The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.