弱选择下局部更新过程的固定时间

FIXATION TIMES FOR LOCAL UPDATE PROCESSES UNDER WEAK SELECTION

双策略2×2对称博弈有限总体的进化动态本质上是一个随机过程.在双策略系统中,如果A策略者占优B策略者,则A策略会在总体中得到扩散,在随机动态下,最终达到总体内全是A策略者或全是B策略者的同源状态.研究在弱选择下的局部更新过程中,总体达到同源状态时的固定时间.结果表明,在弱选择下,A、B两个策略的条件固定时间相等,且仅依赖于两个策略收益差的线性部分,而平均固定时间仅依赖于两个策略收益差的常数部分.最后通过图形表明了固定时间与系统总体数、博弈收益及选择强度间的关系.

An evolutionary dynamics of two strategies games given by 2×2 symmetry matrix in finite populations is essentially a stochastic process.If strategy A dominants strategy B,strategy A will spread in the population.Under stochastic dynamics,a single mutant will sooner or later take over the entire population or go extinct.We mainly analyze the fixation times for local update processes under weak selection in homogeneous populations.The results are that the conditional fixation times of a single A and a single B mutant are identical,they depends only on the density dependent term of the payoff difference of two strategies,and the unconditional mean fixation time depends only on the constant term.Finally,the relationship between population size,payoff matrix and the intensity of selection is illustrated by figures.