IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v368y2006i1p132-146.html
   My bibliography  Save this article

Applications of the Galton–Watson process to human DNA evolution and demography

Author

Listed:
  • Neves, Armando G.M.
  • Moreira, Carlos H.C.

Abstract

We show that the problem of existence of a mitochondrial Eve can be understood as an application of the Galton–Watson process and presents interesting analogies with critical phenomena in Statistical Mechanics. In the approximation of small survival probability, and assuming limited progeny, we are able to find for a genealogic tree the maximum and minimum survival probabilities over all probability distributions for the number of children per woman constrained to a given mean. As a consequence, we can relate existence of a mitochondrial Eve to quantitative demographic data of early mankind. In particular, we show that a mitochondrial Eve may exist even in an exponentially growing population, provided that the mean number of children per woman N¯ is constrained to a small range depending on the probability p that a child is a female. Assuming that the value p≈0.488 valid nowadays has remained fixed for thousands of generations, the range where a mitochondrial Eve occurs with sizeable probability is 2.0492

Suggested Citation

  • Neves, Armando G.M. & Moreira, Carlos H.C., 2006. "Applications of the Galton–Watson process to human DNA evolution and demography," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 132-146.
    • Handle: RePEc:eee:phsmap:v:368:y:2006:i:1:p:132-146
    DOI: 10.1016/j.physa.2005.11.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106001099
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2005.11.055?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. Derrida, Bernard & Manrubia, Susanna C. & Zanette, Damián H., 2000. "Distribution of repetitions of ancestors in genealogical trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 1-16.
    2. de Oliveira, Paulo Murilo Castro, 2002. "Evolutionary computer simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 306(C), pages 351-358.
    3. Chris Stringer, 2003. "Out of Ethiopia," Nature, Nature, vol. 423(6941), pages 693-695, June.
    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. Gravel, Simon & Steel, Mike, 2015. "The existence and abundance of ghost ancestors in biparental populations," Theoretical Population Biology, Elsevier, vol. 101(C), pages 47-53.
    2. Matsen, Frederick A. & Evans, Steven N., 2008. "To what extent does genealogical ancestry imply genetic ancestry?," Theoretical Population Biology, Elsevier, vol. 74(2), pages 182-190.
    3. Paul Jarrett & Robert Scragg, 2020. "Evolution, Prehistory and Vitamin D," IJERPH, MDPI, vol. 17(2), pages 1-7, January.

    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:phsmap:v:368:y:2006:i:1:p:132-146. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.