© 2004 International Council for the Exploration of the Sea
An assessment of Greenland walrus populations
Greenland Institute of Natural Resources PO Box 570, DK-3900 Nuuk, Greenland
*Correspondence to L. Witting: tel: +299 361200; fax: +299 361212. e-mail: ewb{at}dpc.dk.
Recent abundance estimates were combined with historical catches and an age- and sex-structured population dynamic model to perform Bayesian assessments of the walrus (Odobenus rosmarus) populations in West Greenland, the North Water in northern Baffin Bay, and East Greenland. The model assumed density-regulated dynamics and pre-harvest populations in population-dynamical equilibrium. It projected the populations under the influence of the catches to estimate the historical trajectories and the current population status. It was found that the West Greenland and North Water populations have been heavily exploited during the last century with the current abundance being at best only a few per cent of the historical abundance. Apparently these populations are still being exploited above sustainable level. The East Greenland population was heavily exploited after 1889 and during the first half of the 20th century and was depleted to approximately 50% of pristine population size in 1933. After protective measures were introduced in the 1950s this population has increased to a current level close to the abundance in 1889, and the present exploitation appears to be sustainable.
Keywords: Bayesian statistics, density regulation, Greenland, marine mammal, modelling, Odobenus rosmarus, population dynamics, sustainable exploitation, walrus
Received 16 March 2004; accepted 5 November 2004.
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Introduction |
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 Top Introduction MethodResultsDiscussionConclusionsReferences |
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The management of an exploited population of wild animals is often faced with the dilemma between incomplete knowledge on the dynamics and status of the population and the need to determine sound levels of exploitation. If knowledge was complete the implications of a given harvest could be calculated exactly, and it would be relatively easy to set the exploitation to a level where management objectives would be met. In reality, however, the uncertainty trade-off implies that a given harvest can at best be associated with a certain probability that the management goals for the population will be met. In this paper we apply a Bayesian statistical model to the incomplete data on the three exploited populations of Atlantic walrus (Odobenus rosmarus rosmarus) in Greenland, in order to estimate the historical development of the populations, their current status, and sustainable exploitation levels.
The three populations of Atlantic walrus in West, Northwest, and East Greenland have been subject to exploitation for centuries. First at a limited scale by Inuit and then by European whalers and sealers, who tolled heavily on the populations. From the beginning of the 20th century Greenlanders hunted walrus with increasing efforts after the introduction of fire-arms and motorized vessels. The populations are still exploited for subsistence purposes, and for some there are indications of over-exploitation (Born et al., 1995; NAMMCO, 1995). Hence, it seems warranted to attempt an assessment of the present status of the Greenland walrus populations in the light of historical and current exploitation.
The "West Greenland" population of walrus occurs from fall to spring at the edge of the Baffin Bay pack ice from c. 66°30'N to 70°30'N (Born et al., 1994, 1995; Figure 1). Further north in Baffin Bay and Smith Sound walruses occur almost year-round in the North Water polynya and adjacent areas. They are, however, absent from the coastal areas of NW Greenland during the open water season in August–September when they summer along the eastern and southern coast of Ellesmere Island (Canada) and in the Canadian High Arctic archipelago (Born et al., 1995). Walruses in these areas are referred to as "the North Water" population (Born et al., 1995). Walruses occur year-round along the eastern coast of Greenland where they mainly are distributed inside the National Park of North and Northeast Greenland north of the entrance to Scoresby Sound (c. 71°N) (Born et al., 1995, 1997). There is only limited exchange between the East Greenland and neighbouring populations, i.e., West Greenland, North Water, and the Svalbard-Franz Land populations (Born et al., 1995, 2001; Andersen et al., 1998).
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Information on distribution and migration (Born et al., 1994, 1995, 1997) and genetics (Andersen et al., 1998; Andersen and Born, 2000; Born et al., 2001) indicates that the three Greenland walrus populations represent separate population units and therefore should be managed separately (NAMMCO, 1995). Currently, however, there are no management plans or objectives for the exploitation of walruses in Greenland.
For the depleted population of beluga (Delphinapterus leucas) in West Greenland a management scheme or objective has been suggested that allows the population to increase (NAMMCO, 2002). For populations below the maximum sustainable yield level this objective is close to that for the Greenland exploitation of large cetaceans (i.e., minke whale Balaenoptera acutorostrata and fin whale Balaenoptera physalys) that are managed by the International Whaling Commission (IWC). For the aboriginal whaling in Greenland the IWC Schedule (IWC, 2000) states that catches shall be permitted from populations below the maximum sustainable yield level (msyl) as long as the population is above a protection level and the exploitation allows the population to increase toward the msyl. For populations at or above the msyl catches shall be permitted as long as the total removals do not exceed 90% of the maximum sustainable yield (msy). For the purpose of this study we provisionally adopt this management objective, except that we do not specify a protection level.
Previous attempts to model walrus populations include the use of discrete population models to simulate population dynamics of a hypothetical walrus population (DeMaster, 1984; Chivers, 1999). Simple recursive models (Born et al., 1997; Gjertz et al., 1998) have also been used to back-calculate the size of the East Greenland and Franz Josef Land walrus populations, respectively. By combining crude estimates of population size with estimates of current levels of exploitation it was attempted in 1995 to determine the status of the Greenland walrus populations (Born et al., 1995; NAMMCO, 1995).
In this paper we summarize the walrus catch history for the West Greenland, the North Water, and the East Greenland populations for the last century. In the case of the West Greenland population we extrapolated the catch history back to 1820 to investigate the effects on current population status of the length of the period of exploitation. We applied this information, and recent abundance estimates, in a density regulated model with age and sex structure to (i) reconstruct the historical dynamics of the three populations, (ii) evaluate their current status, and (iii) determine sustainable yield levels.
