Maximal sustainable yield in a single population model with strong Allee effects under discontinuous threshold harvesting

Abstract We investigate a single population model incorporating a strong Allee effect and a discontinuous threshold harvesting strategy, where harvesting occurs only when the population exceeds a prescribed management level. The discontinuity in the growth law is resolved using Filippov’s convexification method, which allows us to define solutions as trajectories of a differential inclusion. We prove that for every positive initial condition, a unique global solution exists and remains positive, ensuring biological consistency. Our analysis identifies the supremum of sustainable constant harvest rates as the maximum value of the Allee growth function, attained when the threshold is set slightly below the population density that maximizes per capita growth and the harvest rate is set slightly below that maximum. In addition, we verify our theoretical results through numerical simulations.