A general model for two-locus assortative mating analysis and prediction

The analytical framework to investigate the effect of assortative mating for phenotypes that are determined by two loci is over a hundred years old and well established by Jennings, Wentworth, Remick, Robbins, and Wright. However, some known aspects of assortative mating have not received a concise analytical analysis or clear expression. Chief among these are linkage disequilibrium and identity disequilibrium but also the change in heterozygosity outside of the simple case of PA = PB = 1/2. In order to understand the effects of assortative mating in more detail, a general model is proposed that uses recursive difference equations rather than simulation to solve most assortative mating problems. Using this, we will expand the cases for which an exact or approximate expression for population genetic variables can be determined. In particular, the first closed form expressions for linkage disequilibrium and identity disequilibrium for two-locus assortative mating are given. We also show that assortative mating does not generate linkage disequilibrium when the loci are completely linked. Finally, this model will be used to investigate two possible cases of two-locus assortative mating in human populations regarding variants for non-syndromic deafness and the variants that largely determine blue eye color.