The Northern Yellowstone Elk: Density Dependence and Climatic ...

The Northern Yellowstone Elk: Density Dependence and Climatic ConditionsAuthor(s): Mark L. Taper and Peter J. P. GoganSource: The Journal of Wildlife Management, Vol. 66, No. 1 (Jan., 2002), pp. 106-122Published by: Allen PressStable URL: http://www.jstor.org/stable/3802877Accessed: 01/11/2009 17:58Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=acg.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.Allen Press is collaborating with JSTOR to digitize, preserve and extend access to The Journal of WildlifeManagement.http://www.jstor.org

THE NORTHERN YELLOWSTONELK: DENSITY DEPENDENCEAND CLIMATICONDITIONSMARK L. TAPER,1 Department of Ecology, Montana State University, Bozeman, MT 59717, USAPETER J. P. GOGAN, U.S. Geological Survey, Northern Rocky Mountain Science Center, Department of Ecology, Montana StateUniversity, Bozeman, MT 59717, USAAbstract: We analyzed a time series of estimates of elk (Cervus elaphus) numbers on the northern Yellowstone winterrange from 1964 to 1979 and 1986 to 1995 using a variety of discrete time stochastic population dynamic models.These models included adjustments for density, an increase in the area of winter range used by elk, lagged effectsof the weather covariates of spring precipitation, snow depth and winter temperature, and the impacts of the 1988drought and fires. An information-criteria-based model-selection process strongly supported evidence of densitydependence. The best model, a Ricker model, distinguished between the 2 time periods. The bulk of the differencebetween the 2 periods is attributed to an increase in the amount of winter range used by elk. Inclusion of thecovariates spring precipitation and spring precipitation squared greatly improved the model fit. We detected ashort-lived increase in elk population growth rate following the 1988 drought and fires. Fertility and survivorshipof adults appeared to have different density-dependent forms that together result in a biphasic relationshipbetween population growth rate and density. This study confirms the presence of density-dependent regulation inthe northern Yellowstone elk herd, and enhances our understanding of population dynamics of these ungulates.JOURNAL OF WILDLIFE MANAGEMENT 66(1):106-122Key words: Cervus elaphus, density dependence, elk, Greater Yellowstone Area, information criteria, Montana, nonlinearpopulation dynamics, population dynamics, Wyoming.Yellowstone National Park (YNP) supports 8 elkherds that intermingle on the summer ranges(Mack and Singer 1993) within YNP but are identifiedby use of distinct wintering areas within andbeyond the borders of YNP. With minimum populationestimates exceeding 17,000 during winters1992-1993, 1993-1994, and 1994-1995 (Lemke etal. 1998), the northern Yellowstone elk herd is thelargest of the 8 herds. The herd is supported by ex-tensive areas of grassland and shrub steppes withinand beyond the borders of YNP (Houston 1982).Many researchers have noted changes in the lifehistory parameters of the northern Yellowstoneelk herd that are consistent with a density-dependentresponse (Houston 1982, Merrill and Boyce1991, Cheville et al. 1998, Singer et al. 1998). However,such changes are considered insufficient proofof density dependence (McCullough 1990). Truedensity-dependent population regulation has beenindicated by regressions of growth rate on populationsize (Houston 1982, Merrill and Boyce 1991,Dennis and Taper 1994). Nonetheless, contentionstill exists on the extent to which the herd exhibitsdensity dependence because in recent years populationsizes have increased beyond the ecologicalcarrying capacity predicted by Houston (1982). Followingrelease from artificial controls within the1 E-mail: taper@rapid.msu.montana.edupark, the herd size increased to 14,000-15,000during the 1970s through mid-1980s (Merrill andBoyce 1991), 17,800 during 1985-1988 (Merrilland Boyce 1991), and >19,000 during 1993-1994(Lemke et al. 1998). However, rigorous reevaluationof the data analyzed by Houston (1982) confirmshis calculations (Dennis and Taper 1994).An interplay of dynamic natural ecologicalprocesses and human management activitiesthroughout the range of the northern Yellowstoneelk herd have continued to impact theherd's population dynamics. For example, expansionof the extent of the winter range by con-tinued pioneering of herd segments northwardfrom the park boundary and extensive use ofthese more northerly areas by greater numbers ofelk have been coincident with acquisition andconversion of rangelands from livestock productionto elk winter range (Lemke et al. 1998).Also, the adult sex ratio shifted from one highlyskewed by intense culling activities within YNP ofapproximately 50 males:100 females during the1960s to approximately 25 males:100 females bythe late 1980s (Mack and Singer 1993). The im-pact of the 1988 wildland fires on northern rangeelk numbers have been predicted to be relativelyshort-lived (Turner et al. 1994) or cause a declineof 5-10% during the first 5 years but increasednumbers 15-25 years post-fire (Coughenour andSinger 1996). Similarly, the reintroduction of106

