Multiple Equilibria and Maintenance of Additive Genetic Variance in a Model of Pleiotropy

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Abstract
We describe a multilocus model that incorporates pleiotropic stabilizing selection on a large number of characters. We find many different stable equilibria with different levels of polymorphism and additive genetic variability. The results lend support to Wright's concept of a complex adaptive surface with many peaks of different heights. The model assumes that alleles contribute additively to the characters. We analyze the multilocus model by first considering a two-locus model. The two-locus model depends critically on having loci of different effect and on having the optimum phenotype not be that of a completely heterozygous individual. The effects of different loci need to differ only by less than a factor of two. For the multilocus, multicharacter model, we assume that completely heterozygous individuals do not have the optimum phenotype. By restricting attention to a two-allele model, we also assume that there are no alleles that can affect all characters in all possible combinations of directions.

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