IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v122y2018icp46-56.html
   My bibliography  Save this article

On the joint distribution of tree height and tree length under the coalescent

Author

Listed:
  • Arbisser, Ilana M.
  • Jewett, Ethan M.
  • Rosenberg, Noah A.

Abstract

Many statistics that examine genetic variation depend on the underlying shapes of genealogical trees. Under the coalescent model, we investigate the joint distribution of two quantities that describe genealogical tree shape: tree height and tree length. We derive a recursive formula for their exact joint distribution under a demographic model of a constant-sized population. We obtain approximations for the mean and variance of the ratio of tree height to tree length, using them to show that this ratio converges in probability to 0 as the sample size increases. We find that as the sample size increases, the correlation coefficient for tree height and length approaches (π2−6)∕[π2π2−18]≈0.9340. Using simulations, we examine the joint distribution of height and length under demographic models with population growth and population subdivision. We interpret the joint distribution in relation to problems of interest in data analysis, including inference of the time to the most recent common ancestor. The results assist in understanding the influences of demographic histories on two fundamental features of tree shape.

Suggested Citation

  • Arbisser, Ilana M. & Jewett, Ethan M. & Rosenberg, Noah A., 2018. "On the joint distribution of tree height and tree length under the coalescent," Theoretical Population Biology, Elsevier, vol. 122(C), pages 46-56.
    • Handle: RePEc:eee:thpobi:v:122:y:2018:i:c:p:46-56
    DOI: 10.1016/j.tpb.2017.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580917300552
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2017.10.008?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. 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.
    2. Drmota, Michael & Iksanov, Alex & Moehle, Martin & Roesler, Uwe, 2007. "Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1404-1421, October.
    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. Choi, Kwok Pui & Thompson, Ariadne & Wu, Taoyang, 2020. "On cherry and pitchfork distributions of random rooted and unrooted phylogenetic trees," Theoretical Population Biology, Elsevier, vol. 132(C), pages 92-104.
    2. Kaur, Gursharn & Choi, Kwok Pui & Wu, Taoyang, 2023. "Distributions of cherries and pitchforks for the Ford model," Theoretical Population Biology, Elsevier, vol. 149(C), pages 27-38.
    3. Alimpiev, Egor & Rosenberg, Noah A., 2022. "A compendium of covariances and correlation coefficients of coalescent tree properties," Theoretical Population Biology, Elsevier, vol. 143(C), pages 1-13.

    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. Eldon, Bjarki, 2011. "Estimation of parameters in large offspring number models and ratios of coalescence times," Theoretical Population Biology, Elsevier, vol. 80(1), pages 16-28.
    2. Hobolth, Asger & Siri-Jégousse, Arno & Bladt, Mogens, 2019. "Phase-type distributions in population genetics," Theoretical Population Biology, Elsevier, vol. 127(C), pages 16-32.
    3. Möhle, M., 2010. "Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2159-2173, November.

    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:46-56. 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.