© 2004 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
A risk assessment of the sustainability of the harvest of beluga (Delphinapterus leucas (Pallas 1776)) in West Greenland
a School of Aquatic and Fishery Sciences, University of Washington Box 355020, Seattle, WA 98195, USA
b Greenland Institute of Natural Resources Boks 570, DK-3900 Nuuk, Greenland
*Correspondence to C. M. Alvarez-Flores. Present address: Resource Assessment and Conservation Engineering, Alaska Fisheries Science Center, National Marine Fisheries Service, NOAA, 7600 Sand Point Way N.E. Building 4, Seattle, WA 98115, USA. Tel.: (206)526-4316; fax: (206)526-6723. e-mail: Carlos.Alvarez{at}noaa.gov.
Risk assessments to assess the efficiency of management procedures to regulate removals of marine mammals have rarely been conducted. Using Bayesian methods, we conducted a risk assessment on a harvested beluga population off West Greenland. The population size in recent years was estimated to be 22% of the size in 1954. Results indicate that current catches are unsustainable and that continuation of this situation represents a 90% probability that the population will become extinct in 20 years. The analyses suggest that the harvest should be reduced to no more than 130 animals. Constant catch quotas represent a greater risk of depletion compared with catch limits that are a function of harvest rate and population size. An alternative gradual reduction schedule is proposed as a viable strategy, reducing the harvest in 5 years and adjusting the subsequent quota using a harvest rate of 0.5 of Rmax, with updates in the abundance. This analysis is presented as an alternative for cases where an immediate catch reduction is desirable but not feasible for marine mammal populations that appear vulnerable or in danger and where catch and abundance data are available.
Keywords: beluga hunt, Greenland, risk assessment
Received 25 February 2003; accepted 5 December 2003.
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1 Introduction |
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 Top 1 Introduction 2 Methods3 Results4 DiscussionReferences |
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Management of marine species is not limited to the evaluation of the biological characteristics of the resource, as social and political considerations also play an important role in the final decisions. Therefore, management alternatives should be evaluated in terms of their ability to meet some specific management goals. If a biologically desirable strategy cannot be implemented immediately, the manager should know the risk of departing from the optimum (Hilborn, 1997). Methods for evaluating harvesting strategies for marine mammal populations have incorporated means of accounting for the associated uncertainties but usually offer a single estimate of the maximum allowable removal. These methods include the Potential Biological Removals (PBR; Wade, 1998) used mainly by the US government, and the Revised Management Procedure (RMP; Cooke, 1995) of the International Whaling Commission (IWC). Such methods work efficiently under specific, institutionally dictated management goals.
The beluga (Delphinapterus leucas) has long been part of the Inuit hunting culture, providing meat for humans and dogs, and the nutritious skin and blubber called "mattak" in Greenland or "muktuk" in North America. However, in several areas where large-scale harvesting has taken place (e.g. Svalbard, Cook Inlet, Saint Lawrence river, Ungava Bay, East Hudson Bay, and Cumberland Sound), the beluga stocks have apparently been reduced in numbers and/or there has been a contraction in the spatial distribution (Gjertz and Wiig, 1994; O'Corry-Crowe and Lowry, 1997; Kingsley, 2002). In West Greenland, the introduction of new hunting methods and the subsequent large catches is assumed to have resulted in the disappearance of belugas from most of the area south of 65°N (Heide-Jørgensen, 1994). Apparently, the beluga either abandoned some fjords where they were previously found in large numbers or the fraction of the population with affinity for these fjords were eliminated through overharvesting. Indeed, belugas are no longer found in many areas where they were harvested during their seasonal migrations.
The main winter distribution in West Greenland has recently been monitored as a proxy for indications of changes in population size (Heide-Jørgensen et al., 1993; Heide-Jørgensen and Reeves, 1996). Survey results indicate that the relative abundance of belugas wintering off West Greenland has declined considerably since 1981. The population estimate for 1998–1999 is 7941 individuals (95% CI: 4264–14 789; Heide-Jørgensen and Acquarone, 2002).
