Mathematical performances of management procedure of constant fishing coefficient for fishery stock in a periodical environment

Abstract

An investigation was carried out in order to compare the performance of constant fishing coefficients maximizing some different objective functions for management of fishery stock in a periodical environment. The stock dynamics are expressed by the generalized stock production model incorporating the periodical changes in carrying capacity. The objective functions to be maximized are the average catch over the unit cycle, and the minimum or maximum catch. The performance of the fishing coefficient at the maximum sustainable yield in a steady environment is also examined. The expressions of the average catch and of the annual variation were mathematically analyzed and numerical calculations were carried out using various values of the growth rate of fishery stock and of the amplitude of periodical changes in the carrying capacity. The models were applied to the Pacific stock of the Japanese pilchard Sardinops melanostictus and the chub mackerel Scomber japonicus. From the results, the fishing coefficient at the maximum sustainable yield mathematically maximizes the generalized mean of catch with the negative of the power coefficient of the production model as the exponent, and is not consistent with that for maximizing the average catch. Interpretation of the results and issues to be resolved in the near future are discussed.