The cost of phenotypic evolution

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Abstract
Formulae are developed for the fraction of the population that must be eliminated by selection in each generation in order to account for a given rate of evolution in a metrical trait. A combination of directional and stabilizing selection is assumed. The effects of competition based on phenotypic value are also considered. The formulae are applied to data on evolutionary rates and their variances. It is concluded that most selective elimination is due to stabilizing selection, and that even very rapid evolutionary change in a single character usually involves low levels of additional elimination. It is suggested that long-sustained evolutionary trends are unlikely to be caused either by gradual change of the optimum under stabilizing selection or by the effects of competitive selection in favor of extreme individuals. It is possible that genetic correlations between traits under selection may limit the response of a single trait to directional selection and hence produce very gradual change.