We examine the current harvest in West Greenland, assuming that all belugas in the area belong to a single stock. Alternative management strategies are evaluated for their ability to ensure that the declining trend is stopped, if possible, allowing for some harvest. Although a risk assessment approach is not unknown in the fishery literature (e.g. Punt and Walker, 1998), it has rarely been applied to marine mammals (e.g. Maunder et al., 2000). We present this assessment as a case where management alternatives are weighted by the amount of risk of not meeting pre-determined goals. Options are offered to administrators, providing time and opportunity to develop economic alternatives for the people affected by drastic reductions in a catch that represents an important source of income. This requires an estimate of the sustainability of different catch levels over the next 5–10 years.
Simultaneous with our study, two independent assessments were conducted on the same stock. One used the IWC HITTER-FITTER model (Butterworth et al., 2002), while the other used Bayesian methods and included belugas from Canadian waters (Innes and Stewart, 2002). These studies were restricted to the estimation of population parameters and of potential yields to be recommended as catch limits. In contrast, after estimating population parameters, we considered a range of alternative catch scenarios and evaluated the risk of not achieving a specific management goal. The underlying philosophy of this approach is discussed.
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2 Methods |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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2.1 Harvest statistics
The catch statistics span a time-series from 1954 to 1999. The difficulty in collecting accurate catch data along the entire coastline of West Greenland prohibits conventional estimates of the uncertainty associated with the data. Instead, the available information has been corrected for potential levels of underreporting and for animals struck and lost to provide three sets (low, medium, and high) based on different assumptions (Heide-Jørgensen and Rosing-Asvid, 2002). We selected the average between the high and medium values as an appropriate balance between potential overestimates and underestimates of the true number of kills. The average was assumed to be an accurate observation of the kill with no associated uncertainty (Table 1). The same approach was applied by Butterworth et al. (2002). An alternative approach would be to incorporate a model parameter that accounts for negative bias in the catch as suggested by Innes and Stewart (2002). Their estimate of the correction parameter increased the average catch by 40%, whereas the mean of medium and high catches increased the catch by approximately 30%. Noting that the distribution of the correction parameter was skewed towards smaller values, the two approaches appear to give roughly comparable estimates of the numbers killed.
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The catch in 1954 was noticeably higher than in all other years. This was caused by the occurrence of a phenomenon known as "ice entrapment", during which Arctic cetaceans may get trapped in ice that forms rapidly and prevents access to open water. An ice entrapment in 1954 included about 3000 belugas (Golodnoff, 1956). When an ice entrapment of this magnitude occurs in Disko Bay, it is unlikely to go unnoticed, and hunters take advantage of the situation. Ice entrapments have occurred in other years (Heide-Jørgensen et al., 2002), but none of the recent events was as large as the one in 1954.
2.2 Abundance
Population trends have been monitored through aerial surveys in selected years between 1981 and 1999 (Figure 1) that provide indices of relative abundance (Table 2). The surveys in 1981 and 1982 differed from later surveys in the type of aircraft used, survey design, methods for extrapolation, and personnel involved (Heide-Jørgensen et al., 1993; Heide-Jørgensen and Acquarone, 2002).
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An estimate of absolute abundance is only available for 1998 and 1999, when the correction factor (and its variance) for missed and submerged animals could be estimated. The estimated absolute abundance for 1998/1999 (combining data for the 2 years) is 7941 animals (CV: 0.32; Heide-Jørgensen and Acquarone, 2002). This value was assumed to apply to 1998 in our calculations.
Using the entire series of indices of relative abundance (1981–1999), a first attempt to derive an estimate of the intrinsic rate of population increase (Rmax) yielded a value close to zero, which was considered inconsistent with the available information on beluga biology. This effect could be traced back to the indices for 1981 and 1982. Because survey design and methods were different, data for these years were removed from the analysis initially. However, to make these data usable, separate re-scaling parameters of relative abundance were estimated for 1981, 1982, and 1990–1999.
