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.
Publié le : 2006-05-14
Classification:
Selective sweeps,
genetic hitchhiking,
approximate sampling formula,
random ancestral partition,
diffusion approximation,
structured coalescent,
Yule processes,
random background,
92D15,
60J80,
60J85,
60K37,
92D10
@article{1151592248,
author = {Etheridge, Alison and Pfaffelhuber, Peter and Wakolbinger, Anton},
title = {An approximate sampling formula under genetic hitchhiking},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 685-729},
language = {en},
url = {http://dml.mathdoc.fr/item/1151592248}
}
Etheridge, Alison; Pfaffelhuber, Peter; Wakolbinger, Anton. An approximate sampling formula under genetic hitchhiking. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 685-729. http://gdmltest.u-ga.fr/item/1151592248/