MOLECULAR EVOLUTION MODELED AS A FRACTAL STATISTICAL PROCESS

Modeling the rate of nucleotide substitutions in DNA as a dichotomous stochastic process with an inverse power-law correlation function desc ribes evolution by a fractal stochastic process (FSP). This FSP model agrees with recent findings on the relationship between the variance a nd mean number of synonymous and nonsynonymous substitutions in 49 dif ferent genes in mammals. that being a power-law increase in the ratio of the variance to the mean, the index of dispersion, with the number of substitutions in a protein. The probability of a given number of su bstitutions occuring in a time t is determined by a fractional diffusi on equation whose solution is a truncated Levy distribution implying t hat evolution is a Levy process in time and yields the same functional behavior for the variance in the number of substitutions as does the FSP model. In addition to obtaining these relationships, the FSP model implies lognormal statistics for the index of dispersion as a functio n of the mean number of substitutions in a protein, which is confirmed in the regression of the FSP model to data. Lognormal statistics sugg est that molecular evolution can be viewed as a multiplicative stochas tic process, rather than the linear additive processes of Darwinian se lection and drift. (C) 1998 Elsevier Science B.V. All rights reserved.