We present a discrete-time predator–prey model in which the prey population is assumed to evolve in response to a toxicant. We incorporate frequency-dependent selection into the prey evolution, assuming that an individual's susceptibility to predation depends on both the trait it possesses and the traits of others in the population. When frequency-dependent selection is symmetric, we show that the trait equation is unable to track changes in the fitness landscape, that is, the fitness landscape may change while the trait continues to evolve to the same trait value. As a result, evolution may produce unfit prey populations. Meanwhile, we show that asymmetric frequency-dependence may have a destabilizing effect on the system, resulting in a closed invariant curve via a Neimark–Sacker bifurcation.

中文翻译：

---

捕食者-猎物系统中的频率相关进化

我们提出了一个离散时间的捕食者 - 猎物模型，其中假定猎物种群响应毒物而进化。我们将依赖频率的选择纳入猎物进化，假设个体对捕食的易感性取决于它拥有的特征和种群中其他人的特征。当频率相关选择是对称的时，我们表明特征方程无法跟踪适应度景观的变化，即适应度景观可能会发生变化，而特征继续演变为相同的特征值。因此，进化可能会产生不合适的猎物种群。同时，我们表明不对称的频率相关性可能对系统产生不稳定的影响，通过 Neimark-Sacker 分岔导致闭合不变曲线。