IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v199y2026ics0304414926001079.html

Genealogical transition in the noisy N-Branching Random Walk. How stronger selection may promote genetic diversity

Author

Listed:
  • Schertzer, Emmanuel
  • Wences, Alejandro H.

Abstract

We consider an extension of the noisy N-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical structure into two regimes, which we respectively call the semi-pulled and the fully-pulled regimes. In the fully-pulled regime, the genealogy converges to a discrete time Poisson-Dirichlet coalescent. In the semi-pulled regime, the genealogy converges to the Bolthausen-Sznitman coalescent. We discuss some interesting biological consequences of this result. In particular, our model predicts a non-monotone relation between the selection strength and the effective population size.

Suggested Citation

  • Schertzer, Emmanuel & Wences, Alejandro H., 2026. "Genealogical transition in the noisy N-Branching Random Walk. How stronger selection may promote genetic diversity," Stochastic Processes and their Applications, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:spapps:v:199:y:2026:i:c:s0304414926001079
    DOI: 10.1016/j.spa.2026.104975
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414926001079
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2026.104975?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Schweinsberg, Jason, 2003. "Coalescent processes obtained from supercritical Galton-Watson processes," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 107-139, July.
    3. Rouzine, Igor M. & Brunet, Éric & Wilke, Claus O., 2008. "The traveling-wave approach to asexual evolution: Muller's ratchet and speed of adaptation," Theoretical Population Biology, Elsevier, vol. 73(1), pages 24-46.
    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. 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. Dhersin, Jean-Stéphane & Freund, Fabian & Siri-Jégousse, Arno & Yuan, Linglong, 2013. "On the length of an external branch in the Beta-coalescent," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1691-1715.
    3. Hobolth, Asger & Rivas-González, Iker & Bladt, Mogens & Futschik, Andreas, 2024. "Phase-type distributions in mathematical population genetics: An emerging framework," Theoretical Population Biology, Elsevier, vol. 157(C), pages 14-32.
    4. Huillet, Thierry & Möhle, Martin, 2013. "On the extended Moran model and its relation to coalescents with multiple collisions," Theoretical Population Biology, Elsevier, vol. 87(C), pages 5-14.
    5. Good, Benjamin H. & Desai, Michael M., 2013. "Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution," Theoretical Population Biology, Elsevier, vol. 85(C), pages 86-102.
    6. Birkner, Matthias & Blath, Jochen & Steinrücken, Matthias, 2011. "Importance sampling for Lambda-coalescents in the infinitely many sites model," Theoretical Population Biology, Elsevier, vol. 79(4), pages 155-173.
    7. Hobolth, Asger & Siri-Jégousse, Arno & Bladt, Mogens, 2019. "Phase-type distributions in population genetics," Theoretical Population Biology, Elsevier, vol. 127(C), pages 16-32.
    8. 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.
    9. Eldon, Bjarki & Stephan, Wolfgang, 2018. "Evolution of highly fecund haploid populations," Theoretical Population Biology, Elsevier, vol. 119(C), pages 48-56.
    10. Steinrücken, Matthias & Birkner, Matthias & Blath, Jochen, 2013. "Analysis of DNA sequence variation within marine species using Beta-coalescents," Theoretical Population Biology, Elsevier, vol. 87(C), pages 15-24.
    11. Udomchatpitak, Nantawat & Schweinsberg, Jason, 2025. "The accumulation of beneficial mutations and convergence to a Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    12. Der, Ricky & Epstein, Charles L. & Plotkin, Joshua B., 2011. "Generalized population models and the nature of genetic drift," Theoretical Population Biology, Elsevier, vol. 80(2), pages 80-99.
    13. Hadzibeganovic, Tarik & Liu, Chao & Li, Rong, 2021. "Effects of reproductive skew on the evolution of ethnocentrism in structured populations with variable size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    14. Durrett, Rick & Schweinsberg, Jason, 2005. "A coalescent model for the effect of advantageous mutations on the genealogy of a population," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1628-1657, October.
    15. 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.
    16. Rouzine, Igor M. & Coffin, John M., 2010. "Multi-site adaptation in the presence of infrequent recombination," Theoretical Population Biology, Elsevier, vol. 77(3), pages 189-204.
    17. Eldon, Bjarki & Degnan, James H., 2012. "Multiple merger gene genealogies in two species: Monophyly, paraphyly, and polyphyly for two examples of Lambda coalescents," Theoretical Population Biology, Elsevier, vol. 82(2), pages 117-130.
    18. Blath, Jochen & Cronjäger, Mathias Christensen & Eldon, Bjarki & Hammer, Matthias, 2016. "The site-frequency spectrum associated with Ξ-coalescents," Theoretical Population Biology, Elsevier, vol. 110(C), pages 36-50.
    19. Jakob J Metzger & Stephan Eule, 2013. "Distribution of the Fittest Individuals and the Rate of Muller's Ratchet in a Model with Overlapping Generations," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-10, November.
    20. Miró Pina, Verónica & Joly, Émilien & Siri-Jégousse, Arno, 2023. "Estimating the Lambda measure in multiple-merger coalescents," Theoretical Population Biology, Elsevier, vol. 154(C), pages 94-101.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:199:y:2026:i:c:s0304414926001079. 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.