Excursions Along the Interface Between Disruptive and Stabilizing Selection

When a polygenic character is exposed to natural selection in which the curve giving fitness as a function of phenotype is a mixture of two Gaussian (normal) curves, the population may respond either by evolving to a specialized phenotype near one of the two optimum phenotypes, or by evolving to a generalized phenotype between them. Using approximate multivariate normal distribution methods, it is demonstrated that the condition for selection to result in a specialized phenotype is that the curve of fitness as a function of breeding value be bimodal. This implies that a specialized phenotype is more likely to result the higher is the heritability of the character. Numerical iterations of four-locus models and algebraic analysis of a symmetric two-locus model generally support the conclusions of the normal approximation.