Bioeconomic Model of the Lake Michigan Alewife (Alosa pseudoharengus) Fishery

Abstract

A stochastic bioeconomic model is developed for the Lake Michigan alewife (Alosa pseudoharengus) fishery. This theoretical model possesses an intermediate degree of complexity and realism. Other Lake Michigan fish stocks are included in a simplified way as an aggregate, to account for interspecific predation by salmonids, but competition could be treated as well. Both alewife and aggregate fisheries are modeled by modifications of Beverton–Holt single-cohort models with growth in weight and interspecific interactions. The alewives are also subjected to large random disasters and it is demonstrated that these are density independent. The methodology is stochastic, feedback, optimal control using dynamic programming. Stochastic terms are used to represent random disasters in the alewife population. The computational results are given in terms of the maximal, expected economic values of the combined fishery and the optimal rates of harvest for both the alewives and aggregate fisheries. These results are new in the sense that continuous dynamic programming has been applied to a model for several interacting species undergoing occasional random shocks. The expected, optimal economic value of the combined fishery is much less sensitive to the initial recruitment of alewives than to that of the salmonid aggregate. Comparison with a deterministic model that does not include the random disasters shows that the disasters reduce the economic value of the combined fishery by 10–15%. The results are sensitive to reasonable data estimates and confirm the overexploitation of alewives by both the alewife fishery and salmonid predation. The need for reliable data with a common basis is emphasized with regard to comparing commercial and sport fisheries.