IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v572y2021ics0378437121001667.html
   My bibliography  Save this article

An algorithm to represent inbreeding trees

Author

Listed:
  • Jarne, C.
  • Gómez Albarracín, F.A.
  • Caruso, M.

Abstract

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population (Yengo et al., 2019). This result brings our attention again to a math problem related to inbreeding family trees and diversity. Groups with a finite number of individuals could give a variety of genetic relationships. In previous works (Caruso and Jarne, 2015; Caruso and Jarne, 2014; Jarne and Caruso, 2019), we have addressed the issue of building inbreeding trees for biparental reproduction using Markovian models. Here, we extend these studies by presenting an algorithm to generate and represent inbreeding trees with no overlapping generations. We explicitly assume a two-gender reproductory scheme, and we pay particular attention to the links between nodes. We show that even for a simple case with a relatively small number of nodes in the tree, there are a large number of possible ways to rearrange the links between generations. We present an open-source python code to generate the tree graph, the adjacency matrix, and the histogram of the links for each different tree representation. We show how this mapping reflects the difference between tree realizations, and how valuable information may be extracted upon inspection of these matrices. The algorithm includes a feature to average several tree realizations, obtain the connectivity distribution, and calculate the mean value and standard deviation. We used this feature to compare trees with a different number of generations and nodes. The code presented here, available in Git-Hub, may be easily modified to be applied to other areas of interest involving connections between individuals, extend the study to add more characteristics of the different nodes, etc.

Suggested Citation

  • Jarne, C. & Gómez Albarracín, F.A. & Caruso, M., 2021. "An algorithm to represent inbreeding trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    • Handle: RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001667
    DOI: 10.1016/j.physa.2021.125894
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121001667
    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.2021.125894?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. Loic Yengo & Naomi R. Wray & Peter M. Visscher, 2019. "Extreme inbreeding in a European ancestry sample from the contemporary UK population," Nature Communications, Nature, vol. 10(1), pages 1-11, December.
    2. Ian G. Jamieson & Sabrina S. Taylor & Lisa N. Tracy & Hanna Kokko & Doug P. Armstrong, 2009. "Why some species of birds do not avoid inbreeding: insights from New Zealand robins and saddlebacks," Behavioral Ecology, International Society for Behavioral Ecology, vol. 20(3), pages 575-584.
    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. A Bradley Duthie & Jane M Reid, 2015. "What Happens after Inbreeding Avoidance? Inbreeding by Rejected Relatives and the Inclusive Fitness Benefit of Inbreeding Avoidance," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-22, April.
    2. Patricia Brekke & Jinliang Wang & Peter M. Bennett & Phillip Cassey & Deborah A. Dawson & Gavin J. Horsburgh & John G. Ewen, 2012. "Postcopulatory mechanisms of inbreeding avoidance in the island endemic hihi (Notiomystis cincta)," Behavioral Ecology, International Society for Behavioral Ecology, vol. 23(2), pages 278-284.
    3. Jussi S. Alho & Céline Teplitsky & James A. Mills & John W. Yarrall & Juha Merilä, 2012. "No evidence for inbreeding avoidance through active mate choice in red-billed gulls," Behavioral Ecology, International Society for Behavioral Ecology, vol. 23(3), pages 672-675.
    4. Adeline Loyau & Jérémie H Cornuau & Jean Clobert & Étienne Danchin, 2012. "Incestuous Sisters: Mate Preference for Brothers over Unrelated Males in Drosophila melanogaster," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-6, December.

    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:572:y:2021:i:c:s0378437121001667. 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.