Abstract.-A model is used to study quantitatively the impact of a good genes process and direct natural selection on the evolution of a mating preference. The expression of a male display trait is proportional to genetic quality, which is determined by the number of deleterious mutations a male carries throughout his genome. Genetic variances and covariances, including the covariance between the preference and male trait that drives the good genes process, are allowed to evolve under an infinitesimal model. Results suggest that the good genes process generates only weak indirect selection on preferences, with an effective selection intensity of a few percent or less, If preferences are subject to direct natural selection of the intensity observed for other characters, the good genes process alone is not expected to exaggerate the male trait by more than a few phenotypic standard deviations, contrary to what is observed in highly sexually selected species, Good genes can, however, cause substantial exaggeration if preference genes are nearly selectively neutral. Alternatively, direct selection on preference genes, acting on mating behavior itself or on the genes' pleiotropic effects, can cause mating preferences and male display traits to be exaggerated by any degree. Direct selection of preference genes may therefore play an important role in species that show extreme sexual selection, Key words,-Deleterious mutation, direct selection, good genes, mate choice, mating preferences, sexual selection.Received July 20, 1995. Accepted July 18, 1996 Two forces thought to be involved in the evolution of female mating preferences in many species are direct selection acting on preference genes and the" good genes" mechanism (reviewed by Kirkpatrick and Ryan 1991;Andersson 1994). Direct selection on a preference occurs when genes that affect the preference also have direct effects on survival or fecundity. The good genes mechanism operates when females choose mates using male traits that are genetically correlated with total fitness. A genetic association then naturally develops between preference and fitness alleles, which causes the preference and consequently the male display character to become exaggerated (Fisher 1958;Pomiankowski 1988).Both mechanisms can in theory produce the spectacular extremes of sexual selection seen, for example, in lek-breeding birds. The good genes process favors ever-greater elaboration of the preference and male trait. In the absence of any other constraining factors, it will cause both the preference and trait to become exaggerated without limit (Porniankowski 1988;Heywood 1989). Direct selection can likewise generate extreme preferences and male displays, In the absence of good genes or other effects, direct selection will establish preferences that maximize immediate survival and fecundity. If those preferences happen to favor an exaggerated display that drastically decreases male survival, the result is the same: there is no evolutionary penalty to mating preferences for extreme male tr...