# Abstract

Simple models of molecular evolution assume that sequences evolve by a Poisson process in which nucleotide or amino acid substitutions occur as rare independent events. In these models, the expected ratio of the variance to the mean of substitution counts equals 1, and substitution processes with a ratio greater than 1 are called overdispersed. Comparing the genomes of 10 closely related species of *Drosophila*, we extend earlier evidence for overdispersion in amino acid replacements as well as in four-fold synonymous substitutions. The observed deviation from the Poisson expectation can be described as a linear function of the rate at which substitutions occur on a phylogeny, which implies that deviations from the Poisson expectation arise from gene-specific temporal variation in substitution rates. Amino acid sequences show greater temporal variation in substitution rates than do four-fold synonymous sequences. Our findings provide a general phenomenological framework for understanding overdispersion in the molecular clock. Also, the presence of substantial variation in gene-specific substitution rates has broad implications for work in phylogeny reconstruction and evolutionary rate estimation.