Journal of Mathematical Biology

, Volume 64, Issue 1–2, pp 291–317 | Cite as

The effect of recurrent mutation on the linkage disequilibrium under a selective sweep



A selective sweep describes the reduction of diversity due to strong positive selection. If the mutation rate to a selectively beneficial allele is sufficiently high, Pennings and Hermisson (Mol Biol Evol 23(5):1076–1084, 2006a) have shown, that it becomes likely, that a selective sweep is caused by several individuals. Such an event is called a soft sweep and the complementary event of a single origin of the beneficial allele, the classical case, a hard sweep. We give analytical expressions for the linkage disequilibrium (LD) between two neutral loci linked to the selected locus, depending on the recurrent mutation to the beneficial allele, measured by D and \({\widehat{\sigma_D^2}}\), a quantity introduced by Ohta and Kimura (Genetics 63(1):229–238, 1969), and conclude that the LD-pattern of a soft sweep differs substantially from that of a hard sweep due to haplotype structure. The analytical results are compared with simulations.


Star-like approximation Genealogy Strong positive selection Haplotype structure 

Mathematics Subject Classification (2000)

92D15 60J80 60J85 


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Supplementary material

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Albert-Ludwigs-University FreiburgEckerstraße 1FreiburgGermany

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