Published online by Cambridge University Press: 14 April 2009
The necessary and sufficient conditions for the stability of the equilibrium point with no linkage disequilibrium are obtained for the three locus model with multiplicative fitnesses. It is shown that there are six inequalities that must be satisfied in order for this equilibrium to be stable. Three of the inequalities require that there be heterozygotic superiority at all loci. The other three are exactly those inequalities which are required for each pair of loci to be stable with linkage equilibrium if they are considered to be an isolated two locus system. Thus, all the information needed to determine the stability of this equilibrium with three loci is contained in one and two locus theory.