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Examples of male mate choice are becoming increasingly common, even in polygynous species. We create a series of population genetic models to examine the evolutionary equilibria and dynamics resulting from male mate choice during polygyny, alone and in the context of mutual mate choice by both sexes. We find that unless males with a preference are able to increase their overall courtship output, male preference will be lost. This loss can be counteracted if males choose females not based on arbitrary traits, but based on a trait that indicates high fertility or viability. We also conclude that if male and female preferences and traits are all controlled by different loci, the male and female mate choice systems are decoupled; the presence of a male preference then has no influence on the equilibria or dynamics of female mate choice. If male and female traits are coupled by pleiotropy, it becomes possible for a male preference to be maintained, regardless of whether preferences between the sexes are pleiotropic or controlled by separate loci. [ABSTRACT FROM AUTHOR]