The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure.

Benjamin Allen,Christine Sample,Christopher Paoletti,Yulia Dementieva,Martin A Nowak,Ruben C Medeiros,Carl T Bergstrom

doi:10.1371/journal.pcbi.1004108

Abstract

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. 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.

Highlights

A half-century ago, Zuckerkandl and Pauling [1] discovered that amino acid substitutions often occur with sufficient regularity as to constitute a “molecular clock”
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
Under simple models of evolution, a single neutral mutation has probability 1/N of becoming fixed in a haploid population of size N. It follows that the rate K of neutral substitution per generation—given by the product of the population size N, the mutation probability u per reproduction, and the fixation probability ρ—is equal to u. (A similar cancellation occurs in diploids, leading again to K = u.) In other words, for any neutral genetic marker, the rate of substitution at the population level equals the rate of mutation at the individual level [2]

Summary

Introduction

A half-century ago, Zuckerkandl and Pauling [1] discovered that amino acid substitutions often occur with sufficient regularity as to constitute a “molecular clock”. Theoretical support for this observation was provided by Kimura [2], who argued that observed rates of amino acid substitution could only be explained if the majority of substitutions are selectively neutral. Under simple models of evolution, a single neutral mutation has probability 1/N of becoming fixed in a haploid population of size N. The extent to which these factors compromise the applicability of the molecular clock hypothesis to biological sequence data has been intensely debated [3, 4, 8,9,10,11,12,13,14]

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