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONELK * Taper and Gogan 107wolves (Canis lupus) to YNP has the potential of more, National Park Service, unpublished report).dramatically affecting the size and population Censuses from fixed-wing aircraft began duringparameters of the northern Yellowstone elk herd winter 1967-1968 and continued to 1994-1995.(Garton et al. 1990, Boyce and Gaillard 1992, Boyce The elk herd was counted several times annually1993, Mack and Singer 1993, Messier et al. 1995). from a single fixed-wing PA-18 Supercub fromWe investigated the northern Yellowstone elk 1968 to 1979 (Houston 1982), with the highestpopulation data from the inception of aerial counts obtained between mid-December and midcountsduring 1965 through 1995 to understand January. Annual counts since 1986 have been conthenature of the population dynamics. Rigorous ducted with 4 Supercubs, each covering a segmentevaluation of density dependence in the north- of the northern range (Lemke et al. 1998), ideallyern Yellowstone elk herd is important for scientif- on a single morning. However, in some instances,ic interest but also for evaluating the appropriate- flying conditions and logistical constraints haveness of human management actions. We explored forced the census to be staggered over several daysthe effects of range expansion, wildfires, and cli- (Lemke et al. 1998). The counts are made duringmate on population changes. We addressed the early winter when elk occupy non-forested porquestionsof whether or not the northern Yellow- tions of the northern range and are more readilystone elk herd exhibited density dependence and detected against a snow-covered landscape. Fromassessed the shape of density-dependent functions 1968 to 1975, we combine information from W. J.influencing the population. Such an assessment Barmore (National Park Service, unpublished re-provides a backdrop for understanding the im- port), Houston (1982), and Lemke et al. (1998) aspacts of natural processes and human activities, our source of data for 1976 to 1995 (Table 1).such as hunting and restoration of wolves on thenorthern Yellowstone elk herd.Age and Sex CompositionHerd ageSTUDY AREAand sex composition were determinedeach January from 1968 through 1979Elk of the northern Yellowstone winter range from ground surveys adjusted for under-repreoccupyan area of 1,410 km2 of foothills and valley sentation of adult males by the percent adultbottoms along the Lamar, Yellowstone, and Gar- males sighted during aerial surveys (Houstondiner rivers, with approximately 1,000 km2 within 1982). During winter 1985-1986 through winterthe boundaries of YNP and 500 km2 on the Gal- 1989-1990, herd composition was assessed from alatin National Forest and privately owned lands helicopter covering one-third of the northernnorth of the YNP boundary in Montana (Houston range (Singer et al. 1997) during early winter1982, Coughenour and Singer 1996, Lemke et al. (an) and late winter (mid-Feb through mid-Apr).1998). Elevations range from 1,500 to 2,500 m. During winter 1990-1991, the early winter com-Mean annual precipitation ranged from 35 cm in position was determined from a similar helitheupper Lamar River valley to 24 cm on the Yel- copter count, but the late count was conductedlowstone River at the YNP boundary (Coughenour from the ground. Thus, the proportion of malesand Singer 1996). Vegetation of the area is pri- in this late count is an underestimate (Houstonmarily grassland or sagebrush steppe (Houston 1982). Early and late winter herd composition1982). Dominant plant species of grassland and estimates were made during winter 1991-1992 folsteppeare Idaho fescue (Festuca idahoensis), blue- lowing the sampling regime used by Singer et al.bunch wheatgrass (Pseudoroegneria spicata), and big (1997). No composition counts were conductedsagebrush (Artemisia tridentata; Houston 1982, during winters 1992-1993 or 1993-1994. Only lateTurner et al. 1994). Coniferous forest of Douglas- winter (Mar) composition estimates were madefir (Pseudotsuga menziesii) and lodgepole pine from a helicopter during winters 1994-1995 and(Pinus contorta) occurs at higher elevations at the 1995-1996. In some instances, we found discrepperipheryof, and as isolated stands within, the ancies between early winter composition estimatesgrassland and sagebrush steppe (Houston 1982). determined from the original data sheets on fileat YNP and those reported by Coughenour andMETHODSSinger (1996:582). We present the YNP file datacorrections used in our analyses (Table 2).Census DataThe elk herd was censused from helicopter dur- Data Selection and Adjustmenting winters 1964-1965 and 1966-1967 (W. J. Bar- Several counts (1976-1977, 1988-1989, and

108 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002Table 1. Count and removal adjusted population estimates, northern Yellowstone Elk herd, winters 1964-1965, Montana andWyoming, USA. (Except where otherwise noted, data are from W. J. Barmore, National Park Service, unpublished report; Houston1982; Lemke et al. 1998; and Montana Department of Fish, Wildlife and Parks unpublished annual hunt reports 1985-1995.)Post-hunt Next fall pre-hunt Total Post-count Pre-countWinter period Count estimate estimate removals removals removals1964-19651965-19661966-19671967-19681968-19691969-19701970-19711971-19721972-19731973-19741974-19751975-19761976-19771977-19781978-19791979-19801980-19811981-19821982-19831983-19841984-19851985-19861986-19871987-19881988-19891989-19901990-199119921993199419954,4763,8423,1724,3055,5437,2818,2159,98110,52912,60712,01412,68010,83816,01916,28617,00718,91316,536e14,82912,027e12,85917,58519,04516,7914,8655,2273,8423,1724,3095,5437,2828,2159,98110,52912,60710,82510,741 b11,87810,80715,11415,38716,162d18,73718,94514,50611,33011,07216,01118,83214,7526,4976,5344,2724,3555,5937,3268,29010,13510,73912,75412,35410,96012,94111,14916,47316,88517,90119,31617,02315,80512,33515,58718,06619,35917,2901,9041,2702,6921,100505045751542101471,5292191,063342661376C1,3591,8812,0611,5711,4981,7395792,8961,2991,0054,5152,0555272,538a Includes other winter mortality of 44 (W. J. Barmore, National Park Service, unpublished report).b Houston (1982:23) adjustment.c Corrects typographical error in Lemke et al. (1998).d Addition error corrected from Lemke et al. (1998).e Sightability corrected numbers.00000000001,1890802319058998451762,4093236971,7871,5742132,0391,9041,2702,692a1,100505045751542101473402192613114545998944034879763082,7284813144991990-1991) are marked in the original records asunreliable due to poor census conditions (Lemkeet al. 1998). Growth rates estimated from year-toyeartransitions that include any of these years arenot included in the primary analyses regardingthe strength of density dependence. Furthercomplications occur when we consider the 1988drought and associated wildfires. These wildfiresmay have affected elk demographics. Becausethey are a single event, it is difficult to investigatetheir impact statistically. Also, the 1992-1993transition in elk numbers appears deviant. Theobserved growth rate of 0.49 is a large outlier forthe dataset. Furthermore, this growth rate isslightly greater than the physiologically maximumpossible growth rate (0.46) given the interpolatedsex ratio for this year. Consequently, weremoved the 1992-1993 transition from the primaryanalyses. Last, 1988-1989 through 1991-1992are considered post-fire years and analyzed separatelyfrom the main body of data. Coughenourand Singer (1996) present "corrected" estimates

