68 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



Table 4. — Average size at each age of the southeastern 

 Bering Sea population of adult male king crabs as de- 

 termined from modal progression in size-frequency dis- 

 tribution and from growth per molt multiplied by the 

 molting proportions in each size 



It would be unrealistic to extend the growth 

 model beyond N + 6, because very few crabs greater 

 than 200 nnn. in carapace length are taken in the 

 eastern Bering Sea. In addition, from the curves 

 presented, it appears that in most years the average 

 length is approaching an asymptote, and any 

 further increase in age will not greatly affect the 

 average size of the year class. 



DISCUSSION 



The growth rates calculated from the 1956, 1958, 

 and 1959 data show general agreement, but 1957 

 data suggests an appreciably lower rate. This is 

 due primarily to the apparent lower proportion of 

 molters in the 110- to 150-mm. carapace length 

 range. In view of the discrepancy of the 1957 

 data, and because of the few years for which we 

 have data, no attempt has been made to develop a 

 single growth cui-ve. 



The model assumes that molting rate is a func- 

 tion of size. It might be questionable tiiat crabs 

 of any one size, which did not molt, will exhibit the 

 same molting rate the following year. The molt- 

 ing proportion, P, used in the model are the pro- 

 portions observed in the entire sample (popula- 

 tion), and in the larger sizes undoubtedly includes 

 several year classes with crabs of various shell 

 conditions. The assumption that crabs of a com- 

 mon size, with varying time since the last molt, 

 have equal molting rates is guided by the fact that 

 the P's are averages of all molting rates that oc- 

 cur in the eastern Bering Sea ; that is, the molting 

 rates of new-shell and old-shell and, to a lesser de- 

 gree, very-old-shell crabs make up P. 



If molting rates of the various shell conditions 

 differ widely, they must differ around P; that is. 



any large deviation of the molting rate of one shell 

 type from P must be accompanied by a compensat- 

 ing deviation of one or both of the other. For ex- 

 ample, if the molting rate of old-shell crabs is 

 high, the molting rate of new-shell crabs would be 

 low, and in any particular year of the age-class 

 progression where old-shell crabs predominate, the 

 average size would be greater than that indicated 

 in the model. However, in the following year the 

 increased number of new-shell crabs resulting from 

 the high-molting rate of the old-shell crabs would 

 be subject to the low molting rate of crabs having 

 new shells. The result would be a lower average 

 size of the year class for that year. The growth 

 rate under such a condition would be step-like, 

 and smoothing would result in a cun-e that would 

 approximate that developed by considering P con- 

 stant for size, as we have done. 



Observed molting proportions may also be af- 

 fected by other factors: (1) varying environ- 

 mental conditions, (2) varying year class strength, 

 (3) differential natural mortalities by shell condi- 

 tions, and size. Our studies with respect to the 

 above factors have not progressed sufficiently to 

 measure their effect on molting proportions. 



The model does not consider mortality. Al- 

 though this may be unrealistic, mortality was not 

 included since our measures of mortality rates are 

 not yet definitive, and constant loss would not 

 change the results. 



There is no reason to expect appreciable dif- 

 ferential natural mortality by size or age for the 

 range of size and age being discussed here. It 

 might be expected, however, that there would be 

 a higher death rate of crabs that molt tlian those 

 that do not. The effect of molting mortality is 

 negated by the fact that molting proportions are 

 based on numbers surviving; therefore, after the 

 effect of molting mortality. Although there is 

 some differential mortality due to fishing, since 

 the fishery continually strives to catch tlie larger 

 old-shell male crabs, this mortality is not evalu- 

 ated in the model. The fisheiy operates concur- 

 rently with our sampling efforts, and at present 

 there is no way to assess its effects. In addition, 

 preliminary examination shows that the fishery, 

 through 1959, takes a relatively small proportion 

 of the king crab population as a whole. 



For use in calculation of yield, it would be ex- 

 pedient to express our growth curves as mathe- 



