E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 8 ) 5 1 7 – 5 2 4

ava i l ab l e a t www.sc i enced i rec t . com

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ANALYSIS

Estimating cost functions for the four large carnivoresin Sweden

Göran Bostedt⁎, Pontus Grahn1

Department of Forest Economics, S-901 83 Umeå, Sweden

A R T I C L E I N F O

⁎ Corresponding author. Tel.: +46 90 786 85 11E-mail addresses: goran.bostedt@sekon.slu

1 Present address: S. Slevgränd 108, S-906 22 Recent surveys can be accessed (in Swedi

0921-8009/$ – see front matter © 2008 Elsevidoi:10.1016/j.ecolecon.2008.05.008

A B S T R A C T

Article history:Received 2 July 2007Received in revised form20 February 2008Accepted 7 May 2008Available online 21 June 2008

The Swedish carnivore policy goal for the four large carnivores – wolverine (Gulo gulo), wolf(Canis lupus), brown bear (Ursus arctos) and lynx (Lynx lynx) – is to ensure a minimum viablepopulation on a long-term basis. To reach this goal the policy restricts population regulationactivities, like hunting (prohibited for wolverine and wolf and restricted for brown bear andlynx) in Sweden. For owners of semi-domesticated (i.e. reindeer), and domesticated(livestock) animals this policy and the existence of individuals of these four speciesresults in externalities associated with predation.This paper presents econometric estimates of the predation and the social costs for thesefour species, based on ecological models of functional response. The data on costs is basedon compensation provided to livestock owners by the Swedish government. The paper alsoapplies these econometric estimates to predict the social cost per species when thepopulation goals of the Swedish carnivore policy are reached. Based on out our model thewolverine and the lynx will impose the highest marginal, as well as total costs on society,given the current policy goals. The wolf is an efficient predator, but due to its geographicaldistribution in Sweden, its social costs are less than anticipated. The brown bear is largelyomnivorous, thus resulting in relatively low social costs.

© 2008 Elsevier B.V. All rights reserved.

Keywords:CarnivoresPredationCostsEconomics

1. Introduction

The conservation of large carnivores entails significant costs.Some costs are obvious, such as predation on domesticated, orsemi-domesticated, animals such as sheep (Ovis aries) orreindeer (Rangifer tarandus) (Bjärvall and Franzén, 1990).However, predation on wild ungulates can also represent asocial cost to the extent that these ungulates are attractivehunting game. Further, carnivores are known to attack and killhunting dogs. Specieswith these features can be characterizedas both environmental ‘bads’ and ‘goods’, to the extent that

; fax: +46 90 786 60 73..se (G. Bostedt), pontus.gr7 Umeå, Sweden.sh) at www.viltskadecent

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there also exists a willingness-to-pay to preserve them(Bostedt, 1999). Apart from carnivores interesting examplesinclude wild pigs (Tisdell, 1982) and elephants (Bandara andTisdell, 2003, 2004).

The four so-called “large carnivores” in Sweden –wolverine(Gulo gulo), wolf (Canis lupus), brown bear (Ursus arctos) and lynx(Lynx lynx) – are native Swedish species and have been so sincethe last Ice Age (Bjärvall and Ullström, 1995). The size of thepopulations of these carnivores is however only known fromsystematic surveys for the last 20–30 years.2 The general trendtoday is that these species (with the exception of the lynx) are

ahn@lycksele.se (P. Grahn).

er.com.

.

Fig. 1 –The wolf population 1971–2004. All population dataare compiled from estimates by the County AdministrativeBoards, the Saami Parliament, the Swedish EPA and theSwedish Hunters' Association, cf. Section 4.

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increasing in numbers, due in part to the current Swedishcarnivore policy (cf. Sections 2.1–2.4 below). This policy hasspecific goals concerning the population number and dis-tribution of each species, to ensure the populations above thelevel of the respective minimum viable populations. Thecurrent policy was adopted by the Swedish Parliament in theyear 2000 (Government Bill 2000/01:57, 2000). Former policies,especially in the beginning of the 20th century, had quitedifferent goals, namely to exterminate the carnivore popula-tions. For this, bounties were paid to those who killed any ofthe four large carnivores.

