Quantum Evolution and Punctuated Equilibria in Continuous Genetic Characters

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Abstract
A model of polygenic inheritance is used to study a character evolving in the neighborhood of 2 fitness peaks. If the variance of the character becomes sufficiently large, the population can make a rapid deterministic transition from an equilibrium near 1 fitness peak to a new equilibrium near a higher peak despite the presence of of an intervening valley in the individual fitness function. The transiton 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 severalphenotypic 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.