Multi-locus ESS Models: Non-additive Effects

Hines and Turelli showed that under the extremely severe assumption that all genetic effects are purely additive, the conventional ESS methodology was relevant to multi-locus models. This note explores the degree to which that assumption can be relaxed, for a two-locus two-allele model for the Hawke Dove contest. If all genotypes are always 100% viable, the ESS formulation proves to be relevant in the considerable majority of cases. This relevance drops if viabilities differ, doing so more if differing viabilities are fixed from generation to generation than if they vary randomly with each generation. An alternative form of stable equilibrium is found in which the influences of recombination and of linkage disequilibrium are important. gree to which various genetic effects are present is explored using a standard statistical tool, the Q–Q plot. This plot shows a tendency for comparatively large dominance effects to be present in the no-allele-loss/no-ESS-convergence case.