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A path integral formulation of the Wright–Fisher process with genic selection

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  • Schraiber, Joshua G.

Abstract

The Wright–Fisher process with selection is an important tool in population genetics theory. Traditional analysis of this process relies on the diffusion approximation. The diffusion approximation is usually studied in a partial differential equations framework. In this paper, I introduce a path integral formalism to study the Wright–Fisher process with selection and use that formalism to obtain a simple perturbation series to approximate the transition density. The perturbation series can be understood in terms of Feynman diagrams, which have a simple probabilistic interpretation in terms of selective events. The perturbation series proves to be an accurate approximation of the transition density for weak selection and is shown to be arbitrarily accurate for any selection coefficient.

Suggested Citation

  • Schraiber, Joshua G., 2014. "A path integral formulation of the Wright–Fisher process with genic selection," Theoretical Population Biology, Elsevier, vol. 92(C), pages 30-35.
    • Handle: RePEc:eee:thpobi:v:92:y:2014:i:c:p:30-35
    DOI: 10.1016/j.tpb.2013.11.002
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    References listed on IDEAS

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    1. Baibuz, V.F. & Zitserman, V.Yu. & Drozdov, A.N., 1984. "Diffusion in a potential field: Path-integral approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(1), pages 173-193.
    2. Schraiber, Joshua G. & Griffiths, Robert C. & Evans, Steven N., 2013. "Analysis and rejection sampling of Wright–Fisher diffusion bridges," Theoretical Population Biology, Elsevier, vol. 89(C), pages 64-74.
    3. A. Dawson, Donald & Feng, Shui, 2001. "Large deviations for the Fleming-Viot process with neutral mutation and selection, II," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 131-162, March.
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