FISHERY BULLETIN: VOL. 78. NO. 4 



Table 4.— Reexpressed stock sizes of Table 3 (1978 stock level 



of2,700). 



creasing values of M, lag time, and maximum net 

 recruitment tend to decrease the estimate of ini- 

 tial stock size. 



Vital Parameters 



The natural mortality rate has somewhat less of 

 an effect on initial stock estimates than does the 

 maximum net recruitment rate. This can be seen 

 from Table 4 where initial stock estimates have 

 been reexpressed as deviations from row and col- 

 umn medians. As noted above, net recruitment 

 rates >0.05 often did not result in convergence of 

 the iterative procedure. In general, convergence 

 occurred only if fractions of animals were allowed 

 in Equation (2). If only integer numbers were 

 used, it was virtually impossible to arrive at a 

 prescribed stock level in 1978 from a given stock 

 level. This is because the time series consists of 

 over 100 yr, and rounding-off errors become criti- 

 cal if the convergence criterion is too stringent. We 

 assumed convergence if the difference between 

 two successive initial stock estimates was <0.1. 



Maximum net recruitment rate and lag time are 

 the most sensitive of the parameters we use in the 

 model and natural mortality rate the least. We 

 have used all combinations of the range of values 

 of the parameters, although we recognize that cer- 

 tain combinations are likely to be unreasonable 

 (for instance, a lag time of 1 yr with a maximum 

 net recruitment rate of 0.01 is unlikely and there- 

 fore the initial stock size is unreasonable for these 

 parameter values). 



850 



Bockstoce^" examined a sample of maritime 

 newspapers and logbooks of whaling voyages and 

 estimated that 22,111 bowheads were killed by 

 pelagic whalers in the "commercial" fishery be- 

 tween 1848 and 1915. Mitchell (footnote 4) esti- 

 mated 27,714 whales killed in both the "commer- 

 cial" and the "aboriginal" fisheries during this 

 period. Initial stock size estimates using the data 

 in Bockstoce (footnote 10) for 1848-1915 and our 

 Table 1 for 1916-77 are about 15% lower than the 

 results given in Table 3. 



Recovery Times 



Using the basic model of Equation (2) and as- 

 suming that the maximum net recruitment rate 

 applies in the current season (assuming a popula- 

 tion of 1,500 and 2,700 animals), the time required 

 to recover to one-half of an initial stock level of 

 18,000 was calculated for various parameter val- 

 ues. These are presented in Table 5 as a ratio of 

 time to recover to 9,000 with a constant kill 1 5, 10, 

 15, 20, 25, and 30 animals) compared with the time 

 to recover without a kill. 



If the current stock level were 1,500 animals and 

 the maximum net recruitment rate was 0.05, M = 

 0.04, time lag 3 yr, the stock would take 58 yr to 

 recover to a level of 9,000 with no kill vs. 75 yr with 

 a kill of 30/year. These numbers are increased to 

 94 and 153 yr, when the maximum net recruitment 

 rate is only 0.03 (other parameters unchanged). 



DISCUSSION 



We believe our model is useful but not fully 

 adequate. We have reservations about the data 

 used, limitations of the model, and aspects of the 

 fishery that we did not have time or data to 

 adequately address. 



Limitations of the Data 



The commercial catch data are based mainly on 

 extrapolations of a consistent number of whales 

 caught per ship. The statistics for the number of 

 vessels operating in the bowhead fishery compo- 

 nent of the North Pacific Ocean are also subject to 



'"Bockstoce, J. 1978. A preliminary estimate of the reduc- 

 tion of the western Arctic bowhead whale iBalaena mysticetus) 

 population by the pelagic whaling industry: 1848-1915. Report 

 submitted to U.S. Marine Mammal Commission, Washington, 

 D.C. Available U.S. Dep. Commer., Natl. Tech. Inf Serv., 

 Springfield, VA 22161, as PB-286-797. 



