Lessard Sabin
Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Qué., Canada H3C 3J7.
Theor Popul Biol. 2005 Jul;68(1):19-27. doi: 10.1016/j.tpb.2005.04.001.
For mixed strategies in finite populations, long-term stability is defined with respect to the probability of fixation of a mutant. Under weak selection, necessary and sufficient conditions are obtained using a diffusion approximation of the Wright-Fisher model or exact solutions for the Moran model. These differ from the usual ESS conditions if the strategies affect fertility instead of viability, leading to a game matrix depending on the population size, or if the mutant mixed strategy uses a new pure strategy. In this case, the mutant deviation must not exceed some threshold value depending on the population size. In a diploid population, long-term stability may not occur unless there is partial dominance. In the case of sex allocation, continuous stability of an even sex ratio is ascertained. If sex allocation is random, an evolutionary decrease of the variance is predicted.
对于有限种群中的混合策略，长期稳定性是根据突变体固定的概率来定义的。在弱选择条件下，使用赖特 - 费希尔模型的扩散近似或莫兰模型的精确解可得到必要且充分的条件。如果策略影响的是繁殖力而非生存能力，导致博弈矩阵取决于种群大小，或者突变体混合策略使用了新的纯策略，那么这些条件与通常的ESS条件不同。在这种情况下，突变体偏差不得超过某个取决于种群大小的阈值。在二倍体种群中，除非存在部分显性，否则可能不会出现长期稳定性。在性别分配的情况下，可以确定均匀性别比的持续稳定性。如果性别分配是随机的，则预计方差会发生进化性减小。
