On the theory of selection dependent on two loci

Summary A, a are alleles at one locus. Considered on their own, other alleles being fixed, they display heterosis, so that there exist unique stable equilibrium values p, q for their respective gene frequencies. Let B, b be a second pair of heterotic genes at a second locus, with equilibrium frequencies P, &. Consider models in which the fitnesses are multiplicative (or additive), i.e. the fitness of, for example, AaBB is taken to be the product (or sum) of the fitnesses of Aa and BB considered singly. Assume random mating and separate generations, and the population sufficiently large for random fluctuations to be ignored. Then it is shown that if the recombination fraction between the loci does not differ too much from 1/2, and if all four alleles are originally present in the population, then the population does tend (as might be expected) to a stable equilibrium in which the gene frequencies of A, a, B, b are respectively p, q, P, Q. But this may not happen when linkage is close.