Two locus models of selection and mutation within and among full-sib lines

Summary General models for continued full-sib mating with two diallelic autosomal loci taking account of linkage, mutation and selection within and among lines are considered. The problems are first approached by deriving the full probability transition matrix, taking account of linkage, mutation and within-line selection. Exact solutions to the equilibrium system are possible, but the computational effort is prohibitive, and this is exacerbated by the introduction of between-line selection. A second approach is based on decomposing the transition matrix into blocks whose properties suggest approximations that lead to a rapid iterative solution of the equilibrium system. Extensive numerical analysis of models of within-line selection and of combined within- and between-line selection were made. The results show that equilibrium values are essentially independent of the degree of linkage under models of within-line selection. This is because mutation plays a dominant role in determining equilibrium structure. Results from models of combined within- and between-line selection show that between-line selection has the dominant influence on gene frequency equilibrium. Both within-line and between-line selection produce appreciable linkage disequilibrium only when selection is disruptive. The results also suggest that much of the twolocus equilibrium structure can be predicted from a knowledge of single-locus equilibria.