IDEAS home Printed from https://ideas.repec.org/a/hin/jnijsa/963831.html
   My bibliography  Save this article

Modeling Neutral Evolution Using an Infinite-Allele Markov Branching Process

Author

Listed:
  • Xiaowei Wu
  • Marek Kimmel

Abstract

We consider an infinite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, that is, the proportion of alleles having a given number of copies at a specified time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP with birth and death offspring distribution, we show that the mean of its limiting frequency spectrum has an explicit form in terms of the hypergeometric function. We also derive an asymptotic expression for convergence rate to the limit. Simulations are used to illustrate the results for the birth and death process.

Suggested Citation

  • Xiaowei Wu & Marek Kimmel, 2013. "Modeling Neutral Evolution Using an Infinite-Allele Markov Branching Process," International Journal of Stochastic Analysis, Hindawi, vol. 2013, pages 1-10, March.
    • Handle: RePEc:hin:jnijsa:963831
    DOI: 10.1155/2013/963831
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJSA/2013/963831.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJSA/2013/963831.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/963831?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gunnarsson, Einar Bjarki & Leder, Kevin & Foo, Jasmine, 2021. "Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability," Theoretical Population Biology, Elsevier, vol. 142(C), pages 67-90.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnijsa:963831. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.