adaptive management for reintroductions: updating a wolf recovery model for yellowstone national...

Ecological Modelling 193 (2006) 315339

Adaptive management for reintroductirecovery model for Yellowstone

Nathan Varley , Mark S. BDepartment of Biological Sciences, University of Alberta, Edmonton, Alta., Canada T6G 2E9

Received 23 July 2004; received in revised form 3 September 2005; accepted 7 September 2005

Abstract

Ecologiexamplesanticipatesince wolvdynamicsby hunterswinter sevsmaller remodel prepredationElk harvesis density-models inthe density 2005 El

Keywords:Numerical r

Correspfax: +1 780

E-mail

0304-3800/doi:10.1016Available online 2 November 2005

cal models have their greatest potential for conservation in the context of adaptive management, but there are fewwhere models have been updated as new data have become available. We update a predatorprey model built tothe consequences of wolf (Canis lupus) reintroduction into Yellowstone National Park, with new data accumulatedes were released in 1995. Observed response to wolf recovery allows us to evaluate our ability to predict systemand thereby address concerns about future impacts of predation on elk (Cervus canadensis) numbers and harvest. Structural assumptions of the model include a dynamic carrying capacity for elk, Kelk(t), varying as a function oferity and summer forage production. During severe winters the aerial extent of Yellowstones Northern Range getssulting in density-dependent migration of elk outside the park where they are subject to hunter harvest. The updateddicts that hunter harvest of elk will cause a decline of mean herd size relative to that expected without harvest. Wolfresults in a further 21% reduction in elk herd size with wolf consumption averaging approximately 1035 elk annually.t is reduced by wolves yet annual hunter harvest was sustained at an average of 1089 elk. Predation and hunter harvestdependent providing a stabilizing influence that reduces the risk of severe elk population decline. Using simulationadaptive management of the wolfungulate system in Yellowstone reinforces agency management policies, especially-dependent harvest quota for elk.sevier B.V. All rights reserved.

Adaptive management; Canis lupus; Cervus canadensis; Elk; Experimental management; Functional response; Harvesting; Hunting;esponse; Predatorprey dynamics; Simulation model; Wolves; Yellowstone National Park

onding author. Tel.: +1 406 223 2152/848 2469;492 9234.address: [email protected] (N. Varley).

1. Introduction

Adaptive management has been advocated forspecies reintroductions (Sarrazin and Barbault, 1996;Bearlin et al., 2002; Hirzel et al., 2002) and transloca-tions (Brook et al., 2002; Stockwell and Leberg, 2002),but adaptive management has failed in the majority

$ see front matter 2005 Elsevier B.V. All rights reserved./j.ecolmodel.2005.09.001ons: Updating a wolfNational Park

oyce

316 N. Varley, M.S. Boyce / Ecological Modelling 193 (2006) 315339

of attempted applications (Walters, 1997). Adaptivemanagement often fails to advance from simulationmodeling to subsequent evaluation of the models afterfield experiing is subsparticularlyvalidationwe have ferefined usinfuture mannently in aYellowstondevelopedanticipated1992, 1993Vales and Pand Singerlowstone Nyears of dato recovery

We havdictions foWOLF5 mon data copark. Thewell, undertions thatbecome avmodel, WOwolfpreyferred overwas undereof the estimkills has benumericaldata with dters for WONR. New dpredation sharvest thaelk harvesta harvest oabout the tin the simuated the altOur objectithe model,dation on e

With a narrowed focus on the NR, the projections of theWOLF6 model will be useful for adaptive managementof the Yellowstone ecosystem.

ethod

OLF6escribby B

ariatioand fontrastex str

Elk po

e NReginn; Barmated

1). Thn sizetion b). Bacunpubler anBoyce; Coug).ountsar theex clat thatmonthows (fmonth

Trans

Lefkoructedf any

t) =mentation, and quite often detailed model-tituted for empirical evaluation of models,when the cost of acquiring data for model

can be prohibitive (Walters, 1997). Thus,w cases where models were evaluated andg data from field experimentation to guide

agement. Simulation models figured promi-plan to restore gray wolves (Canis lupus) toe National Park, USA. Several models wereto predict the recovery of wolves and theirnumerical effects on prey (see Boyce, 1990,, 1995; Garton et al., 1990; Singer, 1990a;eek, 1990; Boyce and Gaillard, 1992; Mack, 1993). Wolves were reintroduced to Yel-ational Park (YNP) in 1995 providing 10

ta for examining the predictions made prior.

e evaluated model assumptions and pre-r YNPs Northern Range (NR) from theodel (Boyce and Gaillard, 1992) based

mpiled since wolves were released in theWOLF5 model predicted prey abundanceestimated wolf numbers, and made assump-need adjustment now that new data haveailable. We have updated the simulationLF6, which better characterizes the YNP

system. Elk (Cervus canadensis) were pre-alternate prey in WOLF5, but the preferencestimated relative to current data; about 90%

ated species composition of winter wolfen elk (Smith, 2005). Wolf functional and

responses in WOLF5 were estimated fromifferent assemblages of prey, but parame-LF6 were based on data directly from the

ata also revealed age/sex-specificity of wolfubstantially different from that of huntert was not modeled in WOLF5. Quotas forduring the Gardiner (Montana) late hunt,f NR elk outside the park, were changedime of wolf recovery, requiring refinementlation of harvests. Finally, we have evalu-ernative of potential wolf culls in WOLF6.ve for WOLF6, as with previous versions ofis to forecast the consequences of wolf pre-lk, other ungulate prey, and human harvests.

2. M

Wand ddatedtic vmateIn coand s

2.1.

Ththe b1982fluctuFig.ulatiodetec1997upon(Fowand19932002

Cor ne

age/stion a18old-c30

2.2.

Aconstend o

Nelk(s

is based on the WOLF5 model developeded by Boyce and Gaillard (1992) and vali-

oyce (1995). Both versions include stochas-n simulating year-to-year variation in cli-rage production (Merrill and Boyce, 1991).to WOLF5, version WOLF6 includes age

ucture for elk.

pulation dynamics

elk herd has fluctuated considerably sinceing of record keeping in YNP (Houston,

ore, 2002), and since 1972 counts havearound a mean of 13,716 (Lemke, 2003;ese counts are considered a minimum pop-and have not been corrected for consistentias of approximately 15% (Singer et al.,

kground data for the NR elk herd were basedlished park records and published literatured Barmore, 1979; Houston, 1982; Merrill, 1991; Singer, 1990b; Mack and Singer,henour and Singer, 1996; Taper and Gogan,

of the NR herd were typically collected atend of the calendar year. Therefore, the fivesses were defined to reflect herd composi-time: calves (6 months old), spikes (maless), cows (females 18 months to 9 years),emales 10 years or older) and bulls (maless or older).

ition matrix

vitch projection matrix (Caswell, 2001) wasfor the five-age/sex classes such that at the

given year, t, the total population size was:

5

i

Ni(t) (1)

N. Varley, M.S. Boyce / Ecological Modelling 193 (2006) 315339 317

Fig. 1. Count et al., 1and 1990199

where Ni isold-cow anA(t), whichof the numyields a colyear:

Ncalf

Nspike

Ncow

Nold-cow

Nbull

N

The popthe dominathat Nelk(t+stable age dfied the proan annual t

We definclasses i atto remain ithe probabcurrent clasis the probinto the old

ical ex(P.J. W, so Rt lowe

een Pcs of the Northern Yellowstone elk herd, 19722004, data from Lemke1 were adjusted for poor count conditions.

the number of elk in the i= calf, spike, cow,d bull classes. The square projection matrix,

when post multiplied by a column vectorber of individuals in each stage class, N(t),umn vector for the population the following

0 0 Rcalf.c Rcalf.oc 0

identratesdata)reflecbetwt+1

=

Pcalf.m 0 0 0 0Pcalf.f 0 Scow 0 0

0 0 Pcow Sold 00 Pspike 0 0 Sbull

t

N

N

No

N

ulation growth rate, , can be obtained fromnt eigenvalue of the projection matrix such