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and Gogan 109Table 2. Late winter age and sex composition of the northernYellowstonelk herd, winters 1987-1988 through 1995-1996,Montana and Wyoming. Data are from records archived at YellowstoneNational Park, Mammoth, Wyoming, USA.Calves: Yearling M: Adult M:Year 100 F 100 F 100 F n1987-1988 23 4 15 5,1031988-1989 6 2 13 2,8271989-1990 19 3 12 3,3931990-1991 26 - - 1,9251991-1992 44 - - 3,5301994-1995 33 11 29 3,6131995-1996 28 9 26 2,902of elk numbers for winters 1986-1987 through1990-1991 by adjusting numbers to account forthe proportion of radiocollared elk that were notseen during the standard aerial censuses.Coughenour and Singer's (1996) calculationsindicate that even in good survey years, aerialcensuses post-1986-1987 underestimate the populationlevels on the order of 25%. However, forthe 1988-1989 and 1990-1991 censusesCoughenour and Singer (1996) believe that only49 and 51% of the population was counted,respectively, confirming the census participants'assessments. We reduced the Coughenour andSinger (1996:574) corrected estimates for1988-1989 and 1990-1991 by 25% to make themcomparable with the rest of the count data.Early and Late PeriodsThe census data do not form a continuousrecord. No population estimates were made during1980, 1981, 1983, or 1984. Consequently,growth rates are not available from 1979 to 1984.This divides the time series into an early (i.e.,1964-1979) and a late (i.e., 1986-1995) period.Adjusting for HuntingBecause our intent was to investigate the naturalregulation of the northern Yellowstone elkherd, we corrected for hunting to discern theunderlying natural population dynamics regardlessof whether hunting is density-dependent ordensity-independent. The annual elk cycle in Yellowstonebegins with calving in spring, resultingin a population increase (Fig. 1). Perinatal mortalityreduces the population size somewhat(Singer et al. 1997), and then the populationenters a period with comparatively low naturalmortality until late winter (Green et al. 1997).Superimposed on this cycle are annual total herdcounts at the beginning of each year and annualhunting mortality. This population is subjectedto a regular-season hunt and a late-season hunt.The regular hunt has occurred between lateOctober and late November since the mid-1960s(Erickson 1981). The late hunts have varied fromlate November through early March during themid-1960s, mid-December through mid-Februaryduring the early 1980s, and earlyJanuary to mid-February during the 1990s (Erickson 1981,Lemke et al. 1998). Thus, the count and mosthunt mortality occur during a period of low naturalmortality. This allows us to study densitydependence in this herd as it would haveoccurred in the absence of hunting. We calculatea pre-hunt population estimate by adding all legalharvest plus known illegal kills and lost woundedanimals presumed to have died that occurredbefore the annual count to the estimated herdsize (Lemke et al. 1998). In a similar fashion, apost-hunt population estimate is constructed bysubtracting known subsequent anthropogenicmortality from the census (Table 1). We investigatednatural population regulation by studyingthe statistical dependence of transitions in populationnumbers from post-hunt to pre-hunt thenext year on post-hunt population size.Correcting for Range ExpansionDensity dependence by definition relatesgrowth rates to population densities. Calcula-tions based on raw population counts will not bevalid if range expansions or contractions occur.The winter range for the northern Yellowstoneelk herd increased during the early 1980sPre-huntestimatez Z I /_ \6iPerinatal mortalityAerialcount Post-huntestimateCalving Early Latehunt huntWinter mortalityMay Jul Sep Nov Jan Mar MayJun Aug Oct Dec Feb AprFig. 1. Schematic diagram of annual cycle of elk numbers, timingof natural and human-induced mortality and sampling,northern Yellowstonelk herd, Montana and Wyoming.

110 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002(Coughenour and Singer 1996, Lemke et al.1998). These authors estimated that between1980 and 1985 (between our early and late periods),the extent of the winter range increased41%. In analyses that relate to population densities,we adjust the estimated population numbersduring the late period by dividing by 1.41. Thisexpresses all estimates as densities in units of animalsper pre-1980 winter range.Testing for Density DependenceTo legitimately test for density dependence intime series of population estimates, one musthave a true a priori hypothesis that is null andalternative models that are specified beforeinspecting the data. Following Dennis and Taper(1994), we used a null model of exponentialgrowth and an alternative model of Ricker density-dependentgrowth. We used a parametric bootstraplikelihood ratio (PBLR) test (Dennis andTaper 1994). This procedure regresses populationgrowth rate as a response variable against apredictor variable of population size. The distinctionbetween the PBLR test and a standard regressionis that the PBLR develops the distribution ofthe test statistic under the null hypothesis by simulation.Thus, it gives a true size to the test of densitydependence. The test also is robust againstmeasurement error (Dennis and Taper 1994).Identifying the Form of PopulationDynamicsIdentifying Population Dynamic Process withSchwarz's Information Criterion.-Because legitimatehypothesis testing requires a single pair ofnull and alternative hypotheses, it often is quiteconstraining. Model mis-specification is a majorsource of error in data analysis (Chatfield 1995,Buckland et al. 1997, Burnham and Anderson1998). Model identification is an approach thatminimizes the risk of model mis-specification bycomparing the goodness-of-fit of a whole suite ofmodels. A number of possible criteria for comparingmodels exist. We prefer the informationcriteria methods because of their strong statisticalfoundations (Sakamoto et al. 1986, Burnhamand Anderson 1998) and because the validity ofits application to the identification of populationdynamic models in time-series analysis has beeninvestigated through simulation (Hooten 1995).Although model identification formally selectsa single model from a suite of models, as opposedto testing a single null against a single alternative,the process can still be used to compare classes ofmodels. All the population dynamic models weinvestigated were classified as density-independentor density-dependent models. Thus, if themodel identified as the best model is a memberof the set of density-independent models, thenthe population dynamics are considered to bedensity-independent, while, if the identifiedmodel is a member of the density-dependent set,the population dynamics are classified as densitydependent(Hooten 1995, Zeng 1996, Zeng et al.1998). Because of the multiple models involvedand because explicit P-values are not calculated,such a classification by model identification doesnot per se constitute a hypothesis test. Nonetheless,if the compared models have been includedon an a priori basis, then the comparison retainsmuch of the epistemological standing of ahypothesis test (Burnham and Anderson 1998).There are a variety of possible information criteriato choose from (Hooten 1995). All informationcriteria are constructed as -2*(log-likelihood)+ (an adjustment). The adjustment is afunction of the number of parameters or of thenumber of parameters and the number of observations.The adjustment for Akaike's InformationCriterion (AIC; Akaike 1973) is 2*p (p = the numberof parameters including the error variance),while the adjustment for Schwarz's InformationCriterion (SIC; Schwarz 1978) contains a samplesize correction so that the adjustment is the numberof parameters times the natural logarithm ofthe number of observations. The model with thelowest value for the information criterion used isselected as the best-supported model. However,this selection should not be considered absolute.If the difference in information criteria (IC) valueof 2 models is slight, then it is best to consider themodels more or less equally supported and retainboth for consideration. Differences in informationcriterion values (AIC) of >2 are generallyconsidered to indicate that models are statisticallydistinguishable (Sakamoto et al. 1986).It has been shown both theoretically (Stone1979) and through simulation (Hooten 1995)that the SIC estimates the true order of theunderlying model more accurately than the AIC.Furthermore, the SIC tends to choose models oflower order than the AIC (when the selection differs).In contrasting between density-independentand density-dependent classes of models,this feature will make the identification of densi-ty dependence conservative as the density-dependentmodels contain more parameters than thedensity-independent models (Zeng et al. 1998).

