  Over time, a population acquires neutral genetic substitutions as a
consequence of random drift. A famous result in population genetics asserts
that the rate, $K$, at which these substitutions accumulate in the population
coincides with the mutation rate, $u$, at which they arise in individuals:
$K=u$. This identity enables genetic sequence data to be used as a "molecular
clock" to estimate the timing of evolutionary events. While the molecular clock
is known to be perturbed by selection, it is thought that $K=u$ holds very
generally for neutral evolution. Here we show that asymmetric spatial
population structure can alter the molecular clock rate for neutral mutations,
leading to either $K<u$ or $K>u$. Deviations from $K=u$ occur because mutations
arise unequally at different sites and have different probabilities of fixation
depending on where they arise. If birth rates are uniform across sites, then $K
\leq u$. In general, $K$ can take any value between 0 and $Nu$. Our model can
be applied to a variety of population structures. In one example, we
investigate the accumulation of genetic mutations in the small intestine. In
another application, we analyze over 900 Twitter networks to study the effect
of network topology on the fixation of neutral innovations in social evolution.
