Interaction of selection and biased gene conversion in a multigene family

A model of the evolutionary dynamics of a multigene family in a finite population under the joint effects of selection and (possibly biased) gene conversion is analyzed. It is assumed that the loss or fixation of a polymorphism at any particular locus in the gene family occurs on a much faster time scale than the introduction of new alleles to a monomorphic locus by gene conversion. A general formula for the fixation of a new allele throughout a multigene family for a wide class of selection functions with biased gene conversion is given for this assumption. Analysis for the case of additive selection shows that (i) unless selection is extremely weak or bias is exceptionally strong, selection usually dominates the fixation dynamics, (ii) if selection is very weak, then even a slight conversion bias can greatly alter the fixation probabilities, and (iii) if both selection and conversion bias are sufficiently small, the substitution rate of new alleles throughout a multigene family is approximately the single locus mutation rate, the same result as for neutral alleles at a single-copy gene. Finally, I analyze a fairly general class of underdominant speciation models involving multigene families, concluding for these models under weak conversion that although the probability of fixation may be relatively high, the expected time to fixation is extremely long, so that speciation by "molecular drive" is unlikely. Furthermore, speciation occurs faster by fixing underdominant alleles of the same effect at single-copy genes than by fixing the same number of loci in a single multigene family under the joint effects of selection, conversion, and drift.