The assessment model applied is based on a Bayesian statistical method (Berger, 1985; Press, 1989; Punt and Hilborn, 1997; McAllister and Kirkwood, 1998). Bayesian assessments have recently been applied to marine mammals like the bowhead whale (Balaena mysticetus) in the Bering-Chukchi-Beaufort Seas (Givens et al., 1995; Raftery et al., 1995), the gray whale (Eschrichtius robustus) in the eastern Pacific (Wade, 2002; Witting, 2003), and beluga (Delphinapterus leucas) in Baffin Bay (Innes and Stewart, 2002; Alvarez-Flores and Heide-Jørgensen, 2004) and they are particularly useful when faced with limited or uncertain information on the stocks in question.
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Method |
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TopIntroductionMethodResultsDiscussionConclusionsReferences |
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Model runs
The assessment of Greenland walruses was based on five runs of the Bayesian assessment model. The first three runs were comparable assessments for the three populations based on catch histories from about 1900. Although these catch histories may be considered best estimates, they are not complete because walruses were taken from all three populations earlier than 1900. A sensitivity run was therefore applied to the West Greenland population where it was possible to provide crude estimates of the catches back to 1820. All these runs were based on the assumption of an even sex ratio at birth (Fay, 1982; Born, 2001). There are, however, some indications that at least Pacific walruses (O. r. divergens) may have female biased sex ratios in the breeding population (e.g., Fay et al., 1997). A second sensitivity test was therefore applied to the West Greenland population where the sex ratio at birth was set to the sex ratio in the harvest which apparently had a ratio of 0.4M:0.6F (Born et al., 1994).
Data
Estimates of current abundance, catches, and losses are described for each population separately.
Current abundance
West Greenland
The point estimates obtained from aerial surveys during late March 1990 and early April 1991 of the visible portion of the population in West Greenland were 458 and 631, respectively (mean: 545). About 18% of the walruses observed were in the water and the remainder on the ice (Born et al., 1994). Walruses in water usually spend about 20% of the time at the surface (i.e. upper 0–2 m) (Fay, 1982; Wiig et al., 1993; Born and Knutsen, 1997; Born et al., 2003). If applying a correction factor (i.e. four walruses submerged for every walrus seen in the water) to the mean of the number of walruses in the water (98), the estimate of the total number of walruses that were in the water is 491. By adding this to the number on the ice (447), the estimate of the West Greenland stock is 938, with a CV of 0.48 based on the survey data.
North Water
In order to enumerate the number of walruses in the North Water population, the Department of Fisheries and Oceans (DFO, Winnipeg, Canada) and the Greenland Institute of Natural Resources (GINR, Nuuk, Greenland) jointly conducted an aerial survey during 11–19 August 1999 over terrestrial walrus haul-outs and along the coasts on eastern Ellesmere Island and in the Jones Sound, south Devon Island, and Cornwallis Island-Grinnell Peninsula areas in Canada (DFO and GINR, unpublished data; Dunn, 2000). These are the main summering areas of walruses in the North Water population (Born et al., 1995).
If the maximum counts per area are summed, a total of 452 walruses was observed, of which 73.5% were hauled out. In the Jones Sound and Cornwallis Island-Grinnell Peninsula areas, which were surveyed twice, the minimum counts obtained during one survey were 71% and 83%, respectively, of the maximum counts of the other survey.
These aerial survey counts were corrected in two alternative ways: (i) The number of walruses at sea (120) was multiplied by 5 to include the number that theoretically was submerged (i.e. 80%). The total number of walruses at sea (i.e. 600) was then added to the actual number observed on land (332). (ii) The number observed hauled out (=30%, e.g., Born and Knutsen, 1997; Born and Acquarone, 2005) was simply multiplied by 3.3 to include the fraction not present at the haul-outs.
The resulting estimates of the total number of walruses in the North Water population were (i) 932 and (ii) 1097, indicating that about 1000 walruses were within the surveyed areas during the period 11–19 August 1999. To include walruses in areas not surveyed (southern coasts of Lancaster Sound and Barrow Strait and adjacent areas, and a section of eastern Ellesmere Island where walruses may occur sometimes), this estimate was raised to 1500 for the simulations and the CV of this estimate was arbitrarily set to 0.35 (this CV allows for inclusion of the plausible ranges of the estimate of abundance).
East Greenland
Based on opportunistic and systematic observations, the East Greenland walrus population was estimated to number ca. 1000 (Born et al., 1997). The CV was set to 0.35 for the same reason as given for the North Water population.
Catch data and loss rates
Two catch histories were estimated for each population. A "low" catch history based on reported or landed catch (and in some years estimates of the catch) and a "high" catch history that includes also estimates of non-reported loss, i.e., animals that were struck and lost, and animals that were landed and not reported.
West Greenland
Catch data were extracted from official catch statistics and written sources (Born et al., 1994), and sources given in Table 1.
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Losses were assumed to average 10% (1 lost for every 10 killed) from 1900 until 1930. During this period walruses were mainly taken by traditional means close to the coast and primarily at the terrestrial haul-outs. From 1930 onwards when walruses increasingly were hunted by use of motorized vessels operating in the offshore pack ice (Born et al., 1994) losses were assumed to average 25% (1 lost for every 4 killed). Loss rates of 20–30% are not uncommon during walrus hunts based on small-type vessels (cf. Born et al., 1995 and references therein; Gjertz et al., 1998).