The aim of this paper is to estimate social cost functions forthe four large carnivores in Sweden based on regressionmodels of cost and population numbers founded in ecologicaltheory. These estimates are then used to predict the costs tosociety of achieving the Swedish carnivore policy goals. Itshould be emphasized that due to lack of data this analysisignores the social costs to hunters associated with (1)carnivore competition with humans for game and (2) attackson hunting dogs.

The number of publications on this topic is very limited.The cost study by Boman (1995) is a predecessor to the onepresented in this paper, even though that data set was shorter.Today, the estimates of carnivore populations have greatlyimproved, particularly for the brown bear. Furthermore,Boman et al. (2003) conducted a cost–benefit analysis for theSwedish wolf population, which showed that the spatialdistribution of the wolf population is of great importance inexplaining costs and benefits. More recently, Skonhoft (2006)analyzed the costs and benefits of wolf re-colonization inNorway. Costs were measured in terms of predation on, andthereby reduced availability of, game (mainly moose) forhunting. Benefits were measured in terms of reduced brows-ing damage by these game species. Furthermore, two studiesof predation and cost efficiency in the conservation of Africanwild dogs (Lyacon pictus) in South Africa and Kenya, by Lindseyet al. (2005) and Woodroffe et al. (2005), provide an interestingcomparison with a non-Scandinavian carnivore (this compar-ison is provided below in the Results section).

Concerning cost studies of endangered species other thancarnivores, there is a dearth of empirical studies in refereedjournals, with the well-known exception of the spotted owlstudy by Montgomery et al. (1994). In addition, there was acost–benefit study of the rare Australian mahogany glider(Petaurus gracilis) by Tisdell et al. (2005). This is an interestingfact, especially when contrasted with the wealth of valuationstudies directed at endangered species. Consequently we feelthat this social cost study fills a gap in the literature, sinceboth benefits and costs are needed to make informedeconomic decisions concerning wildlife management.

There are a significant number of publications concerningthe ecology and biology of the four large carnivores in Swedenand Scandinavia. This literature often deals with populationecology, genetics and animal ethology. However, of interesthere is that there are a few ecological studies that presentestimates of the diet and amount of meat required by thepredators, for instance Dahle et al. (1998) and Landa et al.(1999). Therefore we, when necessary, rely on estimates fromcountries outside Scandinavia, for instance the North Amer-ican studies by Sibly and Callow (1986) and Mech (1977).

Webegin the next section by outlining basic biological factsconcerning the four large carnivores, with a focus on species'behavior, demand for nutrition and energy, and the popula-tion and spatial distribution. In the Theory section we outlinethe ecological framework, which provides the basis for ourempirical estimates. The final section contains concludingremarks.

2. Bioeconomic background

This section presents a short biological overview of the fourlarge carnivores in Sweden focusing particularly on thebiological characteristics, the species' capacity to imposeexternalities on private livestock, and the general populationdevelopment in Sweden in the latest decades. This analysisexcludes the Golden Eagle (Aquila chrysaetos), which is some-times is considered the fifth large carnivore in the Swedishfauna.

2.1. Wolf (C. lupus)

The wolf is an efficient carnivore that usually feeds on moose(Alces alces) and other ungulates like reindeer (R. tarandus). Thefact that wolves form packs can make them very effective inhunting large prey (Bjärvall and Ullström, 1995; Persson, 1996).As of 2005, the wolf population numbers approximately 100individuals in Sweden. If Norway, with whom Sweden sharesa common wolf population, is included the populationnumber becomes slightly higher, approximately 100–120individuals. The (first stage) goal of the Swedish wolf policyis that the future population should number 20 annualrejuvenations, which is equal to around 200 individuals. Theofficial policy is, somewhat simplified, that the wolf shouldnot be established in the reindeer herding area in the north ofSweden, due to the potential problems it might cause toreindeer herders (Government Bill 2000/01:57, 2000) (Fig. 1).

