Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4502930 | Theoretical Population Biology | 2007 | 8 Pages |
Abstract
Let ZnZn denote the length of an external branch, chosen at random from a Kingman n -coalescent. Based on a recursion for the distribution of ZnZn, we show that nZnnZn converges in distribution, as n tends to infinity, to a non-negative random variable Z with density x↦8/(2+x)3x↦8/(2+x)3, x⩾0x⩾0.This result facilitates the study of the time to the most recent common ancestor of a randomly chosen individual and its closest relative in a given population. This time span also reflects the maximum relatedness between a single individual and the rest of the population. Therefore, it measures the uniqueness of a random individual, a central characteristic of the genetic diversity of a population.
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Authors
Amke Caliebe, Ralph Neininger, Michael Krawczak, Uwe Rösler,