THE EFFECT OF SOFT SELECTION ON THE VARIABILITY OF A QUANTITATIVE TRAIT

The equilibrium phenotypic variance (σ^2) of a normally distributed quantitative character P under soft selection is studied. This character is assumed to undergo Gaussian stabilizing selection W(p, x) = exp[-(p - x)² /2w² ]. The environmentally determined optimum (x) is a normal variable with variance s² . A stable equilibrium with σ^2=S2-w2 is found, so that σ^2 increases both with increasing environmental heterogeneity and with increasing local intensity of stabilizing selection. It is shown that both genetic and environmental components of the variance are selected until this equilibrium is reached. Habitat selection, supposed to be normal (with variance H² ) around the optimum, also increases the σ^2 value. Nevertheless, relatively intense local stabilizing selection (w < s) and accurate habitat choice (H < s) are required for the initial spread and the evolutionary stability of this habitat selection.