Fisheries management in random environments: Comparison of harvesting policies for the logistic model

Abstract

We describe the growth dynamics of a harvested fish population in a random environment using a stochastic differential equation logistic model, where the harvest term depends on a constant or a variable fishing effort. We consider revenues to be proportional to the yield and costs to be quadratic in terms of effort. We compare the optimal expected profit obtained with two types of harvesting policies, one based on variable effort, which is inapplicable, and the other based on a constant effort, which is applicable and sustainable. We answer two new questions: (a) What is the constant effort that optimizes the expected profit per unit time? (b) How do the two policies compare in terms of performance? We show that, in a realistic situation, there is only a slight reduction in profit when choosing the applicable constant effort policy instead of the inapplicable policy with variable effort.