Biased intrachromosomal gene conversion in a chromosome lineage

A model for the evolution of a family of tandemly repeated genes in a single chromosome lineage under intrachromosomal gene conversion [43] is analyzed further and extended. Direct and diffusion approximations are derived for the exact fixation probabilities, mean time to fixation or loss, and mean conditional fixation time of Nagylaki and Petes [43]. The distribution of the number of variant repeats under the joint action of gene conversion and reversible mutation is investigated; exact and approximate expressions are derived for the stationary distribution. It is shown that conversional bias greatly increases the amount of sequence homogeneity at equilibrium. The diffusion processes studied here also apply to selection and mutation in a finite population, and some new results are established for that classical problem.