ESTIMATED INITIAL POPULATION SIZE OF THE 



BERING SEA STOCK OF BOWHEAD WHALE, 



BALAENA MYSTICETUS: AN ITERATIVE METHOD 



Jeffrey M. Breiwick,' Edward D. Mitchell,^ and Douglas G. Chapman^ 



ABSTRACT 



Initial stock sizes of bowhead whales were calculated iteratively, using an estimate of removals from 

 the Bering Sea stock of bowheads, a range of assumed values for size of current stock, and assumed 

 mortality and recruitment rates of M = 0.04-0.08 and "--Ml^g^ = 0.01-0.05. Estimates of initial 

 stock size range between 14,000 and 26,000. At a kill level of 25 per annum, time to recover to 9,000 

 (50% of 18,000) is a minimum of 40 years if the present stock is approximately 2,700 bowheads. A 

 theoretical model giving the risk of extinction is also discussed. 



The International Whaling Commission has re- 

 cently established quotas on the aboriginal take of 

 the bowhead whale, Balaena mysticetus, in the 

 Bering, Chukchi, and Beaufort Seas. This has led 

 to much discussion of the status of the stock both 

 now and in relation to its original size. 



Bowhead whales are distributed throughout the 

 Arctic in several presumably discrete stock units. 

 Tomilin (1957) recognized four circumpolar stock 

 units and Mitchell'* identified five. Regardless of 

 various interpretations, the Bering-Chukchi- 

 Beaufort Sea stock has been regarded by all au- 

 thors for many years as a discrete stock (Figure 1). 



This stock winters in the Bering Sea, but during 

 the spring it moves through the Bering Strait 

 along the northwestern and northern coasts of 

 Alaska at least as far as the Beaufort Sea. The 

 Beaufort and Chukchi Seas are the main feeding 

 areas. For convenience we will refer to this stock 

 hereafter as the Bering Sea stock. This paper con- 

 centrates solely on this stock, for which commer- 

 cial exploitation began in 1848, the date to which 

 "initial" but not "unexploited" stock refers. Es- 



'College of Fisheries, University of Washington, Seattle, 

 Wash.; present address: Northwest and Alaska Fisheries Center 

 National Marine Mammal Laboratory, National Marine 

 Fisheries Service, NOAA, 7600 Sand Point Way NE., Seattle, WA 

 98115. 



^Arctic Biological Station, 555 St.-Pierre Blvd., Ste. Anne de 

 Bellevue, Quebec, Canada H9X 3R4. 



^College of Fisheries, University of Washington, Seattle, WA 

 98195. 



••Mitchell, E. D. 1977. Initial population size of bowhead 

 whale i Balaena mysticetus) stocks: cumulative catch estimates. 

 Int. Whal. Comm.Doc. SC 29/33, 112 p. The Red House, Station 

 Road. Histon, Cambridge CB4 4NR Engl. 



Manuscript accepted March 1980. 

 FISHERY BULLETIN: VOL. 78, No. 4, 1981. 



kimo utilization of bowhead whales dates back 

 many centuries, hence the Bering Sea stock was 

 subject to human influence prior to 1848. 



After 1848 the Bering Sea stock was rapidly 

 depleted by heavy commercial exploitation — thus 

 following a pattern that had been established ear- 

 lier with respect to the Spitzbergen, Davis Strait, 

 and Hudson Bay stocks and which also was to 

 occur with the putative Okhotsk Sea stock ( Mitch- 

 ell footnote 4). Of all these depleted stocks, that of 

 the Bering Sea is now the most abundant, and the 

 only one from which removals of any consequence 

 are occurring. 



There are few satisfactory estimates of current 

 population size for other bowhead whale stocks; 

 estimates of the population sizes of all stocks at the 

 onset of heavy commercial exploitation are even 

 less reliable. Accordingly, we here present one ap- 

 proach to verify the order of magnitude of the early 

 Bering Sea stock. We have also used some assumed 

 estimates of the vital parameters in a simulation 

 study of the expected time of recovery of this stock 

 with catches at the present level. 



The basis of the method is to start with an as- 

 sumed current stock size and a recruitment rate, 

 which is a function of stock size. The same form for 

 the recruitment function is used throughout — a 

 linear function decreasing from its maximum 

 value at zero stock level to the natural mortality 

 rate, M, at the initial stock level. Given current 

 stock size, maximum net recruitment rate, mor- 

 tality rate, and lag time between birth and age at 

 recruitment into the fishery, the program starts 

 with an estimated initial (1848) level. The pro- 



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