Revisiting logistic population model for assessing periodically harvested closures

Duo Yu, Sanyi Tang, Yijun Lou

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.

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Published: 2016-10-14

How to Cite this Article:

Duo Yu, Sanyi Tang, Yijun Lou, Revisiting logistic population model for assessing periodically harvested closures, Communications in Mathematical Biology and Neuroscience, Vol 2016 (2016), Article ID 14

Copyright © 2016 Duo Yu, Sanyi Tang, Yijun Lou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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