An approximate sampling formula under genetic hitchhiking

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 $O((\log\alpha)^{-2})$ 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 identi cal 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 co mplements recent work of Schweinsberg and Durrett on selective sweeps in the Moran model.