Behavior of Age-Specific, Density-Dependent Models and the Northern California Dungeness Crab (Cancer magister) Fishery

Abstract

A continuous time and age model which reflects the effect of older age-groups on mortality in young is presented. The conditions under which this model is unstable and the characteristics of solutions under various conditions are examined. Results obtained are related to results obtained by others from stock–recruitment models. Analytical expressions for the period of oscillations, the effect of fishing all age-classes, and the effect of the slope of the stock–recruitment curve at the replacement point support earlier simulation results. The effect on the model of size-selective fishing is shown to be a decrease in the stability of the population in some cases. These results are demonstrated with a model that approximately reflects the Dungeness crab (Cancer magister) population in northern California. The cyclic behavior of this population is similar to an unstable mode of the model. Conditions under which this mode arises are derived and potential causes of decreased stability, among which is fishing, are examined. Key words: fishery, model, stability, Dungeness crab, age-specific, density-dependent, stock–recruitment, cannibalism, Carcinonemertes