Revisiting logistic population model for assessing periodically harvested closures

Abstract

Periodically harvested closures are frequently employed within the exploitation frameworks. Logistic model, with its variants, have been extensively investigated on evaluating different harvesting strategies. In this manuscript, we revisit Logistic model to evaluate the population dynamics and harvesting yields under periodically harvested frameworks. Sufficient conditions are obtained for global stability of positive periodic solutions. With the maximum annual-sustainable yield (MASY) as a management objective, the optimal harvest timing (or season) is determined for fixed harvesting effort and MASY is shown to depend solely on the duration of open harvesting season. Combining with the optimal harvesting effort, the higher annual-sustainable yield can be reached if the timing of harvesting is set as early as possible. Furthermore, the optimal harvesting policy, optimal harvesting effort, optimal harvest timing and their biological implications are discussed. Moreover, the paradoxical hydra effect observed in one-dimensional difference equation, where population size increases in response to additional mortality, is excluded for scalar continuous-time model. Our results offer a new perspective on setting the policy of harvesting closures.