تجزیه و تحلیل هزینه فایده از برداشت گوزن شمالی در اسکاندیناوی. یک روش مدل سازی ساختار یافته مرحله ای

A cost-benefit analysis of moose (Alces alces) harvesting in Scandinavia is presented within the framework of an age structured model with four categories of animals (calves, yearlings, adult females, and adult males). The paper aims to demonstrate the economic content of such a wildlife model and how this content may change under shifting economic and ecological conditions. Two different harvesting regimes are explored: landowner profit maximization, where the combined benefit of harvesting value and browsing damage is taken into account, and overall management, where the costs and damages of moose-vehicle collisions are taken into account as well. An empirical analysis of the Norwegian moose stock indicates that the present stock level is far too high compared with the overall management scenario, and that the composition of the harvest could be improved.

The aim of this paper is twofold: first, to demonstrate the economic content of an age structured wildlife population model; and second, to show how this economic content may change under different management scenarios. The wildlife considered is the moose (Alces alces) which is studied in a Scandinavian ecological and institutional context where the landowners obtain the harvesting value and bear the cost of the timber browsing damage, but do not pay for possible other damages. Two basic management schemes are analysed; landowner management and overall management where the cost of moose-vehicle collisions is taken into account as well. Analysing structured wildlife harvesting models, i.e., models where the species are grouped in different classes according to age and sex, has a long tradition within biology. Caswell (2001) gives an in-depth overview; see also Getz and Haigh (1989). However, economic analysis plays a minor role in these works. Economic reasoning is taken into account in Skonhoft et al. (2002) who analysed various management strategies for a mountain ungulate living in a protected area and a hunting area. Four stages were included: females and males within and outside the protected area. However, because of the complexity of this model due to the dispersal mechanism it is difficult to understand the various economic mechanisms influencing harvesting and abundance. The present paper aims to analyse such economic mechanisms more explicitly where a four-stage model (calves, yearlings, adult females, and adult males) is formulated. Ericsson et al. (2000) studied the Swedish moose harvest policy with respect to selective versus random harvest of the different stages. In their simulations, however, they only accounted for hunting profit. Wam and Hofstad (2007) also studied a stage structured moose model in a Scandinavian context. The landowner profit was maximized and the trade-off between meat value and timber browsing damage was considered. Such trade-off will also be analysed here, but, as indicated, traffic damage costs will be taken into account as well. These costs are quite high, and recent estimates indicate that they may be even higher than that of the moose meat value (see below). Another important difference compared to the Wam and Hofstad study is that our model, at least to some extent, is solved analytically. We are thus able to show more directly the driving forces behind the harvesting composition and the various harvesting scenarios. We find that per animal values (meat value plus omitted damage value due to harvesting) are instrumental in determining the optimal harvesting composition. The similarity with the results in the seminal Reed (1980) paper is apparent. In addition, we explicitly model a female-calf harvest restriction as the current code of conduct among hunters prevent that calves are left without their mother their first winter (Section 4). A novelty of our paper is thus to demonstrate the analytical and numerical consequences of imposing such restriction. As in Wam and Hofstad (2007) the model is illustrated numerically where the Norwegian moose stock is used as an example. Just as in Ericsson et al. (2000), we also calculate the benefit of our selective harvesting scheme with a harvest pattern where ‘an animal is an animal’ as considered in the traditional bioeconomic analysis (e.g., Clark, 1990). The paper is organized as follows. In the next section, moose hunting in Scandinavia is briefly described. In Section 3 the population model is formulated while Section 4 demonstrates what happens when the hunting is steered by the traditional landowner goal of maximizing meat value. The landowner exploitation is analysed both with and without including the browsing damage cost. In Section 5 we study the optimal sex and age composition as well as the economic consequences when the harvest is steered by the overall manager, and where the traffic damage cost, in addition to the meat value and browsing damage cost, are taken into account. Section 6 illustrates the models by numerical simulations using Norwegian aggregate data and where the various scenarios are compared with recent harvest and stock data. In the basic model, the meat value is assumed to be given by a fixed meat price, and the unit costs related to forest damage and traffic accidents are assumed to be constant as well. In Section 6.3 these assumptions are relaxed and we show some numerical results when stock dependent hunting costs as well as convex forest damage costs are included. Section 7 finally summarizes our findings.

In this paper we have analysed the cost and benefit of the Scandinavian moose population within a four stage model with density-dependent fertility and density independent mortality and where the cost and benefit functions are approximated by linear functions. Two basic exploitation schemes, landowner exploitation (LO and LOF) and overall management (OM), have been studied. The different ways to compose the harvest, e.g., in yearlings or females, and how the various management regimes induce different composition of the harvest are highlighted. Without a restriction on the female-calf harvest, we find the optimal harvest composition to be determined basically by the same factors as in Reed (1980). With the female-calf restriction included, typically neglected in the existing literature on moose harvesting, we find it to bind. As a consequence, the harvest composition will be substantially different from the situation without this constraint. Therefore, the same number of calves and females should always be harvested (zero or positive) in the optimal solution, irrespective of harvesting regime. The numerical section illustrates the predictions from the theoretical model. In the hunting value only management scheme (LO-scenario), we find that zero calf and female harvest and high yearling harvest are accompanied by a modest male harvest. We also find that under the overall management scenario (OM), no yearling harvest is optimal while calves and females should be harvested. Moreover, the male stage is more aggressively harvested than the other stages in the LOF and OM regime. It is also demonstrated how changing harvest mortality of the different stages is accompanied by significant profitability changes while leaving total harvest more or less unchanged. Comparing the current management regime of moose in Norway (Current) with the overall management (OM) regime studied here shows that the moose stock in Norway generally is far too high. The calculated yearly overall loss is about NOK 30 million. The most significant difference between the two solutions is that the OM management regime suggests that no yearlings should be harvested, while the harvest of yearlings in Current is substantial. Therefore, from an overall perspective, this analysis indicates that the moose stock in Norway is too high causing too much browsing and traffic damage compared to the hunting value income obtained. The massive increase in the moose stock in Scandinavia since the seventies must be seen as a large scale ecological project to maximize meat production. From an economic point of view, maximizing meat production without taking forest and traffic damage costs into account seems strange. Thus, a harvest pattern of the different age classes that maximizes meat production is not in accordance with the economic optimal harvest pattern. Our study is a restricted type of cost-benefit analysis because some values, like non-use values and existence values, are neglected. However, due to the recent high moose population in Scandinavia, such values, on the margin, are probably quite modest and will hence only have small influence on the optimal harvest composition. All our basic conclusions drawn about the harvesting composition is based on linear damage cost and benefit functions. However, when relaxing the linearity assumptions, numerical results indicate that the harvest pattern does not change dramatically. We have also calculated the net benefit when our optimal selective harvesting pattern is replaced by an ‘optimal’ uniform pattern where an ‘animal is an animal’ as considered in the traditional bioeconomic models. We find that such harvesting pattern reduce the economic benefit considerably. Finally, while the present analysis is for a moose population, our results have certainly relevance for the management of other species, cf. the Reed (1980) paper as well as the recent age structured fishery analysis in Tahvonen (2009).