We assumed an even sex ratio in the catch before 1930, while an estimated sex ratio of M:F = 0.4:0.6 was applied to the catch history after 1930 (Born et al., 1994).
North Water
Generally, the catch data from the Thule area of NW Greenland are insufficient in particular prior to 1950 (Teilmann and Kapel, 1998). Hence, to obtain estimates for the early period, catches were inferred from the trend in growth of the human population in the area. Inferred from Gilberg (1976; Figure 19), the Inuit population in the Thule area increased gradually with a rate of ca. 0.8% per year from about 200 at 1900 to about 300 around 1950. If assuming a proportional relationship between (i) the size of the human population, (ii) the fraction of hunters (29–34% of the human population were men aged 15–64 years; Gilberg (1976; Table 25)) in this population, and (iii) the number of walrus caught per hunter, the annual catch of walrus during the year 1900–1950 was back-calculated from an average of about 200 in 1939–1940 (Vibe, 1950): Catch (c) in year x – 1 = cx0.9918; Table 2.
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Losses were assumed to average 5% from 1900 until 1950. During this period walruses were mainly taken by traditional means and only few motorized vessels were available for hunting. Furthermore, the walruses were harpooned before being shot. For the period 1951–1969, a loss rate of 15% was applied taking into account an increased use of vessels during the open water period where walruses hauling out on ice fioes can be shot at before they are harpooned. After 1970, an overall loss rate of 25% (1 lost for every 4 killed) was used based on observations in the late 1970s (Born et al., 1995).
An age-structured catch (Table 3) is available from a sample of the Greenlanders catch of walruses (0–29 years of age) in the North Water (1987–1991). The sex ratio in this sample (F: n = 179; M: n = 197), which did not differ from unity (
2 = 0.43, p = 0.512, d.f. = 1), was applied to the catch history for the entire period.
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East Greenland
Catches in East Greenland were extracted from Born et al. (1997); Table 4. An average loss rate of 20% was applied to the catch by the European sealing vessels (Chapskii, 1936; Gjertz et al., 1998). An overall loss rate of 27% and 23% was applied to the catches taken by European trappers and Greenlanders, respectively (Born et al., 1997).
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Information is not available on the sex ratio in the catches taken by European sealers prior to 1956 when walruses were completely protected in NE Greenland north of ca. 72°N (Born et al., 1997) – effectively prohibiting the catch of walrus in East Greenland by foreigners. Hence, for the period 1889–1955 an even sex ratio in the catch was assumed. South of 72°N the Greenlanders' recent catch consists of ca. 90% male walrus (Born et al., 1997), and we therefore applied a 0.9M:0.1F ratio for the catch in East Greenland after 1956.
Population dynamic model
An age- and sex-structured model with direct density regulation on the birth rate is applied. The number of animals in age classes larger than zero is
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| (1) |
is the number of males/females of age a at the start of year t, 
is the catch of males/females of age a during year t, with the age distribution of the catches being sex-specific and proportional to the product between the age- and sex-specific abundance 
and an age- and sex-specific catch selectivity factor 
. The proportionality of the age-structured catch to the product 
can be obtained for all age classes only when the total catch is so low that the catch from any sex-specific age class does not exceed the abundance in that class. If instead the estimated catch exceeds the abundance in an age class, the catch in that age class is set to the abundance of that class, while the remaining catches are reallocated to the remaining classes in proportion to the age- and sex-specific selectivity factors and abundances. If necessarily, this redistribution of the catches continues until it is possible to redistribute the remaining catches in an age and sex structure where the catch from any class does not exceed the number of individuals in that class. The annual survival rate of adults (sad) applies to all animals older than two years (s2+), the survival of juveniles during the second year (s1) is sjuv, and the survival during the first year (s0) is sjuvsad, assuming that first year survival depends also on the survival of the mother.
The number of births at the start of year t is
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| (2) |
and 
are the number of female and male births in age class a. These births are
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| (3) |
is the fraction of females at birth, bt is the birth rate for mature females at time t, and 
is the number of mature females in age class a at the start of year t, defined as
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| (4) |
The component of the population that imposes density regulation is the one plus component
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| (5) |
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| (6) |
Although not explicit parameters of the model, the maximum sustainable yield level (msyl) and the maximum sustainable yield rate (msyr) are treated as parameters in the analysis. The msyl depends mainly on the compensation parameter z, and to speed computation the three parameters are defined relative to the mature component of the population, denoted by the symbol 
. Hence, the birth rate is
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| (7) |
is the depletion ratio. Given no changes in the sex ratio with age, from the steady state Ñt+1 = Ñt with 
, the sustainable yield is
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| (8) |
is survival from birth to age of reproductive maturity. The 
relative to the depletion ratio 
is then
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| (9) |
, the 
is
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| (10) |
being the 
at the 
.
Statistical methods
The model was fitted to the abundance estimate by projecting the population from the first year with harvest under the influence of the historical catches, assuming that the pre-harvested population was in dynamic equilibrium. A Bayesian statistical method (e.g., Berger, 1985; Press, 1989) was used, and posterior estimates of the model parameters and other management related outputs were calculated. This implied an integration of the product between a prior distribution for each parameter and a likelihood function that links the probability of the data to the different parameterizations of the model.
The method of De la Mare (1986) was used to calculate the likelihood L under the assumption that observation errors are lognormally distributed (Buckland, 1992)
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| (11) |
the point estimate of the observed total abundance at time t, and CVt is the coefficient of variation of the abundance estimate at time t.
