When sexual selection through mate choice depletes versus exaggerates genetic variation: Unraveling the 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 preferences. However, sexual traits often have higher genetic variation than nonsexual traits. This contradiction, and, relatedly, how costly preferences and display traits are maintained, is called the "lek paradox." Using infinitesimal models and individual-based simulations, we show that variation in male traits and female preferences often mutually exaggerate each other under sexual selection, 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 preference variance is not too small relative to trait variance. Increases in trait variance are more likely under directional than stabilizing preferences, but also occur under stabilizing preferences if preferences are not too weak. When mate choice does reduce trait variation, the effect is generally slight provided loci are highly polymorphic under random mating. However, when loci are already near fixation under random mating, increases or decreases in trait variance by mate choice become more pronounced due to changes in segregation variance. It is under situations such as lekking, where mate discrimination is effectively strong with weak fitness costs, that sexual selection may be most powerful in exaggerating male display variance.