Journal of Molecular Evolution

, Volume 67, Issue 4, pp 418–426 | Cite as

Divergence and Polymorphism Under the Nearly Neutral Theory of Molecular Evolution

  • John J. WelchEmail author
  • Adam Eyre-Walker
  • David Waxman


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.


Genetic drift Distribution of mutant effects Neutrality index Special functions 



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


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • John J. Welch
    • 1
    • 2
    Email author
  • Adam Eyre-Walker
    • 2
  • David Waxman
    • 2
  1. 1.Institute of Evolutionary Biology, School of Biological SciencesUniversity of EdinburghEdinburghUK
  2. 2.Centre for the Study of Evolution, School of Life SciencesUniversity of SussexFalmer, BrightonUK

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