The evolutionary significance of sexual selection.

A model for the joint evolution of a secondary sexual male trait Z and a female mating preference Y is discussed. Recurrence relations for the moments of (Z, Y) are given under the assumption that the traits are binormally distributed. It is shown that female preference for a male character can lead to an equilibrium distribution of the male trait with non-zero variances. The conditions under which the distribution is stable, are given. Unstable situations, in which a continued exaggeration of the male trait occurs, are described. It is demonstrated that the effect of sexual selection on the evolution of the male trait depends on the intensity of natural selection, i.e. the effect of the sexual selection increases when the intensity of natural selection is reduced. The effect of the female preference on the male trait also increases with increasing availability of males. This provides a link to several ecological conditions which have generally been known to be correlated with the degree of sexual selection. Furthermore, it is demonstrated that perturbations away from the equilibrium may cause rapid evolution of the male character, eventually leading to speciation.