2.3 Model structure
A simple discrete generalized logistic model was used to represent the dynamics of the population. The particular form used was a difference equation variant of the Pella and Tomlinson (1969) model:
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2.4 Parameter estimation
Population parameters were estimated in two different ways, by maximum likelihood (MLE; Punt and Hilborn, 1996; Hilborn and Mangel, 1997) and by Bayesian integration (Gelman et al., 1995; Punt and Hilborn, 1997). MLE was based on non-linear fitting of the model to both the relative and the absolute abundance estimates, assuming that their residuals are normally distributed. This choice is arbitrary because the number of strata in the aerial surveys (n=8) is not large enough to approximate normality, but being an estimate obtained by pooling, a lognormal is even more unlikely. Anyway, the predicted trends obtained based on one assumption about error distribution or the other should not differ by much. Likelihood profiles (Punt and Hilborn, 1996; Hilborn and Mangel, 1997) were also generated. Parameter estimates were obtained by minimization of the negative log likelihood of the objective function:
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is the vector of parameters in the model (Equation (1)), 
Ay is the standard error associated with each estimate of absolute abundance, and subscript y refers to year.
The year-specific likelihood for any estimate of relative abundance is given by:
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Iy is the standard error associated with each estimate of relative abundance, qi is the re-scaling parameter for periods i=1 to 3 (1981, 1982, 1991–1999), and qixNy is the associated expected index of relative abundance at year y. Posterior probability distributions for population parameters were calculated by means of Bayesian integration using the Markov Chain Monte Carlo (MCMC) method (Gelman et al., 1995). Prior probability distributions were uniform, bounded between 0.01 and 0.08 for Rmax and between 14 000 and 120 000 for K. An additional parameter q was estimated that re-scales the relative abundance in relation to the absolute estimate. The prior distribution for q was completely uninformative (uniform and unbounded). Two approaches were followed to estimate q. One single q is estimated if the 1981 and 1982 indices of abundance are removed from the series. In the other option, q values are estimated separately for 1981 and 1982 and for the period 1990–1999.
A Bayesian posterior distribution was also obtained for a derived parameter specified to evaluate the actual state of depletion of the population as a consequence of the harvest: the ratio of the population size in the last year with catch data to the estimated abundance in 1954 (K1954).
MLE, likelihood profile calculation and MCMC simulation for Bayesian estimation of parameters were conducted using AD Model Builder (© Otter Research).
2.5 Risk assessment
Derived parameters (Vp), which represent the ratios of the population size after p years of harvest against the population size at the time when the catch limits were introduced, were calculated to evaluate the consequences of future catch restrictions. These parameters are obtained by first saving a sample of the sets of individual model parameters obtained during the MCMC process. When a large number of simulations are run and convergence in the Markovian chain is achieved (a large sample is also desirable), the sample closely resembles the joint posterior distribution of the parameters. The population is then projected without process error (natural variability is not considered) using all the sampled sets of parameters. This assumption could lead to underestimation of the risk, particularly if no feedback is obtained through future surveys. During the projections, a proposed catch scheme is subtracted from each population trajectory (one for each set of parameters sampled from the Markovian chain), resulting in the posterior distribution of future population size after a number of years. For a future trend scenario presented by each set of parameters, the final population is compared to what it was right before a policy is implemented, evaluating in this way the effect of future harvests. The total risk of not meeting a management goal (e.g. stop population decline) is calculated by constructing the cumulative probability of population change. This procedure incorporates the uncertainty around the parameters into the process of calculating the future status of a population. This is a useful way to propose that the specific outcome for the application of a policy is not absolute, and that the real situation can differ from the prediction.
