Recombination, selection, and the evolution of tandem gene arrays

Multi-gene families – immunity genes or sensory receptors, for instance – are often subject to diversifying selection. Allelic diversity may be favoured not only through balancing or frequency dependent selection at individual loci, but also by associating different alleles in multi copy gene families. Using a combination of analytical calculations and simulations, we explored a population genetic model of epistatic selection and unequal recombination, where a trade-off exists between the benefit of allelic diversity and the cost of copy abundance. Starting from the neutral case, where we showed that gene copy number is Gamma-distributed at equilibrium, we derived also mean and shape of the limiting distribution under selection. Considering a more general model which includes variable population size and population substructure, we explored by simulations mean fitness and some summary statistics of the copy number distribution. We determined the relative effects of selection, recombination and demographic parameters in maintaining allelic diversity and shaping mean fitness of a population. One way to control the variance of copy number is by lowering the rate of unequal recombination. Indeed, when encoding recombination by a rate modifier locus, we observe exactly this prediction. Finally, we analyzed the empirical copy number distribution of three genes in human and estimated recombination and selection parameters of our model.