Variable effort fishing models in random environments

We study the growth of populations in a random environment subjected to variable effort fishing policies. The models used are stochastic differential equations and the environmental fluctuations may either affect an intrinsic growth parameter or be of the additive noise type. Density-dependent natural growth and fishing policies are of very general form so that our results will be model independent. We obtain conditions on the fishing policies for non-extinction and for non-fixation at the carrying capacity that are very similar to the conditions obtained for the corresponding deterministic model. We also obtain conditions for the existence of stationary distributions (as well as expressions for such distributions) very similar to conditions for the existence of an equilibrium in the corresponding deterministic model. The results obtained provide minimal requirements for the choice of a wise density-dependent fishing policy.