1) =Nelk(t), when the population is in aistribution (Caswell, 2001). We have modi-jection matrix to make it time varying, withime step.e Ri(t) to be the recruitment of calves fromtime t, Si(t) is the probability of survivingn the same class i at time t+ 1 and Pi(t) isility of surviving and advancing from thes into the next class at time t+ 1 (e.g. Pcowability of a cow surviving and advancing-cow class) The Rcalf.c and Rcalf.oc terms are

and differeOn average(Houston, 1vival for aprobability

While thindividualsthan 1 yeacows. In ththe probab(Scow) andto the next s998 and Taper and Gogan (2002); counts in 19881989

calf

cept for the effect of differential pregnancyhite, National Park Service, unpublished

calf.oc was reduced to 90.85% of Rcalf.c tor pregnancy rates in old-cows. Differencesalf.f and Pcalf.m reflect the effect of sex ratiospike

cow

ld-cow

bull

t

(2)

ntial survival of male and female calves., 47% of yearlings at 18 months are males982), thus Pcalf.m is the probability of sur-

calf multiplied by = 0.47, and Pcalf.f is theof survival of a calf multiplied by (1 ).e projection interval of the matrix is 1 year,in the cow class stay in that class for more

r before advancing to the next class, old-is case, annual survival was partitioned intoility of surviving and staying in the stagethe probability of surviving and advancingtage (Pcow). We used the method of (Crouse


et al., 1987; see also Caswell, 2001) to estimate Scowand Pcow as follows:

Scow =(

1 pdcow1cow1 pdcowcow

)pcow (3)

and

Pcow = pdcowcow (1 pcow)

1 pdcowcow(4)

where pcow is the annual survival for cows and dcow isthe duration in years of the cow class, dcow = 9. Sum-ming Scow and Pcow gives pcow, the annual probabilityof survival for cows. The probabilities of transition,reproduction, and survival in the transition matrix weretime-varyinmate as des

2.3. Densi

Survivalto be strong1979; MerTaper and GResearch CGogan, 20reported bysity depend

Si(t) =Qi

where Si(t)ing in classscale densiDensity-deand the reeled simila

Fig. 2. Density dependence for five classes of Northern Range elk,cows, old-cows, bulls, calves (06 months) and yearlings (618

s). Elk

cientsndentikes sstantonse tariabconsi

ion ofepend

hardt (ated fcompodata.

bull raears wand Tand 1995, up to the period of wolf recovery. Forty dependence of bulls, we chose to simulate thegraphics observed for the period beginning 5

Table 1Density-depe r the five classes of elk

Probability fu

Green summer phytomass Winter severity

Z W

Rcalf 0.0003 0.070Pcalf 0.0001 0.050pcow 0.0025 0.200Sold-cow 0.0045 0.095Sbull 0.0080 0.160g functions of population density and cli-cribed in Sections 2.3 and 2.4.

ty dependence

and fecundity of NR elk have been shownly density-dependent (Fowler and Barmore,rill and Boyce, 1991; Singer et al., 1997;

ogan, 2002; Garrott et al., 2003; Nationalouncil, 2002) and non-linear (Taper and02). We adopted a non-linear equationClutton-Brock et al. (2002) to model den-

ence for all classes,

1(t) + exp[Xi + YiNelk(t)] (5)

is the probability of surviving and remain-i to time t+ 1. The constants Qi, Xi and Yi

ty dependence for each class, i (Table 1).pendent transition functions, Pi(Nelk)cruitment functions, Ri(Nelk), were mod-rly to survival functions, Si(Nelk), but with

month

coeffidepeof spa con

Respwas v

to befunctsity dEberestimherdof thecow:

19 y19791987densidemo

ndent, summer phytomass and winter severity scaling coefficients fo

nction Scaling coefficients

Density dependence

Q X Y2.30 6.0 0.00043201.20 7.5 0.00055001.00 8.5 0.00030001.00 7.5 0.00033001.15 6.2 0.0003025density is the number of elk per km2.

fit accordingly. All vital rates were density-with the exception of Pspike, the probabilityurviving to become bulls, which was 0.98,reported in life tables by Houston (1982).o population density in all other elk classesle (Fig. 2), and coefficients were estimatedstent with observed class composition as apopulation density. The sequence of den-

ence in vital rates follows that suggested by2002). The coefficients, Qi, Xi and Yi wereor each class by iterative adjustment untilsition predicted by the model matched thatReference data for cow:calf, cow:spike andtios were taken from Houston (1982) forhen data was available between 1930 andaper and Gogan (2002) for 7 years between


years after the implementation of natural regulationmanagement (Boyce, 1998; Singer et al., 1998), or19731995. Data previous to this period includedeffects ofService (Hbuffer wassex ratios t

2.4. Clima

Summe1991; Merweather (FPicton, 198Boyce, 199ence elk poand yearlinity and poMerrill andet al., 2003the conditiovival and gBoyce, 199NR is availfraction ofthey are suhunt. Thisto the dens

Like WOter severityrandom nuWinter sevewhich wasprecipitatiothe NR. Foage tempersubtractiontively affecitation poswas modelmally distrdeviation oceous phytSAT imagecapita elk p(1991). Thedent randomof zero and

Winter severity and summer phytomass were incor-porated into the density-dependent functions of sur-vival, recruitment and transition in a way that essen-

pertubility

=Q

lass iity ats phytesponity, remethoi andrated ily linestimaill ands repolationdecrealationl, iteramodeata for.V. fr

Elk ha

arvestR elk

; Barmery m). Oursts, Heachx, A(t(t), sp1) =

e Momana

of thehuntmodeartificial reductions by the National Parkouston, 1982; Barmore, 2003), so a 5-yearchosen to allow culling-induced skewed

o normalize (Mack and Singer, 1993).

tic variation

r forage production (Boyce and Merrill,rill and Boyce, 1991) and severe winterowler and Barmore, 1979; Houston, 1982;4; Clutton-Brock et al., 1987; Merrill and1; Garrott et al., 2003) significantly influ-pulation dynamics. Survival of elk calvesgs is often a function of both winter sever-pulation density (Sauer and Boyce, 1983;

Boyce, 1991; Garton et al., 1990; Garrott). High-quality summer forage can enhancen of reproducing females and improve sur-rowth of calves and yearlings (Merrill and1). As winter severity increases, less of theable for foraging by elk, resulting in a higherthe herd dispersing north of the park wherebject to human harvest in the late-season

process links stochastic variation in climateity-dependent process.

LF5, WOLF6 simulated variation in win-and summer plant growth variables using

mber generation (see Boyce, 1992, 1995).rity was represented by Lambs Index, L(t),calculated from winter temperature and

n measurements for the past 50 years onr each standard deviation from the aver-

ature and precipitation, integer additions ors were made. Increased temperature nega-ts Lambs Index, whereas increased precip-itively affects it. Lambs Index in WOLF6ed as an independent random variable, nor-ibuted, with mean of zero and standardf 6.5. Mean and variance of green herba-omass (kg/ha) was estimated from LAND-ry (Merrill et al., 1993) and related to peropulation growth rates by Merrill and Boycephytomass term, P(t), also was an indepen-variable, normally distributed, with mean

standard deviation of 309 kg/ha.

tiallyproba

Si(t)

for csever

ceou

the rsever

TheQi, Xillustimatewas e

Merrvaluepopusity,the reSmaluntilthe dand C

2.5.

