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A selective sweep describes the reduction of diversity due to strong positiveselection. If the mutation rate to a selectively beneficial allele issufficiently high, Pennings and Hermisson (2006a) have shown, that it becomeslikely, that a selective sweep is caused by several individuals. Such an eventis called a soft sweep and the complementary event of a single origin of thebeneficial allele, the classical case, a hard sweep. We give analyticalexpressions for the linkage disequilibrium (LD) between two neutral loci linkedto the selected locus, depending on the recurrent mutation to the beneficialallele, measured by $D$ and $\hat{\sigma_D^2}$, a quantity introduced by Ohtaand Kimura (1969), and conclude that the LD-pattern of a soft sweep differssubstantially from that of a hard sweep due to haplotype structure. We compareour results with simulations.

The Effect of Recurrent Mutation on the Linkage Disequilibrium under a Selective Sweep