The integration was obtained by the sampling-importance-resampling routine (Berger, 1985; Rubin, 1988), where n1 = 2 000 000 random parameterizations 
i(1 
i n1) were sampled from an importance function h() (Oh and Berger, 1992; McAllister et al., 1994; McAllister and Ianelli, 1997). The importance function was set to the joint prior, so that the importance weight is given simply by the likelihood. To generate a random sample of the posterior distribution, the n1 parameter sets were then resampled n2 = 5000 times with replacement, with the sampling probability of the i(th) parameter set being
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| (12) |
If the importance function is adequately specified, the mean of the importance sample for each parameter should approach the mean from the true posterior distribution, given a sufficiently large sample. To illustrate whether the sampled posterior quantities can be assumed to be representative of the true posterior distribution, convergence diagnostics were calculated. One such diagnostic is the maximum importance weight of a parameter set relative to the total summed importance weight over all n1 draws. For example, McAllister et al. (2001) suggest that the maximum importance weight needs to have dropped below 1% of the total sum. And in line with Wade (2002), we also calculated the total number of unique parameter sets in the resample of n2 parameter sets, as well the maximum number of occurrences of a unique parameter set in the resample.
Probability of meeting the objective
Given future annual catches c in the period 2005–2009, we applied the objective
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| (13) |
i of the random sample of the posterior distribution of size n2, we have perfect knowledge of the status of the population so that it can be determined if Equation (13) is true or false. Hence, the probability p(ob) of meeting the objective is
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| (14) |
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Age-selective catch
Assuming that the age- and sex-specific catch selectivity factor 
increases linearly with age from age class zero to x, and that it remains constant thereafter, it follows that the complete age selectivity curve is described by the selectivity ratio c0/cx. Given this model and an assumed stable age structure, the catch will decline with age for a 
x. For the age- and sex-structured catch in the North Water during 1987–1991 (Table 3), this decline begins from age class 10 in both males and females, suggesting a similar catch pattern for both sexes. Lumping the data for the two sexes, 17 animals were caught from age class zero and 44 animals from age class 10. Estimates of the survival rates from an initial run of the assessment model for the North Water population with an uniform age and sex structured catch, suggested that the number of animals in age class 10 is 33% of the number in age class zero. Hence, a c0/c10 ratio of 0.13 can be expected for the North Water, and assumed here also for West and East Greenland.
Prior distributions
Prior probability distributions were assigned to adult survival (sad), juvenile survival (Sjuv), the maximal birth rate (bmax), the age of reproductive maturity (am), the maximum sustainable yield level (msyl), the equilibrium abundance (N*), and the catch history parameter (
). Although the msyl is not an explicit parameter of the model, a uniform prior was assigned to it. This was possible since no prior distribution was assigned to the compensation parameter z; given values for msyl and the other parameters of the model, a unique value is given for z. The fraction of females at birth () was a fixed parameter across all model iterations.
The parameter sets a prior on the catch history, where the catch history that is applied in the parameterized iteration i is given by a linear scaling between the low and the high catch histories, where the catch in year t of parameterization i is
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| (15) |
= 0, and the high catch history when = 1. All the priors were uniform. The age of reproductive maturity was a discrete variable, while all other priors were continuous. The range of values for the priors (Table 5), together with the value for the fraction of females at birth, were based on various studies of walrus populations and previous modelling of walrus population dynamics (Fay, 1982; DeMaster, 1984; Fay et al., 1989, 1997; Chivers, 1999). The annual natural survival rate of adults (sad) is unknown for walrus but was set in this study to range between 0.90 and 0.98 with constant survival rate for all adult age classes. The juvenile annual survival rate (sjuv), that is also unknown, was set to 0.56–0.96. However, for each randomly selected parameter set, the upper bound on the juvenile survival rate was always set to be smaller than or equal to the randomly selected value for the adult survival rate.
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The maximal birth rate (bmax), i.e, the maximal number of offspring per female per year, was set to range between 0.33 and 0.50 (Mansfield, 1958; Fay, 1982; Born, 2001), reflecting the assumption that each female produces one offspring every second or third year. The age of reproductive maturity (am) is set to 5–9 (Mansfield, 1958; Fay, 1982; Born, 2001), and the maximum sustainable yield level (msyl) to 0.50–0.80 (Eberhardt, 1992). The prior for the equilibrium abundance was set for each population separately with ranges wide enough to encompass plausible values given the estimates of current abundance.
The fraction of females at birth () was set to the fixed value of 0.5 for all primary runs. However, an alternative run was performed for West Greenland walrus where was set to 0.60 (i.e., the fraction of females in the catch).
Realized priors, or post-model-pre-data probability distributions, were generated by discarding any parameterization i that would not generate a viable model with a maximal population dynamic growth rate above zero. In result the discarded parameterizations were given zero likelihood, and the n1 sampled parameterizations include only realistic models with positive maximal growth rates.
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Results |
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TopIntroductionMethodResultsDiscussionConclusionsReferences |
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Posterior distributions
The maximum importance weights relative to the total sum of importance weights for the 2 000 000 parameter sets were less than 0.0% for each of the five Bayesian runs. The number of unique parameter sets in the resample of 5000 parameter sets was above 4400 for all runs, and the maximum occurrences of a unique parameter set in the resample was no more than five (Table 6).
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The median and 90% credibility intervals (CI) of the posterior parameter estimates are given in Table 7. As each model was fitted to only one abundance estimate there is hardly any information in the data to update the realized priors to new posterior estimates. This is exemplified for the West Greenland population (Figure 2), where nearly all the posterior parameter estimates resemble the realized priors. The exception is the equilibrium abundance, where the posterior clearly differs from the realized prior, showing that the model is fitting to the abundance data by adjusting the equilibrium abundance.