Hthe N2002recov

2005harvefrommatritor, N

N(t +Th

Parksnorthlatewasrbed the carrying capacity. For example, theof survival for stage class i at time t was

1i + exp{Xi + [YiNelk(t)] [ZiP(t)] [WiL(t)]}

(6)

in which L(t) is Lambs Index of wintertime t, and P(t) is the summer green herba-omass at time t. The terms Zi and Wi scalese to variability in phytomass and winterspectively, for each stage class (Table 1).d for obtaining deterministic estimates ofYi is described above with the functions

n Fig. 2. The range of values for the approx-ar middle portion of the curve for each class

ted from the linear relationships reported byBoyce (1991). Intercepts were anchored atrted in life tables by Houston (1982) for thewhen it was at low density, and at high den-sing, non-linear survival was used to reflectships described by Taper and Gogan (2002).tive changes in the coefficients were made

l output converged with the relationships inboth herd composition and population meanom 1973 to 1995.

rvest

by humans has a significant influence onherd (Houston, 1982; Taper and Gogan,

ore, 2003; Eberhardt et al., 2003), and wolfay impact elk harvests (White and Garrott,simulations included a column vector of

(t), of the number of individuals harvestedsex/age class subtracted after the projection), was post multiplied by the population vec-ecifically,

A(t)N(t) H(t). (7)ntana Department of Fish, Wildlife andges winter elk hunts on the NR immediatelypark. Hunter harvest of elk in the Gardiner

(Unit 313) during January and Februaryled using the harvest objectives outlined


Table 2Harvest goals for northern Yellowstone elk herd in Gardiner late hunt (Unit 313) as set by Montana Department of Fish, Wildlife, and Parks(abbreviated, see Lemke, 2003), and the corresponding numerical adjustments for the WOLF6 modelSeason type ed elk h

LiberalStandard 30Conservative

a L(t) is the

by Montannumber ofnumber ofand simulahunter part

Permitsuary and Ffemales forbetween 231991 and 1to 2870 induced, thenally decline

Severe wof YNP int(National Rwas modeleseverity towinters, ca

h(t) = 30L

in which hLambs Indstant, 30, wnormal distto 1995, 96harvest, H(added to copopulationthe absence

The colyearly harage/sex cla(see Lemke9% of totalWhile 18%these calveof these in

h malles) ine wasion ofest aprecov

Altern

urrentR pacprey fb). Wspecie(Odorn shame

nus) an WOded inse po

to indet al.e andof th

; Boycndents forF5 (Tth ratcient

is oTotal elk count Permits issued Estimat

>15000 >2700 >12301000015000 20002700 91012


Table 3Population, functional response and numerical response coefficients for each of four ungulate prey species and five elk classes used in WOLF6

Prey K Fmaxa Attack rate Handling Body size Densityependenoefficie

Winter Summer Growth

ElkCalfSpikeCowOld-cowBull

Bison .0002Moose .0001Deer .0003

a Maximum ar.b See Table

2.7. Preda

Predatio(Canis latrgrizzly beacant to preyto the undeand alternapossible efother predaenced by ca2003; Wilmbehaviour oincorporate

2.8. Funct

Predatioresponse,killed as aModel simtion columresponse tethe numbervector F(t)sition vectomultipliedSo, simulation includ

N(t + 1) =

e empl respoms an. (200le fitls, bund imls (Ha, 1997terpretor (Camo

), andsearc

ethodt requtime coefficient, R dc

8.5 0.000002 0.02 0.05 b2.3 0.0000001 0.035 0.06 b7.5 0.00000003 0.04 0.075 b6.3 0.0000004 0.04 0.075 b1.8 0.000003 0.0425 0.082 b

800 2.9 0.000000005 0.1 0.13 0800 2.6 0.00000006 0.045 0.09 03000 57.6 0.000000006 0.009 0.015 0

functional response, greatest number of prey taken per wolf per ye1 for scaling coefficients of elk classes.

tors

n by cougars (Felis concolor), coyotesans), black bears (Ursus americanus) andrs (Ursus arctos), while probably signifi-populations, were assumed to be intrinsic

rlying population dynamics modeled for elkte prey prior to wolf reintroduction. Thefects of wolves on predation rates of thesetors, or the predation rate of wolves influ-rrion loss to scavengers (see Wilmers et al.,ers and Getz, 2004), and carcass-usurpingf bears (see MacNulty et al., 2001) was notd into WOLF6.

ional response

WtionaAbraet alsonabmodeics amode1994be inpredability1996whiletive mdo non by wolves was modeled as a functionalor the per capita rate at which prey isfunction of prey availability (Taylor, 1984).ulations with predation included a preda-n vector, F(t), containing the five functionalrms (one for each class) multiplied timesof wolves, Nwolf(t). The predation column

was subtracted from the population compo-r after the projection matrix had been post

by N(t) and reduced by hunter harvest, H(t).tions that included both harvest and preda-ed reductions by both, H(t) and F(t):A(t)N(t) H(t) F(t). (9)

and Ginzbudependenteffects of wsuggested breproductivthe time scaand prey).

There isprey abundvulnerabletion mechaet al., 2003a Type III rever, Waltefor a similacent, 1

severitycoefficient, 2

phytomasscoefficient, 3

rate, r0

b b n/ab b n/ab b n/ab b n/ab b n/a

0.0079 0.0002 0.230.01 0.0001 0.20.009 0.0003 0.4

loyed a multi-species prey-dependent func-nse (Crawley, 1992; Abrams, 1993, 1994;

d Ginzburg, 2000). We note that Vucetich2) and Eberhardt et al. (2003) found rea-s of data to ratio-dependent predatorpreyt we could not reconcile the peculiar dynam-plausible assumptions of ratio-dependentnski, 1991; Oksanen et al., 1992; Abrams,). Although ratio-dependent models mightted to accommodate group hunting by theosner et al., 1999), variation in vulnera-

ng individual prey (Abrams and Walters,aggressive encounters between predators

hing for prey (Beddington, 1975), alterna-s exist for modeling these phenomena that

ire such unreasonable assumptions (Abrams

rg, 2000). Our approach was to use a prey-

functional response while accounting for theolf density in the numerical response. Asy Abrams (1994), this works well when thee period of the predator and prey matchesle of the model (t= 1 year for both predator

clear evidence that wolf density is related toance through a complex interaction betweenprey availability and intra-specific limita-nisms (Fuller, 1989; Messier, 1994; Fuller). For mammals, functional response is oftenesponse, or logistic (S-shaped) curve; how-rs et al. (1981) used a Type II disc equationr wolfprey model. Messier (1995) suggests


that Type II is the correct version to use, but it is not pos-sible to distinguish between a Type II and Type III withlimited existing data on prey at low densities (Marshaland Boutinconstant prdata over asystems, annot decreasfar (Whitevariation aelk densityenough varesponse ovprey densitcentury.

There ichanges wi2000; Vuceform of thBoyce (199alternate pof the abuIncreased sType III funtors, whiledecrease set al., 199can switchity, which(Scheel, 19tion (FryxeLundberg,and PetersoYNP. Increscarce in Yresponse tomigratory mof scat (Smsonally avavulnerablegests that eNR; the usritories hasLewis and MbehaviourFortin et alnomena lepredation a

response. The form we used was:

AiNi

Nj

1 + T

e Fi iable, Athe sutime

ly estate fue, 199olves

to parary byded for condSmithntire yx = 32, 30%ce, 19ficantln ratestor deasona

; Smier wo

ttack re com

9952h et al; Smitg midperio

ows ation foh et aseaso

rtionsroportlls inide wut noston,ionalivelyon of p, 1999). Eberhardt et al. (2003) advocate aedation rate as better supported by available

wide range of prey densities in multipled observed per capita predation rates haveed with decreasing elk density in YNP thusand Garrott, 2005). However, the moderateround the mean that has been observed in

since wolf recovery may not representriation to measure long-term functionaler the wide range of primary and alternate

ies that might be expected during the next

s no agreement on how predation rateth prey or predator density (Eberhardt, 1997,tich et al., 2002), so we chose the logistic

e Type III functional response justified by2) on the basis that predators confronting

rey species will switch prey as a functionndance of various prey (Murdoch, 1969).tability in prey numbers are expected underctional and numerical responses for preda-

Type II functional and numerical responsestability, i.e. they are antiregulatory (Dale4). In multiple ungulate systems, wolvesto alternate prey in response to availabil-is influenced by abundance, vulnerability93; Abrams and Walters, 1996), migra-ll et al., 1988), use of refugia (Fryxell and1998) and anti-predator behaviour (Mechn, 2003). These factors may be present inased use of bison by wolves where elk areNP (Smith et al., 2000b) is an example of adiffering abundance, and increased use ofule deer during summer found by analysisith, 2005) demonstrates wolf use of sea-ilable prey. Use of low wolf-use areas byelk classes (White and Garrott, 2005) sug-lk seek to minimize predation risk on the

e by prey of refugia between wolf pack ter-been found in other systems (Mech, 1977;urray, 1993). Some forms of anti-predator

by YNP elk have been documented (e.g.., 2005). Individually and in sum, these phe-ad to the prediction of density-dependents characterized by a Type III functional