Three different trials (A, B, and C) were conducted to evaluate the risk of not meeting a management goal (Table 3). The management goal in the trials A and B was to stop the population decline (reference point: Vp=1). In trial C, the goal was to avoid extinction (reference point: Vp=0).
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Trial A compared the performance of two choices for setting catch limits: (1) constant annual catch quota or (2) quota set as a function of population size and a constant harvest rate, applied over both a 5-year and a 10-year period. This evaluation was conducted before information on the catch for 1998 was available and therefore parameter estimates used in the simulations (Bayesian means: K=30 610 and Rmax=0.035) differ slightly from the final estimates shown in Table 5. Given that differences were small, we decided not to redo these trials, because the comparison of the performances of the two approaches, our main purpose, remains valid.
Constant catch limits were set to 150, 200, 300, and 500 removals per year. Catches based on harvest rates were specified as for PBR:
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t considered the "best" available estimate; 
is a constant that determines the percentile of the lognormal distribution represented by Nmin, fixed to 0.842 for the 20th percentile.
Additional harvest rates were set to correspond to 0.5Rmax and 0.75Rmax,coinciding with MSY rates if the shape parameter z equals 1 and 3 (default), respectively. If a harvest rate is applied, the estimate of abundance for 1998 is used to calculate the catch for the following 5 years (
). If the trial projects the population for 10 years, then in year 2004, an estimate of abundance (e.g. from a survey) is simulated by sampling from a lognormal distribution with a mean equal to the predicted value for the year and a CV of 0.2. This simulated estimate of abundance is multiplied by the harvest rate to obtain the new catch level.
In a first approach, catch options were calculated using harvest rates by direct utilization of the Bayesian means of Rmax calculated without the 1981–1982 abundance data but with catch data up to 1999 (because catch data for 1999 were incomplete, we assumed a kill of 600 animals). As an alternative management scheme to mitigate the effects of a drastic reduction in the catch and to give managers and hunters time to develop economic alternatives, trial B involved gradual catch reductions and an evaluation of the outcome after 10 years. Because the priority at this point is to prevent further depletion of the population, the reference point for evaluation is the probability that the population after 10 years is smaller than in 2001. Because management policies in our scenario will be applied from 2001 onwards, catches had to be assumed for 1999 (600) and 2000 (700). The situation under a constant removal of 700 animals (option 1) is compared to five alternative scenarios (Table 4).
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The same analysis was conducted again under the same catch options as those applied for the first 5 years, but adjusting catches for the remaining 5 years to a new "observation" of abundance obtained in 2005 (see above). The use of new estimates of abundance represents the common feedback mechanism in situations where new catch limits (based on harvest rates) are estimated based on updated knowledge about the managed stock. The same four (constant) harvest rate alternatives tested in trial A were used in this case. In addition, this experiment was repeated projecting 30 years ahead for: (1) the scenario that is proposed as the "best" alternative (option 3, see Results) and (2) for the scenario where such action is delayed for 2 years (option 5). In both cases, catches after year 2005 are calculated using harvest rates applying PBR with Fr=1. Population "estimates" are again obtained every 5 years by simulation to adjust the catch.
In trial C, the probability that the population will become extinct was calculated projecting the population forward during 10, 20, 30, 40, and 50 years. In each case, catches were kept constant at 100, 300, 500, 700, and 1000 animals.
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3 Results |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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3.1 Parameter estimates and current status of the stock
Figure 2 shows the likelihood profiles and posterior probability distributions for the estimated parameters. The posterior probability of Rmax was very similar to the prior within the interval 0.01–0.08. To better demonstrate the degree of uncertainty associated with this parameter, another estimation was conducted, expanding the upper bound to 0.15, and the resulting profile and posterior distribution are shown in Figure 2A. The posterior probabilities and profiles for the other parameters are better defined than those for Rmax.