2.2. Brown bear (U. arctos)

The brown bear (U. arctos) is found mainly in the northernparts of Sweden. The Scandinavian brown bear is an

Fig. 3 –The wolverine population in Sweden 1971–2004.

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omnivorous species that predominantly eats non-meat food(Bjärvall and Ullström, 1995), such as blueberries, ants andplants (Dahle et al., 1998). However, in the spring, followinghibernation, the bear is known to seek meat in order to meetprotein demands. At this time it is more likely to predate onmoose (A. alces) and reindeer (R. tarandus), particularlysince the calves of these species are also born in the springand provide easy prey. A trend shown by a number of studiessuggests that the brown bear prefer a larger amount of meatwith increasing latitude (Persson et al., 2001; Kaleckaya, 1973).

As of 2005, the Swedish brown bear population is estimatedat between 1600 and 2800 individuals. This represents aseemingly rapid increase in the population between 2000 and2005, yet it has been argued that this change is not realisticand is likely due to the development of estimation techniques,rather than ecologically favorable conditions (Solberg et al.,2006). The reason is that the brown bear population untilrecently has been very hard to estimate because it does notleave tracks during the winter. Estimation techniques havechanged and developed over the years and new DNAtechniques have made it possible to estimate the populationsize with a higher degree of accuracy (Solberg et al., 2006; NFS2004:17; NFS 2004:18).

The Swedish carnivore policy goal for the brown bearestablished that the population should be larger then 1000individuals. As of 2005, this goal has been reached (Fig. 2).

2.3. Wolverine (G. gulo)

Thewolverine (G. gulo) mainly inhabits themountain region inScandinavia, with some exceptions. This species is welladapted to the climate conditions in this area, and is anefficient carnivore with a diet mainly consisting of reindeer.Its advantage over this prey is due to, among other things, itsvery large feet, if the overall size and weight of the animal areconsidered, which gives it a great advantage over reindeer onsnow covered ground. During summer, the diet is less known,but is thought to include smaller prey and carcass (Landa et al.,1997, 1999). The wolverine population was estimated tocontain around 420 individuals in 2005 according to theSwedish Environmental Protection Agency. The (first stage)goal of the Swedish carnivore policy for the wolverine is thatthe population should number at least 90 rejuvenationsannually, which is thought to be equal to about 575 individuals(Ericsson et al., 2007) (Fig. 3).

Fig. 2 –The brown bear population in Sweden 1971–2004.

2.4. Lynx (L. lynx)

The lynx is the only large wild cat found in Scandinavia. Thelynx has been shown to have a significant effect on thepopulation numbers of roe deer (Capreolus capreolus), animportant prey in some parts of Sweden (Liberg and Andren,2005). Due to the high populations of roe deer the largestdensity of lynx is found in the middle-part of Sweden.However, the lynx is also found in the northern parts ofSweden. As a carnivore in the southernmost parts ofScandinavia, the lynx prefers roe deer and small prey specieslike hares (Odden et al., 2006). Lynx in the northern part ofScandinavia also predate on reindeer and smaller mammalslike mountain hare (Lepus timidus), as well as birds likegrouses (Lagopus lagopus and Lagopus mutus) (Pedersen et al.,1999).

Due to historic government policies that alternativelyencouraged and prohibited hunting, the lynx population hasvaried over the years. Today, when limited hunting has beenallowed since the mid 1990s, the population is stable orsomewhat decreasing. The goal of the Swedish lynx policy isthat the population should exceed 1500 individuals — a goalwhich has been reached as of 2005 (Fig. 4).

3. Theory

Theoretically defining and empirically estimating the relationbetween the population of a certain carnivore and the social

Fig. 4 –The lynx population in Sweden 1971–2004.

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costs it imposes in terms of predation on domesticatedanimals involve at least two steps:

Step 1: Estimating the relation between the populationlevel of the carnivore in a specific area and the expectednumber of domesticated animals of different sex and agegroups that may be lost to predation to this carnivore pertime period. This will be explained below in terms of func-tional response models.

