标题： 有限种群中的确定性进化博弈动力学 显示英文标题

标题： Deterministic evolutionary game dynamics in finite populations

摘要： 进化博弈动力学描述了在繁殖个体群体中成功策略的传播。 通常，策略传播的微观定义是随机的，因此只有在无限大的种群中动力学才变为确定性的。 在这里，我们引入了一种新的微观出生-死亡过程，在任何大小的均匀混合种群中，该过程在强选择极限下具有完全确定的动力学。 此外，在弱选择下，从这个新过程中可以恢复频率依赖的莫兰过程。 这使其成为弱选择下常规进化动力学的自然扩展。 我们找到了在两个玩家和两个策略的进化博弈中，新过程的固定概率和平均固定时间的简单表达式。 对于两个玩家和三个策略的循环博弈，我们表明结果的确定性动力学以一种非平凡的方式严重依赖于初始条件。 显示英文摘要

摘要： Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic only in infinitely large populations. Here, we introduce a new microscopic birth--death process that has a fully deterministic strong selection limit in well--mixed populations of any size. Additionally, under weak selection, from this new process the frequency dependent Moran process is recovered. This makes it a natural extension of the usual evolutionary dynamics under weak selection. We find simple expressions for the fixation probabilities and average fixation times of the new process in evolutionary games with two players and two strategies. For cyclic games with two players and three strategies, we show that the resulting deterministic dynamics crucially depends on the initial condition in a non--trivial way.