Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics with fluctuations due to random drift. A selection advantage which depends on a changing environment will introduce additional possibilities for the dynamics. We analyse a simple model in which a random environment allows competing species to coexist for a long time before a fixation of a single species happens. In our analysis we use stability in a linear combination of competing species to approximate the stochastic dynamics of the system by a diffusion on a one dimensional co-existence region. Our method significantly simplifies approximating the probability of first extinction and its expected time, and demonstrates a rigorous model reduction technique for evaluating quasistationary properties of stochastic evolutionary dynamics.

中文翻译：

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随机演化博弈中共存子空间上的扩散动力学。

频率相关的选择反映了不同物种在环境中争夺有限资源时的相互作用。在随机进化博弈中，物种相对适应度会指导由于随机漂移而引起波动的进化动力学。取决于不断变化的环境的选择优势将为动力学带来更多可能性。我们分析了一个简单的模型，其中随机环境允许竞争物种在固定单个物种之前很长时间共存。在我们的分析中，我们使用竞争性物种的线性组合中的稳定性，通过在一维共存区域上的扩散来近似系统的随机动力学。我们的方法大大简化了首次灭绝的概率及其预期时间，