The probability of fixation of a single mutant in an exchangeable selection model
The probability of fixation of a single mutant in an exchangeable selection model
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DOI：
10.1007/s00285-007-0069-7
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发表时间：
2007-05-01
影响因子：
1.9
通讯作者：
Ladret, Veronique
中科院分区：
文献类型：
--
作者：
Lessard, Sabin;Ladret, Veronique
将离散时间有限种群的Cannings可交换模型推广到包含选择的情形。在弱选择的假设下研究了突变类型的固定概率。推导出一个精确的公式，这个概率的导数相对于选择的强度，并在一个单一的突变体的情况下开发。该公式用中性条件下的平均聚结时间表示，假设突变类型的选择系数相对于选择强度具有导数，该导数相对于突变类型的频率呈多项式形式。在该导数是突变频率的连续函数且种群规模较大的情况下，得到了近似值。这种近似是一致的扩散近似矩条件下的一个单一的个人在一个时间步长的后代的数量。有限种群进化博弈论的应用。
The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula is expressed in terms of mean coalescence times under neutrality assuming that the coefficient of selection for the mutant type has a derivative with respect to the intensity of selection that takes a polynomial form with respect to the frequency of the mutant type. An approximation is obtained in the case where this derivative is a continuous function of the mutant frequency and the population size is large. This approximation is consistent with a diffusion approximation under moment conditions on the number of descendants of a single individual in one time step. Applications to evolutionary game theory in finite populations are presented.