## The Annals of Applied Probability

### An approximate sampling formula under genetic hitchhiking

#### 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 modeled by a structured coalescent in a random background. For large selection coefficients α 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.

#### Article information

Source
Ann. Appl. Probab., Volume 16, Number 2 (2006), 685-729.

Dates
First available in Project Euclid: 29 June 2006

https://projecteuclid.org/euclid.aoap/1151592248

Digital Object Identifier
doi:10.1214/105051606000000114

Mathematical Reviews number (MathSciNet)
MR2244430

Zentralblatt MATH identifier
1115.92044

#### Citation

Etheridge, Alison; Pfaffelhuber, Peter; Wakolbinger, Anton. An approximate sampling formula under genetic hitchhiking. Ann. Appl. Probab. 16 (2006), no. 2, 685--729. doi:10.1214/105051606000000114. https://projecteuclid.org/euclid.aoap/1151592248

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