Effect of Individual Growth Rates on Expected Behavior of the Northern California Dungeness Crab (Cancer magister) Fishery

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Abstract
Cycles in the northern California Dungeness crab (Cancer magister) fishery may be caused by density-dependent recruitment or a cyclic environmental variable. Investigation of these potential causes requires knowledge of the age(s) at which crabs enter the fishery. Behavior of this fishery has previously been analyzed using mathematical models that include density-dependent recruitment and describe changes in age structure with time. From data available on the northern California crab population and a review of previous studies elsewhere it appears that a single year-class of crabs enters this fishery over several years rather than in one year as described by models with only age structure. The realism of models of this fishery can therefore be increased by including size structure. Behavior of size-specific models is in general different from that of age-specific models. However, it is shown here that an effective survival rate can be derived from a size-specific model that enables interpretation as an age-specific model. This is used to demonstrate that inclusion of size dispersion in a population model increases stability, but if the mean age of the population is not changed, it will not substantially change the period of cycles. Because the growth pattern developed here changes the mean age of entry into the fishery it results in cycles with a longer period than determined in previous analyses. With regard to environmental causes, this growth pattern implies time lags of 4 and 5 yr between an environmental factor affecting recruitment and its effect on the catch record.