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Table 5 provides a summary of the point estimates of population parameters obtained with the complete data set (assuming a catch of 600 in 1999) and without the 1981–1982 indices of relative abundance. Using the Bayesian means (Rmax=0.034 and K=31 522) obtained without the 1981–1982 abundance (but after including the 1998 catches) to estimate the replacement yield of the population (NtRmax(1–Nt/K)), a plot of the replacement yield and catch, both standardized by dividing by K, shows that the kill consistently has exceeded the sustainable catch (Figure 3). The conclusion must be that the stock historically has been overexploited and that the actual kill is still too high. This result is in agreement with the point estimate (Bayesian mean) of the level of depletion that, despite differences in parameter estimates, consistently shows a population size that is near 20% of the original size (Table 5). Under the assumptions of the model, there is a 95% probability that the population is currently
38% of the size in 1954.
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3.2 Probability of extinction
If 1000 animals are caught per year, there is a 99% probability that the population will be extinct in 20 years (Figure 4). At the actual catch level (around 700 animals), the estimated probability of extinction is 90% after 20 years, and 99% after 50 years. A catch of 100 animals shows a small probability (3%) of extinction after 50 years.
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3.3 Alternative management strategies and allowable catch
Figure 5 summarizes the population response under the uncertainty associated with the knowledge that can be extracted from the data about the parameters. The figure compares the cumulative posterior probability distributions of population status after 5 and 10 years of implementing different quota regimes under the two management strategies (fixed quota and fixed harvest rates). In these figures, a Vp value of 1 corresponds to the management objective of "stop decline". Larger V values imply that the population is increasing and thus the management objective has been met; lower values indicate a decline.
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A fixed catch of 500 animals will cause the population to continue to decline with high probability (Figure 5A, B). When this strategy is used, there is no feedback mechanism to adjust the catch to changes in population size. Under these conditions and given the uncertainty, the longer the time an overharvesting policy is applied, the greater the probability that the population will decline. Even a small constant catch of 150 animals implies a total risk of about 20% that the population will not grow.
In contrast, if future catch limits are based on a constant harvest rate and an updated estimate of absolute abundance, the risk of continued population decline is of concern only when harvest rate is set at 0.75Rmax (Figure 5C, D). Use of any of the lower harvest rates implies, at the most, a small risk of population decline. Because the catch is adjusted in time with the acquisition of new information on the population response, the probability of a decline in population size becomes smaller as time progresses.
Table 6 compares the catch levels that result by applying alternative harvest rates directly to the actual stock size estimated for 1999 (7941). The most aggressive policy under the most optimistic scenario suggests a sustainable catch of about 200 animals given the current population size, while a more conservative approach under less optimistic scenarios suggests a sustainable catch of <100 animals per year. A moderate approach using a harvest rate of half the Bayesian mean of Rmax defines a sustainable catch of about 130 animals.
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The maximum probabilities of population decline under different strategies considered are presented in Table 7. These probabilities must be interpreted as the upper bound of an open interval such that the actual probability of decline is smaller than the bound and indicate that if the management goal is to prevent decline in 10 years, the only way to be 100% sure that the population will not have declined after 10 years is by either banning any catch or immediately reducing the catch to the PBR value obtained with an Fr of 0.5. The next lowest probabilities are achieved if the annual catch is reduced to 100 animals for the first 5 years and harvest rates are used for the following 5 years (option 4) or by exclusively using harvest rates. However, if the management goal is expanded to prevent population decline after 30 years, the feedback effect of the application of harvest rates during the following 25 years reduces the uncertainty, and the probability of a decline under the combination of catch option 3 and PBR with Fr of 0.5 is reduced from 37% to 17%.
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4 Discussion |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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Estimates of population parameters are in general consistent with each other, except the Bayesian means for Rmax and K using the entire data set (Table 5). We have not examined these differences and cannot explain them formally, but they may be related to the added uncertainty of two extra parameters (q1, q2, and q3 instead of a single q) for estimation. The estimate of Rmax with the complete data set but only one q estimated was close to zero, a situation that could occur only if the production was extremely low or if natural mortality was very high. To our knowledge, there is no evidence of either one except the observed ice entrapment events that do not occur very often. Whatever the causes, these results indicate that the indices of relative abundance obtained in the past are not strictly comparable, which is probably related to recorded changes in survey design and methods.
