledtototalarea(¢aughley 1977). 'memmberofeJJcseenwithinaparticllarconiferclassofeadl streumwerestmnedmflthetotalcorrectedusingthepredictim procedure found to be most appropriate, based on sightability data 32 collectedin1988-89. Assad» 12 distinctcamtswerecorrected, l for eadiofthe4cmiferclasseswithiheachofthe3densitystrata(i.e. coniferclasslofthelmstramm,cmiferc1ass2ofthemedilm straum,arriconiferc1asssofthehighstraum). 'mecorrectedcotmts foreadiconiferclasswithinaparticllarstraumweresmmedtoarrive atatotalcorrectedcomtforthatstraum. Correctedelkcourrtswere mltipliedbytheinvereeperoentageofareaacmallyflownwithineadi stratlm,providirqanestinateofthemmberofelkpresentwithinead1 stratum. Smirgtheixdivimalstraumestimatesprovidedanestimate fortotalelkmmbersovertheentirerange. Anodifiedrui-respmsenorvitzdnmsmestimator,aspresentedby SteinhorstandSannl(1989),wasusedtoestimtevariancefran populationhelicopterszmveys. 'meestimatorpartitimstotalvariance intocmpmentsofalrveyerror,sigtrtabilityerror,ardnodelerror. ‘meslmveycmpmentestimteserrorduetosurveynetlndologyand sampling effort allocation. 'Ihe sightability cmponent estimates error duetovisibility bias, that is, theimability ofaerialcotmtersto sigrrtallanimalspresent. 'memdelcauponentestimteserror associatedwiththesightabilitymodelusedtocorrectelkcounts. Varianceestimteswerecalwlatedforeadlofuie3densitystrata arrithensmunedasanestimteofcverallmiitvariance. Iotalvariarice msthenusedtoconstruct95%and90%cmfidenoeintervalsat60 degrees of freedan. A coefficient of variability (Steel and 'Ibrrie 1980:27) was calculated frun population and variance estimates for cmparison with similar estimates frcm other aerial wildlife census research. 33 M %Q 'IotalcostswereestimatedforbcththeclrrentnidiiganDRelk censusingtedmiqueanithestratifiedaerial sanplingmethodusedin thisstudy. Adirectcmparismwasmadebetweenthesetwoestimtes using the following paralleters: I-Ielicqater rental - $150.00/hr Helicopter fuel - $1.85/gallm Pilot lodging - $65.00/day m personnel salary - $25.00/tnm/man Snowmobile rental - $78/mchine/day Midliganchensuscostestimtes includehelicopterrerrtal for 17-31 hours, fuel costs for 2—4 days (75 gallows/day) of flight, pilot lodging for 1-3 nights, ZOMENRpersormel salaries for 2-4 days (9 hours/day), and rental of 7 Miles for 2-4 days. Stratified aerial census cost estimates include helicopter rental for 31-45 hours, helicopter fuel costs for 4-6 days (150 gallons/day) of flight, pilot lodging for 3-5 nights, ardZMENRpersmnel salaries for 4-6 days (9 hours/day). Since the stratified aerial method requires no snowmobile rental, thisadditimalexpenseneednotbeimluded. DJBtO difficulties in ascertaining the cost of operating wheeled vehicles this expelfiiturehasnotbeenincluded fortheMIlchensusmethodcost estimate. Elam Fifty-five sampling units (17 different) were flown on 18 days in 1988 and 1989 for sightability model development. A total of 775 elk in 79grolpsmreobservedfruntheair, thegromd, orboth. Atotalof 638e1kin529roups (12.3 elk/group) wereseenbyaerialcreas, while 137elkin27groups (5.1e1k/group) werenotseendurihgflycvers. 0f theelkgroupsseen, 32 (61.5%) minvegetatimwhereconifercover wasnortmorethan25% (coverclassl), 13 (25%) wereinstandsof26- 50% conifer cover (cover class 2), 5 (9.6%) were in starris of 51-75% conifercover (coverclass3), andz (3.8%) veroinstardswterecmifer coverwaSmorethan75% (coverclass 4). Offlleelkgroupsnotseenby aerial crews, 4 (14.8%) were in cmifer cover class 1, 3 (11.1%) were in conifer cover class 2, 6 (22.2%) were in conifer coverclass 3, and 14 (51.9%) were in conifer cover class 4. Appendix Table A2 summarizes the data collected for sightability model developnent. Helicoptersurvey flightsweremadetoestinatebetneensampling unitvariance, ardtodetennihetheoptimalallocatimofsanpling