The Annals of Applied Probability

An approximate sampling formula under genetic hitchhiking

Alison Etheridge, Peter Pfaffelhuber, and Anton Wakolbinger

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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

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

First available in Project Euclid: 29 June 2006

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Zentralblatt MATH identifier

Primary: 92D15: Problems related to evolution
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes [See also 92Dxx] 60K37: Processes in random environments 92D10: Genetics {For genetic algebras, see 17D92}

Selective sweeps genetic hitchhiking approximate sampling formula random ancestral partition diffusion approximation structured coalescent Yule processes random background


Etheridge, Alison; Pfaffelhuber, Peter; Wakolbinger, Anton. An approximate sampling formula under genetic hitchhiking. The Annals of Applied Probability 16 (2006), no. 2, 685--729. doi:10.1214/105051606000000114.

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