| Summary: | <p>Abstract</p> <p>Background</p> <p>A frequent observation in molecular evolution is that amino-acid substitution rates show an index of dispersion (that is, ratio of variance to mean) substantially larger than one. This observation has been termed the overdispersed molecular clock. On the basis of <it>in silico </it>protein-evolution experiments, Bastolla and coworkers recently proposed an explanation for this observation: Proteins drift in neutral space, and can temporarily get trapped in regions of substantially reduced neutrality. In these regions, substitution rates are suppressed, which results in an overall substitution process that is not Poissonian. However, the simulation method of Bastolla et al. is representative only for cases in which the product of mutation rate <it>μ </it>and population size <it>N</it><sub>e </sub>is small. How the substitution process behaves when <it>μN</it><sub>e </sub>is large is not known.</p> <p>Results</p> <p>Here, I study the behavior of the molecular clock in <it>in silico </it>protein evolution as a function of mutation rate and population size. I find that the index of dispersion decays with increasing <it>μN</it><sub>e</sub>, and approaches 1 for large <it>μN</it><sub>e </sub>. This observation can be explained with the selective pressure for mutational robustness, which is effective when <it>μN</it><sub>e </sub>is large. This pressure keeps the population out of low-neutrality traps, and thus steadies the ticking of the molecular clock.</p> <p>Conclusions</p> <p>The molecular clock in neutral protein evolution can fall into two distinct regimes, a strongly overdispersed one for small <it>μN</it><sub>e</sub>, and a mostly Poissonian one for large <it>μN</it><sub>e</sub>. The former is relevant for the majority of organisms in the plant and animal kingdom, and the latter may be relevant for RNA viruses.</p>
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