Models of clines in sexual selection by female choice

Most models of sexual selection by female choice have considered discrete, homogenous populations. This paper studies the evolution of a female preference along a cline in the frequency of a preferred male trait. Single alleles control both the preference and preferred character.
Fisher's process initially causes the preference to spread to some 'maximum' frequency with a corresponding rise in character gene frequency. At this stage, the cline in preference does not necessarily mirror that of the trait. Then, however, preference frequency usually decreases, albeit very slowly, and the preference cline always comes to mirror that of the preferred character. Eventually, preference is completely lost from the cline and the character cline decays to that seen under random mating. This loss can only be prevented if the preference is initially frequent enough to push the character to fixation throughout the cline.
Consequently, a preference that arises after the preferred trait may increase very little in frequency itself and have a negligible effect on trait frequency before being lost from the population. Special conditions, such as cyclical natural selection, may be necessary to explain the spread of a preference in a cline from a low initial frequency to frequencies as high as those observed. A preference that predates the preferred trait can enter the population at a high frequency and radically alter a cline in the frequency of a preferred male trait, albeit often transiently.