Optimal harvesting strategies for ecological population dynamics

What is the optimal way to harvest an ecological population sustainably is a fundamental problem in natural resource management. Here we use the framework of the stochastic logistic model which captures random birth-death of individuals to determine the optimal harvesting strategy that maximizes the integrated yield over time. Harvesting is assumed to occur at either a constant or state-dependent rate, and individuals are harvested with a certain probability whenever a harvesting event occurs. A special case of state-dependent harvesting is a threshold-based strategy, where harvesting is done when the population crosses a threshold. We use moment closure schemes to develop analytical formulas quantifying the mean and optimal yield. Moreover, as populations are susceptible to extinction at high harvesting rates, the Finite State Projection (FSP) method is used to estimate the probabilities of extinction across strategies and parameter regimes. Our results show that the threshold-based strategy is most effective in maximizing the yield as it suppresses population fluctuations and minimizes extinction events.