A contagion model of a fishery and its use in analyzing catch-effort data

Abstract

A stochastic model of a fishery which recognizes a contagion effect in the fishing process (i.e. the fact that the events of individual fish being caught are not independent) is developed and is used to establish how the probability distribution of the aggregated annual catch of the fishery depends upon the aggregated annual fishing effort. From this relationship, and the assumption of deterministic, non-linear population dynamics, it is possible to determine analytically a likelihood function of the various model parameters (catchability coefficient, two parameters of the Ricker stock-dynamic model and a contagion parameter). Maximum likelihood estimates and likelihood ratio confidence intervals for these model parameters can then be obtained numerically. The method is applied to two sets of catch-effort data. The performance of the method is assessed by comparing predictions of catch and catch-per-unit-effort with observed values for reserved data which were not used for model fitting. Also confidence estimates of the maximum sustainable yield are obtained and the credibility of such estimates discussed.