This step involves several sub-steps including: disentan-gling the effect of different carnivore species that predate onthe same prey species; estimating the prey death rate —referred to as the functional response; consideration of acarnivore's preference for prey species when several differentchoices of prey exist; and spatial concerns, such as the effectof dispersal of prey by the carnivore.

Step 2: Estimating the welfare loss associated withpredation of a particular animal, given its species type, sexand age group. This will be explained below in terms of op-portunity costs.

Importantly, the welfare loss associated with predationupon a domesticated animal, such as a sheep or a reindeer,shouldnot always be restricted to themeat valueof theanimal.For example, if the killed individual is a valuable breeder thenthe welfare loss should also include the lost opportunity topass on its genetic information to future offspring.

3.1. Step 1 — functional response models

Conventionally, general first-order differential equations (i.e.Lotka–Volterra typemodels3) are used to describe predator–preydynamics (cf. Gutierrez, 1996; Abrams and Ginzburg, 2000):

dNdt

¼ r Nð ÞdN� g N;Pð ÞdP ð1Þ

dPdt

¼ f g N; Pð Þ; P½ �dP ð2Þ

where Eq. (1) is the growth rate of the prey species, N, whileEq. (2) is the corresponding growth rate for the predator species,P. r(N) is the per capita birth rate of the prey species, whichdecreases with N in most models. Furthermore, g(N, P) is thepredator per capita consumption rateofprey,while the functionf(·) represents the predators' numerical response. To proceedwith step 1 it is necessary to focus on the function g(N, P), whichis commonly known as the predator functional response. Asdemonstrated in Eqs. (1) and (2) there is a feedback effect in thesense that the prey population influences the growth rate of thepredator, through the numerical response. However, whenmultiple prey species are available this relationship will appearless interactive, meaning that the predator will not respondnumerically to variations in the population of a particular preyspecies. Furthermore, both prey and predator densities areheavily influenced by current management regimes. Thenumerical response is therefore in the following neglected andthe sizes of thepredator populationsare determinedoutside themodel.

3 These models were initially developed by Lotka (1925) andVolterra (1931) independently.

Ecological theory usually distinguishes between threetypes of functional responses (cf. Abrams and Ginzburg, 2000):

Preydependent response : Na ¼ g Nð ÞdP

where Na is the number of prey killed by a population ofpredators. Here the prey density alone determines thefunctional response. Evidently, this response is linear in P (e.g.Lotka, 1925; Volterra, 1931; Nicholson and Bailey, 1935; Hasseland May, 1974). The simplest of these models also assume thatfor a given predator density, prey mortality increases linearlywith prey density up to some saturation level where thepredator simply cannot kill more prey, i.e. g(N)=sN if g(N)bNa

max.

Predatordependent response : Na ¼ g N; Pð ÞdP

Here both predator and prey populations affect theresponse. These functional responses were first described byHolling (1959). In these models g(N, P) is usually assumed tobe convex in N, so that ∂g(N, P) /∂NN0 and ∂2g(N, P) /∂N2b0. Inthe limit, as N→∞, the number of prey killed approaches thesaturation level, i.e. Na→Na

max. Another alternative is toassume that the functional response has a sigmoidal shapein N, so that ∂g(N, P) /∂NN0 and ∂2g(N, P) /∂N2N0 if NbN⁎ and∂2g(N, P) /∂N2b0 if NNN⁎. Again, in the limit, as N→∞,the number of prey killed approaches the saturation level,i.e. Na→Na

max. Since predator dependent response models arevery difficult to estimate empirically, wewill concentrate on preydependent response models in the following, and will furtherassume that prey density is below the predator saturation level.

