Preferential mating in symmetric multilocus systems: stability conditions of the central equilibrium

Several multilocus models that incorporate both preferential mating and viability selection are studied. Specifically, a class of symmetric heterozygosity models are considered that assign individuals to phenotypic classes according to which loci are in heterozygous state regardless of the actual allelic content. Otherwise, an arbitrary number of loci, number of alleles per locus, and arbitrary recombination scheme, viability parameters and preferential mating pattern based on phenotypes are allowed. The conditions for the stability of a central polymorphism are indicated and interpreted. The effects of viability and preference selection may be summarized in a single quantity for each phenotypic class, a generalized fitness. Preferential assortative mating alone can produce stability for a central polymorphism as in the case of viability selection when sexual attractiveness or general fitness increases with higher levels of heterozygosity. The situation is more complex with sexual selection.