Honesty, perception and population divergence in sexually selected traits

We investigate the evolution of female preference for one and two male ornaments, to address two issues in sexual selection: (i) what factors affect the evolution of female preferences; and (ii) how do preferences diverge between isolated populations, leading to speciation? We assume that the male traits are costly indicators of male condition (`handicaps'), and that females benefit directly from a high-condition mate. We find that optimal female preference for a single male trait equals (benefit of condition) $\times $ (detectability of male trait) $\times $ (honesty of male trait)/(costliness of preference). With two male traits to choose from, females should prefer the one with greatest honesty $\times $ detectability, and ignore the second. These results highlight the role of perception in the evolution of both male ornaments and female preferences, and provide a theoretical illustration of `sensory drive'. They confirm that a less honest male trait can displace a more honest trait if its detectability is sufficiently high. Environmental differences can drive evolutionary divergence between populations in both the male trait and female preference. Even small differences between habitats in detectability of male traits can trigger dramatic change in the female preference. Finally, populations may drift apart in arbitrary directions if choice of different male traits yields equivalent benefits to females.