The evolution of quantitative characters can be described by the equation Δz¯=GP−1S where Δz¯ is the vector of mean responses, G is the matrix of additive genetic variances and covariances, P is the matrix of phenotypic variances and covariances and S is the vector of selection differentials. This equation can be used to predict changes in trait values or to retrospectively estimate the selection gradient and is thus a central equation of evolutionary quantitative genetics. Genetic variances and covariances will be reduced by stabilizing selection, directional selection and drift, and increased by mutation. Changes in trait values resulting from directional selection that are comparable with differences observed among species are readily obtainable in short geological time spans (<5000 generations) with selection intensities so small that they would have an insignificant effect on the G matrix (of course it is possible that such changes came about by strong selection over a few generations, followed by long periods of stasis; there is insufficient evidence to presently distinguish these two possibilities). On the other hand, observed effective population sizes are sufficiently small that considerable changes in G can be expected from drift alone. The action of drift can be distinguished from selection because the former produces a proportional change in G whereas the latter, in general, will not. A survey of studies examining variation in G suggests that the null hypothesis that most of the variation can be attributed to drift rather than selection cannot be rejected. However, more research on the predicted statistical distribution of G as a result of selection and/or drift is required and further development of statistical tests to distinguish these two forces needs to be made.