IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v122y2018icp22-29.html
   My bibliography  Save this article

A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci

Author

Listed:
  • King, Léandra
  • Wakeley, John
  • Carmi, Shai

Abstract

The population-scaled mutation rate, θ, is informative on the effective population size and is thus widely used in population genetics. We show that for two sequences and n unlinked loci, the variance of Tajima’s estimator (θˆ), which is the average number of pairwise differences, does not vanish even as n→∞. The non-zero variance of θˆ results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by gene genealogies at all loci. We derive the correlation coefficient under a diploid, discrete-time, Wright–Fisher model, and we also derive a simple, closed-form lower bound. We also obtain empirical estimates of the correlation of coalescence times under demographic models inspired by large-scale human genealogies. While the effect we describe is small (Varθˆ∕θ2≈ONe−1), it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci.

Suggested Citation

  • King, Léandra & Wakeley, John & Carmi, Shai, 2018. "A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci," Theoretical Population Biology, Elsevier, vol. 122(C), pages 22-29.
    • Handle: RePEc:eee:thpobi:v:122:y:2018:i:c:p:22-29
    DOI: 10.1016/j.tpb.2017.03.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580917300394
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2017.03.002?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. Eriksson, A. & Mahjani, B. & Mehlig, B., 2009. "Sequential Markov coalescent algorithms for population models with demographic structure," Theoretical Population Biology, Elsevier, vol. 76(2), pages 84-91.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Severson, Alissa L. & Carmi, Shai & Rosenberg, Noah A., 2021. "Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population," Theoretical Population Biology, Elsevier, vol. 139(C), pages 50-65.

    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. Haipeng Li & Thomas Wiehe, 2013. "Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation," PLOS Computational Biology, Public Library of Science, vol. 9(5), pages 1-14, May.
    2. Miroshnikov, Alexey & Steinrücken, Matthias, 2017. "Computing the joint distribution of the total tree length across loci in populations with variable size," Theoretical Population Biology, Elsevier, vol. 118(C), pages 1-19.
    3. Jerome Kelleher & Alison M Etheridge & Gilean McVean, 2016. "Efficient Coalescent Simulation and Genealogical Analysis for Large Sample Sizes," PLOS Computational Biology, Public Library of Science, vol. 12(5), pages 1-22, May.

    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:122:y:2018:i:c:p:22-29. 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.