Evolution of a large population under gene conversion

The dynamics of allelic frequencies at a single multiallelic locus under gene conversion is studied. Generations are discrete and nonoverlapping; the diploid monoecious population mates at random; selection, mutation, and random drift are negligible. Analytical and numerical investigation indicates the following. (i) If gene conversion is biased within at least one pair of alleles, then the frequency of at least one allele must become arbitrarily small. (ii) If conversion is biased within every pair of alleles, then the frequency of at most one allele can fail to become arbitrarily small. Although allelic frequencies may become repeatedly small instead of remaining small, the biological ubiquity of small random perturbations (due, e.g., to random genetic drift) guarantees the ultimate loss of at least one allele in case i and of all alleles but one in case ii. The decay of genetic variability is often sufficiently rapid to imply that biased gene conversion can be an important mechanism for the genetic divergence of isolated populations.