The index of dispersion of molecular evolution: Slow fluctuations

The most simple neutral model of molecular evolution predicts that the numb er of substitutions within a lineage in T generations ought to be Poisson d istributed. Therefore, the variance in the number of substitutions ought to equal the mean number. The ratio of the variance to the mean number of sub stitutions is called the index of dispersion, R(T). Assuming infinite sites , no recombination model of the gene, and a haploid, Moran population struc ture, R(T) is derived for a general stationary model of molecular evolution . R(T) is shown to be affected by fluctuations in parameters only when they occur on a very slow time scale. In order for parameter fluctuations to ca use R(T) to deviate significantly from one, the time between parameter chan ges must be roughly as large, or larger, than the time between substitution s. (C) 2000 Academic Press.