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 choice of 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 and thus ultimately diminish strong preferences. In fact, sexual traits often have higher genetic variation than non-sexual traits. The puzzle presented by this pattern, and, relatedly, how costly preferences and display traits are maintained, is known as the “lek paradox”. Using infinitesimal models, we show that, contrary to prior suppositions, sexual selection through mate choice may exaggerate genetic variance in male display traits and female preferences, provided that the variance of female preferences relative to the male trait at the stage of mate choice is not too small and preferences are not too weak. In fact, even if preference variation is substantially smaller than trait variation, trait variation can still increase over the case of random mating, as long as selection on the trait is sufficiently strong compared to that on preferences. When trait variation does decrease, we find this reduction to be generally slight. It is under situations such as lekking, in which females can simultaneously choose from many males so that mate discrimination tends to be effectively strong and the cost of choice weak, that sexual selection through mate choice should be expected to be the most powerful in exaggerating genetic variance in male displays.