The Stability of an Equilibrium and the Average Fitness of a Population

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Abstract
For a Mendelian population in which each genotype has a fixed selective value, there may exist equilibrium values of the gene frequencies other than complete homozygosis. It was shown that the average fitness (W) of a population determines the number, nature, as well as location, of the nontrivial equilibriums. Every maximum point in the W curve (or surface) corresponds to a stable equilibrium value of gene frequency (q) and every minimum point of W corresponds to an unstable equilibrium value. Several models of selection scheme have been examined and illustrated. The cases in which there is inbreeding or the genotypic selective values vary with gene frequencies have also been discussed.