IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i11p3757-3766.html
   My bibliography  Save this article

Coalescence in the recent past in rapidly growing populations

Author

Listed:
  • Athreya, K.B.

Abstract

In a rapidly growing population one expects that two individuals chosen at random from the nth generation are unlikely to be closely related if n is large. In this paper it is shown that for a broad class of rapidly growing populations this is not the case. For a Galton–Watson branching process with an offspring distribution {pj} such that p0=0 and ψ(x)=∑jpjI{j≥x} is asymptotic to x−αL(x) as x→∞ where L(⋅) is slowly varying at ∞ and 0<α<1 (and hence the mean m=∑jpj=∞) it is shown that if Xn is the generation number of the coalescence of the lines of descent backwards in time of two randomly chosen individuals from the nth generation then n−Xn converges in distribution to a proper distribution supported by N={1,2,3,…}. That is, in such a rapidly growing population coalescence occurs in the recent past rather than the remote past. We do show that if the offspring mean m satisfies 1

Suggested Citation

  • Athreya, K.B., 2012. "Coalescence in the recent past in rapidly growing populations," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3757-3766.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:11:p:3757-3766
    DOI: 10.1016/j.spa.2012.06.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001433
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2012.06.015?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. Grey, D. R., 1979. "On regular branching processes with infinite mean," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 257-267, May.
    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. Liu, Rong-Li & Ren, Yan-Xia & Wang, Yingrui, 2024. "Coalescence times for critical Galton–Watson processes with immigration," Statistics & Probability Letters, Elsevier, vol. 210(C).

    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.

      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:spapps:v:122:y:2012:i:11:p:3757-3766. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

      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.