Asymptotic sampling formulae for -coalescents
Asymptotic sampling formulae for -coalescents
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发表时间：
2012
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通讯作者：
J. Berestycki;V. Limic
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作者：
J. Berestycki;V. Limic
我们提出了一种稳健的方法，它将关于从谱系树的无穷大下降的速度的信息转化为潜在总体的抽样公式。我们将这些结果应用到种群动力学中，其中家谱由�合并者给出。这使我们能够推导出当样本量趋于∞时，位置和等位基因频谱的渐近行为以及分离位置的数量的精确公式。我们的一些结果适用于从无穷远处下来的一般�-聚合体的情况，但我们在正则变化假设下获得了更精确的信息。在这种情况下，我们得到了关于随机选择的突变产生的时间的独立感兴趣的结果。这在α=3/2时表现出相变，其中α∈(1，2)是规则变化的指数。AMS 2000科目分类。60J25、60F99、92D25
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a �coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to ∞. Some of our results hold in the case of a general �-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at α = 3/2, where α ∈ (1,2) is the exponent of regular variation. AMS 2000 Subject Classification. 60J25, 60F99, 92D25