Alvarez L H
Institute of Applied Mathematics, University of Turku, Finland.
Math Biosci. 1998 Aug 15;152(1):63-85. doi: 10.1016/s0025-5564(98)10018-4.
We consider the derivation of the optimal harvesting strategy maximizing the expected cumulative yield from present up to extinction, under the assumption that the harvested population fluctuates stochastically and is subjected to an Allee-effect. By relying on both stochastic calculus and the classical theory of linear diffusions, we derive both the optimal harvesting thresholds at which harvesting should be initiated at full capacity and the value of the optimal strategy. In contrast to ordinary models which are absent of critical depensation, we show that the presence of an Allee-effect leads to the introduction of a lower harvesting threshold at which the population should be immediately depleted under the optimal policy. Moreover, we demonstrate that discounting increases the incentives to harvest and, therefore, increases the probability of a soon extinction of the harvested population.
我们考虑在收获的种群随机波动且受到阿利效应影响的假设下，推导使从当前到灭绝的预期累积产量最大化的最优收获策略。通过运用随机微积分和线性扩散的经典理论，我们得出了应满负荷开始收获的最优收获阈值以及最优策略的价值。与不存在临界补偿的普通模型不同，我们表明阿利效应的存在导致引入了一个较低的收获阈值，在最优策略下种群应在此阈值时立即被耗尽。此外，我们证明贴现增加了收获的动机，因此增加了收获种群很快灭绝的概率。
