IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v132y2020icp33-46.html
   My bibliography  Save this article

The Wright–Fisher model with efficiency

Author

Listed:
  • González Casanova, Adrián
  • Miró Pina, Verónica
  • Pardo, Juan Carlos

Abstract

In this article, we propose a Wright–Fisher model with two types of individuals: the inefficient individuals, those who need more resources to reproduce and can have a higher growth rate, and the efficient individuals. In this model, the total amount of resource N is fixed, and the population size varies randomly depending on the number of efficient individuals. We show that, as N increases, the frequency process of efficient individuals converges to a diffusion which is a generalization of the Wright–Fisher diffusion with selection. The genealogy of this model is given by a branching–coalescing process that we call the Ancestral Selection/Efficiency Graph, and that is an extension of the Ancestral Selection Graph (Krone and Neuhauser, 1997a,b). The main contribution of this paper is that, in evolving populations, inefficiency can arise as a promoter of selective advantage and not necessarily as a trade-off.

Suggested Citation

  • González Casanova, Adrián & Miró Pina, Verónica & Pardo, Juan Carlos, 2020. "The Wright–Fisher model with efficiency," Theoretical Population Biology, Elsevier, vol. 132(C), pages 33-46.
    • Handle: RePEc:eee:thpobi:v:132:y:2020:i:c:p:33-46
    DOI: 10.1016/j.tpb.2020.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580920300149
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2020.02.003?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. Parsons, Todd L. & Quince, Christopher & Plotkin, Joshua B., 2008. "Absorption and fixation times for neutral and quasi-neutral populations with density dependence," Theoretical Population Biology, Elsevier, vol. 74(4), pages 302-310.
    2. Baake, Ellen & González Casanova, Adrián & Probst, Sebastian & Wakolbinger, Anton, 2019. "Modelling and simulating Lenski’s long-term evolution experiment," Theoretical Population Biology, Elsevier, vol. 127(C), pages 58-74.
    3. Robert E. Beardmore & Ivana Gudelj & David A. Lipson & Laurence D. Hurst, 2011. "Metabolic trade-offs and the maintenance of the fittest and the flattest," Nature, Nature, vol. 472(7343), pages 342-346, April.
    4. González Casanova, Adrián & Kurt, Noemi & Wakolbinger, Anton & Yuan, Linglong, 2016. "An individual-based model for the Lenski experiment, and the deceleration of the relative fitness," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2211-2252.
    5. Kluth, Sandra & Baake, Ellen, 2013. "The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation," Theoretical Population Biology, Elsevier, vol. 90(C), pages 104-112.
    6. Mark J. Fitzpatrick & Elah Feder & Locke Rowe & Marla B. Sokolowski, 2007. "Maintaining a behaviour polymorphism by frequency-dependent selection on a single gene," Nature, Nature, vol. 447(7141), pages 210-212, May.
    7. Mano, Shuhei, 2009. "Duality, ancestral and diffusion processes in models with selection," Theoretical Population Biology, Elsevier, vol. 75(2), pages 164-175.
    8. Lenz, Ute & Kluth, Sandra & Baake, Ellen & Wakolbinger, Anton, 2015. "Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution," Theoretical Population Biology, Elsevier, vol. 103(C), pages 27-37.
    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. Cordero, Fernando, 2017. "Common ancestor type distribution: A Moran model and its deterministic limit," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 590-621.
    2. Wirtz, Johannes & Wiehe, Thomas, 2019. "The Evolving Moran Genealogy," Theoretical Population Biology, Elsevier, vol. 130(C), pages 94-105.
    3. Ivana Gudelj & Margie Kinnersley & Peter Rashkov & Karen Schmidt & Frank Rosenzweig, 2016. "Stability of Cross-Feeding Polymorphisms in Microbial Communities," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-17, December.
    4. Olga A Nev & Richard J Lindsay & Alys Jepson & Lisa Butt & Robert E Beardmore & Ivana Gudelj, 2021. "Predicting microbial growth dynamics in response to nutrient availability," PLOS Computational Biology, Public Library of Science, vol. 17(3), pages 1-20, March.
    5. Wakeley, John & Sargsyan, Ori, 2009. "The conditional ancestral selection graph with strong balancing selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 355-364.
    6. Wei Fan & Jingchao Yuan & Jinggui Wu & Hongguang Cai, 2023. "Effects of Straw Maize on the Bacterial Community and Carbon Stability at Different Soil Depths," Agriculture, MDPI, vol. 13(7), pages 1-15, June.
    7. Bossert, S. & Pfaffelhuber, P., 2018. "The fixation probability and time for a doubly beneficial mutant," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4018-4050.
    8. González Casanova, Adrián & Kurt, Noemi & Wakolbinger, Anton & Yuan, Linglong, 2016. "An individual-based model for the Lenski experiment, and the deceleration of the relative fitness," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2211-2252.
    9. Heinrich, Lukas & Müller, Johannes & Tellier, Aurélien & Živković, Daniel, 2018. "Effects of population- and seed bank size fluctuations on neutral evolution and efficacy of natural selection," Theoretical Population Biology, Elsevier, vol. 123(C), pages 45-69.
    10. Hermann, Felix & Pfaffelhuber, Peter, 2020. "Markov branching processes with disasters: Extinction, survival and duality to p-jump processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2488-2518.
    11. Baake, Ellen & González Casanova, Adrián & Probst, Sebastian & Wakolbinger, Anton, 2019. "Modelling and simulating Lenski’s long-term evolution experiment," Theoretical Population Biology, Elsevier, vol. 127(C), pages 58-74.
    12. Kluth, Sandra & Baake, Ellen, 2013. "The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation," Theoretical Population Biology, Elsevier, vol. 90(C), pages 104-112.
    13. Etheridge, A.M. & Griffiths, R.C., 2009. "A coalescent dual process in a Moran model with genic selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 320-330.
    14. Lenz, Ute & Kluth, Sandra & Baake, Ellen & Wakolbinger, Anton, 2015. "Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution," Theoretical Population Biology, Elsevier, vol. 103(C), pages 27-37.
    15. Kobayashi, Yutaka & Wakano, Joe Yuichiro & Ohtsuki, Hisashi, 2018. "Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution," Theoretical Population Biology, Elsevier, vol. 123(C), pages 18-27.
    16. Pokalyuk, Cornelia & Pfaffelhuber, Peter, 2013. "The ancestral selection graph under strong directional selection," Theoretical Population Biology, Elsevier, vol. 87(C), pages 25-33.
    17. Baake, E. & Esercito, L. & Hummel, S., 2023. "Lines of descent in a Moran model with frequency-dependent selection and mutation," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 409-457.

    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:132:y:2020:i:c:p:33-46. 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.