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and Gogan 111(AIC)Ricker, 2 a, & lb,v (0.00)Ricker, 1 a, b, & v (0.43)Ricker, 2 b, & 1 a,v (0.75)Ricker, 2 a, b, & 1 v (0.80)Gompertz, 2 a, b, & 1 v (2.00)Gompertz, 2 b, & 1 a,v (2.75)Gompertz, 1 a, b, & v (3.36)Ricker, 2 a, b, & v (3.48)Gompertz, 2 a, b, & v (4.59)Exp single model (5.74)Gompertz, 2 a, & 1b,v (6.60)Exp double model (11.16)Random walk (18.68)Two stationary dist (41.21)Single stationary dist (59.70)-25 -20 -15 -10 -5 -0SIC valuesFig. 2. Schwarz Information Criteria (SIC) selection for appropriatemodels to describe observed trends in populationchange, northern Yellowstonelk herd, 1965-1995, Montanaand Wyoming. Values of SIC for each model are given inparentheses on the Y-axis. Numbers of intercept (a), slope(b), and error (v) terms indicated.On the other hand, selection by minimum AIC isasymptotically equivalent to selection by minimumprediction error (Stone 1977). Becauseour primary intention is to identify the underlyingform of population dynamics of the northernYellowstone elk herd and not to make explicitpredictions, use of the SIC is appropriate.Models Considered.-Density-independent modelclasses are random walk and exponential growthmodels. Included in the density-dependent classare Gompertz (1825) and Ricker (1954) models.We included models that differentiated populationdynamics in the early and late periods fordensity-independent and density-dependentgrowth model classes. For example, we consideredRicker and Gompertz growth models withintercept, slope, and variance parameters commonto the early and late periods, and Ricker andGompertz models that allowed >1 of these parametersto differ between the periods. In Rickermodels, the relationship between growth rateand population density is linear, while for Gomnpertzmodels, growth rate is linearly associatedwith the logarithm of population size (Fig. 2).We also included the stationary statistical distri-bution models. This class of models does notassume any dependence of population size at agiven time on the population size at any previoustimes. Population sizes are simply assumed to bedrawn from some random distribution.Surprisingly, in such a situation, growth rateswill be negatively correlated with population size.This phenomenon was first pointed out by Eberhardt(1970), and has been discussed recently byWolda and Dennis (1993) and by Wolda et al.(1994). Wolda and Dennis (1993) demonstratethat rainfall can yield a significant result in a testof density dependence. This may be disturbing tobiologists. However, stationary statistical distributiondoes not necessarily indicate an absence ofdirect causal density dependence. For example, aGompertz growth model with a growth rate parameterof 1 will generate a log-normal stationarydistribution of population sizes where populationsize at a given time is independent from populationsize at any previous time. We have explicitlyincluded the stationary statistical distributionmodel class to alleviate the uncertainty generatedby this situation. If a model is identified as a density-dependentmodel but is strongly distinguishablefrom a stationary distribution, then a caveatthat could be raised against deciding the populationdynamics represents biological densitydependence has been removed.Recent work has successfully used nonparametriccurve fitting and generalized additive modelsto investigate density dependence in natural populations(Bj0rnstad et al. 1999). These techniquesare data intensive; for example, Bj0rnstadet al. (1999) analyzed a composite dataset with250 observations. Such an approach cannot besuccessfully applied to the northern Yellowstoneelk herd because of the paucity of data.Assessing the Impacts of EnvironmentalFactorsTo determine the impact of weather on thepopulation dynamics of the northern Yellowstoneelk herd, we include weather variables as covariatesin some population dynamic models. Fames'(1996) weather severity index is a weighted sumof 3 normalized components: winter forage avail-ability, snow depth, and winter temperature. Allcomponents are constructed so that higher num-bers indicate milder winters. Thus, a high valuefor the snow component indicates low snow levels.We do not use Fames' full index, but insteaduse his 3 components directly. This enables themost effective weightings to emerge from thedata. Weather variables used (Table 3) comefrom Fames' most recent revision of his compilationof 30 of Yellowstone climate data (P. Fames,Soil Conservation Service, personal communica-tion). We consider these 3 variables, their l-yearlags (previous year's values), and all squares ofthese variables in looking for the effect of weatheron elk population dynamics. We also considerthe current spring's precipitation and its square.

112 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002Table 3. Winter condition indices for the lower northern Yellowstonewinter range, Wyoming (after Fames [1996] and P.Fames, Soil Conservation Service, 1998 [personal communication]).Season19641965196619671968196919701971197219731974197519761977197819791980198119821983198419851986198719881989199019911992199319941995Temperatureindex0.7-2.62.42.91.22.12.41.41.3-2.82.4-0.9-0.72.91.8-4-0.63.60.32.9-3.4-3.50.9-0.40.1-2.91-2.41.6-0.81.60.7Snowindex-0.1-3.23.2-3.8-1.9-1.1-1.6-3.3-3.23-3.6-2.8-3.83.3-2.7-1.61.33.8-1.70.82.10.723.53.1-1.6-1.11.621.72.1-0.8Forageindex-0.62.52.5-2.432.41.91.4-3.21.9-2.7-3.30.91.7-0.7-3.5-2.9-0.42.51.323.2-1.22.53.3-3.7-2.2-2.8-3.943.7-0.4Winter forage was not directly measured, butFames assumed the previous spring's precipitationcan act as a surrogate. Coughenour andSinger (1996) demonstrated a correlation betweenthe previous spring's precipitation andwinter forage. Thus, previous spring's precipitationshould affect overwinter survival, while currentspring's precipitation might be expected toinfluence perinatal mortality. Weather variableswere included as covariates (Rothery et al. 1997,Dennis and Otten 2000) in Ricker and Gompertzdensity-dependent models and in exponentialgrowth density-independent models. SchwartzInformation Criterion values were comparedamong regressions of all possible subsets of predictorvariables (Neter et al. 1996). To avoidselection bias (Zucchini 2000, Taper 2002), nomodel was considered that had >8 variablesincluding error variance, intercept, populationdensity, and weather variables. Thus, there werealways >2x as many data points (year-to-year transitionsin herd numbers) as variables estimated.Delayed Density DependenceDelayed density dependence has beenobserved in red deer (Cervus elaphus; Forchhammeret al. 1998). To investigate the impact ofdelayed density dependence in the northern Yel-lowstone elk herd, we perform a model identificationanalysis on a reduced dataset of all transitionsfor which the previous year's density alsohas been observed (3 consecutive yearly popula-tion estimates). This reduces the number ofobservations from 17 to 13 transitions. All possiblesubsets regression was performed as abovebut with the inclusion of the previous year's populationdensity as a possible predictor variableand the current year's density.Assessing the Impacts of 1988 Droughtand FiresWe compare population estimates for the postfireyears (1989-1996) with predictions based onthe pre-1988 data to discern the impact of the1988 drought and wildfires on the northern Yellowstoneelk herd's population dynamics. We inspectedthe magnitude and direction of residualsof observations from predictions for evidence ofdrought and fire influence.Post hoc AnalysesThe analyses described above are true a priorianalyses decided on before inspection of the data.The following analyses were inspired by featuresin the data we became aware of during detailedinvestigation. Epistemologically, these analyseshave the standing of exploratory data analyses.The Interaction of Density and Life History Traits.-Because growth rate is a synthetic parameter aris-ing from more fundamental demographic rates,an observed dependence of growth rate on populationsize implies there must be density dependencein some combination of underlying demographictraits. We investigated fertility andsurvival rate directly for indications of densitydependence. Density-dependent immigrationand emigration have been indicated to be importantin the dynamics of some species (Stacey and