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Population dynamics
Assuming post 1999 catches equal to the catch in 1999, the following dynamics was obtained.
West Greenland
For walruses in West Greenland, the model based on the catches from 1900 suggested a population decline from an estimated equilibrium abundance of 16 300 (CI: 10 500–21 500; Table 7) individuals in 1900 to a projected extinction in 2000 (Figure 3 top). The yearly replacement yield had a maximum of 65 (CI: –10–142) individuals in 1934 (Figure 3 middle), while the replacement yield was estimated to be zero (CI: 0–0) in 2005. The annual birth rate reached a maximum of 0.41 calf per year after 1976 (Figure 3 bottom). Projection to extinction before 2010 was also the case with a female fraction at birth of 0.6, and for the model based on catches from 1820. In these cases the equilibrium abundance was estimated to be 13 900 (CI: 8330–18 600) and 16 800 (CI: 10 500–26 100) individuals, respectively (Table 7).
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North Water
The model suggested that the North Water population declined almost linearly from an estimated equilibrium abundance of 15 100 (CI: 7800–22 300; Table 7) individuals in 1900, to a projected abundance of 349 (CI: 0–2230) individuals in 2010 (Figure 4 top). The population is predicted to be most severely depleted in 2010 with a depletion ratio of 0.02 (CI: 0.00–0.21), while the depletion ratio in 2005 was estimated to be 0.07 (CI: 0.01–0.24). The yearly replacement yield had a maximum of 119 (CI: 23–196) individuals in 1948, while the yield in 2005 was estimated to be 11 (CI: –4–92) (Figure 4 middle). The annual birth rate grew steadily to a maximum of 0.41 (CI: 0.34–0.49) calf per year at the end of the projection period (Figure 4 bottom).
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East Greenland
The model indicated that the East Greenland walrus population declined from an equilibrium abundance of 1610 (CI: 941–2860; Table 7) individuals in 1889 and reached a maximal depletion of 0.60 (CI: 0.34–0.95) in 1933. The population then increased steadily to an estimated abundance of 1310 (CI: 808–2200) in 2010 (Figure 5 top). The projected abundance in 2005 is close to the equilibrium, with an estimated depletion ratio of 0.97 (CI: 0.38–1.00). The yearly replacement yield had a maximum of 28 (CI: –16–93) individuals in 1889, while the yield in 2005 was estimated to 10 (CI: 8–19) (Figure 5 middle). The annual birth rate had a maximum of 0.34 (CI: 0.19–0.47) calf per year in 1933 (Figure 5 bottom).
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Meeting management objectives
Only in the case of the East Greenland walrus population could the management criteria applied in this study be met (Figure 6). For this population the probability of meeting the management objectives was 0.93 with future total removals (i.e., catch and loss) similar to the current removal of 10 individuals per year, and the probability was 0.84 and 0.78 for a future annual removal of 15 and 18 individuals, respectively. For the North Water population, where the annual total removal from 1990 to 1999 varied between 123 and 381 individuals (average = 208 walrus per year), the probability of meeting the management objectives was larger than 0.50 only for total removals below 22 individuals per year. The probability was 0.85 for an annual removal of nine individuals, 0.91 for an annual removal of seven individuals, and 0.95 for an annual removal of five individuals. For the West Greenland population, given a female fraction at birth of 0.50, the probability of meeting the management objectives was below 0.01, even with the removal of only a single individual. The reason that the management objectives could not be fulfilled even with no catch was because the population was predicted to become extinct. And with a female fraction at birth of 0.60, the probability of meeting the management objectives with the harvest of a single individual was only 0.03.
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Discussion |
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TopIntroductionMethodResultsDiscussionConclusionsReferences |
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The model
Previous attempts to simulate walrus population dynamics have used discrete models with density regulations for modelling hypothetical populations (DeMaster, 1984; Chivers, 1999). Chivers (1999) applied an individual, age-based population model with density-dependent changes in rates of juvenile survival, birth, and maturation. This model also differed from previous modelling efforts for walrus populations by incorporating senescence in the survival rates and by making calf survival dependent on the survival of its mother.
Born et al. (1997) and Gjertz et al. (1998) used a simple recursive relationship to back-calculate the size of the East Greenland and Franz Josef Land walrus populations, respectively. This method used estimates of current population size, total removals, and fixed values for maximum net recruitment rate. We extended this calculation to include also West Greenland and North Water walruses, and we made the simulation more realistic by incorporating both age and sex structure as well as density regulation in the birth rate. Like Chivers (1999), we made calf survival during the first year depend on the survival of the mother, although this was done at the population level. We did not elaborate an individual-based model, because this adds much complexity to the model, while only providing a marginal advantage unless the population is so small that the effects of demographic stochasticity are strong. This is unlikely for populations above a few hundred individuals (Lande et al., 2003).
Although the priors of the model were initially drawn from uniform distributions, an approximately uniform realized prior was found only for equilibrium abundance, while the other parameters showed realized priors that clearly differed from uniform. The reason is the model constraint of a positive maximal growth rate that limited the set of possible parameter combinations. Combinations of low survival, low maximal birth rate, and a high age of reproductive maturity are generally in conflict with a positive maximal growth rate.
