On the divergence of genes in multigene families

Abstract

Statistical properties of the amount of divergence of genes in multigene families are studied. The model considered is an infinite-site neutral model with unbiased intrachromosomal conversation, unbiased interchromosomal conversion, and recombination. By considering the time back to the most recent common ancestor of two genes, both the probability of identity and the moments of S, the number of sites that differ between two sampled genes, are obtained. We find that (a) if recombination rates are large or conversion is always interchromosomal, then the expectation of S is 4Nµn where N is the population size, µ is the rate of mutation per generation per gene and n is the number of genes in the gene family, (b) as the conversion rates approach zero, the moments of divergence do not approach the moments of divergence with conversion rates equal to zero, and (c) it is possible for a decrease in the rate of intrachromosomal conversion to result in a higher probability of identity, but a greater mean divergence of the two genes.