The Optimal Harvesting Policy With Seasonal Closures

Fishery and aquaculture are crucial resources of global development by provid-ing nutritious food and employment positions in ancillary activities. However, most fish stocks are reported as fully exploited or overexploited. And fish stocks are in ur-gent need of effective fishery management. In the fishery policies, seasonal closures are frequently employed within the exploitation frameworks. A closed season of a single species is the banning of fishing activity for a few weeks or months, usually to protect juveniles or spawners. For instance, the spring closures in Yangtze River and the summer closures in the Yellow Sea in China. Management of harvesting and banning for fixed period is proved to be effective on protecting juveniles, there-fore, enhancing the population persistence and harvested yields of fishery products. Despite the widespread popularity of seasonal closures on harvesting strategies, the benefits of it have been largely untested from the population dynamic point of view.Logistic model, with its variants, has been extensively investigated on evaluat-ing different harvesting strategies. With the assumption that each year is divided into two periods of time, namely, closed season and open season, we perform a piecewise mathematical model to explore the optimal harvesting policy for strate-gies with seasonal closures. In this study, sufficient conditions are obtained for global stability of positive periodic solutions both in constant and periodically fluctuant environment.With the maximum annual-sustainable yield (MASY) as a management objec-tive, the optimal harvest timing (or season) is determined for fixed harvesting effort. 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 both in constant and fluctuant environment. This result is consistent with the results obtained in re-lated studies before. Furthermore, the optimal harvesting policy, optimal harvesting effort, optimal harvest timing and their biological implications are discussed.In chapter 2, the optimal harvesting policy is explored in constant environment. When the harvesting intensity is small, namely harvesting effort not exceed intrinsic growth rate, then the population persists regardless of the length of open season. If the harvesting effort is greater than intrinsic growth rate, suitable length of closed season is needed to ensure population persistence. When the harvesting effort is greater than half of intrinsic growth rate, then there exists a unique optimal harvest timing which can maximize the annual-sustainable yield.The optimal harvesting policy in periodically fluctuant environment is analyzed in chapter 3. The optimal harvesting effort is determined regardless the length of closed season. However, there exists two harvest timings ?<?2 such that the av-erage optimal harvesting effort reach its minimum and maximum value respectively. And when harvesting timing between these two critical values, the harvest tim-ing has moderate effect on the maximum annual-sustainable yield which is mainly determined by the optimal harvesting effort.Moreover, the effect of intrinsic growth rate and its fluctuation on optimal har-vesting timing and average harvesting effort are discussed. The paradoxical hydra effect observed in one-dimensional difference equation, where population size increas-es in response to additional mortality, is excluded for scalar continuous-time model. The results offer a new perspective on setting the policy of harvesting closures.