The uncertainty around Rmax is very large (Figure 2), resulting in a poorly defined posterior distribution (and likelihood profile) within the original bounds of the prior (0.01–0.08). This is an indication of the limitations of the information contained in the available data (i.e. poor contrast in the abundance data). However, the point estimates between 0.03 and 0.04 (Table 5) are in accordance with the expectations based on information for a long-lived species with similar life history characteristics (Reilly and Barlow, 1986). Also, simulation studies using beluga life history parameters derived from field data predicted that populations could potentially grow at 2–3% (Beland et al., 1988).
From the management point of view, the resulting narrow posterior distribution of the level of depletion of the population (N1999/N1954) is more important. This result is consistent with earlier simulations suggesting that the estimate of this depletion parameter is usually robust and reliable (Alvarez-Flores, 2002). Most of the probability density in the posterior distribution of depletion level is observed in population sizes much lower than the MNPL (
0.6K; cf Figure 2D). This is consistent with the permanent state of overexploitation since 1954 (Figure 3). Continuation of this trend represents a serious threat for the beluga population.
Three alternative ways to manage the hunt for belugas in West Greenland may be considered. Although decisions on management alternatives are a political rather than a scientific issue, we comment on them because of the strong biological implications of each one and their potential socio-economic effects. In the first scenario that no action is taken at all, belugas most likely will go extinct in West Greenland and with them all future economic, cultural, and nutritional benefits from this resource. If this alternative is selected, hunters should be advised to take measures to find alternative sources of future income to compensate for the loss of profit of a restricted catch. Even if hunters do so, it is unlikely that this alternative would provide an acceptable long-term solution given the biological, cultural, and economic loss.
The second alternative is to immediately impose a sharp reduction of harvest level. This may be the more desirable solution from the conservation point of view. If the catch is drastically reduced or even eliminated, the stock should start to recover immediately. Unfortunately, the recovery of a marine mammal stock is slow and it will take decades before the hunters may enjoy the benefits of the recovery. The decision here revolves around the question of whether the hunters can and must give up the current levels of benefit to ensure that future generations can use the resource sustainably at a safe maximum potential.
The third alternative provides an intermediate solution that combines a gradual catch reduction plan, thereby allowing managers and hunters to develop economic alternatives to buffer the transition from a high-catch regime to a low-catch regime, with the primary objective of at least having a low risk of further decline of the stock.
Given the uncertainty associated with parameter estimates, we analysed the relevant question of what level of catch may be recommended from different perspectives. Depending on which harvest rate and estimation method was used, catch options at the present stock size ranged between 74 and 202 animals (Table 6), suggesting a median value around 130. Because of the inertia involved in updating appropriate catch limits for the following years, situations where 100 animals or more were annually removed were tested and compared to catch quota based on harvest rates that were adjusted with new survey data of abundance after 5 years. The results indicate that complete ignorance of parameter values and abundance propagates any positive or negative effects on future population size: the longer the constant catch policy is applied, the larger the uncertainty about the future population. On the contrary, use of a harvest rate strategy reduces the uncertainty because of the feedback provided by new estimates of population size. Even if the population is projected 5 years forward with a fixed-catch policy, predictions of future population sizes are better if they are followed by a harvest rate strategy than those obtained when continuing the fixed-quota policy. The reason for this is that the uncertainty in parameter values is being incorporated in the update. Therefore, each trial results in a different catch limit. For the same reasons, and contrary to the results using fixed quota, applying harvest rates enhances our certainty about the potential outcomes in time. This characteristic has been previously suggested in the context of a description of ways to ensure that management procedures are robust to associated uncertainties (Butterworth et al., 1997).