effort through low, medium, and high density strata. Fourteen of 17 high density units, totalling 150.4 1on2 (83.18 of total strata area, 82.4% of strata units), were surveyed, camting 252 elk in 25 groups. Fourteen of 32 medium density units, totalling 139.8 1on2 (42.6% of 34 35 strata area, 43.75% of strata units), were surveyed, calming 101 elk in 13 grmlps. men of 45 low density units, totalling 97 m2 (19.2% of strata area, 22.2% of strata units) were surveyed, coimtirg 74 elk in 10 groups. Apperdix'l‘ableAB mizesthedata collected forthe estimtim of populatim size and variance. W m A sightability model was developed based on logistic regression analysis and included the calculated coefficients for factors found to significantly (P < 0.10) influence elk visibility frun the air. Five possible sources of visibility bias were recorded durirg data collection aniusedas irriepenientvariablesmringregressim: conifercover class, group size, conifer age class, dominant vegetation (stand) age class, andanimalbehaviorclass. 'nledependentvariable forregression analysis was the dichotanous classification of elk groups as "seeri" or "not seen". Before sightability modelling was initiated, animal behaviordatawasjudgedtobeinccmpatiblewiththerestdfthedata setandwasnot included inthelogistic regression analysis; the initial step of the logistic regressim analysis indicated that only conifer cover class (P < 0.001) significantly influenced elk visibility. Elk group size, conifer age class, and stand age class slaved no significant influence on sightability. Final coefficients, thus, imluded the regression constant (3.698), and the conifer cover class coefficient (-1.333) . Model 1 was constructed using these coefficients arr! took the form: u - 3.698 - (1.333) (conifer cover class) 36 'mefimlcoefficientforconifercoverclassesmsmgativeduetothe inverse relationship between cmifer cover and animal visibility fran theair(Caughley1974). Correctimfactorespecificforeadlconifercoverclasswerethen calculatedasdescribedbySamleletal. (1987). Tincorrectimforelk groupsseeninconifercoverclasslms:(l.094)(£$),wierePS-the totalmmberofelkseeninthatcoverclass. 'nlecorrectionforelk grwpsseenincoverclassesz,3,and4mre: (1.355)(ES), (2.353)(ES), and(6.l35)(ES),respectively. Correctedelkcamtsforeadlcmifer coverclassarepresentedinAppendixTableM. Six adiitimal models were developed using logistic regression analysisbyeliminatirg specificindependentvariables, orby eliminatirgportimsofthedatasetheforeanalysis. Allmdelswere caetructedusingsaneorallofthedefimdcmifercoverclass,except models3ani4,whidlcmbineddatafranclasse33and4intoasirgle classrepresentirgcalifercoverofsofkormore. 'IableZsmnnarizestheconditimsinposedmthedatasetpriorto regressim analysis. Table 4 simmrizes the final coefficients of factors significantly influencing elk visibility, as detemined with 7 logisticregressimanalyses. Models2through6werebuiltusing significant variable coefficientsinthesanemamlerasrodel 1, andas descr'ibedinthemthcds. Sincecoverclass4wasanittedfranthedatasetusedtomfld mode15,elkpredictionsforthisclassweremadewithamathaietica1 probability calculation (Appendix II). All models were judged for accuracybycmparingthetotalmmberofelklmowntobepresentin 37 Table 4 . Significant logistic regressicn coefficients of 7 sightability mdelsdevelopedfortheaerialoensusirqofelkinuichigan. Model Constant Cover Class Group Size 1 3.698 -1.333 (p < 0.001) 2 2.481 -1.168 (P < 0.001) 0.119 (P < 0.125) 3 4.207 -2.374 (P < 0.007) 0.344 (P < 0.037) 4 4.041 -1.634 (p < 0.001) 5 3.338 -1.115 (p < 0.007) 6 2.847 -1.664 (p < 0.003) 0.345 (P < 0.036) 7 5.108 -1.764 (P < 0.069) 38 eadicmifercoverclasswithellcmmaerspzedictedbyeachmdel. Only thoseelkgrwpsthatwereacmallyseenbyaerialcrwswereusedin ead1modeltopredictell