Fi =

wheravailNjdlingviousestimBoycfor wableNR vrecor

undesity (the e(FmaYNP(Boysignidatiopredaby se2000summ

Aon thfor 1Smit2001durinstudyold-cselecSmitotherpropothe pof bucoincrut, b(HoufunctiteratportihiAi

N2j(10)

s the functional response for the ith preyi the attack rate by wolves on the ith prey,

m of all available prey and Thi is the han-for the ith prey (Table 3). Kill rates pre-imated for other populations were used tonctional response terms in WOLF5 (see0, for review); however, kill rate estimatesin YNP (Smith et al., 2004) were avail-

ameterize WOLF6. Predation rates on theseason and year, but the highest rate was

r a 30-day sampling period in March 1997itions of severe winter and high prey den-, 1998; Mech et al., 2001). If extrapolated toear, this represents a theoretical maximumelk/wolf/year) for wolf predation on elk inhigher than in WOLF5 where Fmax = 25

90, 1995). However, the yearly rate would bey lower than Fmax = 32, because yearly pre-will be affected by variation in prey density,nsity and prey vulnerability as influenced

lity (Messier, 1994, 1995; Eberhardt, 1997,th et al., 2004). Messier (1994) estimatedlf predation rates were 70% of winter rates.ates on each elk class were estimated basedposition of wolf kills reported from YNP

003 (Phillips and Smith, 1997; Smith, 1998;., 1999, 2000a,b, 2001, 2003; Mech et al.,h and Guernsey, 2002). Wolf kills on the NR-November to mid-December and Marchds included 41% calves, 11% cows, 27%nd 21% bulls. These values characterizer winter months only (Mech et al., 2001;

l., 2004) and few data were available forns of the year. Needing to extrapolate these

for an entire year, we chose to reduceion of bulls to 10% due to high incidencewinter kills collected during periods that

ith high bull elk vulnerability following thermally low mortality during other seasons1982; Barmore, 2003). Attack rates in theresponse term of the WOLF6 model wereadjusted until the following observed pro-rey classes taken by wolves were predicted:


Fig. 3. Functional response, or rate of elk consumption per wolf peryear, for five classes of elk: calf, spike, cow, old-cow and bull. Elkdensity is the number of elk per km2.

44% calves, 6% spikes, 11% cows (includes yearlingfemales), 2ing attack rresponse wing 19952(Fig. 1).

Handlinsize of thefrom theseerated forspecies (Fi(Table 3) wof the curvresulted w

Fig. 4. FunctiFmax = 10, 20tively. Prey de

Attack rates for alternate prey were adjusted to reflectthe low levels of predation observed since wolf reintro-duction (Table 4). Current consumption is estimated tobe betweenfor all threfrom the da

Surpluswolves andYNP (Smiin excess owinter is sabundant pof predatiotive due toto succumbBallard, 19was not spe

2.9. Nume

e nummed

iple-splation

f(t + 1e Nword termes. Thconve

e size9% old-cows and 10% bulls. While estimat-ates, the available elk used in the functionalas 12,215 elk the mean elk, population dur-003 when wolf kill data were collected

g times were scaled relative to mean bodyprey. Functional response curves derivedattack rates and handling times were gen-each elk class (Fig. 3) and alternate preyg. 4). The Fmax for each of the prey classesas derived from the asymptotic maximum

es in Figs. 2 and 3. For elk, an Fmax of 26.2hen all elk age/sex classes were summed.

Thconsu

multpopuwas

Nwol

wherrewa

wolvwere

on thonal response curves for bison, moose and deer whereand 110 individuals taken per wolf per year, respec-nsity is number of prey per km2.

Tr =

(Bfor the ithprey, whercapita rateof the fiveand Bi is thof each ith

Recentulation grois high, inincreased,has decreaindicate thand spatia0.1 and 0.35 individuals per wolf per yeare species of alternative prey as estimatedta in Table 4.killing, when excessive prey are killed by

left unconsumed, has been observed inth, 1998). In late winter, wolves may killf their food requirements particularly if theevere with deep, crusted snow pack andrey in poor condition; however, this kindn tends to be rare and tends not to be addi-the poor condition of prey and the tendencyor migrate during severe winters (Eide and82; Miller et al., 1985), so surplus killingcifically modeled in WOLF6.

rical response

erical response is the rate at which preyinfluences predator population growth. Aecies numerical response was used for wolfgrowth. The form of the numerical response

) = Nwolf(t) exp(Tr Tdd) (11)lf(t) is the wolf population at time t, Tr the

and Tdd is the density-dependent term fore reward term was the rate at which preyrted to predator population growth basedand number of prey taken, such that

iFi(t)) (12)elk sex/age class and alternative ungulate

e Fi is the functional response (yearly perat which respective prey was taken) for eachclasses of elk, and species of alternate prey,e reward coefficient scaled to the body massprey item (Table 3).demographic data indicate that wolf pop-wth in YNP has subsided: adult mortalityter-pack and intra-pack aggression has

mean pack size has increased and dispersalsed (Smith, 2005). These observationsat the population is experiencing sociall constraints (Fuller et al., 2003); hence,


Table 4Proportion of elk, bison, deer and moose taken by the number of estimated wolves during winter sampling periods since reintroduction in 1995,data summarized in Smith (2005)Year

2003200220012000199919981997

Mean proport

a Estimatesb Proportion r, and e

the populacapacity. Tdescribed timposed by

Tdd = rwoKwo

where theobserved g(Smith, 20Kwolf, wasrelationshiprates for wwhich the lgrowth ratThe initial17 and 10respectivelin the park

2.10. Wolf

About htem has beevehicle coltually, the sharvest throNR outsideof wolves fremoved pshould be infrom the po

e sour-basewoul

uota we quotQuotaes usie NRty is lality, drable

esults

itial er effoopulaton haProportion of known kills (%), nElk Bison Deer

84, 291b 6, 21 1, 487, 311 2, 6 2, 687, 281 3, 10 1.5, 587, 276 4, 14 1, 286, 197 2, 5 3, 698, 46 1, 1 1, 198, 50 0, 0 0, 0

ion (%) 89.6 2.6 1.4

of population in Yellowstone National Park from Smith (2005).of prey species in sample of wolf kills from March, late-Novembe

tion appears to be approaching carryinghe density dependence term for wolves

he numerical limitation of wolf populationssocial and spatial constraints, given by

lf

lfNwolf(t) (13)

constant, rwolf = 0.77, was the maximumrowth rate for the YNP wolf population05). The carrying capacity for wolves,

estimated by plotting the density-dependentbetween the yearly population growth

olves on the NR and population size, forinear relationship intersects zero per-capitae at Kwolf = 131 (Smith, 2005: Fig. 6).release of Nwolf(t) in 1995 was 14, withwolves added the two successive years,

y, to reflect the total of 41 wolves released(Phillips and Smith, 1997; Smith, 1998).

of thquotaquotathe qof thtion.wolvof thdensiritorivulne

3. R

Inearlieelk pducticulling

alf of wolf mortality in the YNP ecosys-n human-caused due to depredation control,lisions and poaching (Smith, 2005). Even-tate of Montana may implement controlledugh hunting and trapping of wolves on theof the national park. To model the removalrom all human sources, a quota of wolveser year was implemented. The quotaterpreted as the number of wolves removedpulation each year by humans, irrespective

taking climnumbers o2030% (Funderestimical simulais poor (Ebthe data subetween pstriking ag(Boyce andhave simuleffects on edation rateEstimated populationa

Moose Wolf

0, 0 1740.5, 1 1481, 4 1322, 7 1191, 3 721, 1 831, 1 80

0.9

arly December; number of kills.

ce. We assumed density dependence in thed removal, so that when Nwolf > 90, the fulld be removed, when 50


Table 5Projections from various versions of the WOLF model since 1990Reference Model version Area Nwolf Reduction in elk herd size (%) Reduction in elk C.V. (%)Boyce (1990, 1993) WOLF YNP* 50120 1525Boyce (1992) WOLF YNP* 90140 1525Boyce (1992, 1995), Boyce

and Gaillard (1992)WOLF5 GYA* 114; 50170 520

Current article WOLF6 NR* 110122 21

* GYA, Greater Yellowstone Area; YNP, Yellowstone National Park; NR, Yellowstone

Fig. 5. Time sGaillard, 199Northern Ran

The firsWOLF6, edeterministwolves. Webeginning(phase 3) sand finally(with/witho

Fig. 6. Time sand Gaillard,the Yellowsto19952005.