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and Gogan 113Taper 1992, Stacey et al. 1997). Unfortunately,data are not available for us to verify the existenceof permanent long range movements inthis population or to determine the densitydependentnature of the process. However, lowdispersal rates for the northern Yellowstone elkherd have been documented (Houston 1982).Fertility.-Fertility often is defined as the numberof female offspring produced/female thatsurvive to the first population census or estimatefollowing birth (Keyfitz 1985, Caswell 2001).However, because the herd composition surveysdo not identify calf sex, we define fertility as thenumber of calves produced/female that surviveto the first census. Fertility is calculated as theratio of the estimated number of calves in thepopulation at the time of the next winter's compositionsurvey divided by the number of femalesestimated in the post-hunt population of the previouswinter. The composition surveys do not dis-tinguish yearling females from reproductivelymature females. Our demographic model incor-porates these data to minimize the consequencesof this constraint.Survival Rate. We define adult survival rate asthe ratio of the estimated number of adults in thepre-hunt estimate for the following year to theestimated number of adults in the post-hunt estimate.We are unable to separately estimate thesurvival of males and females; the hunt data donot completely break the kill down into malesand females. Because this estimate of survivaldoes not follow marked cohorts but depends onraw population estimates, survival rate estimates>1 can and do occur.Curve Fitting.-The estimates for fertility andsurvival rate are plotted against population den-sity. Based on these plots, we decided on appropriatefunctional forms for recruitment and survivalrate and estimated the parameters of thesemodels using nonlinear curve fitting. We usedMarquardt's (1963) algorithm to fit the curves.Composition counts are sporadic during thelate period. As a consequence, there are only afew years during the late period where recruitmentand survival rates were estimated. We baseour estimates of survival and fertility/densitydependence curves solely on data from the earlyperiod.A Simple Demographic ModelTo incorporate the nonlinearity in the northernYellowstone elk herd population dynamics thatour initial analysis discovered, we constructed asimple demographic model of population growth.Population growth rate (rt) is modeled as:rt= n ( (N) fNt + s (Nt)Nt)Nt(1)where Nt is population size, m(Nt) is fertility, ft isproportion of females in the population at time t,and s(Nt) is survivorship.This simple formulation allows for separatedensity dependence in survivorship (s[Nt]) andin fertility (m[Nt]). The major drawback of thisapproach is that the model does not distinguishbetween yearling females and reproductivelymature females. On average, this is incorporatedin the estimate of fertility. However, some of theyear-to-year variation in observed growth rate maybe due to variation in the proportion of the populationof females in the pre-reproductive stage.We used appropriate parametric forms for survivorship(s[Nt]) and fertility (m[Nt]) derivedfrom inspection of the estimated rates. Marquardt'salgorithm had convergence problems sowe fit equation 1 with the Nelder/Mead downhillsimplex method, a very robust technique for nonlinearregression (Nelder and Mead 1965, Presset al. 1992). We also investigated nonlinearity inthe elk population dynamics, using a 0-Rickermodel (Gilpin and Ayala 1973, Thomas et al.1980, Hooten 1995)Interpolation of the Proportion of Females. Theproportion of adult females in the population isa necessary parameter for predicting growth rateusing the demographic model. This informationis missing for 1992-1993 and 1993-1994. However,there is noticeable continuity in the proportion offemales in the population through time. Therefore,we constructed estimates of the proportionof adult females in the population for those 2 yearsfrom surrounding data using linear interpolation.RESULTSTesting for Density DependenceThe 17 transitions that comprise the time seriesare divided into 4 unbroken sub-series (Table 1).The parametric bootstrap of the Dennis andTaper (1994) test was conditioned on the initialpopulation sizes for each sub-series. Despite thetime series' brevity and its division into multiplesub-series, both of which should reduce thepower of a test, a 1-sided test was significant atapproximately P = 0.009 (2-sided test P= 0.018).This justifies rejecting the a priori null hypothe-

