The Molecular Clock of Neutral Evolution Can Be Accelerated or Slowed by Asymmetric Spatial Structure

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. Our results apply to a general class of haploid, asexually reproducing, spatially structured populations. 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 ≤ 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.Author Summary: Evolution is driven by genetic mutations. While some mutations affect an organism’s ability to survive and reproduce, most are neutral and have no effect. Neutral mutations play an important role in the study of evolution because they generally accrue at a consistent rate over time. This result, first discovered 50 years ago, allows neutral mutations to be used as a “molecular clock” to estimate, for example, how long ago humans diverged from chimpanzees and bonobos. We used mathematical modeling to study how the rates of these molecular clocks are affected by the spatial arrangement of a population in its habitat. We find that asymmetry in this spatial structure can either slow down or speed up the rate at which neutral mutations accrue. This effect could potentially skew our estimates of past events from genetic data. It also has implications for a number of other fields. For example, we show that the architecture of intestinal tissue can limit the rate of genetic substitutions leading to cancer. We also show that the structure of social networks affects the rate at which new ideas replace old ones. Surprisingly, we find that most Twitter networks slow down the rate of idea replacement.