Structural instability of models of sexual selection

Models for sexual selection by the coevolution of female preference and a male trait have as a generic feature the existence of a neutrally stable line of equilibria up and down which the system can drift at random. However, this feature is structurally unstable since it is destroyed by introducing either mutation or weak direct selection on female preference into the model, to be replaced by a single equilibrium (or a finite set of disconnected equilibria). This process is investigated in detail under a simple but general population genetic model. It is concluded that the level of female preference is determined by mutation, selection, and genetic drift acting directly on it, and drags the male trait along with it along the line of equilibria. More attention should be paid to selective forces acting directly on female preference.