On Richerson and Boydʹs Model of Cultural Evolution by Sexual Selection

Richerson and Boyd proposed a model of sexual selection in which both the male trait and the female preference are culturally transmitted. We generalize their model by introducing sex-dependent oblique transmission rates and a fairly comprehensive female preference rule. The model differs markedly from the standard genetic models in that the male trait and the female preference are uncorrelated. Hence, there can be no “sexy son” effect to offset the assumed fertility cost to choosy females. Nevertheless, the cultural processes can support a stable polymorphic equilibrium at which the choosy females are present. Also of interest are the cyclical dynamics observed in the neighborhood of the internal equilibrium.