Biological parameters
The ranges chosen by us for the various prior distributions were based on previous knowledge of the biology of Atlantic and Pacific walrus and estimates of their vital parameters. Although recognized as two geographically and taxonomically distinct subspecies (e.g., Fay, 1985), the life history of Atlantic and Pacific walrus appears to be very similar. However, in both cases the segregation of different sex and age classes for most of the year, and the selective hunting pattern make it difficult to obtain unbiased samples for determining biological parameters (Fedoseev and Goltsev, 1969; Fay, 1982; DeMaster, 1984). The posterior estimates of the biological parameters were generally in good agreement with estimates in other studies, even though the data signal of the single abundance estimates for the three walrus populations was not sufficiently strong to update the realized priors to new posterior estimates (Figure 2). These values are discussed in detail below.
The sex ratio in walrus populations is not well known. On the assumption that walruses are polygynous, an adult sex ratio of one male to three females has been suggested in the population of Pacific walrus (Fay, 1982; Fay et al., 1984; Sease and Chapman, 1988). DeMaster (1984) adopted this sex ratio in his modelling of the dynamics of a hypothetical walrus population. The sex ratio in the Pacific walrus changed from (M:F) 1:1.7 to 1:3 between 1960 and 1985 during a period of population increase according to Fay et al. (1997), a pattern that is actually expected from density and frequency dependent natural selection (Witting, 1997, 2000).
To our knowledge there are no indications of the sex ratio being severely skewed towards females in Atlantic walrus sub-populations, and we therefore assumed that it was even in the evaluation of the Greenland situation. An exception was West Greenland, where we also made a simulation of the population dynamics assuming a surplus of females (based on small recent sample of the catch and historical information). Although the female biased version of the model estimated a population that was slightly better in sustaining the historical harvest, the change in sex ratio was not sufficient to avoid a prediction of the extirpation of the population in 2010.
In Pacific walrus total annual mortality for adult males has been estimated at 8–13% (Burns, 1965; Fedoseev and Goltsev, 1969). DeMaster (1984) suggested an annual mortality of about 9% for adult males and considered it likely that total annual mortality of adult females was much lower.
The natural mortality rate in walrus is not well established but is assumed to be low because productivity is low and longevity is relatively high (Fay, 1982; Fay et al., 1997). Natural mortality rate has been estimated to be 3% to 5% for the entire population of Pacific walrus (DeMaster, 1984; Fay et al., 1989). Fay et al. (1994) suggested that natural mortality in adults was higher than 1%, but probably not higher than 2% per year. A natural mortality rate of 1.5% per year was applied in simulations of Bering Sea walruses (Fay et al., 1997). Chivers (1999) used an estimate of survival in adults between 9 and 24 years to 0.98 (it then decreased until 40 years of age).
Survival in calves until their second year of life (during this year suckling ceases) has been estimated to range between 0.5 and 0.9 (Chivers, 1999, and references therein). A survival rate in calves up to two years of age of 0.66 to 0.88 was used by Chivers (1999) for simulations of walrus population dynamics.
We used 0.90 to 0.98 for the prior for annual adult survival rate (i.e., annual natural mortality: 2% to 10%), and 0.56 to 0.96 in calves. The resulting estimate of survival obtained by the posterior median was 0.94 (West Greenland) to 0.96 (East Greenland) in adults, and 0.75 (West Greenland) to 0.81 (East Greenland) in calves.
Our prior of maximum annual fecundity ranged between 0.33 and 0.5 cal per mature female per year, with the posterior median being 0.41 or 0.42 for the different model runs. Based on analyses of reproductive organs, rates of fecundity have been estimated at between 0.29 and 0.40 in walruses (Mansfield, 1958; Fay, 1982; Garlich-Miller and Stewart, 1999; Born, 2001). According to Mansfield (1958), the reproductive cycle of the female Atlantic walrus in Foxe Basin was basically biennial, but, to an unknown extent, older females may give birth at three- or four-year intervals. According to Fay (1982), female Pacific walruses tend to breed at two-year intervals or less often, and hence maximum fecundity was thought to be 0.5 (Fay et al., 1997).
The priors for age at maturity (i.e., first birth) ranged between five and nine years of age, and the posterior median was seven years for all populations. Mansfield (1958) found that the age at first ovulation varied from 5 to 10 years, but that the majority of females in his Canadian sample became sexually mature at the age of seven. Born (2001) found that the average age at sexual maturity was six years in Atlantic walruses from the North Water and stated that attainment of sexual maturity in female Atlantic walruses is similar to that in the Pacific subspecies. By the age of six years, two-thirds of the female Pacific walruses have ovulated at least once, and by the 8th or 9th year practically all have ovulated (Fay, 1982).
Our fixed parameter for sex ratio at birth (1:1) was in accordance with findings in Atlantic walrus from the North Water (Born, 2001) and in Pacific walrus from the Bering Strait region (Fay, 1982; Fay et al., 1984).
In most populations of large marine mammals, msyl is thought to be within the (0.50; 0.80) range chosen for the prior distributions in this paper (Anon., 1986; Eberhardt, 1992). The median posterior estimate of msyl was almost identical at 0.62 (CI: 0.51–0.74) for all Greenland populations.
The population birth rate (fraction of neonates in the total population) has been estimated at 0.07 (Mansfield, 1966) or 0.11 (Mansfield, 1973) in Atlantic walrus and between 0.12 and 0.17 in Pacific walrus (Fedoseev and Goltsev, 1969; Fay, 1982). Instantaneous net growth rate of the population of Pacific walruses during the late 1950s to mid-1970s was estimated at 0.067 (Tavrovski, 1971; Sease and Chapman, 1988), indicating a finite growth rate of about 7% per year for a population in a phase of growth under favourable environmental conditions with no food limitations. Chivers (1999) modelled an annual maximum growth rate of 8% but stressed that because survival rates are unknown for walrus, the models growth rate should not be considered an estimate of maximum growth rate for walrus.
