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May 2006 An approximate sampling formula under genetic hitchhiking
Alison Etheridge, Peter Pfaffelhuber, Anton Wakolbinger
Ann. Appl. Probab. 16(2): 685-729 (May 2006). DOI: 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 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.


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Alison Etheridge. Peter Pfaffelhuber. Anton Wakolbinger. "An approximate sampling formula under genetic hitchhiking." Ann. Appl. Probab. 16 (2) 685 - 729, May 2006.


Published: May 2006
First available in Project Euclid: 29 June 2006

zbMATH: 1115.92044
MathSciNet: MR2244430
Digital Object Identifier: 10.1214/105051606000000114

Primary: 92D15
Secondary: 60J80, 60J85, 60K37, 92D10

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.16 • No. 2 • May 2006
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