ABSTRACT Prolonged exposure to disturbances, such as toxicants, has the potential to result in evolutionary responses in a population. These evolutionary responses may impact not just that species but also other species with which the population interacts. In this paper, we develop a discrete-time predator–prey model and establish conditions for the existence and stability of equilibria, as well as conditions for the persistence of the prey and predator populations. We then extend this model to an evolutionary model which couples the population dynamics with the dynamics of an evolving phenotypic trait that provides a measure for the level of toxicant resistance developed by the prey. We study the persistence dynamics of this model and establish conditions for when the prey evolves toxicant resistance. We show that the evolution of toxicant resistance may allow both the predator and prey to persist when, without the evolution, both may go extinct.

中文翻译：

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离散时间捕食者-猎物模型的持久性和稳定性分析：种群和进化动力学研究

摘要 长期暴露于干扰物，如毒物，有可能导致种群的进化反应。这些进化反应可能不仅会影响该物种，还会影响与种群相互作用的其他物种。在本文中，我们开发了一个离散时间的捕食者-猎物模型，并建立了平衡存在和稳定的条件，以及猎物和捕食者种群持续存在的条件。然后，我们将该模型扩展到一个进化模型，该模型将种群动态与进化表型特征的动态相结合，为猎物产生的毒物抗性水平提供了衡量标准。我们研究了该模型的持久性动态，并建立了猎物何时进化出毒药抗性的条件。