Runaway sexual selection when female preferences are directly selected

We introduce models for the runaway coevolution of female mating preferences and male display traits. The models generalize earlier results by allowing for direct natural selection on the preference, arbitrary forms of mate choice, and fairly general assumptions about the underlying genetics. Results show that a runaway is less likely when there is direct selection on the preference, but that it is still possible if there is a sufficiently large phenotypic correlation between the female's preference and the male's trait among mated pairs. Comparison of three preference functions introduced by Lande (1981) shows that open-ended preferences are particularly prone to a runaway, and that absolute preferences require very large differences between females in their preferences. We analyze the causes of the runaway seen in a model developed by Iwasa and Pomiankowski (1995).