The additio14) reduc

3.1. Elk po

The deteequilibriumelk (Table

alone19901), thclimatd herd:cow a

ult fentageeries projections from the WOLF5 model (Boyce and2; Boyce, 1995) compared with survey data for thege elk population (Lemke, 2003), 19952005.

t phase of our analysis of the current model,ntailed studying the basic framework as a

ratesearly(Fig.milddictespikeby adperceic model without climate, elk harvest, orthen incorporated stochastic perturbations,

with climate (phase 2), then hunter harvestimulating conditions prior to wolf recovery,wolves (phase 4), which included variationsut elk harvest, with/without wolf culling).

eries of five projections of the WOLF5 model (Boyce1992; Boyce, 1995) compared with survey data ofne National Park wolf population (Smith, 2005),

1 projectio45% estim1970s.

Climaticter severityphase 2 caution to 14,7inability ofmortality i(Boyce ancaused stoclate populaobserved therd (HousMerrill, 19productionWithout otharvest anddependencpopulationmate and d(Merrill an303010

10

s Northern Range.

n of each component to the model (phasesed average elk population size.

pulation dynamics

rministic version of the model predicted anpopulation for the NR elk herd of 16,243

6), resulting from density-dependent vital. Although counts in the late 1980s ands of elk numbers were in excess of 18,000ese large counts likely occurred because ofic conditions (Taper and Gogan, 2002). Pre-composition, as reflected in low calf:cow,nd bull:cow ratios (Table 6), was dominated

males more so than other phases. Also, theof old-cows in the herd was highest in phasens (55%); this estimate was higher than theated by Houston (1982) for the herd in the

influences (i.e. stochastic variation in win-and summer forage quality) were added insing a decrease of 9% in the mean popula-

29 (n= 25; Fig. 7). The decrease is due to thea population to match climate-influenced

n bad years with growth in good yearsd Daley, 1980). The addition of climate-hastic variation resulted in substantial ungu-tion fluctuations over time, as has been

hroughout the recorded history of the NRton, 1982; Singer et al., 1989; Boyce and91). Winter severity and summer forage

influenced both survival and recruitment.

her sources of mortality in the model (i.e.wolves), the interaction between density

e and climate caused high variability in(C.V. = 0.20). The interaction between cli-ensity has been reported for this elk herdd Boyce, 1991; Singer et al., 1997; Taper


Table 6Projections of elk population and composition for four simulation phases of the WOLF6 modelSimulation phase NElk S.D. C.V. Percent

old-cowsaCalves:100 Bulls:100 Spikes:100

1. Deterministic 16243 552. Climate n= 25 14728 2913 0.20 433. Harvest n= 25 12254 2304 0.19 504a. Wolves, with harvest n= 25 9713 1696 0.17 414b. Wolves, with no harvest n= 25 12727 2274 0.18 40

a Percent of all adult females (>18 months) that are in the old-cow class (>10 years).

and Gogan, 2002) and other ungulate herds (Picton,1984; Clutton-Brock et al., 1987; Choquenot, 1991).For a non-harvested elk herd in a different region ofYNP, calf recruitment was inversely correlated withsnowpack (Garrott et al., 2003). Combined with highadult survival, variable recruitment caused this herd tobe maintained in a dynamic equilibrium (Garrott et al.,2003). Taper and Gogan (2002) estimated populationequilibriumbe 20,000in WOLF6lation undeprojection o100 years,in a 100-ye

In phaseWOLF6 melk the pro17% to 12

Fig. 7. A phawide populatiin climate.

from count13,716, buThe WOLFindicatinglower elk pyears. Becahigh popullow popula

educe. = 0.19o incre 6) anas a re

omposing dat for:cow (with

ata forogan

ng org yeabiase

relativonshiprical rfor the NR herd in the absence of harvest to25,000 elk. Density dependence as modeledpredicts a lower long-term average popu-r these conditions. In Fig. 7, the WOLF6f population size surpassed 18,000 in 15 of

but large fluctuation in population resultedar mean of 14,729.3, hunter harvest of elk was added to the

odel; with mean annual harvest of 1228jected 100-year population mean decreased,254. The observed minimum population

vest r(C.Vvest t(Tablherd

Cexistoutpuspikeparedical dand Gmissidurinhavedatarelatiempise 2 projection of the Northern Range elk herd withon fluctuation due to density dependence and variation

Duringrecovery. Wulation 21%dation suppwolves thaper year (Fwas reducewolf predadecreased41%, but hcows cows cows

18 11 222 12 429 34 929 21 824 16 5

s between 1973 and 2003 (Fig. 1) averagedt this was with a mean harvest of 1092 elk.6 projection gave a lower population size

that current harvest patterns will result inopulations on average relative to the past 30use harvest rate was density-dependent (i.e.ations coincided with higher harvests whiletions were subjected to lower harvests), har-d the among years variation in elk numbers). Current hunting regulations cause har-

ease calf:cow, bull:cow and spike:cow ratiosd reduced the proportion of old-cows in thesult of selection for cows in the harvest.ition of the elk herd was compared withta to assess model performance. Phase 3calf:cow (Fig. 8), bull:cow (Fig. 9) andFig. 10) ratios relative to density were com-the same relationships from available empir-19302003 from Houston (1982) and Taper(2002). Some data from this period were

excluded purposefully (e.g. bull:cow ratiosrs in which artificial herd reduction mightd composition), but despite having fewere to model output, these herd compositions for the model were nearly identical to the

elationships (Figs. 810).

phase 4 we examined scenarios under wolf

olves decreased long-term mean elk pop-from 12,254 to 9713; this level of pre-

orted a 100-year mean population of 109t consumed an average total of 1035 elkig. 11, Table 6). Variance in elk numbersd, C.V. = 0.17, indicating that an effect oftion was to stabilize elk numbers. Wolvesthe proportion of old-cows in the herd toad little other effects on herd composition.


Fig. 8. Comparison of the density-dependent relationship between calves per cow (female yearling, cow and old-cow) and elk population fromphase 3 simulation of WOLF6 vs. data from 1973 to 1994 from Houston (1982) and Taper and Gogan (2002).

Fig. 9. Comparison of the density-dependent relationship between bulls per cow (female yearling, cow and old-cow) and elk population fromthe phase 3 simulation of WOLF6 vs. data from 1973 to 1994 from Houston (1982) and Taper and Gogan (2002).

Fig. 10. Comparison of the density-dependent relationship between spikes per cow (female yearling, cow and old-cow) and elk population fromphase 3 simulation of WOLF6 vs. data from 1973 to 1994 from Houston (1982) and Taper and Gogan (2002).


with cli

3.2. Harve

Wolvesfrom 1228two causednumbers (Cremoval ofprojectionshunter harvin hunter hGaillard, 1was simulalessened, aelk numbermore elk w1277 per yprey availaslightly wihunter harvNwolf = 12alternativethat hunterity causingharvests ofmore old-celk harvest

ue to tws inin thewith

st atery deationsFig. 11. A 100-year projection of the Northern Range elk herd

st implications

decreased mean annual harvest by 12%to 1089 elk, while the combination of thethe greatest reduction in variability in elk.V. = 0.17) with a combined mean annual2107 elk (Fig. 12). Previous WOLF model

Dto cobullsbinedharverecov

regul

also showed that wolf recovery decreasedestWOLF5 projected up to 10% decline

arvests in the greater YNP area (Boyce and992). The option to discontinue elk harvestted in phase 4, and the effect of wolves wasreduction of 13% (versus 21%) in mean

s from 14,729 to 12,727. Wolves took 19%ithout hunter harvest of elk than with it,

ear versus 1035 per year, due to increasedbility. Variability in elk herd size increasedthout harvest (C.V. = 0.18), and removingest of elk resulted in more wolves, with2. Composition of the herd (Table 7) andprey taken (Table 8) changed suggestingharvest alters proportional prey availabil-wolves to alter selection. With no hunter

elk, wolves took fewer bulls and calves andows compared to simulations that includeds.

