We previously studied a good genes handicap model in which male quality was heritable and improved offspring viability. We extend our analysis to species in which males provide direct benefits (e.g. parental care, better resources, the absence of contagious diseases). Male quality now affects female fitness by increasing female reproductive success. For this good parent handicap to work, the male signal must have condition-dependent expression. The equilibrium strength of female preference is controlled by the product of signal transmission efficiency, phenotypic variance of male quality and the effectiveness of male quality in improving female reproductive success. The equilibrium resulting from the good parent handicap has exactly the same form as with the good genes handicap. This allows us to compare the relative importance of these two forces in the evolution of female preferences. The handicap models (both good genes and good parent) also show cyclic evolution, as happens with the pure Fisherian model. However, we predict that the handicap process is often strong enough to lead to a stable equilibrium. This leads to the conclusion that cyclic evolution is less likely to occur for handicap than Fisherian traits.
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