Functional response models can easily be expanded toinclude several predator or prey species. For instance, a preydependent response model can be adapted for two prey types:

Multispeciesdependent response : Na1 ¼ g s1dN1 þ s2dN2ð ÞP

where the lower case indices 1 and 2 indicate the two differentprey species, and s1 and s2 are constants which indicate preypreference by the predator. For statistical purposes theequation above shows how the population of one prey speciescan contribute to explaining social costs on another preyspecies. It is important to note that predators are more likelyto exhibit prey preference when food is not limiting. Conse-quently, all preference models may fail under conditions ofextreme hunger. As noted by Abrams and Ginzburg (2000),very few empirical studies of functional responses in naturalsettings exist, despite considerable debate around theseresponses. Notable exceptions are the studies of functionalresponses of wolf on moose by Messier (1994) and Vucetichet al. (2002). In the study by Messier (1994) killing rates wereshown to be increasing asymptotically in moose populationdensity to a specific level and were not significantly explainedby wolf population density, i.e. a prey dependent response,while Vucetich et al. (2002) showed that predator densityexplained more variation in kill rate than did prey density.

3.2. Step 2 — opportunity cost

The relevant cost term in this type of welfare analysis is theopportunity cost, which is used to place a value on the inputs

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that could be used to produce other things of value to people.With reference to Boardman et al. (1996) opportunity cost canbe defined in the followingway: “The opportunity cost of usingan input to implement a policy is its value in its best alternativeuse” (emphasis added). A common assumption is that the bestalternative use of a domesticated animal, other than as foodfor a wild carnivore, is the market value of the animal. If thekilled individual is a valuable breeder then the lost opportu-nity to pass on its genetic information to future offspringshould be reflected by this market value.

Ideally,market prices for live domesticated animals times thenumber of carnivore caused deaths of these animals should beused to estimate the welfare loss, measured as the opportunitycost. In the absence of such information government compensa-tions can be an alternative, given that the very reason for theseschemes are to compensate the owner for the welfare lossassociated with predation. However, it should be borne in mindthat in many countries, including Sweden, livestock ownerscomplain that government compensations are inadequate.

In addition to domesticated animals, carnivores likewolvesand wolverines may also predate on valuable game species,creating an opportunity cost on hunters by reducing theharvestable population. For the carnivore populations ofconcern in this analysis, the four large carnivores in Sweden,the main relevant game species is the moose and roe deer.Locally, certain carnivore species may have a strong impact,although there exist no national statistics on the effect of the“four large” on the Swedish moose, or roe deer, populations.The opportunity cost on hunters is therefore excluded in theempirical analysis. For this reason the opportunity costestimates should be seen as a lower bound measure of thetrue welfare loss caused by these carnivores.

4 According to the homepage of the Swedish Saami Parliamentwww.sametinget.se.5 The actual damage in terms of found livestock or reindeer

killed or injured by a large carnivore.

4. Method

The data used in this paper is in the form of time series for thecarnivore populations, as well as for the annual economiccompensations for the period 1971–2003. However, the dataseries contain gaps for the years 1981, 1982, 1984–86, 1988,1989, and 1992–1996, due to unavailable data at some CountyAdministrative Boards that were responsible for the statisticsbefore 1996. The estimation of the population numbers forwolf, wolverine and lynx is conducted by using either radiotagged animals or the amount of animal footprints producedby the individuals of the different species. For brown bear, theDNA technique was used to estimate the population levels,but in this case, the “footprints” were brown bear droppings(NFS 2004:17; NFS 2004:18). We have chosen to use theeconomic compensations to livestock owners as a representa-tion of the welfare loss associated with predation. Thisimplicitly assumes that the government compensations arecorrectly set, which is not known with certainty. Reindeerherders and other livestock owners in Sweden have com-plained about the low level of these compensations, suggest-ing that theymay not represent an overestimate of thewelfareloss, as we indicate above. However, it could also representstrategic behavior on the part of herders and livestock owners.