overall haras 15% of hbut when cincreased telk annuall

Phase 4with wolvelower theso in combever, extincany modelEberhardt eper year. Thwe modelevest requirpopulationwill recovedictions arein that highmatic variation, harvest and wolves.

he steep density dependence of bulls relativeFig. 2, culling cows affected the number ofherd (Fig. 13). Cow culling of 812% com-varying levels of bull harvest maximized12001500 elk (Fig. 14). Although wolfcreased projected hunter harvest, changingto permit harvest of more bulls could allowvest to increase. Bull harvest was modelederd total in all phases of model projections,ow harvest is decreased and bull harvest

o 20%, a higher overall yield of nearly 1600y could be achieved (Fig. 14).results include a harvest of the NR elk herds present in the system. Wolf predation willlong-term mean number of elk, and moreination with current harvest regimes. How-tion of the NR herd was not predicted byprojection as it was for a harvest model byt al. (2003) (Fig. 5) with removal of 1500 elke difference that led to this disparity is that

d and documented a density-dependent har-ing that managers reduce elk harvest whens are low, thereby ensuring the populationr from low densities. Qualitatively, our pre-

similar to those of Eberhardt et al. (2003)harvests can cause elk numbers to drop to


f the N

low levels;the populaensures thaa moderate1089 elk pvariation inconsistentyear-to-yea

Actual helk (Lemkhigh durinvests (>2819881989numbers ofexposed toto 1988 waa 75% incr(Lemke, 20ter of 1991projectionate between1989. Elk hof Fish, Wvest in WOharvest decpast. Seasotive types

F6 pre hunst exc

Altern

us faprey,

es (TaFig. 12. WOLF6 100-year projections of yearly removal of elk o

however, the ability of managers to monitortion and change harvest levels accordinglyt elk numbers can be maintained even withharvest. Our model projected a harvest of

er year with wolf predation, and reducedelk population size allowing reasonably

numbers of hunting permits to be issuedr.arvests during 19762003 averaged 1081

WOLin fivharve

3.3.

Thmaryspecie, 2003). The population was relativelyg this period and above average har-00) coincided with severe winters, e.g., 19911992 and 19961997 when largeelk moved out of the park where they werehunter harvests. Mean harvest from 1976s lower, 743 elk per year; but since 1989,ease occurred with 1302 elk taken per year03). The largest harvest occurred in the win-

1992 with 4515 elk removed. With wolves,of mean harvest in WOLF6 was intermedi-

the means for the periods before and afterarvest goals set by the Montana Departmentildlife and Parks and used to simulate har-LF6 (Table 2) are sustainable but with meanreasing significantly relative to the recentns fell within the standard or conserva-as few yearly elk counts exceeded 15,000 in

WOLF6 mon alternat(Table 8). Hbined to cawolves prespecies thasince wolfon the altepled with won alternat

3.4. Wolf p

At thewas estimawolves onmodel projnumbers trorthern Range by wolves and harvest.

ojections (Fig. 11), resulting in less than oneting seasons considered liberal in whicheeded 1230 elk.

ative prey

r, wolves have focused on elk as the pri-and little predation has occurred on otherble 4). Using these data to calibrate theodel resulted in little to no effect of wolvese prey species: bison, moose and mule deer

owever, climate, wolves, and harvest com-use elk numbers to decrease, resulting in

ying relatively more often on alternate preyn has been observed during the first 10 yearsreintroduction. Elk harvest had little effectrnate prey species in the model, and cou-olves, had little effect on predation levels

e prey.

opulation dynamics

end of 2004, the YNP wolf populationted to number 169, with approximately 85the NR (Smith, 2005, Fig. 5). The WOLF6ected a mean of 109 wolves on the NR. Wolfacked elk numbers over time (Fig. 11), with

330 N. Varley, M.S. Boyce / Ecological Modelling 193 (2006) 315339Ta

ble

7Fu

nctio

nalr

espo

nse

fore

lkag

e/se

xcl

asse

sfro

m10

0-ye

arpr

ojecti

onso

fthe

WO

LF6

mo

del

F cal

fCa

lves

take

n

pery

ear

F spi

keSp

ikes

take

n

pery

ear

F cow

Cow

sta

ken

pery

ear

F old

-cow

Old

-cow

s

take

npe

ryea

rF b

ull

Bul

lsta

ken

pery

ear

F elk

Tota

lelk

take

n

pery

ear

Phas

e4

simul

atio

nso

fthe

WO

LF6

mo

del,

with

wo

lves

and

elk

harv

est,n

=25

Mea

n4.

0745

00.

3942

1.18

128

2.49

275

1.24

138

9.38

1035

Perc

enta

geto

tal

424

1626

12

Phas

e4

simul

atio

nso

fthe

WO

LF6

with

wo

lves

and

no

elk

harv

est,n

=25

Mea

n4.

0549

40.

3542

1.83

225

3.04

378

1.09

1.36

10.3

712

77Pe

rcen

tage

tota

l39

318

3010

Ref

eren

cepr

opor

tions

estim

ated

from

data

(%)a

1995

200

2a43

513

2811

aD

ata

from

Phill

ipsa

nd

Smith

(1997

),Sm

ith(19

98),S

mith

etal

.(199

9,20

00a,

b,20

01,2

003)

and

Smith

and

Gue

rnse

y(20

02).

Fig. 13. Number of bulls (males, >18 months) as a function of pro-portion of females culled from harvest projections in the WOLF6model.

periods of low wolf population preceded by periods ofdecline in the elk population and high wolf populationpreceded by growth in elk numbers. Wolf numbers wereaffected bynamely dentic variatiothat WOLFtions weretrophic leveVucetich an

Fig. 14. Totalproportion ofthe factors that influenced elk numbers,sity dependence, climate-induced stochas-

n and hunter harvest of elk. This suggests6 simulations of wolf population projec-influenced at least in part by bottom-upl perturbations (Boyce and Anderson, 1999;d Peterson, 2004).elk harvest as a function of the proportion of bulls andcows removed from projections of the WOLF6 model.


Table 8The 100-year population mean, functional response (prey per wolf per year), and total removal by wolves of alternate prey speciesStochastic model version, n= 25 Nbison Fbison Bison taken Nmoose Fmoose Moose taken Ndeer Fdeer Deer taken

Phase 4a: wol 0.40Phase 4b: wo 0.39

Table 9Wolf quota, q Nwolf,harvest per ye

Wolfquota

Qo

.V. Nwo

0 .165 .16

10 .1715 1 .1720 1 .1825 1 .1928 2 .2030 2 model35 2 model40 3 model50 3 ic mode

Cullingmodel to retions persisculling quocaused extiexceeded 5likely. Woldeclines inal., 1987), a(Boyce, 19so wolf pacwith the prfive wolvesin the elk p

4. Discuss

Experimgested decical proceswith far-retion and m

arch Cper year

ves, harvest 811 0.05 5.53 974lves, no harvest 811 0.06 6.97 974

uota percent of Kwolf, Nwolf/Kwolf, wolves culled per year, C.V. ofar from 25 runs of phase 4a of the WOLF6 model.uota %f Kwolf

Nwolf/Kwolf Nwolf Wolves culledper year

C

0 0.83 109 0.00 04 0.79 103 5 08 0.74 97 9 01 0.70 91 13 05 0.66 86 16 09 0.62 81 19 01 0.60 78 20 03 Extinction occurred in 1 of 25 runs of the stochastic7 Extinction occurred in 2 of 25 runs of the stochastic1 Extinction occurred in 6 of 25 runs of the stochastic8 Extinction occurred in 23 of 25 runs of the stochast

of wolves was predicted by the WOLF6 Rese

duce wolf population size (Table 9). Popula-ted at yearly quotas of up to 28 wolves. Wolftas in excess of 30, or about 23% of Kwolf,nction in some projections, and when quotas0, extinction of the wolf population becamef harvests of >40% have been found to causewolf populations (Keith, 1983; Ballard etnd in previous versions of the WOLF model90, 1993). Most of the NR lies within YNPks may not be subject to high culling levelsesence of this refuge. For each increase ofin the quota, a mean increase of about 1%

opulation and elk harvest was projected.

ion

ental wolf restoration in YNP was sug-ades ago as one way to restore an ecolog-s (Leopold, 1944; Despain et al., 1986),aching effects on prey population regula-ulti-level trophic dynamics. The National

1986; SarraFieberg aning advantin YNP toevaluate thagement asVarley, 199fundamentprocess, anremain a tothe implicaof elk.