114 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002L.cICll0n ..a I I0.50.0-0.52,0 )00 7,000 12,000 17,000 22Minimum winter count1. .w0.50.0A BIX,) ( i IIIII1 II I I I In .. --U,02,000i Ii i iI IIIII()!~ ~ !(3~IIIIII1 1IIII7,000 12,000 17,000 22Minimum winter densityFig. 3. Estimated carrying capacities, marked by verticaldashed lines for the northern Yellowston elk herd, Montanaand Wyoming, based upon counts (a, upper panel) and correctedfor increase in size of the winter range (b, lower panel).Note that the X-axis is total count in the upper panel and densityin the lower panel. Circles indicate observations from theearly period, while squares indicate the late period.sis of growth rate independent of population andaccepting the alternative hypothesis that growthrate declines with population density.Identifying the Form of Population DynamicsThe best density-independent model found wasexponential growth with the same parameters inthe early and the late periods (Fig. 2). The bestdensity-dependent model in the set explored wasa Ricker model with separate intrinsic growthrates (a) in the 2 periods, but single coefficient ofdensity-dependent decline (b) and single processerror for both periods. The difference in theinformation criteria (AIC) between these modelsis 5.74. Differences of >2 generally are consideredsignificant (Sakamoto et al. 1986), while differencesof >5 are deemed extremely significantby Burnham and Anderson (1998). Thus, modelidentification using SIC supports the presence ofdensity dependence in the population dynamicsof the northern Yellowstone elk herd. A differenceof 2.0 between the best SIC values for Rick-er models over Gompertz models provides somesupport for Ricker-like density dependence overGompertz-like density dependence. The verylarge differences between the stationary distribu-tion models and our best models indicate thatthe observed density dependence is biological,and not a statistical artifact. The poor performanceof the stationary distribution models canbe attributed to the long stretch of continuousgrowth in the early period.The best model (Fig. 2) distinguishes betweenthe early and late periods in that some parametersare fit separately for the periods. However,there is so little difference (AIC = 0.34) betweenthis model and a Ricker model fit over the entiredataset that the models are not statistically distinguishable.With only 5 usable transitions in thelate period, our ability to characterize the populationdynamics of this period is weak. If countsin the late period are not adjusted to densities toaccount for the increase in area of winter rangeoccupied in the late period, the results are differentwith the best 2-period model (Ricker) beingsuperior (AIC = 4.2) to the best single-periodmodel (Gompertz). Thus, the bulk of the apparentdifferences between the periods can be attributedto the increase in the amount of winterrange used by the northern Yellowstone elk herd.In a comparison of the best model for the unadjusteddata (Fig. 3a) with the best model for therange expansion adjusted data (Fig. 3b), approx-imately 60% of the population increase isaccounted for by range expansion. The remainingincrease in population size is due to an increasein density at the estimated equilibrium.However, exactly quantifying how much of theincrease in elk abundance is due to range expansionis complicated by the uncertainty in modelselection. Considering the 4 statistically indistin-guishable best models (Fig. 2), 2 models indicatethat range expansion accounts for almost all ofthe observed population increase (Figs. 4b,d)while 2 models indicate that increases in densityare involved (Figs. 4a,c). Density dependence isa component of all of these models, but the portionof population increase accounted for byrange expansion varies from 60 to 100%. Regressionequations for all parametric a priori modelsare given in Table 4.The Impact of Weather on Elk DynamicsBecause density has a large effect on elk populationdynamics, it is included in the set of potentialvariables with weather variables. The SIC best

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and Gogan 1150I-In , , I Iq I, , ,0.5AIC = 0 aIto , ^^ ^II I-II0mAIC = 0.43 1 bI-0.5I _0)LI0.0Annre2,000---''--_-i i i i8,000 14,000Minimum winter densityII20,0000_Ih.I0.0_n._lCp [X InII2,000 8,000 14,000Minimum winter density004.'I-00)h.I8,000 14,000Minimum winter density20,0008,000 14,000Minimum winter densityFig. 4. Display of best 4 a priori models to describe observed trends in population change, northern Yellowstone elk herd,1965-1995, Montana and Wyoming. Note that the difference between early and late estimates of population equilibrium varieswidely among these statistically indistinguishable models.model out of all possible models of order

116 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002Table 4. Regression equations for a priori models to describe observed trends in population change, northern Yellowston elkherd, 1965-1995, Montana and Wyoming. N is population size, X is In(N), and Z is Gaussian random variable with mean 0 andvariance 1. IE and IL are indicator functions for the early and late periods, respectively. Arguments to the indicator functions areonly expressed for observations from that period.Model nameRegression equationRicker, 2a, & lb,v IE(0.375) + IL(0.483) - (3.009 x 10-5)N + 0.084ZRicker, 1a, b, & v 0.330 - (2.124 x 10-5)N + 0.093ZRicker, 2b, & 1 a,v 0.373 + IE([-2.942 x 10-5] N) + 0.086ZRicker, 2a, b, & lv IE(0.357 - [2.76 x 10-5] N) + IL(1.017 - [7.477 x 10-5] N) + 0.079ZGompertz, 2a, b, & 1vIE(1.790 - 0.186 x 10-5]X) + IL(8.900 - 0.902 x 10-5] X) + 0.082ZGompertz, 2b, & la,v 1.550 + IE(-0.158X) + IL(-0.147X) + 0.102ZGompertz, la, b, & v 1.118 - 0.107X + 0.101ZRicker, 2a, b, &v IE(0.357 - [2.762 x 10-5] + 0.082Z) + IL(1.017 - [7.477 x 10-5] + 0.071Z)Gompertz, 2a, b, &vIE(1.790 - 0.188X + 0.086Z) + IL(8.90 - 0.902X + 0.071Z)Exp single model 0.146 + 0.118ZGompertz, 2a, & lb,vIE(3.051) + IL(3.323) - 0.329X + 0.102ZExp double modelIE(0.155 + 0.119 Z) + IL(0.124 + 0.111Z)Random walk 0.187Z(1989-1992) with predicted growth rates forthose years based on our best model of densityand environmental effects (Fig. 6). In the first 2years following the fire, the observed growthrates are below predicted values, while in thethird and fourth seasons, growth rates are considerablyabove the predicted values. The residualsfor the last 2 years of the time series seemlarger than the pre-fire portion of the time series.It appears that the major effects of the 1988 firesp p2N (0.00) IT p p2N (0.92)p s2p2N (1.06)ps2F2p2N (1.26)Sp p2N (1.44)TSpp2N (1.95)t p p2N (1.98)(AIC) , I , II I I I 1-27.0 -26.5 -26.0 -25.5 -25.0 -24.5SIC values__Fig. 5. Schwarz Information Criteria (SIC) selection for appropriatemodels to describe the impacts of density and weatheron population growth rate, northern Yellowstone elk herd,1965-1995, Montana and Wyoming. Values of SIC for eachmodel are given on the Y-axis. Symbols: t, s, and f are temperature,snow, and forage for the current winter; T, S, and Fare temperature, snow and forage for the previous winter; p isprecipitation for the current spring.on elk population dynamics were brief. It shouldbe noted that although the observed 1989 growthrate is below the predicted growth rate, the residualis quite small. Caution should be taken ininterpreting these post-fire residuals because theanalysis depends heavily on sightability correctionsthat have very large uncertainties.Density Dependence in Component LifehistoryTraitsWe examined the estimated demographic ratesversus density for the early period. Fertility (Fig. 7)was fitted using a log-linear model. Adult sur-vivorship (Fig. 8) is fit with a nonlinear regressionmodel, S(N) = exp(a - bN). The parameter a wasconstrained not to exceed 0 so that survivorshipcannot appear to exceed 1 as population sizegoes to 0. Data points from the late period areincluded in the fit. Our decision to eliminate thelate period from the fit for fertility while includ-aL 0.40 a.(D0.6-0.20.0-0n!+ +? la A+~00!9+ e9 + +A+t-* +M. I . I . I . I . Il . I . .65 70 75 80Year85 90 95Fig. 6. Patterns of observed (circles, squares), predicted(crosses) and immediate post-fire observed (triangles) growthrates, northern Yellowstone elk herd, 1965-1995, Montanaand Wyoming. Single Ricker model with density, spring precipitationand spring precipitation squared as covariates.

