  Genetic hitchhiking describes evolution at a neutral locus that is linked to
a selected locus. If a beneficial allele rises to fixation at the selected
locus, a characteristic polymorphism pattern (so-called selective sweep)
emerges at the neutral locus. The classical model assumes that fixation of the
beneficial allele occurs from a single copy of this allele that arises by
mutation. However, recent theory (Pennings and Hermisson, 2006a; Pennings and
Hermisson, 2006b) has shown that recurrent beneficial mutation at biologically
realistic rates can lead to markedly different polymorphism patterns, so called
soft selective sweeps. We extend an approach that has recently been developed
for the classical hitchhiking model (Schweinsbergand Durrett, 2005; Etheridge,
Pfaffelhuber, Wakolbinger, 2006) to study the recurrent mutation scenario. We
show that the genealogy at the neutral locus can be approximated (to leading
orders in the selection strength) by a marked Yule process with immigration.
Using this formalism, we derive an improved analytical approximation for the
expected heterozygosity at the neutral locus at the time of fixation of the
beneficial allele.

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