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At macroevolutionary time scales, and for a constant mutation rate, there isan expected linear relationship between time and the number of inferred neutralmutations (the "molecular clock"). However, at shorter time scales a number ofrecent studies have observed an apparent acceleration in the rate of molecularevolution.  We study this apparent acceleration under a Jukes-Cantor model applied to arandomly mating population, and show that, under the model, it arises as aconsequence of ignoring short term effects due to existing diversity within thepopulation. The acceleration can be accounted for by adding the correction termh_0e^{-4mu*t/3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{-4mu*t/3}),where h_0 is the expected heterozygosity in the population at time t=0. Thetrue mutation rate mu may then be recovered, even if h_0 is not known, byestimating mu and h_0 simultaneously using least squares.  Rate estimates made without the correction term (that is, incorrectlyassuming the population to be homogeneous) will result in a divergent ratecurve of the form mu_{div}=mu+C/t, so that the mutation rate appears toapproach infinity as the time scale approaches zero. While our quantitativeresults apply only to the Jukes-Cantor model, it is reasonable to suppose thatthe qualitative picture that emerges also applies to more complex models. Ourstudy therefore demonstrates the importance of properly accounting for anyancestral diversity, as it may otherwise play a dominant role in rateoverestimation.

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