Abstract
Theoretical analyses of deterministic population models have shown that the maximum sustained harvest of density dependent populations occurs at the population density with maximum growth rate. This traditional approach to harvesting does not include the effects of a variable environment. Here we analyse by means of diffusion theory the dynamics of populations at risk of extinction from demographic and environmental stochasticity as well as harvesting. These dynamical results are used to derive approximate formulas for the expected cumulative harvest before extinction and the mean and standard deviation of the annual harvest. Analyses of these expressions show that the optimal strategy is to harvest at the maximum rate when the population size is above a critical size c, with no harvest below c. Numerical analyses show that c is relatively independent of the form of density dependence. However, the threshold c decreases with the degree of environmental fluctuations and when the maximum rate of harvest is decreased.
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