Despiteparameterpredictionsmodels conicant effeconce believmous effecas has beennity (Frittsmoderate rper year per year

43.55 3048 0.26 28.7047.22 3048 0.31 38.46

elk population, elk taken by wolves per year, and elk

lf Nelk Elk taken bywolves

Elk harvestper year

9702 1033 10749857 988 1093

10005 940 111310168 895 112710327 853 113610457 813 114410530 785 1151

l

ouncil (2002) and others (Despain et al.,

zin and Barbault, 1996; Singer et al., 1997;d Jenkins, in press) have encouraged tak-age of the opportunities of wolf recoverylearn about predatorprey dynamics and toe ramifications of ecological-process man-practiced in YNP (Boyce, 1998; Huff and9). Updating the WOLF model has been a

al contribution to this adaptive managementd combined with future field studies, shouldol for anticipating wolfelk dynamics andtions of these dynamics on hunter harvest

many differences in model structure andestimates, the updated WOLF6 model gave

similar to its predecessors. The WOLFsistently have predicted neither an insignif-t of wolves on elk numbers as some haded (Houston, 1971; Cole, 1971), or enor-

ts that are tantamount to ecological collapsepopularized outside the scientific commu-

et al., 2003). Rather, the predictions are ofeductions in elk numbers with a sustainable,


moderate hunter harvest. The changes in WOLF6 ulti-mately failed to produce qualitatively different resultsfrom other WOLF models, which implied that the pre-dictions ofrobust.

Contrary(2003, p. 3WOLF moperformeddata. Wolfand elk harhad been ofor these doccurred dearlier verstion beyondexpandinget al., 1998the elk popversion ofthe model r(Boyce, 19subsequentby transienulation groprojectionin the firstaccount forics resultinmay adjusttion (Klein(2002) suggtake longerabsent, or ademographnecessary ton elk vital

Disparitother recenet al., 2003in press) mtiveness ofdifferent magers assesdilemma, hdictions amkey featureadaptive m

of the differences among models have been discussedelsewhere (White and Garrott, 2005), but differences inthe structure and intent of these models are fundamen-

the dgth ofval, ren is tlationtorpity dell docore, 1; Tapemode

dependlk herprovidrates; Tapendentrecov

opulateffecdata)thatimpro

hat dec, 1994betwecil, 20uring tf the(Huffajor dty ann, 200e ecolarticu

placedston,arch Cty-depn andpulatite stilplem

lk, wiat fosearlier versions of the model were generally

to unsubstantiated claims by Boitani33) and Fuller et al. (2003, p. 187) that thedels were problematic, previous versionsreasonably at predicting the most currentnumbers had been slightly underestimatedvest and the use of alternate prey by wolvesverestimated. Several reasons may accountiscrepancies. Increases in harvest quotasuring the 1990s that were unforeseen inions of the WOLF models, and land acquisi-

YNP made winter range available therebythe carrying capacity of the NR herd (Lemke; Taper and Gogan, 2002). Age structure inulation had been dropped from the WOLF5the model due to lack of data and to makeun fast on early vintage personal computers95). Comparisons with current data acquiredto wolf reintroduction may be confoundedt dynamics coinciding with irruptive pop-wth (White and Garrott, 2005); a WOLF6of a 20% increase over the long-term mean10 years was noted (see Fig. 12), and coulda skewed perspective of long-term dynam-g from current data. In fact, the systemfor many years subsequent to wolf restora-, 1995). The National Research Councilested that achieving stable dynamics mightthan the period during which wolves werebout 70 years. Continued monitoring of elkic parameters and wolf predation will beo evaluate the degree to which initial datarates represent transient dynamics.

y among predictions from WOLF6 andt YNP wolf recovery models (e.g. Eberhardt; Wilmers and Getz, 2004; Vucetich et al.,ight be seen to cast doubt on the effec-simulation modeling for management. If

odels yield contrary results, how can man-s which is reliable? Rather than presenting aowever, we argue that the differences in pre-ong models are useful in helping to resolves of the system, exactly as prescribed by theanagement paradigm (Walters, 1986). Some

tal tostrensurvidatiopopupredaDensis weBarm1991in thesitythe ethatvital1991depewolfelk pthesesitionwaysas an

sity tet al.linkCoun

Dtion omentthe mdensiGogaof thand ption(HouResedensidatioof poclimaBy imfor eicy thifferences among model predictions. Thedensity dependence operating through elkproduction, hunter harvest and wolf pre-

he most influential factor determining thedynamics and resilience of the WOLF6

rey system (Fieberg and Jenkins, in press).pendence in vital rates and hunter harvestsumented for the NR elk herd (Fowler and979; Houston, 1982; Merrill and Boyce,r and Gogan, 2002), giving us confidencel predictions. Our ability to document den-ence for this elk herd was facilitated by

d reductions of the 1960s (Houston, 1982)ed a broad range of densities over whichwere then monitored (Merrill and Boyce,r and Gogan, 2002). While little density-

response has been seen in elk vital rates sinceery (White and Garrott, 2005), the range ofion densities has been insufficient to detectts (Figs. 810 present comparative compo-. Density dependence also may appear in

are not reflected in these vital rates, suchved individual elk condition at lower den-reases vulnerability to wolf predation (Dale; Wilmers and Getz, 2004) and the strong

en density and harvest (National Research02).he nearly 30 years between the implementa-natural regulation policy for elk manage-and Varley, 1999) and wolf reintroduction,

rivers in elk population dynamics have beend climate (Singer et al., 1998; Taper and2). Severe winters resulted in compressionogical carrying capacity (Houston, 1979),larly at high densities, subsequent migra-elk outside the park in areas of harvest

1982; Singer et al., 1997, 1998; Nationalouncil, 2002). Thus, climate enforced aendent source of mortality by hunting. Pre-

harvest both work to decrease the magnitudeon fluctuation, but the stochastic effects ofl alter carrying capacity from year-to-year.enting density-dependent harvest guidelinesldlife managers have implemented a pol-ters the resilience and sustainability of the


system, as has been recognized recently in an exploitedmarine system (Hughes et al., 2005).

Eberhardt et al. (2003) suggested the data do notsupport climapparentlyhunter harvdence, climFig. 2 was cthese effecrately in pdensity-depenforced bphase 3 wekill, but parpresent inphase 1. Hclimate dicthe park alinduced pedation reduthe stabilizfacilitate sosequent harharvest (Fielk harvest(Table 2) a

Two meof wolf preresponse anterritorial bprimarily rconsistentwolves takprey popuand in YNThe additicontributedcaused byharvest. Hailar mean ndifferentialto reduce eOther recenet al., in pavoid accevest and pnot modelabundance

Low use of alternate prey in WOLF6 projections(Table 8) suggests a moderately dense elk populationcan occur with little prey switching by wolves. The wolf

rical r90% o(1994nal Paof cahigh

and rsuggehing iet al

e at lowwolf p, the Nties wrimarly lim) withsocia

, 2003n adus self-th.ture

de refiof altend vuto si

ge onynamavera

of par diselk couquantopteslationew (ets are rarasitns (Wella aion cose frorne etreat toate-driven population fluctuation, but theyfailed to recognize the effect of climate onest. The inextricability of density depen-ate, and harvest in the data used to constructonfounding; we were unable to fully isolatets even though they were presented sepa-hases 13 of the model. Specifically, theendent vital rates in phase 1 are ultimatelyy an interaction with hunter harvests. Ininjected the numerical effects of the huntert of the dynamical consequences are alreadythe density-dependent structure formed atarvest is density-dependent (Table 2), buttates years when movements of elk outsidelow for a harvest. We predict that climate-rturbations will continue but with wolf pre-cing the magnitude of fluctuations. In fact,ing effect of wolf predation on the NR mayme consistency in permits offered and sub-vest. Altering the proportion of bulls in the

g. 14) also may help to mitigate the reduceds resulting from fewer liberal season typesfter wolf recovery.chanisms enforce the stabilizing influencedation in WOLF6: the Type III functionald density dependence of wolves caused byehaviour and social interactions. Wolves

emoved elk calves and old-cows, which iswith many studies that have documenteding mostly the non-productive segment oflations elsewhere (Peterson et al., 1998)P (Mech et al., 2001; Smith et al., 2004).on of age structure in the elk population

to dampened fluctuations in elk numbersclimate and amplified the consequences ofrvest and wolf predation often removed sim-umbers of elk in the model (Fig. 12), butselection of classes caused hunter harvest

lk numbers more than predation (Table 6).t models (Eberhardt et al., 2003; Vucetich

ress) advocate lower elk harvest targets tolerated population decline due to both har-redation mortality, but these authors didharvest as self-correcting with changes in.

