Effect of assortative mating on genetic change due to selection

Two mathematical models (A and B) were used to study joint effects of selection and assortative mating on genetic change. Computer simulation was used to verify and extend the results. In each model, the genotype was additive with equal effects at each of N loci and the environmental distribution was N(0, σ(2)). In Model A, each locus had two alleles; in Model B, allelic effects at each locus followed a normal distribution. Using Model A, genetic change with assortative or random mating of selected parents was evaluated for combinations of number of loci (N = 1, 2, 3), heritability in base population (H([0]) = 0.2, 0.5, 0.8), allelic frequency in base population (p = 0.1, 0.5), and proportion selected (α = 0.20, 0.85). Using Model B, genetic change with or without assortative mating was calculated for combinations of N (1, 2, 3, 5, 10, 100, H([0]) (0.2, 0.5, 0.8) and α (0.20, 0.85). Response to selection under both mating systems in a finite population was estimated using Model A from 200 replications of a computer simulation; this was done for all combinations of N (1,2, 3, 5, 10) and α(0.20, 0.85), with H([0]) = 0.5 and p = 0.1. Results obtained with both models indicate that the effect of assortative mating on genetic change increases with H([0]) and α, and decreases with p. With Model A, the relationship between N and the effect of assortative mating on genetic change was not clear; with Model B, however, the advantage of assortative over random mating increased with N, as expected. Simulation results were in agreement with theory of Model A. This study indicates that selection with assortative mating can have a sizable (10 to 20%) long-term advantage over selection with random mating of parents when H([0]) is high, p is low and α is large.