大群体中的固定：一个离散问题的连续视图
Fixation in large populations: a continuous view of a discrete problem
摘要：
我们研究固定在大型，但有限的，人口有两种类型，和动态的出生-死亡过程。通过考虑这样的过程的一个限制类，我们得到一个连续的近似固定的概率是有效的弱选择（WS）限制之外。从连续的近似，然后，我们得到渐近近似的演化动力学与最多一个平衡，在选择驱动的制度，不排除弱选择制度。作为应用，我们研究了无限种群极限具有内部进化稳定策略（ESS）时的注视模式：（i）我们证明了Hawk and Dove博弈的注视模式满足我们称之为二分之一定律：如果进化稳定策略（ESS）在$\sfrac{1}{2}$附近的一个小区间之外，则注视为优势型;（ii）我们还表明，在弱选择制度之外，大种群的长期动态与无限种群的情况几乎没有相似之处;此外，我们还提出了两个平衡的情况下的结果。最后，我们提出了连续重述的两个经典概念，自然定义在离散的情况下，大人口有效：（i）的定义的$\textsc{ESS}_N$策略;（ii）的定义的风险主导的战略。然后，我们提出了这些重述的两个应用：（i）我们获得了一个在准中性制度下有效的渐近定义，该定义恢复了线性适应度下的三分之一定律和$d$玩家游戏的广义三分之一定律;（ii）我们扩展了（广义）三分之一定律以外的准中性制度，作为推广，我们介绍了临界频率的概念;（iii）我们恢复了$d$ -玩家博弈的风险占优策略的分类。
英文摘要：
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation that is valid beyond the weak-selection (WS) limit. From the continuous approximations, we then obtain asymptotic approximations for evolutionary dynamics with at most one equilibrium, in the selection-driven regime, that does not preclude a weak-selection regime. As an application, we study the fixation pattern when the infinite population limit has an interior Evolutionary Stable Strategy (ESS): (i) we show that the fixation pattern for the Hawk and Dove game satisfies what we term the one-half law: if the Evolutionary Stable Strategy (ESS) is outside a small interval around $\sfrac{1}{2}$, the fixation is of dominance type; (ii) we also show that, outside of the weak-selection regime, the long-term dynamics of large populations can have very little resemblance to the infinite population case; in addition, we also present results for the case of two equilibria. Finally, we present continuous restatements valid for large populations of two classical concepts naturally defined in the discrete case: (i) the definition of an $\textsc{ESS}_N$ strategy; (ii) the definition of a risk-dominant strategy. We then present two applications of these restatements: (i) we obtain an asymptotic definition valid in the quasi-neutral regime that recovers both the one-third law under linear fitness and the generalised one-third law for $d$-player games; (ii) we extend the ideas behind the (generalised) one-third law outside the quasi-neutral regime and, as a generalisation, we introduce the concept of critical-frequency; (iii) we recover the classification of risk-dominant strategies for $d$-player games.
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