IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v92y2014icp30-35.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580913001135
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2013.11.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fatheddin, Parisa & Xiong, Jie, 2015. "Large deviation principle for some measure-valued processes," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 970-993.
    2. F. Gamboa & A. Rouault, 2010. "Canonical Moments and Random Spectral Measures," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1015-1038, December.
    3. da Silva, Telles Timóteo & Fragoso, Marcelo D., 2008. "Sample paths of jump-type Fleming-Viot processes with bounded mutation operators," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1784-1791, September.
    4. Kumar, Vinod & Menon, S.V.G., 1987. "Branch selectivity in a system crossing a bifurcation point: Fokker-Planck equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(2), pages 574-584.
    5. Gómez-Ordóñez, J. & Morillo, M., 1992. "Numerical analysis of the Smoluchowski equation using the split operator method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(4), pages 490-507.
    6. Griffiths, Robert C. & Jenkins, Paul A. & Spanò, Dario, 2018. "Wright–Fisher diffusion bridges," Theoretical Population Biology, Elsevier, vol. 122(C), pages 67-77.
    7. Thierry E. Huillet, 2016. "Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin," Mathematical Population Studies, Taylor & Francis Journals, vol. 23(3), pages 164-200, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:92:y:2014:i:c:p:30-35. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.