Quantitative genetic models of female choice based on “arbitrary” male characters

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Abstract
Multivariate, quantitative genetic models are developed for the evolution of female mating preferences in situations where males contribute only their gametes to their progeny. Although female mating preferences may not be directly subject to selection, they can evolve via genetic correlations with other characters that are undergoing evolutionary change. The first set of models examines the evolutionary origin of mating preferences directed at one or more traits that may or may not be expressed only in males. When several selected characters possess additive genetic variance, an indirect selective force exists for the evolution of multivariate mating preferences. The magnitude of this force is proportional to the covariance between a female's relative preference for a given male's phenotype and the expected viability of his progeny. The contribution of any single character to this covariance determines its potential value as a mate choice criterion. The pattern of genetic and phenotypic covariation may cause selectively unimportant traits to be useful in mate choice. In the extreme, selectively neutral characters may become the objects of mating preferences, if they are relatively immune to random environmental variation and genetically correlated with selectively important characters. The second set of models examines the dynamic evolution of such a selectively neutral ("arbitrary") character that is both the object of a mating preference and genetically correlated with a third trait that affects viability. The outcome of evolution in this three character system is highly indeterminate. As in other sexual selection models, there exists a line of neutral equilibria wherein the mean of the criterion character matches the mean level of mating preference within the population, while the viability trait equilibrates at the phenotypic value conferring maximum viability. This line of equilibria, however, is not likely to be stable unless females choose mates according to absolute mating preferences. Thus, mating preferences that initially may arise as a mean of increasing offspring viability may nevertheless lead to indeterminate and potentially maladaptive evolutionary outcomes.