Evolution of sexual preferences in quantitative characters.

An analysis of equilibria and dynamics of the means, variances, and covariances of female mating preference for a quantitative male secondary sexual character following a Gaussian model is presented. For many combinations of viability and sexual selection parameters the evolving Gaussian distribution of phenotypes can diverge. The results on the cases of convergence and their limiting forms suggest some reinterpretations of Fisher's "runaway" process of sexual selection. One possibility is to interpret Fisher's postulated "initial advantage not due to female preference" as a shift in viability selection where runaway evolution occurs if the mean preferred trait evolves beyond its new viability optimum (due to sexual selection). This definition is contrasted with situations in which the new viability optimum is undershot. The quantitative and qualitative conclusions differ from models that approximate genetic covariance evolution involving a constant covariance.