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An exact steady state solution of Fisher’s geometric model and other models

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  • Sella, Guy

Abstract

Because nearly neutral substitutions are thought to contribute substantially to molecular evolution, and much of our insight about the workings of nearly neutral evolution relies on theory, solvable models of this process are of particular interest. Here, I present an analytical method for solving models of nearly neutral evolution at steady state. The steady state solution applies to any constant fitness landscape under a dynamic of successive fixations, each of which occurs on the background of the population’s most recent common ancestor. Because this dynamic neglects the effects of polymorphism in the population beyond the mutant allele under consideration, the steady state solution provides a decent approximation of evolutionary dynamics when the population mutation rate is low (Nu≪1). To demonstrate the method, I apply it to two examples: Fisher’s geometric model (FGM), and a simple model of molecular evolution. Since recent papers have studied the steady state behavior of FGM under this dynamic, I analyze its behavior in detail and compare the results with previous work.

Suggested Citation

  • Sella, Guy, 2009. "An exact steady state solution of Fisher’s geometric model and other models," Theoretical Population Biology, Elsevier, vol. 75(1), pages 30-34.
    • Handle: RePEc:eee:thpobi:v:75:y:2009:i:1:p:30-34
    DOI: 10.1016/j.tpb.2008.10.001
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    References listed on IDEAS

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    1. Justin C. Fay & Gerald J. Wyckoff & Chung-I Wu, 2002. "Testing the neutral theory of molecular evolution with genomic data from Drosophila," Nature, Nature, vol. 415(6875), pages 1024-1026, February.
    2. Nick G. C. Smith & Adam Eyre-Walker, 2002. "Adaptive protein evolution in Drosophila," Nature, Nature, vol. 415(6875), pages 1022-1024, February.
    3. Peter Andolfatto, 2005. "Adaptive evolution of non-coding DNA in Drosophila," Nature, Nature, vol. 437(7062), pages 1149-1152, October.
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    Cited by:

    1. Van Cleve, Jeremy & Lehmann, Laurent, 2013. "Stochastic stability and the evolution of coordination in spatially structured populations," Theoretical Population Biology, Elsevier, vol. 89(C), pages 75-87.

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