Intrachromosomal gene conversion, linkage, and the evolution of multigene families

The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the "homogeneous" approximation to this "exact" model, end effects are disregarded; in the "exchangeable" approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that the exchangeable and homogeneous models are both qualitatively correct, the exchangeable model is sometimes too inaccurate for quantitative conclusions, and the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.