To assess the reasonableness of using government com-pensation as the measure of opportunity cost in this analysis,

we conduct a rough comparison between compensations perkilled reindeer and the slaughter (i.e.meat) value of an averagereindeer. In 2006, SEK 42.5 million was paid in compensations(Viltskadecenter, 2006), and approximately 30,000 reindeer werekilled by carnivores during this period4 (exact figures areunavailable), resulting in an average compensation of approxi-mately SEK 1400/reindeer. Recent (2004) reindeermeat prices arearound SEK 40/kg (including SEK 12/kg in government pricesubsidy) (Svensson and Nergård, 2005). With an averageslaughterweight of 31.58 kg (Bostedt, 2001), this gives a slaughtervalue of SEK 1263/reindeer, suggesting that compensationsapproximately cover the loss in slaughter value. However, wenote that the livestock killed by carnivoresmight not be the onesintended for slaughter (e.g. valuable breeders), and that theexistence of carnivores results in higher livestock managementcosts (e.g. surveillance and rounding up scared animals).

The current Swedish system for damage compensation toowners of semi-domesticated and domesticated animals canbe divided into two separate parts: one part for domesticatedanimals, such as sheep, cows, horses, dogs, etc., and one partfor the reindeer, which is considered a semi-domesticatedanimal in Sweden. The compensation to reindeer herderstoday is administrated by the Saami Parliament, a Swedishgovernment body that gives the Saami a limited amount ofautonomy. Before 1993 this compensation was based on theactual damage done by the carnivores.5 However, since 1996the compensation system for reindeer is related to the numberof carnivores in the sense that the number of carnivores andcarnivore rejuvenations is the base for the amount of moneythat is transferred to the reindeer herders. The compensationfor predation on other types of livestock is administrated bythe County Administrative Boards, and is still based on theactual number of carnivore-killed animals. The data on theeconomic compensation in this analysis is collected from theSaami Parliament and the Wildlife Damage Center in Grimsö.

5. Results

The results presented in this section describe our econometricestimates of the social costs of the Swedish carnivore policy.As shown in the Theory section the predation, and thus costs,are likely to be explained by the number of carnivores, as wellas the amount of prey. Furthermore, the shape of the costfunctions can be nonlinear. Given the unknown, but likelymultiplicative form of the predator functional response, g(N,P), we have chosen to consequently take the natural logarithmof both the dependent and independent variables. For all costfunctions an interaction term, ln(N) · ln (P), is also tested. Foreach species, three different time series have been chosen torepresent N, the population of prey, namely the Swedishreindeer population, the annual cull of roe deer (used as aproxy for the population of roe deer), and the annual cull of

,

Table 1 – Ordinary least squares estimates of costfunctions for the “four large” carnivores in Sweden(t-values within parenthesis)

ln(Bearcost)

ln(Wolfcost)

ln(Wolverine

cost)

ln(Lynxcost)

Constant −2.138 7.838 −13.049 −5.095(− .778) (.883) (−3.122) (−2.863)⁎

ln(Bear pop.) 1.661(5.58)⁎⁎⁎

ln(Wolf pop.) 17.111(2.526)⁎

ln(Wolverine pop.) 1.349(5.796)⁎⁎⁎

ln(Lynx pop.) 1.280(6.769)⁎⁎⁎

ln(Roe deer) 1.035(6.119)⁎⁎⁎

ln(Moose) .446 .231(1.496) (.280)

ln(Reindeer) 1.796(4.582)⁎⁎⁎

ln(Wolf pop.) ⁎ ln(Moose) −1.420(−2.401)⁎

Degrees of freedom 18 17 18 18F-test value 20.50 12.17 48.78 63.81Adjusted R2 .661 .626 .827 .862Mean cost (SEK) 868,089 174,796 5,961,663 5,950,406

⁎Significant at 5% level, ⁎⁎significant at 1% level, ⁎⁎⁎significant at .1%level.

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moose (used as a proxy for the population of moose).6 Theresults in Table 1 present the models with the best F-testvalues for the four carnivore species. All estimates have beencorrected for heteroscedasticity using White's consistentestimator, see White (1978), and all cost data have beendeflated to the year 2000.