Based on the current status of the population, the analyses favour a drastic reduction in the catch and use of a harvest rate to set future catches. The required reduction is so large that opponents could argue that the estimate of Rmax is negatively biased (e.g. through severe underestimation of abundance) and that this error would disproportionately affect the hunters. Therefore, it is useful to consider the consequences of underestimating Rmax. Assuming that the West Greenland population could maintain life history characteristics that are distinct from other populations, Rmax values >0.07 (upper bound for the prior set at 0.08) would require either a calving interval of <3 years (which is unlikely; Hazard, 1988), or unrealistically high survivorship values relative to a longevity of 30 years. Assuming Rmax=0.07 and applying a harvest rate of 0.5 of Rmax with the current estimate of population size, the catch limit would be 277 animals, less than half of the current harvest. Clearly, the population cannot sustain the present harvest pressure and if the trend continues, the population will soon become extinct.
Proceeding with a catch reduction for a resource with great social and cultural value is a difficult matter. Imposing an immediate severe catch limit is likely only to be eventually exceeded, given the limitations in monitoring the cumulative catch during a hunting season, but a biologically acceptable limit implies a severe and sharp reduction from the current kill levels. The controversy about how much the catch must be reduced increases because alternative scenarios (defined by the ranges in the posterior probabilities of the parameters) suggest that the catch could be greater than the suggested 130. Although overoptimistic scenarios are associated with high risk and their use requires extreme caution, the catch for the next years even under the most optimistic scenario should not exceed 200 animals.
A gradual reduction program combined with quota based on harvest rates and a feedback every so often has good chances of succeeding in achieving the goal of recovery (Table 7). If ultimate recovery is the primary goal, the time that this may take will have to be established in terms of a combination of socio-economic and biological factors. If the management goal is to prevent any further decline in 10 years (NAMMCO, 2000), the probability that this goal will not be met may be relatively high (taking, for example, option 3 and PBR Fr-0.5: 37%; Table 7) even if the most likely event is no decline. However, this is to some extent an artificial perspective. When using a feedback control, the probability of not meeting the management goal becomes smaller as the policy is applied longer. For instance, the probability of population decline after 30 years for option 3 is reduced to 17%.
We stress that the alternative of a gradual reduction plan differs from an immediate severe reduction in that the transition time may make the effects less difficult to cope with for the hunters. Of course, the population will be reduced even further and recovery to maximum sustainable levels will take longer. On the other hand, the development of an economic alternative should be an essential element of management. If the beluga catch would be completely banned, the hunting effort may be redirected to other species without planning. Then, the problem would simply be relocated, not eliminated.
Previous attempts to determine the allowable catch of monodontid populations have been restricted to the calculation of limits on numbers taken as fixed proportions of population size (Sergeant, 1981; Kingsley, 1989).
The relevant parameter estimates presented are similar to those reported by Innes and Stewart (2002) and Butterworth et al. (2002). For example, the Bayesian mean of the level of depletion is here estimated to be near 20%, with relatively small variations depending on model structure, which is in the upper range of values estimated by Butterworth et al. (2002). However, these authors made each estimate of depletion dependent on a specific assumption about a parameter used as a proxy for the maximum growth rate, while we estimated the posterior probability distribution for the intrinsic rate of increase from the data, avoiding any assumptions about population growth rates. Innes and Stewart (2002), also using Bayesian methods, estimated that the mean of the posterior distribution of the maximum rate of population change was 1.037. This value is approximately equivalent to 0.037 if expressed as intrinsic growth rate, which is close to our own Bayesian mean estimate (0.034). Both Innes and Stewart (2002) and Butterworth et al. (2002) offer estimates of sustainable yield and use these as limits to be considered "to secure against possible further reduction of the population over the immediate future" (Butterworth et al., 2002). Despite this assertion, they did not consider specific management goals.
