An approximate sampling formula under genetic hitchhiking

Details An approximate sampling formula under genetic hitchhiking An approximate sampling formula under genetic hitchhiking

2005-03-23

arxiv.org/abs/math/0503485v3

Annals of Applied Probability 2006, Vol. 16, No. 2, 685-729

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000114 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000114

For a genetic locus carrying a strongly beneficial allele which has just fixed in a large population, we study the ancestry at a linked neutral locus. During this ``selective sweep'' the linkage between the two loci is broken up by recombination and the ancestry at the neutral locus is modeled by a structured coalescent in a random background. For large selection coefficients $\alpha$ and under an appropriate scaling of the recombination rate, we derive a sampling formula with an order of accuracy of $\mathcal{O}((\log \alpha)^{-2})$ in probability. In particular we see that, with this order of accuracy, in a sample of fixed size there are at most two nonsingleton families of individuals which are identical by descent at the neutral locus from the beginning of the sweep. This refines a formula going back to the work of Maynard Smith and Haigh, and complements recent work of Schweinsberg and Durrett on selective sweeps in the Moran model.

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