IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i8p2211-2252.html
   My bibliography  Save this article

An individual-based model for the Lenski experiment, and the deceleration of the relative fitness

Author

Listed:
  • González Casanova, Adrián
  • Kurt, Noemi
  • Wakolbinger, Anton
  • Yuan, Linglong

Abstract

The Lenski experiment investigates the long-term evolution of bacterial populations. In this paper we present an individual-based probabilistic model that captures essential features of the experimental design, and whose mechanism does not include epistasis in the continuous-time (intraday) part of the model, but leads to an epistatic effect in the discrete-time (interday) part. We prove that under some assumptions excluding clonal interference, the rescaled relative fitness process converges in the large population limit to a power law function, similar to the one obtained by Wiser et al. (2013), there attributed to effects of clonal interference and epistasis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:8:p:2211-2252
    DOI: 10.1016/j.spa.2016.01.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491600020X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.01.009?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. 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. Champagnat, Nicolas, 2006. "A microscopic interpretation for adaptive dynamics trait substitution sequence models," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1127-1160, August.
    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. 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.
    2. 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.
    3. 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.

    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. 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.
    2. Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    3. 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.
    4. Manhart, Michael & Haldane, Allan & Morozov, Alexandre V., 2012. "A universal scaling law determines time reversibility and steady state of substitutions under selection," Theoretical Population Biology, Elsevier, vol. 82(1), pages 66-76.
    5. Eldon, Bjarki & Stephan, Wolfgang, 2018. "Evolution of highly fecund haploid populations," Theoretical Population Biology, Elsevier, vol. 119(C), pages 48-56.
    6. 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).
    7. 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.
    8. González-Forero, Mauricio, 2024. "A mathematical framework for evo-devo dynamics," Theoretical Population Biology, Elsevier, vol. 155(C), pages 24-50.
    9. Etheridge, Alison M. & Griffiths, Robert C. & Taylor, Jesse E., 2010. "A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit," Theoretical Population Biology, Elsevier, vol. 78(2), pages 77-92.
    10. Abraham, Romain & Delmas, Jean-François & He, Hui, 2021. "Some properties of stationary continuous state branching processes," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 309-343.
    11. Möhle, Martin, 2024. "On multi-type Cannings models and multi-type exchangeable coalescents," Theoretical Population Biology, Elsevier, vol. 156(C), pages 103-116.
    12. Smadi, Charline, 2015. "An eco-evolutionary approach of adaptation and recombination in a large population of varying size," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 2054-2095.
    13. Pokalyuk, Cornelia & Wakolbinger, Anton, 2020. "Maintenance of diversity in a hierarchical host–parasite model with balancing selection and reinfection," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1119-1158.
    14. Champagnat, Nicolas & Hass, Vincent, 2023. "Existence, uniqueness and ergodicity for the centered Fleming–Viot process," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    15. 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.
    16. 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.
    17. 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.
    18. Hobolth, Asger & Siri-Jégousse, Arno & Bladt, Mogens, 2019. "Phase-type distributions in population genetics," Theoretical Population Biology, Elsevier, vol. 127(C), pages 16-32.
    19. 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.
    20. Fritsch, Coralie & Campillo, Fabien & Ovaskainen, Otso, 2017. "A numerical approach to determine mutant invasion fitness and evolutionary singular strategies," Theoretical Population Biology, Elsevier, vol. 115(C), pages 89-99.

    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:126:y:2016:i:8:p:2211-2252. 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.