Abstract
Natural selection and random genetic drift are modeled by using diffusion equations for the mean phenotype of a quantitative (polygenic) character in a finite population with two available adaptive zones or ecological niches. When there is appreciable selection, the population is likely to spend a very long time drifting around the peak in its original adaptive zone. With the mean phenotype initially anywhere near the local optimum, the expected time until a shift between phenotypic adaptive peaks increases approximately exponentially with the effective population size. In comparison, the expected duration of intermediate forms in the actual transition between adaptive peaks is extremely short, generally below the level of resolution in the fossil record, and increases approximately logarithmically with the effective population size. The evolutionary dynamics of this model conform to the pattern of current paleontological concepts of morphological "stasis" and "punctuated equilibria."