Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, USA.
Dana-Farber Cancer Institute, Boston, Massachusetts, USA.
Phys Rev E. 2017 Feb;95(2-1):022407. doi: 10.1103/PhysRevE.95.022407. Epub 2017 Feb 13.
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the associated mean fixation times can be more intricate, especially when selection is strong. The intuition is that fixation of a beneficial mutant happens fast in a dominance game, that fixation takes very long in a coexistence game, and that strong selection eliminates demographic noise. Here we show that these intuitions can be misleading in structured populations. We analyze mean fixation times on the cycle graph under strong frequency-dependent selection for two different microscopic evolutionary update rules (death-birth and birth-death). We establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size. Depending on the underlying game, we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring (death-birth update). In contrast, if selection for an offspring occurs before random removal (birth-death update), then strong selection can remove demographic noise almost entirely.
基于图的进化博弈描述了策略相互作用和种群结构如何决定进化成功，这可以通过单个突变体接管种群的概率来量化。与均匀混合的情况相比，图结构可以通过增加或减少有益突变体的固定概率来放大或抑制选择。相关平均固定时间的特性可能更加复杂，尤其是在选择较强时。直觉是在优势博弈中，有益突变体的固定速度很快，在共存博弈中固定速度非常慢，而强选择消除了人口统计学噪声。在这里，我们表明这些直觉在结构化种群中可能具有误导性。我们分析了在强频率依赖选择下，两种不同微观进化更新规则（死亡-出生和出生-死亡）下循环图上的平均固定时间。我们为强选择下的固定时间建立了精确的解析结果，并表明存在共存博弈，其中在种群大小的多项式时间内发生固定。根据基础博弈，如果在选择后代出生之前随机死亡（死亡-出生更新）驱动过程，则即使在强选择下也会存在人口统计学噪声的内在性。相比之下，如果选择后代出生之前发生随机移除（出生-死亡更新），则强选择几乎可以完全消除人口统计学噪声。
