Runaway sexual selection with paternal transmission of the male trait and gene-culture determination of the female preference

Sexual selection is modeled with a male viability-reducing trait and a female mating preference for that trait both of which are culturally transmitted. Both the male trait and the female preference are transmitted only between same-sex individuals, so that non-random association between the trait and the preference, which would give rise to a Fisherian runaway process, cannot arise. Inclusion of an autosomal gene that confers a female predisposition to acquire a certain preference is shown to allow the coevolution of the male trait and the female preference by a Fisherian process. This holds true even when the female preference has a slight viability cost, provided the male cultural transmission is not perfect. It is also suggested that a Fisherian process can be more easily initiated in these models than in the conventional genetic models. Furthermore, a Fisherian process may cause cultural transmission of female preference to evolve. Additionally, polymorphism can be maintained at the predisposition locus if heterozygous females have a stronger predisposition to acquire the preference than homozygotes. Our models may be applicable to the case when the male trait is a Y-linked genetic or environmentally determined trait.