For a panmictic population of constant size evolving under neutrality, Kingman's coalescent describes the genealogy of a population sample in equilibrium. However, for genealogical trees under selection, not even expectations for most basic quantities like height and length of the resulting random tree are known. Here, we give an analytic expression for the distribution of the total tree length of a sample of size n under low levels of selection in a two-alleles model. We can prove that trees are shorter than under neutrality under genic selection and if the beneficial mutant has dominance h<1∕2, but longer for h>1∕2. The difference from neutrality is O(α2) for genic selection with selection intensity α and O(α) for other modes of dominance.

中文翻译：

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选择水平较低时的家谱距离。

对于在中性条件下不断发展的恒定规模的恐慌种群，金曼的联合描述了处于平衡状态的种群样本的家谱。但是，对于正在选择的家谱树，甚至对于大多数基本数量（如生成的随机树的高度和长度）的期望都未知。在这里，我们给出了在两个等位基因模型中低选择水平下大小为n的样本的总树长分布的解析表达式。我们可以证明，在基因选择下，如果有益突变体的优势度为h <1∕2，则树木比中性条件下短，而对于h> 1∕2，则更长。对于基因选择，与中立性的差异为O（α2），对于其他主导模式，选择强度为O（α）。