On the number of segregating sites in genetical models without recombination

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Abstract

The distribution is obtained for the number of segregating sites observed in a sample from a population which is subject to recurring, new, mutations but not subject to recombination. After allowance is made for the different effective population sizes, the results apply approximately to three population models, due to Wright, Burrows and Cockerham, and Moran. Included as extreme special cases are the distributions of the number of segregating sites in the whole population and of the number of heterozygous sites in a diploid individual. Some results of Fisher, Haldane, Kimura, and Ewens concerning the means of the distributions for different models are confirmed, but the variances, and the distributions themselves, are new.

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