Cannings模型中的Halfton公式：中等强选择的情况
Haldane's formula in Cannings models: The case of moderately strong selection
摘要：
对于一类Cannings模型，我们证明了Haldinger的公式，$π(s_N) \sim \frac{2s_N}{ρ^2}$，为固定概率的一个单一的有益的突变体在限制大总体规模$N$和制度的适度强选择，即$s_N \sim N^{-b}$和$0< b<1/2$。这里，$s_N$是携带有益类型的个体的选择优势，而$ρ^2$是（渐近）后代方差。我们的假设上的复制机制允许耦合的有益等位基因的频率过程与轻微的超临界Galton-Watson过程中的早期阶段的固定。
英文摘要：
For a class of Cannings models we prove Haldane's formula, $π(s_N) \sim \frac{2s_N}{ρ^2}$, for the fixation probability of a single beneficial mutant in the limit of large population size $N$ and in the regime of moderately strong selection, i.e. for $s_N \sim N^{-b}$ and $0< b<1/2$. Here, $s_N$ is the selective advantage of an individual carrying the beneficial type, and $ρ^2$ is the (asymptotic) offspring variance. Our assumptions on the reproduction mechanism allow for a coupling of the beneficial allele's frequency process with slightly supercritical Galton-Watson processes in the early phase of fixation.
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