A.M. Etheridge, P. Pfaffelhuber, A. Wakolbinger
An Approximate Sampling Formula Under Genetic Hitchhiking
Preprint series: ESI preprints

MSC:

92D15 Problems related to evolution

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

60J85 Applications of branching processes, See also {92Dxx}

60K99 None of the above but in this section

92D10 Genetics, {For genetic algebras, See 17D92}

Abstract: 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 modelled 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 non-singleton 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.

Keywords: Selective sweeps, genetic hitchhiking, approximate sampling formula, random ancestral partition, diffusion approximation, structured coalescent, Yule processes, random background
Notes: second and final version