Question Marks About the Period of Punctuation

Aviv Bergman and Marcus W. Feldman

Working Papers from Santa Fe Institute

Abstract: In a recent publication (Bergman et al., 1995) we used a diploid version of the NK model of fitness landscapes (Kauffman and Levin, 1987; Kaufman, 1989) to investigate properties of Wright's shifting balance theory of evolution (reviewed in Wright, 1977). The NK model is a relatively simple way to extend the majority of earlier analyses, which had concentrated on fitness surfaces with two peaks, to the case of multiple fitness peaks. The ruggedness of the fitness landscapes is controlled by the parameter K which for any of the N genes determines the number of other genes that contribute to its marginal fitness. Among the main conclusions of Berman et al. (1995) was that for a given K the time trajectory of the average over 25 fitness surfaces of the population's mean fitness depends critically on the amount of dispersal. In fact, this average mean fitness is strongly influenced by both K, which can also be viewed as a measure of epistasis, and the dispersal distance. These interact in such a way that for rugged fitness surfaces, intermediate levels of dispersal result in a higher average mean fitness, a result found earlier by Barton and Rouhani (1993) and Moore and Tonsor (1994) in the two-peak case.

Date: 1996-02
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