Quantitative Variability and Multilocus Polymorphism Under Epistatic Selection

We study multilocus polymorphism under selection, using a class of fitness functions that account for additive, dominant, and pairwise additive-by-additive epistatic interactions. The dynamic equations are derived in terms of allele frequencies and disequilibria, using the notions of marginal systems and marginal fitnesses, without any approximations. Stationary values of allele frequencies and pairwise disequilibria under weak selection are calculated by regular perturbation techniques. We derive conditions for existence and stability of the multilocus polymorphic states. Using these results, we then analyze a number of models describing stabilizing selection on additive characters, with some other factors, and determine the conditions under which genetic quantitative variability is maintained.