Patel Swati, Schreiber Sebastian J
Department of Evolution and Ecology and Graduate Group in Applied Mathematics, University of California, Davis, CA, 95616, USA.
Faculty of Mathematics, University of Vienna, Vienna, Austria.
J Math Biol. 2018 Jul;77(1):79-105. doi: 10.1007/s00285-017-1187-5. Epub 2017 Oct 26.
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks.
物种既经历与诸如性状进化等内源性因素的内部反馈，也经历与诸如天气等外源性因素的外部反馈。这些反馈在决定种群是否持续存在或物种群落是否共存方面可能发挥重要作用。为了提供一个研究这些效应的通用数学框架，我们针对考虑内部和外部反馈的生态模型开发了一个共存定理。具体而言，我们使用平均李雅普诺夫函数和莫尔斯分解来为稳健持久性（一种对种群密度的大扰动和模型的小结构扰动具有鲁棒性的共存形式）开发充分必要条件。我们说明了如何应用我们的结果来验证非自治模型、结构化种群模型（包括具有频率依赖反馈的模型）以及生态进化动力学模型中的持久性。在这些应用中，我们讨论了我们的结果与具有特定类型反馈的模型的先前结果之间的关系。
