On the evolution of dominance, over-dominance and balanced polymorphism

Abstract

Recurrence relations are derived for the natural selection of a selective coefficient that is subject to additive genetic variations. Mathematical models are set up of the natural selection of the selective coefficient of the heterozygote. A general computer model of genetical populations is described and populations are set up to simulate genetic variation of the heterozygote. The theoretical models are applied to the spread of a gene under natural selection. If the heterozygote is initially intermediate between the 2 homozygotes, the evolution of semi-dominance, dominance or over-dominance depends on the genetic variance in fitness. Over-dominance evolves if the standard deviation in fitness due to genetic causes is about 0.7 times the difference between the initial heterozygote and homozygote fitnesses. The heterozygote will then continue to increase in fitness until the characters that determine the fitness are at their optimum values. Thus the polymorphism tends to become more stable. The fitness of the heterozygote of a recurrent mutation will also be raised by natural selection. Dominance still evolves though it takes many thousands of generations. Eventually over-dominance, too, evolves and a balanced polymorphism is thus established. This will explain many polymorphisms, like the sickle cell trait in man, which have a highly deleterious homozygote. Selection slowly raises the fitness of the heterozygote to an optimum above that of the wild-type.