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Divergence and Polymorphism Under the Nearly Neutral Theory of Molecular Evolution

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Abstract

The nearly neutral theory attributes most nucleotide substitution and polymorphism to genetic drift acting on weakly selected mutants, and assumes that the selection coefficients for these mutants are drawn from a continuous distribution. This means that parameter estimation can require numerical integration, and this can be computationally costly and inaccurate. Furthermore, the leading parameter dependencies of important quantities can be unclear, making results difficult to understand. For some commonly used distributions of mutant effects, we show how these problems can be avoided by writing equations in terms of special functions. Series expansion then allows for their rapid calculation and, also, illuminates leading parameter dependencies. For example, we show that if mutants are gamma distributed, the neutrality index is largely independent of the effective population size. However, we also show that such results are not robust to misspecification of the functional form of distribution. Some implications of these findings are then discussed.

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Acknowledgments

It is a pleasure to thank Laurence Loewe, Andrea Betancourt, and Fraser Lewis for their help with this work.

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Authors and Affiliations

  1. Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JT, UK

    John J. Welch

  2. Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Falmer, Brighton, BN1 9QG, UK

    John J. Welch, Adam Eyre-Walker & David Waxman

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  1. John J. Welch
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  2. Adam Eyre-Walker
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  3. David Waxman
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Correspondence to John J. Welch.

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Welch, J.J., Eyre-Walker, A. & Waxman, D. Divergence and Polymorphism Under the Nearly Neutral Theory of Molecular Evolution. J Mol Evol 67, 418–426 (2008). https://doi.org/10.1007/s00239-008-9146-9

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  • DOI: https://doi.org/10.1007/s00239-008-9146-9

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