An Age-Structured Open-Access Fishery Model

Abstract

A dynamic model for open-access fisheries is presented. In addition to density dependence in recruitment and fishing effort changing in proportion to the level of profit fishermen earn which characterizes previous open-access models, it incorporates full age structure for the fish stock, lognormal environmental recruitment variability, and gear selectivity. The predator–prey cycling solution of the original Schaefer dynamic model, and subsequent open-access models, persists for these model extensions. Density dependence in recruitment induces greater global stability. Environmental recruitment variability, common in marine populations, is destabilizing in the neighborhood of the open-access equilibrium. These two influences, combined in the open-access fishery model, generate robust long-lasting irregular cycles of stock and effort. Volterra proved for the original Lotka–Volterra model that the time averages of the variables over one cycle were exactly equal to their equilibrium steady states. This is shown to extend as a good approximation for the model presented here. Approximating model steady states of effort and catch by the corresponding averages from data time series underlies a new algorithm of parameter evaluation, applied here to an open-access model of the Georges Bank sea scallop (Placopecten magellanicus) fishery.