nume

over

et al.NatiorangetimespreybeenswitcMechstablhighilarlydensithe pmate1995beinget al.tion ileavegrow

Fuincluandsity ausedchanNR dfrommenttial foand ebeen(Sarcpopuare feffecand pulatio(Bruccollisdisea(Thono thesponse stabilized with elk still constitutingf the individual prey taken by wolves. Dale, 1995) found wolves in Gates of the Arcticrk, Alaska, did not switch prey over a wideribou (Rangifer tarandus) densities and atmoose densities. Vulnerability of preferredisks associated with attacking moose havested as factors responsible for lack of preyn such multi-prey systems (Dale et al., 1994;., 1995). The caribou population remained

density, albeit a density sufficient to absorbredation rates without serious decline. Sim-R elk were projected to sustain moderate

ith wolves relying substantially on them asy prey. Wolf density is thought to be ulti-ited by vulnerable prey density (Mech et al.,some of the proximate causes of limitationl mechanisms, such as territoriality (Fuller). A significant proportion of the elk popula-lt stages is consistently invulnerable, whichlimiting mechanisms to cap wolf population

updating of WOLF6 parameters shouldned estimates of seasonal predation ratesrnate prey use with changing prey den-

lnerability. Average climate conditions weremulate future climate; however, climatethe millennia scale has had a large effect onics (Bartlein et al., 1997). Climate deviationsge in the next century would call for adjust-rameters in the model. Similarly, the poten-ase and parasitic outbreaks with both wolvesld change predictions. While not much has

ified, canine parvovirus and sarcoptic mangescabiei) are noted potential factors in wolflimitation; however, examples to draw upon.g. Peterson, 1995) suggesting populationare (Fuller et al., 2003). Relatively few viral

ic infections affect North American elk pop-orley, 1991). While rare, bovine brucellosisbortus) in elk and bison places the herd on aurse with intensive efforts to eradicate this

m domestic and wild sources in the regional., 1991). On its own, brucellosis imposesthe elk population (Krebs, 2002). Chronic


wasting disease has not yet been found in the YNPregion but occurs at very low prevalence in southeast-ern Wyoming (Miller et al., 2000).

The sucspecies reiwhich to dbecause emoccurs (Wafully underbeen usefuLindenmayof WOLFgathering bmodels havment (somement, see WYellowstonthe results oactions werof these preand then pethe modelthe respons

Adaptivmany potenfor golden(OToole ein Scotlanoriginal moimprove thof which hfor reintrodcolor coryimanagememacquariecompositiohemionus)and creatiosamango mAfrica (Swefforts in sto be able tcompetitioEquus sppwalskii) re2005). ReinSwitzerlanal., 2004) le

creation of additional brood-rearing habitat may help.Occasionally, updated models can affirm the recoveryeffort is proceeding without major needs or impedi-

s (e.g.s havever podeemality olocatioons ofccessfdensitundeto preodele

ts (Saer lyn

in pat patcelingmics pain into su

tamaneed fer.

e trassfuliningth, 20ing plationto simm tols thaur un

iterativbilityand tre consular,

throug) inclu4 Ca

lationling aises toativescess of adaptive resource management forntroductions has had few examples uponraw (Sarrazin and Barbault, 1996), in partpirical testing of predictive models seldomlters, 1997). The models that have success-gone empirical testing and updating havel and insightful (e.g. Mills et al., 1997;er et al., 2001, 2003). After six revisionsmodels over 15 years and continued datay the National Park Service, the WOLFe been an integral part of adaptive manage-times referred to as experimental manage-alters, 1986, 1997) for wolf recovery in the

e ecosystem. Models were built to predictf experimental wolf recovery, managemente carried out based in part on the reassurancedictions (i.e. wolves were released in YNP),rformance of the model was evaluated and

revised based on subsequent monitoring ofe to wolf recovery.e management for wildlife recovery hastial applications. Recent recovery projects

eagles (Aquila chrysaetos) in Irelandt al., 2002) and beavers (Castor ber)

d (South et al., 2000) can now evaluatedels and refine them. These evaluations cane success of recovery programs, examplesave included: curbing human developmentuced northern Florida panthers (Puma con-; Cramer and Portier, 2001), altering fisherynt for Australian trout cod (Maccullochellansis; Todd et al., 2004), altering the agen of Asiatic wild ass translocations (Equusin Israel (Saltz and Rubenstein, 1995),n and maintenance of patch corridors foronkeys (Cercopithecus mitis) in South

art and Lawes, 1996). Species recoveryome cases require further empirical worko evaluate model predictions. For example,n and possible hybridization with domestic. may challenge takhi (Equus ferus prze-covery in Mongolia (King and Gurnell,troduced white storks (Ciconia ciconia) in

d suffered low juvenile survival (Schaub etading to the suggestion that conservation or

mentothera beaandmorttransportiunsu

preycases

stageical mefforfurthhingehabitModdynain Spcient(Busthe nmann

Thsucce

susta(Smiplannpopuusedsystemodetest oandour a

tionfuturpartiction2003tries,popumodepromalternSaltz, 1998; Bar-David et al., 2005), whileindicated the opposite. In the Netherlands,pulation was evaluated after reintroduction

ed only marginally viable due to highf adults (Nolet and Baveco, 1996). Then of lynx (Lynx canadensis) to southerntheir USA range was later predicted to be

ul on the basis that habitat lacked minimumies (Steury and Murray, 2004). The latterrscore the need for models at the planningdict its outcome, but unfortunately, ecolog-rs have been involved in few reintroductionrrazin and Barbault, 1996). Direction forx (Lynx lynx) recovery efforts in Germanyart on current modeling assessments ofh viability (Kramer-Schadt et al., in press).of bearded vulture (Gypaetus barbatus)rior to reintroduction to isolated mountainsdicated captive populations were insuffi-

pport the translocations that were requiredte, 1998). In sum, these examples illustrateor and value of modeling in an adaptive

nslocation of wolves to YNP has been(sensu Griffith et al., 1989) with a self-

population well established within 10 years05; White and Garrott, 2005). During thehase, after reintroduction, and through torecovery, the WOLF models have beenulate probable dynamics of a multi-speciesinform management alternatives. Buildingt predict the outcomes of species recoveryderstanding of the ecology of the system,e revisions of models gradually improveto predict system dynamics. Reintroduc-anslocation is likely to increase to meetervation demands (Griffith et al., 1989), inwolves continue to expand their distribu-h conservation efforts worldwide (Boitani,ding, but not limited to, 14 European coun-nadian provinces and 11 US states wheres are increasing (Boitani, 2003). Predictives a framework for adaptive managementassist with the evaluation of managementfor future population recovery efforts.


Acknowledgements

We thank the National Park Service, National Geo-graphic Society, National Science Foundation (grant#0078130), USGS Biological Resources Division,NSERC and Alberta Conservation Association forfinancial support. P.J. White, G.J. Wright, R.O. Peter-son and D.W. Smith provided unpublished data. E.H.Merrill, M.J. Kauffman, L.T. Thurston, P.J. White, M.Hebblewhite, G.P. Frame, D.W. Smith, D.R. Stahler,L.S. Mills and G. Plumb provided valuable discussion.Two anonymous reviewers provided helpful commentson an earlier draft.

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