The neutrality theory predicts that the rate of neutral molecular evolution is constant over time, and thus that there is a molecular clock for timing evolutionary events. It has been observed that the variance of the rate of evolution is generally larger than expected according to the neutrality theory, which has raised the question of how reliable the molecular clock is or, indeed, whether there is a molecular clock at all. We have carried out an extensive investigation of three proteins, glycerol-3-phosphate dehydrogenase (GPDH), superoxide dismutase (SOD), and xanthine dehydrogenase (XDH). We have observed that (i) the three proteins evolve erratically through time and across lineages and (ii) the erratic patterns of acceleration and deceleration differ from locus to locus, so that one locus may evolve faster in one than another lineage, whereas the opposite may be the case for another locus. The observations are inconsistent with the predictions made by various subsidiary hypotheses proposed to account for the overdispersion of the molecular clock.T he hypothesis of the molecular clock of evolution emerged from early observations that the number of amino acid replacements in a given protein appeared to change linearly with time (1). Indeed, if proteins (and genes) evolve at constant rates they could serve as molecular clocks for timing evolutionary events and reconstructing the evolutionary history of extant species; and for delimiting the choices among mechanistic descriptions of the amino acid (and nucleotide) substitution process. A notable feature of the hypothesis of the molecular evolutionary clock is empirical multiplicity: every one of the thousands of proteins or genes of an organism would be an independent clock, each ticking at a different rate but all measuring the same events. Kimura's neutrality theory of molecular evolution provides a mathematical foundation for the clock (2, 3). The theory states that the rate of substitution, k, of adaptively neutral alleles is precisely the rate of mutation, u, of neutral alleles, k ϭ u. The neutrality theory predicts that molecular evolution behaves like a stochastic clock, such as radioactive decay, with the properties of a Poisson process; therefore, the variance of the number of substitutions, V, should be equal to the mean, M, so that the ''index of dispersion'' R ϭ V͞M ϭ 1. A common observation, however, is that genes and proteins evolve more erratically than allowed by the neutral theory (the so-called overdispersed molecular clock; refs. 4 and 5), which casts doubts on the validity of the molecular clock model (5, 6). Several subsidiary hypotheses have been proposed that modify the predictions of the neutrality theory, allowing for greater variance in evolutionary rates (6).Here we present an analysis of the rates of evolution of three genes: glycerol-3-phosphate dehydrogenase (GPDH; EC 1.1.1.8), Cu,Zn superoxide dismutase (SOD; EC 1.15.1.1), and xanthine dehydrogenase (XDH; 1.1.1.204). We have previously analyzed the evolutionary rates of GPDH and...