DeMaster (1984) estimated that the maximum sustainable yield of adult females (four years and older) would be 5.1% of the total population of females. He suggested that an adult female harvest of 1% to 5% could be sustained. Fay (1985) suggested that an annual hunting mortality of 5% to 7% of the total population of walrus would be sustainable. Gjertz et al. (1998) suggested a net maximum recruitment rate of 5% to be the most plausible and in compliance with the estimates of current abundance of walruses at Franz Josef Land. Assuming an even sex ratio, our estimate of msyr for the mature component of the population was 0.02 (CI: 0.00–0.07) for the West Greenland and North Water walrus populations, and 0.04 (CI: 0.00–0.10) for the East Greenland population.
Abundance and population identity
Inevitably our modelling exercise was influenced by the uncertainties about current abundance, delineation of populations (in particular in West Greenland), and total removal.
The surveys for determination of abundance in western Greenland were conducted in 1990 and 1991 during late March and early April. The majority of walruses observed were hauled out on the ice. Walruses tend to haul-out during relatively warm and calm days (Fay and Ray, 1968), and they are generally difficult to detect in the water (Estes and Gilbert, 1978; Born et al., 1994), partially due to their cryptic colour. Likely, an unknown number of walruses was missed by the observers in West Greenland. Hence, we expect that these estimates of abundance were not corrected for observer bias or missed observations (Born et al., 1994) and it cannot be precluded that particularly walruses in water were missed. Hence, we suspect that the estimates of abundance were negatively biased (i.e., minimum estimates). This is also suggested by our analysis which, based upon the abundance estimate, predicts population extirpation before 2000, while walruses are still being caught in West Greenland.
For the purpose of the present study we applied a correction factor to include walruses that were submerged during the surveys. The general correction factor (surface:subsurface ratio of 1:4) used here is consistent with most observations of feeding walruses (Fay, 1982; Wiig et al., 1993; Born and Knutsen, 1997; Born et al., 2003). Most of these observations have been made during summer when walruses feed intensively. Walruses feed in western Greenland (Born et al., 1994) but information on surface:subsurface ratios in walruses during March–April, when the surveys were flown, are not available. However, an adult male walrus equipped with a satellite-transmitter in Northeast Greenland (2000/2001) spent an average of 19.3% of its time in the upper 2 m of the water column in December–January (16.3% and 23.1%, respectively) (Born, unpublished data). This supports the notion that walruses generally dive in a highly stereotypic manner, and also that the correction factor used by us is appropriate.
Irrespective of general uncertainties associated with abundance estimates obtained from aerial surveys of walruses, not only in West Greenland but also in other studies (cf. Gilbert, 1989; Udevitz et al., 2001), we believe that the estimate used in the present study for the total group of walruses wintering in West Greenland is in the right order of magnitude.
It was attempted to enumerate the North Water population during five days in August 1999 when the coasts of eastern Ellesmere Island (north to Flaggler Bay), Jones Sound, Cornwallis and Bathurst Islands, and Grinnell Peninsula were surveyed by helicopter and ground counts (DFO and GINR, unpublished data; Dunn, 2000). The surveys covered all areas where walruses from the North Water population are known to haul-out on land during summer (Born et al., 1995). However, the number of walruses hauling out on land on any given day may fluctuate (Hills, 1992; Born and Knutsen, 1997) making any short-period census sensitive to daily fluctuations in numbers. Furthermore, walruses can move up to 100 km from their terrestrial haul-outs to feed (e.g., Born and Knutsen, 1992, 1997; Born and Acquarone, 2005) meaning that surveys that follow coastlines may miss an unknown proportion of walruses at sea. We applied general correction factors to include the fraction of walruses not present at the haul-out and/or submerged. By more or less arbitrarily adding another 500 to account for walruses in unsurveyed areas we derived at an estimate of the total population of 1500. Based on miscellaneous ground counts and aerial surveys since 1976, Born et al. (1995) suggested that the North Water population of walrus numbers approximately 1700–2000 and perhaps as many as 3000. Given the uncertainties about the fraction present at the haul-out during the surveys, and the fact that walruses far out at sea inevitably were missed, we cannot exclude the possibility that the estimate of abundance of the North Water population used in this study is negatively biased.
The estimate of abundance in East Greenland was based on Born et al. (1997) who derived at a rough estimate of 500–1000 walruses from miscellaneous ground and aerial counts north of approximately 74°N. They argued that the highest bound of this estimate was the most likely (Born et al., 1997).
Born et al. (1997) used a simple recursive relationship to back-calculate the size of the East Greenland walrus population, using an estimate of current population size of 500–1000. Their estimates of the population size in 1889 ranged between 676 and 1934 walruses for different combinations of parameters (Born et al., 1997). The estimate in the present study of the equilibrium abundance in 1889 was 1610 (95% CI: 941–2860).
The results in the present study are influenced by assumptions about whether the populations considered represent separate demographic units or not. We assumed that they did.
Information on distribution and occurrence indicates that when walruses were more abundant in the Baffin Bay area during the beginning of the 20th century, walruses in this region (including the West Greenland and North Water animals) were part of one large population (Born et al., 1995, and references therein). However, recent data on migration and distribution (Born et al., 1994, 1995) and genetic analyses (Andersen and Born, 2000) indicate that there is very limited exchange between walruses in West Greenland and in the North Water area.
