POPULATION DYNAMICS AND EXPLOITATION OF SEALS 175 



Also, where tj is the total annual mortality rate, mj is the annual rate of 

 hunting mortality, and rij is the annual rate of natural mortality of the age- 

 group y, then: 



1 — Sj = tj = ntj + «;• — f^jfJj (2) 



Where a population is sampled at random, the age composition of the catch 

 may be used to determine the age-specific rates of total mortality (tj). 

 Unfortunately, samples from south-west Baffin Island, while extensive, are 

 by no means random. There is considerable under-representation of the first- 

 year seals, which are largely born in inaccessible areas. Immature seals 

 probably become harder to catch and tend to spend the winter under the 

 fast ice as they get older. Adult seals become increasingly under-represented 

 in the catch due to local hunting and to their progressive withdrawal to the 

 more suitable breeding grounds. However, selected catch curves or certain 

 sections of the overall catch curve may be used to give rates of total mortality 

 for some age-groups. For example, after the age of 15, year-groups of seals 

 are probably equally accessible and equally easily caught, and samples of 

 them may be compared to give mortality rates from year to year. Likewise 

 older immature seals and young adults are probably adequately represented 

 in summer-killed samples. 



The estimates of hunting mortality in each age-group depend on the 

 combination of local and seasonal age-samples with local and seasonal catch 

 statistics. The derived age structure of the total annual kill (including loss by 

 sinking), which averages around 7,000 seals along the Hudson Strait coast of 

 Baffin Island, is thought to be sufficiently accurate. 



Thus we now have the means of constructing hypothetical balanced 

 populations which will have annual yields of 7,000 seals. This can be done 

 by setting up an initial cohort (Xq) and changing its size to satisfy equation 

 (i), while making various assumptions about natural mortahty in the first 

 year and the proportionate effects of decreasing catchabihty and natural 

 mortahty as these affect the empirical catch curve of the immature seals, 

 but always staying within the limits imposed by known hunting mortahties, 

 the reliable total mortahty rates of some age classes, and the reproductive 

 rates. In operation the method involves tedious and inelegant iteration and 

 successive approximation, but the results are valuable in indicating that 

 suitable populations can only vary in size between rather narrow hmits, in 

 which the annual kill is between about 7 per cent and 10 per cent of the total 

 population at the beginning of the seal-year. The lower hmit may be taken 

 as quite safe, and since the population estimate of a region is based on censuses 

 performed later in the seal-year, we may consider that a sustainable kill of 

 at least 8 per cent will be obtainable from ringed seal populations with the 



