A Diploid "Sexy Son" Model

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Abstract
The "sexy son" hypothesis proposes that female mating preferences have evolved in such a way that in a polygynous mating system some females preferentially mate with males having high attractiveness and low fertility. Kirkpatrick''s (1985) analyses of haploid and additive polygenic models have discredited the sexy-son hypothesis, suggesting that neither the genetic disposition to become a sexy male nor the tendency to mate with them will normally increase under selection (except in a "runaway" process). Analysis of haploid models has also led to the claim that polymorphism of sexually selected traits and female mating preferences cannot be maintained at equilibrium. Here, we present results of a diploid sexy-son model, demonstrating by counterexample that generalizations from haploid and additive polygenic models are not valid. The diploid model allows trade-offs between fertility and sexual selection, stable polymorphisms for both male traits and female mating preferences, and increase of sexy males from low initial frequencies. The maximization principles derived from other models can be violated in the diploid case. The general problem of model sensitivity to ploidy and other genetic assumptions is discussed.