A comparison of walruses from the Hudson Strait-eastern Hudson Bay region indicated that they differ genetically from those in West Greenland (Andersen and Born, unpublished data). Furthermore, walruses from West Greenland differed in lead isotope ratios from walruses in these two areas (Outridge et al., 2003). However, the absence of walruses from West Greenland during summer and scattered observations of walruses in Davis Strait midway between Southeast Baffin Island and Central West Greenland (Born et al., 1994) indicate a connection between walruses in those two areas. In that case the group of walruses that winters in West Greenland represents a part of a population which ranges over eastern Baffin Island but for which numbers are unknown (Born et al., 1995).
The study of regional variation in lead isotope ratios in walruses indicated a sub-structuring and subdivision in some of the populations identified from distribution and genetics (Outridge et al., 2003). For example, walruses that winter in West Greenland and summer at SE Baffin Island may mix with but not mate with walruses occurring in Baffin Island year-round. The breeding season of Atlantic walruses is March–April (Born, 2001, 2003) when walruses are found in West Greenland.
Walruses are caught by the Inuit at southeastern Baffin Island (Born et al., 1995; NAMMCO, 1995). Therefore West Greenland walruses may be subject to hunting while summering there. However, owing to lack of specific information on hunting practices in Baffin Island, we did not include catches from there in our simulations of the West Greenland population.
Despite uncertainties about the delineation of the West Greenland population, we decided to take a precautionary approach by treating it as a separate population unit.
Information on distribution (Born et al., 1995) and genetic (Andersen and Born, 2000) and isotopic variation (Outridge et al., 2003) indicates that the North Water population constitutes a separate demographic unit. However, some fine-scale sub-structuring of the population was indicated (Andersen and Born, 2000; Outridge et al., 2003).
Similar information indicates that the East Greenland population is a distinct population with little exchange with the neighbouring groups (Born et al., 1997; Andersen et al., 1998; Born et al., 2001).
Removals
The modelling was influenced by the fact that catch data were insufficient for several years and periods. Furthermore, losses were estimated in most cases.
Catches from the West Greenland population were reported for most years since 1900. However, the system of reporting until 1987, based on Hunters Lists of Game, was inadequate. The new system of reporting ("Piniarneq") that started in 1993 also suffers from uncertainties about the actual takes (for a description of the Greenland catch reporting systems, see Born et al. (1994); Kapel and Rosing-Asvid (1996); Teilmann and Kapel (1998)). In particular the sudden fourfold increase in reported catch for West Greenland from 1993 and onwards is critical for our assessment. Furthermore, for years with no reporting we had to estimate the catch. This was particularly the case for the North Water population.
Until about 1910, Scottish whalers caught walruses in the Baffin Bay region including in West Greenland and the North Water areas (Ross and MacIver, 1982). Norwegian sealers and whalers took walruses between ca. 1910 and 1923 offshore in West Greenland, and made large catches around the 1950s presumably in northern Baffin Bay (Born et al., 1995, and references therein). For all three walrus populations great uncertainty exists about the numbers taken by European whalers and sealers. Furthermore, there are uncertainties about location and numbers in the original sources. A general lack of information about the catch of walrus by foreigners precluded us from pursuing this matter further. For this reason, the catches used in the present study are negatively biased to an unknown extent. However, in West Greenland we attempted to estimate the catches also by foreigners back to 1820. However, doing so did not alter the conclusions about the pristine population and current status.
The catch of walruses in East Greenland by foreigner sealers was intense during the last decade of the 19th century and the first decades of the 20th century (Born et al., 1997). Those researchers extracted information on catches from published and unpublished sources. However, because information in many cases was insufficient on numbers of vessels participating in the hunt and number of walrus taken historical catches were underestimated. For the same reason the equilibrium population (i.e., pristine population) may have been underestimated in the present paper.
We tried to incorporate the uncertainty in the catch histories into the analysis by applying a uniform prior scaling between a low and a high catch history. Irrespectively of the catch history assumed, the main results of the simulation basically remained the same.
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TopIntroductionMethodResultsDiscussionConclusionsReferences |
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The Bayesian approach to modelling walrus populations proved valuable in this study because in the existence of non-ideal data it allowed us (i) to simulate the historical development and current status of the three walrus populations in Greenland, and (ii) to quantify the trade-off between the uncertainties inherent in data and the probability of meeting the management objectives. Owing to the lack of specific management objectives for the exploitation of walruses in Greenland, we used management objectives defined by IWC for the sustainable management of aboriginal exploitation of large whales.
The study indicated that the West Greenland population was heavily exploited during the last century and that the current abundance is at best only a few per cent of the historical abundance. The population is still being exploited far above a sustainable level. Further, the North Water population has been subject to intense hunting during the same period, where it has declined to a current depletion of less than 10% of the 1900 level. The current removal is apparently unsustainable, with a drastic reduction in the removal required if this population should increase again. Finally, the East Greenland population was heavily exploited late in the 19th century and in the first half of the 20th century, where it was depleted to approximately 50% in 1933. The abundance has since increased to a current level close to the abundance in 1889, with the current catch being sustainable.
These conclusions suffer from a lack of adequate information on population size, delineation of populations, and catch and losses. Future research must aim at providing information on in particular (i) the delineation of the walrus population that is exploited in West Greenland, (ii) abundance of all three Greenland walrus populations, and (iii) catch levels and site and method specific losses.
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Acknowledgements |
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We thank Michael Kingsley (Greenland Institute of Natural Resources), Carryn Cunningham (University of Cape Town), Østein Wiig (University of Oslo), and an anonymous reviewer for many helpful comments.
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