Discrete polymorphisms due to disruptive selection on a continuous trait--I: the one-locus case

We have investigated, numerically and analytically, long-term evolution under frequency-dependent disruptive selection of a continuous trait varying in a finite range and controlled by one diploid mendelian locus. We found that evolution converges towards a unique long-term equilibrium where only two extreme phenotypes are present with frequencies identical to those of the mixed strategy that would be the unique ESS of the game defined by the basic fitness function of the model. As long as this precise phenotypic composition is preserved, any genetic configuration of the polymorphism is equally acceptable (selectively neutral) at the equilibrium. Thus the number of alleles and their dominance pattern may vary considerably among different equilibrium populations. If genetic expression of the trait is variable but the amount of variability is genetically modifiable, disruptive selection, acting on such modifiers, produces a steady increase of expression variability before the equilibrium is attained. In this case a population at the long-term equilibrium might even be genetically monomorphic, with the phenotypic dimorphism resulting from purely random individual variation.