Variable effort harvesting models in random environments: generalization to density-dependent noise intensities

In a previous paper [Math. Biosci. 156 (1999) 1], we have studied quite general stochastic differential equation models for the growth of populations subjected to harvesting in a random environment. We have obtained conditions for non-extinction and for the existence of stationary distributions (as well as expressions for such distributions) similar to conditions for non-extinction and for the existence of a stable equilibrium in the corresponding deterministic model. The models were quite general, considering density-dependent natural growth functions and harvesting policies of very general form, so that our results would be model independent and provide minimal requirements for the choice of a wise density-dependent harvesting policy. Those models, however, although quite general on all other respects, have a serious limitation. In fact, the ways environmental fluctuations affect the population per capita growth rate are poorly known and those models only considered two possible ways, namely the noise intensity could be constant or proportional to that rate. To overcome this limitation, in this paper we generalize the previous results to density-dependent positive noise intensities of very general form so that they also become independent from the way environmental fluctuations affect population growth rates.