  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_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. The
true mutation rate mu may then be recovered, even if h_0 is not known, by
estimating mu and h_0 simultaneously using least squares.
  Rate estimates made without the correction term (that is, incorrectly
assuming the population to be homogeneous) will result in a divergent rate
curve of the form mu_{div}=mu+C/t, so that the mutation rate appears to
approach infinity as the time scale approaches zero. While 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, as it may otherwise play a dominant role in rate
overestimation.
