Hilker Frank M, Liz Eduardo
Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany.
Departamento de Matemática Aplicada II, Universidade de Vigo, 36310, Vigo, Spain.
J Math Biol. 2019 Oct;79(5):1927-1951. doi: 10.1007/s00285-019-01415-7. Epub 2019 Sep 3.
Threshold-based harvesting strategies tend to give high yields while protecting the exploited population. A significant drawback, however, is the possibility of harvesting moratoria with their socio-economic consequences, if the population size falls below the threshold and harvesting is not allowed anymore. Proportional threshold harvesting (PTH) is a strategy, where only a fraction of the population surplus above the threshold is harvested. It has been suggested to overcome the drawbacks of threshold-based strategies. Here, we use discrete-time single-species models and rigorously analyze the impact of PTH on population dynamics and stability. We find that the population response to PTH can be markedly different depending on the specific population model. Reducing the threshold and allowing more harvest can be destabilizing (for the Ricker and Hassell map), stabilizing (for the quadratic map), or both (for the generalized Beverton-Holt map). Similarly, management actions in the form of increasing the threshold do not always improve population stability-this can also be due to bistability. Our results therefore emphasize the importance of a rigorous analysis in investigating the impact of PTH on population stability.
基于阈值的捕捞策略往往能在保护被开发种群的同时实现高产。然而，一个显著的缺点是，如果种群数量降至阈值以下且不再允许捕捞，就有可能出现捕捞禁令及其带来的社会经济后果。比例阈值捕捞（PTH）是一种策略，即仅捕捞阈值以上种群剩余量的一部分。有人认为它可以克服基于阈值策略的缺点。在此，我们使用离散时间单物种模型，并严格分析PTH对种群动态和稳定性的影响。我们发现，根据具体的种群模型，种群对PTH的反应可能会有显著差异。降低阈值并允许更多捕捞可能会导致不稳定（对于里克模型和哈塞尔映射）、稳定（对于二次映射）或两者皆有（对于广义贝弗顿 - 霍尔特映射）。同样，以提高阈值形式的管理行动并不总是能改善种群稳定性——这也可能是由于双稳态造成的。因此，我们的结果强调了在研究PTH对种群稳定性影响时进行严格分析的重要性。
