Linkage and selection: new equilibrium properties of the two-locus symmetric viability model

Abstract

In the two-locus symmetric viability model with recombination, conditions for the existence and stability of a new class of polymorphic equilibria are given. These "unsymmetric" equilibria, which exist for relatively loose linkage, can be explicitly obtained, in contrast to the previously known symmetric equilibria which are generally given by the solutions of a cubic equation. For sufficiently tight linkage, there is always at least one stable symmetric equilibrium. Seven is the precise maximum for the number of interior equilibria. The qualitative consequences of these results are briefly examined. In particular it is pointed out that since for some linkage values no stable polymorphic equilibria exist, there is no "overdominance theorem" comparable to the single-locus case.