Correcting the apparent mutation rate acceleration at shorter time scales under a Jukes-Cantor model

At macroevolutionary time scales, and for a constant mutation rate, there is an expected linear relationship between time and the number of inferred neutral mutations (the "molecular clock"). However, at shorter time scales, a number of recent studies have observed an apparent acceleration in the rate of molecular evolution. We study this apparent acceleration under a Jukes-Cantor model applied to a randomly mating population, and show that, under the model, it arises as a consequence of ignoring short-term effects due to existing diversity within the population. The acceleration can be accounted for by adding the correction term h(0)e(-4μt/3) to the usual Jukes-Cantor formula p(t) = 3/4(1 - e (-(-4μt/3), where h(0) is the expected heterozygosity in the population at time t = 0. The true mutation rate μ may then be recovered, even if h(0) is not known, by estimating μ and h(0) simultaneously using least squares. Rate estimates made without the correction term (i.e., incorrectly assuming the population to be homogeneous) will result in a divergent rate curve of the form μ(div) = μ + C/t, so that the mutation rate appears to approach infinity as the time scale approaches zero. Although our quantitative results apply only to the Jukes-Cantor model, it is reasonable to suppose that the qualitative picture that emerges also applies to more complex models. Our study, therefore, demonstrates the importance of properly accounting for any ancestral diversity, because it may otherwise play a dominant role in rate overestimation.