Even though the three papers assessed the current status of the beluga population off West Greenland and results were similar overall, our work differs fundamentally. Although we agree that the population is overexploited and that catches must be substantially reduced, we considered it unrealistic to suggest that such course of action could be implemented immediately. Therefore, we formally evaluated a wide range of alternative scenarios, ranging from no action to a complete ban.
To our knowledge, the only evaluation of alternative management options in a formal risk assessment in relation to marine mammals refers to the by-catch of Hooker sea lions in the squid fishery of New Zealand (Maunder et al., 2000). These authors evaluated the ability of alternative decisions to reach a goal of population recovery simultaneously with economic losses associated with these decisions.
A stepwise approach has been applied to gradually reduce the by-catch mortality of dolphins in the tuna fishery (IATTC, 1997). The management action was not evaluated in terms of its ability to reach a specific population size of dolphins, because the ultimate goal was a by-catch close to zero. What is relevant here is that the parties involved recognized the impossibility of reducing the by-catch in the immediate short term and realized that the only way to reach an agreement was to propose a gradual reduction programme.
Although the simplicity of our population model may be subject to debate, the principles proposed can also be applied if a model of higher complexity is required. The most important lesson is that a formal risk evaluation of the full range of alternative management options, with incorporation of different sources of uncertainty, is possible. This range should cover the entire array of views of all parties involved so that the consequences of reaching the conservation goal can be weighed against the consequences for the people using the resource.
We acknowledge that there are sources of uncertainty other than those incorporated in the analysis. (1) Kills by hunters during ice entrapment events (Siegstad and Heide-Jørgensen, 1994; Heide-Jørgensen et al., 2002) may be considered as part of the natural mortality if the animals would not survive anyway. To what extent the effects of "natural" mass mortality are represented in the estimated intrinsic rate of increase remains unknown and additional modelling may be required. (2) The population has been exploited for centuries and the population in 1954 is undoubtedly a biased estimate of pre-exploitation population size. Although catch data for earlier years are available, they require a substantial review (Heide-Jørgensen and Rosing-Asvid, 2002) before they could be used. An alternative approach would be to account for bias in K, but this would require the estimation of a large number of additional parameters. (3) The possible existence of sub-stocks (cf. Palsbøll et al., 2002) has been ignored because of insufficient knowledge. (4) Intrinsic model performance in relation to particular characteristics of the data used (Punt, 1995) has not been addressed. (5) Trying to quantify the overall uncertainty associated with the bias in the catch data would be in line with the intention of our analysis. The problem with incorporating formal bias parameters is that their sheer number may prohibit estimation. (6) The decision about an appropriate value of the shape parameter (z; associated with the relative population size at which the Maximum Sustainable Yield may be taken: MNPL/K) is a difficult one. A sensitivity analysis indicated that MNPL/K values <0.5 or >0.8 are unlikely for marine mammals (Taylor and DeMaster, 1993). These authors also showed that multiple factors affect the value of z, that their individual effect is not easily inferred, and that empirical data are scarce. From the perspective of incorporating all possible sources of uncertainty, it would have been more appropriate to release the assumption and to use a semi-informative prior. We opted to assume a shape parameter resulting in a MNPL/K value of 0.63, within the range of 0.6–0.7 applied in sensitivity analyses testing the performance of methods to calculate allowable catches of marine mammals (IWC, 1992; Wade, 1998).
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Acknowledgements |
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This study was funded by the Greenland Institute of Natural Resources. We thank Laura Litzky, Glenn VanBlaricom, Robert Suydam, and two anonymous reviewers for their valuable input.
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Footnotes |
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1 Present address: National Marine Mammal Laboratory, Alaska Fisheries Science Center, National Marine Fisheries Service, NOAA, 7600 Sand Point Way N.E. Building 4, Seattle, WA 98115, USA.
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References |
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Top1 Introduction2 Methods3 Results4 DiscussionReferences |
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