Constant effort and constant quota fishing policies with cut-offs in a random environment

Abstract

ABSTRACT. Consider a population subjected to constant effort or constant quota fishing with a generaldensity-dependence population growth function (because that function is poorly known). Consider environmental random fluctuations that either affect an intrinsic growth parameter or birth/death rates, thus resulting in two stochastic differential equations models. From previous results of ours, we obtain conditions for non-extinction and for existence of a population size stationary density. Constant quota (which always leads to extinction in random environments) and constant effort policies are studied; they are hard to implement for extreme population sizes. Introducing cut-offs circumvents these drawbacks. In a deterministic environment, for a wide range of values, cutting-off does not affect the steady-state yield. This is not so in a random environment and we will give expressions showing how steady-state average yield and population size distribution vary as functions of cut-off choices. We illustrate these general results with function plots for the particular case of logistic growth.