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONELK * Taper and Gogan 1170.71.1-0.600Early period1.0-.SEarly period._0.4-0.3 '.0* 4zr.20.S00.200.803,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000Post-hunt density0.7t I3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000tFig. 7. Changes in estimated fertility with population density,northern Yellowstone elk herd, 1965-1980, Montana andWyoming. E(F) = exp(-0.108 - 0.00102*Nt).Post-hunt densityFig. 8. Changes in estimated adult survivorship with populationdensity, northern Yellowstonelk herd, 1965-1980, Montanaand Wyoming. E(S) = exp(-0.219*N3 77).ing the late period in the fit for survivorship isbased on inspection of the data and the observationthat the only environmental effects indicatedto be important by model identification usingthe linear regression were current spring precipitationand current spring precipitation squared.These variables are expected to influence fertilitybut not adult survivorship. Calculation of survivorshipfrom population counts does not allowdistinguishing mortality from emigration.Inserting the above submodels for fertility andsurvivorship into the simple demographic modelof equation 1 produces a model with an SIC ofonly -12.8. Alternatively, one can fit the parametersof this model directly to the population transitiondata using the Nelder/Mead downhill-simplexalgorithm. The fit is similar, although notquite as good (SIC = -11.4). Clearly, the demographicmodel is not supported over the simpleRicker model of population dynamics. Nonetheless,density dependence in both fertility andadult survivorship is strongly suggested (Figs. 7,8). We believe the demographic model is notsupported because it requires 2 extra parameters;this is a heavy penalty to pay with so few datapoints, and the demographic model requires theuse of the herd composition assessments. Thisintroduces new measurement errors and biasesto the analysis and probably degrades the performanceof the model.One of the consequences of density dependencein fertility and adult survivorship (Figs. 7,8) is a biphasic relationship between populationgrowth rate and density (Fig. 9). At low density,population growth rate is dominated by densitydependence in fertility, while high density populationgrowth rate is dominated by density dependencein adult survivorship (Fig. 9). This demonstratesthe biphasic nature to growth rateimposed by separate density dependence in fer-tility and survivorship. Curvature in the relationshipbetween growth rate and density can bemodeled in a simple fashion using a 0-Rickermodel (Gilpin and Ayala 1973, Thomas et al.1980, Hooten 1995). The SIC for this model is-22.58 with AIC = 1.99, indicating this model isnot clearly distinguishable from our best model.Thus, density dependence may be nonlinear inthe northern Yellowstone elk herd.00.4-0.3-0.2? 0.10.0-0.1%5,~ ^ Early period'., I* Observed r ,- - - Predicted r " *- Predicted r with average sex ratio *\I I I j3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000Post-hunt densityFig. 9. Biphasic density dependence in the northern Yellowstoneelk herd, 1965-1980, Montana and Wyoming. Thedashed line plots the growth rate predicted by the demographicmodel (Equation 1) using the observed sex ratio foreach year. The solid line plots the growth rate derived fromthe model assuming that the sex ratio is constant throughout.

118 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002DISCUSSIONDensity dependence in the population growthrate of the northern Yellowstone elk herd isstrongly supported by several aspects of ouranalysis. First, a true a priori test (Dennis andTaper 1994) rejects the null hypothesis of densityindependence. This is more significant than thetest of density dependence for this populationreported in Dennis and Taper (1994). Two differencesbetween the current analysis and that ofDennis and Taper (1994) account for this change.First, we include the late period in our analysis,while Dennis and Taper (1994) worked just withthe early period. Second, we adjust for huntingmortality while Dennis and Taper (1994) did not.Perhaps, more appropriately, model identificationalso strongly supports density dependence inthe elk herd. In comparing the best density-independentmodel to the best density-dependentmodel, we find a AIC of 5.74. This indicates densitydependence is more than 300x more stronglysupported by the data than is the absence ofdensity dependence.Currently, the Yellowstone northern elk populationis capable of regulating itself. The populationequilibrium numbers in the absence of hunting(based on minimum counts) seem to besomewhere between 20,000 and 25,000 elk for thesize and quality of the current winter range.Undoubtedly, this underestimates the equilibriumpopulation size somewhat because of sightabilityissues.Our analysis indicates that although estimatesof the area of expansion are crude, the bulk ofthe population increase can be attributed to theexpansion of winter range to the north of YNP.Range expansion directly reduces density by increasingthe denominator in the ratio of populationsize to area occupied. Further, range expansionmay have a negative density-dependenteffect as the energetic demands of longer migrationsincrease at greater population sizes(Messier et al. 1988).Environmental changes have been involved to alesser extent in the increase in ecological carryingcapacity in the late period. Spring precipitationof the current year and spring precipitationsquared were identified as contributing effects.Calf:female ratios have been correlated positivelywith winter and summer precipitation 2 years earlierand negatively correlated with the previousyear's spring precipitation for 1970-1971 through1990-1991 (although the latter relationship wasonly marginally significant; Coughenour andSinger 1996). Other variables are included inmodels not statistically distinguishable from themodel including only current spring precipitationand density (Fig. 5). Further, the weathervariables are correlated, and thus, the identificationof predictive variables is not stable (Neter etal. 1996). A more secure statement is that environmentalfactors do contribute to elk populationdynamics.Singer et al. (1997) reported that Fames'(1996) winter severity index for the current yearwas not correlated with over-winter survival of elkcalves for winters 1968-1969 through 1991-1992.However, between 1987-1988 and 1990-1991,summer survival of radiocollared elk calves wasnot correlated with current year precipitationand over-winter survival of these calves was correlatedwith Fames' (1996) winter severity index forthe current winter. This may indicate an interactionbetween the effects of density and environmentalvariation in which winter severity has amore profound impact on calf (and adult) survivalunder conditions of high density. This patternhas been reported in other ungulate populations(Clutton-Brock et al. 1987, Choquenot1991). Winter carcass surveys during the lateperiod (Green et al. 1994) show a strong (adjustedR2 = 0.73) and significant (P= 0.02) regressionof elk carcasses on Fames' winter severity index(C. Schwartz, U.S. Geological Survey, personalcommunication).Our comparison of predicted and observedgrowth rates following the 1988 fire corroboratesthe simulation findings of Turner et al. (1994)that predicted a mild, but short-lived, increase inelk growth rate due to fire. Boyce and Merrill(1996) also modeled a post-fire peak and declinein the population size of the northern Yellowstoneelk herd. However, the timing of the peakand the rate of return to background levels weobserve are much more rapid than thoseassumed by Boyce and Merrill (1996). Thus, inagreement with empirical work (Pearson et al.1995, Boyce and Merrill 1996, Vales and Peek1996) and the simulations of Turner et al. (1994)and Wu et al. (1996), we found that the 1988 firewas not responsible for the large decline in theherd from 1989 to 1990. The high 1988 populationsize and severe spring drought accounted forvirtually the entire decline. We also support theconclusions of these researchers that there was ashort-lived enhancement to elk habitat after thefire. This boost seems to have been in effect duringthe 1991-1992 and 1992-1993 years.

