A bioeconomic model of the pacific whiting

Abstract

The Pacific whiting (Merluccius productus) is a highly migratory fish occupying the continental shelf and slope off the west coast of North America. The species spawns in January off southern California and northern Mexico. During spring and summer the older and larger fish will migrate as far north as central Vancouver Island. Recruitment is highlys variable, with strong year classes often supporting the commercial fishery during several years of low recruitment. The level of recruitment appears to be independent of the size of the spawning population.

A simple bioeconomic model of the Pacific whiting is constructed with independent recruitment. Fishery production functions are estimated from data on U.S. catch, average annual biomass and the number of vessels in the U.S. fleet. A stochastic optimization problem, seeking to maximize the expected value of industry profit, is formulated. Its solution would require a joint distribution on future recruiment and other bioeconomic parameters. Such a distribution is problematic. As an alternative, the certainty-equivalent problem is solved yielding solution values for the stochastic equilibrium and an approximately-optimal rule that sets allowable catch based on an estimate of current-year biomass.

Adaptive management can result in large changes in fleet size and allowable catch from year to year. The whiting fishery might be characterized as an opportunistic fishery, requiring a generalist fleet to expand or contract as bioeconomic conditions warrant. It is possible that longrun conditions would not support a profitable fishery, but that short-run fishing is profitable based on previous years of strong recruitment. The situation is not dissimilar to that facing the owner of a marginal gold mine that opens or closes depending on the price of gold. In the case of the whiting fishery, the optimal level of short-run fishing will depend not only on price, but on current biomass, the annual cost of fishing, the discount rate and vessel productivity. A simple interactive program is provided for would-be managers.