As is evident from Table 1, different prey species contributeto different carnivore cost functions. Note that humanhunting of wild ungulates such as roe deer and moose inSweden results in great quantities of slaughter offal (animalremains) being left in the forest, which is thought to be animportant food source for the four large carnivores. This couldcontribute to carnivore population growth and thus indirectlyto social cost through predation on livestock. For the brownbear cost function the annual moose cull – as a proxy for themoose population – was used, but did not contributesignificantly to explain cost (probability of rejecting the nullhypothesis that the β-coefficient is equal to zero was 84.8%).The marginal cost of an increase in the bear population,evaluated at the 2003 national population level of bears (2000)andmoose cull (103,185) is approximately SEK 5120.7 However,should the recent brown bear population increase be over-

6 Roe deer and moose are included as substitute preys for thepredator, which intuitively has an effect on the predation onlivestock and reindeer, and thus, the economic compensation.7 Using the parameter estimates in Table 1 the cost function is:

C=e[−2.138+1.661 ⁎ ln(Bearpop)+ .446 ⁎ ln(Moosecull)]. Taking the first deriva-tive of the cost function and evaluating at the 2003 levels give themarginal cost estimate. The other marginal cost estimates werecalculated in a corresponding way.

estimated (due to changes in estimation techniques discussedin Section 2.2) this figure would likely be an underestimate.

The cost function for wolves shows signs of hete-roskedasticity8 when regressed on the wolf population andthe annual cull of moose. This can partly be explained by thehigh dispersal capacity of wolves combined with theirefficiency as a predator. A few wolves in the “wrong” placecan cause large social cost. Thus, the geographical distributionof wolves is of great importance, whichwas also highlighted inBoman et al. (2003). The moose cull variable is not significantby itself but contributes significantly through an interactionterm. The marginal cost of an increase in the wolf population,evaluated at the 2003 population level of wolves (85) andmoose cull (103,185) is SEK 7480, which is more than 2.5 timesthe marginal cost of bears. This should come as no surprisehowever, given the omnivorous nature of the brown bear. Thewolfmarginal cost figure can also be comparedwith estimatedcosts of conserving African wild dogs (another pack-huntingcanine carnivore) in northeastern South Africa from Lindseyet al. (2005). Estimates ranged from 18 to 27 packs per USD100,000 or – with an average of 7 wild dogs per pack – USD 793to 1020 per wild dog. Using an exchange rate of 7 SEK per USDthis gives approximately SEK 5500 to 7000 per wild dog, whichis comparable to the estimated cost figure for wolves inSweden. Note, however, that the Lindsey et al. (2005)estimates are based on prey profiles composed entirely ofwild prey (i.e. lost recreational hunting opportunities) andthat they are average cost estimates while the carnivorecost function approach in this paper allows for marginal costestimates.

The wolverine cost function includes both the wolverineand reindeer populations, which are both significant at the 1%level. The marginal cost of an increase in the wolverinepopulation, evaluated at the 2003 population levels ofwolverines (375) and reindeer (245,000), is a staggering SEK109,700. This relatively large figure can be attributed to thenatural habitat and present population distribution of theSwedish wolverine population, which brings it in directconflict with the reindeer herding industry. Without doubt iswolverine conservation one of the greatest challenges facingSwedish wildlife management.

Finally, the lynx cost function gives the best fit andincludes the lynx and roe deer populations. The marginalcost of an increase in the lynx population, evaluated at the2003 population levels of lynx (1550) and roe deer cull(162,000), is SEK 15,120, which is considerably lower than themarginal cost for wolverines but is twice the marginal cost forwolves. Table 1 also gives themean value of the compensationcosts used as dependent variable. This shows that wolverineand lynx compensations are approximately 34 times higherthan the compensations for wolf predation. This is due to thefact that wolf population in Sweden has been found mainlyoutside the reindeer herding area and outside other areas withextensive livestock management, e.g. free-ranging sheep.