J. Wildl. Manage. 66(1):2002DENSITY DEPENDENCE IN YELLOWSTONELK * Taper and Gogan 119During recent years, there has been a growing iarityinterest in understanding the potential of nonlinearityin density-dependent population dynamics(Fowler 1994, Clutton-Brock et al. 1997, Higginset al. 1997, Ellner et al. 1998, McCullough 1999).An important aspect of this study is that fertilityand adult survivorship have distinct nonlinearrelationships with density. When these 2 relationshipsare coupled through a simple demographicmodel, a biphasic or ramped density dependencecurve emerged. Ramps in growth rate/densitycurves have been considered by other authors(Fowler 1980, 1981; McCullough 1990, 1992,1999). In these papers, the ramp was generatedby a physiological maximum to reproductive rate.Thus, our observation that different demographicrates can have distinct density-dependent rela-tionships, which can combine to yield rampeffects, is a previously unidentified mechanismfor generating nonlinearity in growth rates.These datasets are unusual in following growth ofa population from very low levels to near carryingcapacity. Most studies are restricted to a muchnarrower range of population sizes making it difficultto detect ramp effects or density dependencein adult survival (Gaillard et al. 1998). Yetpredictions of expected time to recovery of adepleted population or expected time to extinctionmay be biased by neglecting these changesin the slope of density dependence function (Pascualet al. 1997).Eberhardt (1977) suggested that density-dependentresponses in life history should follow theorder: (1) juvenile survival, (2) age of first reproduction,(3) adult reproductive rate, and finally(4) adult survival. We are not able, given thedata, to distinguish life-history stages 1 through 3.They all contributed to the fertility we estimate.However, the onset of density dependence inadult survival is at a much higher population levelthan for fertility (Figs. 7, 8). An interesting fea-ture of the density dependence of fertility is it isconcave (Fig. 7). This contrasts with observationson a number of other ungulate species reviewedby Fowler (1994). A further contrast between thisstudy and reviews of ungulate dynamics is thepresence of density dependence in adult survival.Gaillard et al. (1998) indicated that densitydependence in adult survival seems rare.Our analysis is unable to distinguish betweenmortality and emigration. Thus, it is possible thatthe declines in adult survivorship observed athigh densities are the result of adults permanentlyleaving the herd. Experts with long famil-with the herd do not believe this is the case(D. B. Houston, U.S. Geological Survey, personalcommunication). Smith and Anderson's recentstudy (2001) of dispersal in the nearby Jacksonelk herd (Grand Teton National Park) indicatesthat mature adult elk are extremely herd faithful.The little dispersal that did occur was by juveniles,and did not appear in their study to have adensity-dependent component. Further, mortalityof dispersers from the Jackson herd was muchgreater than that of nondispersers.MANAGEMENT IMPLICATIONSManagement of the northern Yellowstone elkherd has been controversial throughout the 20thcentury. Between 1935 and 1968, annual reductions(by trapping and shooting) inside and outsideYNP removed 1,500animals from the northern Yellowstone elk herdby sport hunters (Lemke et al. 1998).The increase in the size of the northern Yellowstoneelk herd has been concomitant with amajor expansion of the herd's winter rangebeyond the YNP boundaries (Lemke et al. 1998).At present, a variable portion of the herd movesduring each fall and winters north of YNP onother public (chiefly USDA Forest Service) andprivate lands where management authorityresides with the Montana Department of Fish,Wildlife and Parks (MDFWP; Lemke et al. 1998).This expansion has been in part facilitated and sup-

120 DENSITY DEPENDENCE IN YELLOWSTONE ELK * Taper and GoganJ. Wildl. Manage. 66(1):2002ported by establishment of the Dome MountainWildlife Management Area by MDFWP and acquisitionof other private lands north ofYNP by sporthuntingorganizations. The MDFWP is responsiblefor establishing harvest quotas during aregular fall hunt and a late winter hunt. Huntersuccess is influenced by a combination of the timingand numbers of elk leaving the park, weather,and MFWP regulations. The MFWP has steadilyincreased the legal harvest of northern range elkin both the regular and late hunts. An average of>1,500 elk were taken each year by huntersbetween winters 1975-1976 and 1996-1997 (Lemkeet al. 1998). During winters 1991-1992 and1996-1997, numbers removed (Lemke et al. 1998)approximated the lower levels of elk removals withinYNP during the 1950s and 1960s during the controlperiod (W. J. Barmore, National Park Service,unpublished report). The extent to which currentremovals mimic prehistoric winter dispersalof elk from the northern range remains unknown.ACKNOWLEDGMENTSThe data analyzed herein were secured by thehard work and dedication of biologists of theNational Park Service, Montana Department ofFish, Wildlife and Parks, U.S. Forest Service, andthe U.S. Geological Survey. Since 1983, theseefforts have been coordinated through theNorthern Yellowstone Cooperative Wildlife WorkingGroup. We are particularly grateful to T. W.Lemke, J. A. Mack, and D. Tyers for their collaborativeefforts to gather the recent data. Inpreparation of this manuscript, we benefitedfrom discussions of the topic of density dependencein ungulate populations with D. B. Houston,D. R. McCullough, C. W. Fowler, M. S. Boyce,and B. Dennis. Many of these individuals alsoprovided comments on earlier drafts of the manuscript.C. Jerde produced the figures. 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