When does sexual selection through mate choice deplete versus exaggerate genetic variation: is there a lek paradox?

The evolution of female preferences for male display traits relies on females receiving indirect benefits from their mate. This requires substantial genetic variation in display traits or male quality. Nevertheless, sexual selection through mate choice has been assumed to deplete this genetic variation, ultimately diminishing strong preferences. However, sexual traits often have higher genetic variation than non-sexual traits. This contradiction, and, relatedly, how costly preferences and display traits are maintained, is called the “lek paradox”. Using infinitesimal models, we show that sexual selection through mate choice allows variation in male display traits and female preferences to mutually exaggerate each other, in a process analogous to runaway sexual selection but in terms of genetic variation. Therefore, contrary to prior suppositions, sexual selection may increase equilibrium genetic variance in display traits and preferences over that under random mating, provided that the variance of female preferences relative to male traits during mate choice is not too small and preferences are not too weak. Notably, even if equilibrium preference variation is substantially smaller than trait variation, trait variation can still increase over that under random mating, provided selection on the trait compared to the preference is sufficiently strong. Furthermore, when trait variation does decrease, this reduction is generally slight. It is under situations such as lekking, where females can simultaneously choose from many males so that mate discrimination is effectively strong and fitness costs of choice weak, that sexual selection through mate choice may be most powerful in exaggerating genetic variance in male displays.