Some additional results about polymorphisms in models of an additive quantitative trait under stabilizing selection

The existence of two stable? symmetric (allelic frequency 0.5 in each locus) polymorphic states is demonstrated for a two-locus model of an additive quantitative trait under strong Gaussian selection. Linkage disequilibrium at one of the states is negative whereas it is positive at the other state. For a three-locus model, it is shown that in order to maintain a stable polymorphism in all three loci, selection must be sufficiently but not excessively strong relative to recombination. Also, positive linkage disequilibrium can be maintained in a three-locus model under stabilizing selection that is not very strong.