Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain.
Departamento de Matemática Aplicada II, Universidade de Vigo, 36310, Vigo, Spain.
J Math Biol. 2021 Jan 19;82(1-2):3. doi: 10.1007/s00285-021-01557-7.
One-dimensional discrete-time population models are often used to investigate the potential effects of increasing harvesting on population dynamics, and it is well known that suitable harvesting rates can stabilize fluctuations of population abundance. However, destabilization is also a possible outcome of increasing harvesting even in simple models. We provide a rigorous approach to study when harvesting is stabilizing or destabilizing, considering proportional harvesting and constant quota harvesting, that are usual strategies for the management of exploited populations. We apply our results to some of the most popular discrete-time population models (quadratic, Ricker and Bellows maps). While the usual case is that increasing harvesting is stabilizing, we prove, somehow surprisingly, that increasing values of constant harvesting can destabilize a globally stable positive equilibrium in some cases; moreover, we give a general result which ensures that global stability can be shifted to observable chaotic dynamics by increasing one model parameter, and apply this result to some of the considered harvesting models.
一维离散时间种群模型通常用于研究增加捕捞对种群动态的潜在影响，众所周知，适当的捕捞率可以稳定种群丰度的波动。然而，即使在简单的模型中，增加捕捞也可能导致不稳定。我们提供了一种严谨的方法来研究捕捞何时稳定或不稳定，考虑了比例捕捞和固定配额捕捞，这是对受捕捞种群进行管理的常用策略。我们将我们的结果应用于一些最流行的离散时间种群模型（二次、里克尔和波纹管图）。虽然通常情况下，增加捕捞是稳定的，但我们有些出人意料地证明，在某些情况下，增加固定捕捞值会使一个全局稳定的正平衡点失稳；此外，我们给出了一个一般结果，该结果可以通过增加一个模型参数将全局稳定性转移到可观察的混沌动力学，并且将该结果应用于一些考虑的捕捞模型。
