Optimal strategies for sustainable harvesting of ecological populations: A stochastic approach

Determining the optimal way to sustainably harvest an ecological population is a key challenge in natural resource management. Our contribution employs the stochastic logistic model, which accounts for random birth-death processes, to identify optimal harvesting strategies that maximize the integrated yield over time while considering nonzero probability of extinction. Harvesting is modeled to occur at either a constant or state-dependent rate with individuals being harvested with a certain probability at each harvesting event. A special case of state-dependent harvesting is a threshold-based strategy, where harvesting occurs once the population exceeds a specific threshold. Using moment closure schemes, we approximate analytical formulas to quantify mean and optimal yield. We verify these approximations using the Finite-State Projection (FSP) method. Through this numerical method, we estimate not only the optimal harvesting rate, but also the extinction probabilities over a given time interval. Our results show that the threshold-based strategy is most effective in maximizing yield by reducing population fluctuations and minimizing extinction events.