Stable Cycles in Multistage Recruitment Models: An Application to the Northern California Dungeness Crab (Cancer magister) Fishery

Abstract

This study illustrates, through the modeling of the Northern California Dungeness crab fishery, a diagnostic approach to the inference of multistage density-dependent recruitment mechanisms operating in animal populations. Northern California Dungeness crab landings have exhibited a strikingly regular cycling pattern since the early 1940s, but with increasing amplitude swings as the fishery has expanded suggesting the possibility of an eventual crash. A variety of mechanisms have been proposed, involving either biological feedback controls or exogeneous environmental effects, to account for the regular cycling and its possible destabilization by fishing. This study examines the plausibility of various alternative biological control mechanisms by incorporating them, one by one, into a multistage dynamic recruitment model, of nonlinear renewal type, based on general qualitative features of the crustacean's life history. A total of 48 plausible model variants are examined, reflecting differences in intensity and timing of possible feedback controls and uncertainty about exploitation and survival rates.Model analysis incorporates two complementary approaches to test out the range of alternative hypotheses incorporated in these variants. The first approach is based on examination of qualitative features of model dynamics: period and amplitude of stable cycles, and the model's response to varying levels of exploitation. The second is based upon extracted estimates of probable historic year-class strength and assesses the fit of model variants by least-squares regression techniques. These twin diagnostic procedures allow elimination of most model variants, and support the hypothesis that recruitment must be determined in the very early life stages, egg, or larval.The last phase of analysis is to further probe the model by numerical experimentation, including a simulation of the institution of female harvest. Finally, the implications of the modeling exercise are drawn, for future field studies and for second generation modelling.Key words: bifurcations, Dungeness crab, Cancer magister, stable cycles, multistage recruitment models, stock-recruitment