At this stage it is of interest to use the regression modelsfrom Table 1 to forecast the social costs of the four large

8 The null hypothesis of homoscedasticity can be rejected at the13% level through the Breusch–Pagan test.

Table 2 – Forecasts of social costs for the “four large”carnivores in Sweden (SEK)

Carnivorespecies

Populationgoal

Cost whenpopulation

goal isreached (A)

Current(2003)cost (B)

Difference(A−B)

Brown bear 1000 1,952,000 6,174,000 −4,222,000Wolf 200 1,639,000 886,000 752,000Wolverine 575 54,279,000 30,493,000 23,785,000Lynx 1500 17,559,000 18,312,000 −753,000Sum 75,429,000 55,866,000 21,194,000

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carnivores in terms of predation when the current Swedishcarnivore policy population goals are reached. Our estimatesare presented in Table 2 and include a comparison with thecurrent (2003) costs. All figures have been deflated to the year2000.

Note that the figures for brown bear and lynx in therightmost column are negative. This is because the 2003population figures for these species are actually above thegovernment population goal; i.e. reaching the population goalimplies reducing the populations. In total, reaching thegovernment goal would imply a 35% increase in social costs.The table also illustrates that the social cost of reaching thegovernment population goal is almost solely attributable toone species: the wolverine. However, this conclusion dependsto a large extent on the current population distribution ofthe Swedish wolf population. A permanent establishment ofwolves in the reindeer herding area in northern Sweden – fromwhich it is now excluded – would likely imply a dramaticincrease in predation costs.

6. Conclusion

Carnivore conservation and, in some countries, reintroduc-tion, bring with them significant social costs. This paperestimates individual cost functions for carnivore speciesbased on time series data on populations of the four largecarnivores in Sweden, and costs of predation (measured bygovernment compensations to livestock owners), andtogether with ecological models of functional response. Insome cases, notably in the estimation of the wolf costfunction, there are problems with heteroscedasticity, whichcan largely be explained by variations in the spatial distribu-tion. For example, a few wolves maymigrate into the reindeerherding areas in one year, but then disperse from this area inthe following year. During years when they are inside thereindeer herding area, costs are high due to the wolves'efficiency as a predator and to the fact that reindeer herding isthemost widespread form of extensive livestockmanagementin Sweden.

Marginal cost estimates based on these functions showthat an expansion of the Swedishwolverine population comeswith a large price tag attached. The marginal cost forexpanding the lynx population is also high, but given thatthe current Swedish carnivore policy this is less of an issuesince the target lynx population level is already reached, these

costs are not expected to be incurred. In spite of the incessantpublic debate about the expanding Swedish wolf populationthe marginal costs for increasing the population are relativelymodest by comparison. However, these estimates are basedon the 1971 to 2003 geographical population distribution ofwolves. It is important to note that the costs of an expansion ofthe wolf population into the reindeer herding area in northernSweden cannot be forecasted using the cost functionsestimated in this paper. Furthermore, it should be noted thatpolitical pressure might result in greater relative compensa-tion for the wolf, being a “politically sensitive” carnivore,which might slightly bias findings for this carnivore.

In total, expanding the Swedish carnivore population toreach the population goals decided upon by the SwedishParliament would imply a more than 50% increase in socialcosts, compared with the 2003 level. This cost is almost solelycaused by the wolverine population. For this increase incarnivore populations to be socially worthwhile in an eco-nomic sense this cost should be weighed against the possiblebenefits in terms of use and non-use values of thesecarnivore populations. Recent Swedish attempts at esti-mating non-market benefits of carnivore conservation canbe found in Ericsson et al. (2007, in press) and Bostedt et al.(2008).

This paper has shown that theoretical models from popula-tion ecology – in this case functional response models – canbe applied to estimate welfare costs associated with wildlifeconservation. This type of interdisciplinary effort is likely tobe fruitful given the challenge of making informed policydecisions on the benefits and costs of conserving our mega-fauna, despite the real externalities associated with them(e.g. carnivores in Scandinavia and North America or elephantsin Africa).

Acknowledgements

Weacknowledge funding fromtheMountainMistra (“FjällMistra”)research program. We appreciate comments by Mattias Boman,Southern Swedish Forest Research Centre, Swedish Universityof Agricultural Sciences, Alnarp, and Jens Persson, Dept. ofConservation Biology, Swedish University of AgriculturalSciences, Grimsö. We are also grateful for English editing byScott Cole.

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