A Theory of Sustainable Harvesting
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TL;DR
Numerical solutions are obtained using adaptive boundary-value solvers and numerical integration to assess the accuracy of an approximate solution that is based upon simpler “canonical” problems.
Abstract
A problem of sustainable harvesting is formulated. The effects considered include continual small fluctuations in environmental conditions (Brownian motion), rare but large population decreases (Poisson noise), and uncertainty about the intrinsic growth rate for the population. The harvesting rate is a control variable that is chosen to keep the probability of early collapse or extinction below a prescribed level. Numerical solutions are obtained using adaptive boundary-value solvers and numerical integration. These are used to assess the accuracy of an approximate solution that is based upon simpler “canonical” problems.