Abstract
A model of polygenic inheritance is used to study a character evolving in the neighborhood of two fitness peaks. The major conclusion reached is that if the variance of the character becomes sufficiently large, the population can make a rapid deterministic transition from an equilibrium near one fitness peak to a new equilibrium near a higher peak despite the presence of an intervening valley in the individual fitness function. The transition can be initiated by either a change in the environment (the individual fitness function) or a change in the internal (mutational or developmental) properties of the character that increase its variance in the population. During such an adaptive transition the mean of the character can change several phenotypic standard deviations in a few tens or hundreds of generations. The pattern of evolution generated by this process accords well with the punctuated equilibria description of the fossil record.
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