IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v82y2012i1p66-76.html
   My bibliography  Save this article

A universal scaling law determines time reversibility and steady state of substitutions under selection

Author

Listed:
  • Manhart, Michael
  • Haldane, Allan
  • Morozov, Alexandre V.

Abstract

Monomorphic loci evolve through a series of substitutions on a fitness landscape. Understanding how mutation, selection, and genetic drift drive this process, and uncovering the structure of the fitness landscape from genomic data are two major goals of evolutionary theory. Population genetics models of the substitution process have traditionally focused on the weak-selection regime, which is accurately described by diffusion theory. Predictions in this regime can be considered universal in the sense that many population models exhibit equivalent behavior in the diffusion limit. However, a growing number of experimental studies suggest that strong selection plays a key role in some systems, and thus there is a need to understand universal properties of models without a priori assumptions about selection strength. Here we study time reversibility in a general substitution model of a monomorphic haploid population. We show that for any time-reversible population model, such as the Moran process, substitution rates obey an exact scaling law. For several other irreversible models, such as the simple Wright–Fisher process and its extensions, the scaling law is accurate up to selection strengths that are well outside the diffusion regime. Time reversibility gives rise to a power-law expression for the steady-state distribution of populations on an arbitrary fitness landscape. The steady-state behavior is dominated by weak selection and is thus adequately described by the diffusion approximation, which guarantees universality of the steady-state formula and its applicability to the problem of reconstructing fitness landscapes from DNA or protein sequence data.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:thpobi:v:82:y:2012:i:1:p:66-76
    DOI: 10.1016/j.tpb.2012.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580912000469
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.tpb.2012.03.007?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. 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.
    2. Shimon Bershtein & Michal Segal & Roy Bekerman & Nobuhiko Tokuriki & Dan S. Tawfik, 2006. "Robustness–epistasis link shapes the fitness landscape of a randomly drifting protein," Nature, Nature, vol. 444(7121), pages 929-932, December.
    3. Frank J. Poelwijk & Daniel J. Kiviet & Daniel M. Weinreich & Sander J. Tans, 2007. "Empirical fitness landscapes reveal accessible evolutionary paths," Nature, Nature, vol. 445(7126), pages 383-386, January.
    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. McCandlish, David M. & Epstein, Charles L. & Plotkin, Joshua B., 2015. "Formal properties of the probability of fixation: Identities, inequalities and approximations," Theoretical Population Biology, Elsevier, vol. 99(C), pages 98-113.
    2. Patrick C F Buchholz & Catharina Zeil & Jürgen Pleiss, 2018. "The scale-free nature of protein sequence space," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-14, August.

    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. Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    2. Zachary R Sailer & Sarah H Shafik & Robert L Summers & Alex Joule & Alice Patterson-Robert & Rowena E Martin & Michael J Harms, 2020. "Inferring a complete genotype-phenotype map from a small number of measured phenotypes," PLOS Computational Biology, Public Library of Science, vol. 16(9), pages 1-27, September.
    3. Alicia Sanchez-Gorostiaga & Djordje Bajić & Melisa L Osborne & Juan F Poyatos & Alvaro Sanchez, 2019. "High-order interactions distort the functional landscape of microbial consortia," PLOS Biology, Public Library of Science, vol. 17(12), pages 1-34, December.
    4. 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.
    5. Krishnendu Chatterjee & Andreas Pavlogiannis & Ben Adlam & Martin A Nowak, 2014. "The Time Scale of Evolutionary Innovation," PLOS Computational Biology, Public Library of Science, vol. 10(9), pages 1-7, September.
    6. Jordan Yang & Nandita Naik & Jagdish Suresh Patel & Christopher S Wylie & Wenze Gu & Jessie Huang & F Marty Ytreberg & Mandar T Naik & Daniel M Weinreich & Brenda M Rubenstein, 2020. "Predicting the viability of beta-lactamase: How folding and binding free energies correlate with beta-lactamase fitness," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-26, May.
    7. Beerenwinkel Niko & Knupfer Patrick & Tresch Achim, 2011. "Learning Monotonic Genotype-Phenotype Maps," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, January.
    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. Roger D Kouyos & Gabriel E Leventhal & Trevor Hinkley & Mojgan Haddad & Jeannette M Whitcomb & Christos J Petropoulos & Sebastian Bonhoeffer, 2012. "Exploring the Complexity of the HIV-1 Fitness Landscape," PLOS Genetics, Public Library of Science, vol. 8(3), pages 1-9, March.
    10. Khadraoui, Khader, 2015. "A simple Markovian individual-based model as a means of understanding forest dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 1-23.
    11. Van Cleve, Jeremy, 2015. "Social evolution and genetic interactions in the short and long term," Theoretical Population Biology, Elsevier, vol. 103(C), pages 2-26.
    12. Shidong Wang & Renaud Foucart & Cheng Wan, 2014. "Comeback kids: an evolutionary approach of the long-run innovation process," Papers 1411.2167, arXiv.org, revised Jul 2016.
    13. Lavallée, François & Smadi, Charline & Alvarez, Isabelle & Reineking, Björn & Martin, François-Marie & Dommanget, Fanny & Martin, Sophie, 2019. "A stochastic individual-based model for the growth of a stand of Japanese knotweed including mowing as a management technique," Ecological Modelling, Elsevier, vol. 413(C).
    14. González-Forero, Mauricio, 2024. "A mathematical framework for evo-devo dynamics," Theoretical Population Biology, Elsevier, vol. 155(C), pages 24-50.
    15. Steven Schulz & Sébastien Boyer & Matteo Smerlak & Simona Cocco & Rémi Monasson & Clément Nizak & Olivier Rivoire, 2021. "Parameters and determinants of responses to selection in antibody libraries," PLOS Computational Biology, Public Library of Science, vol. 17(3), pages 1-24, March.
    16. Sagitov, S. & Mehlig, B. & Jagers, P. & Vatutin, V., 2013. "Evolutionary branching in a stochastic population model with discrete mutational steps," Theoretical Population Biology, Elsevier, vol. 83(C), pages 145-154.
    17. Blath, Jochen & Tóbiás, András, 2020. "Invasion and fixation of microbial dormancy traits under competitive pressure," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7363-7395.
    18. Billiard, Sylvain & Smadi, Charline, 2017. "The interplay of two mutations in a population of varying size: A stochastic eco-evolutionary model for clonal interference," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 701-748.
    19. Jingzhi Lou & Weiwen Liang & Lirong Cao & Inchi Hu & Shi Zhao & Zigui Chen & Renee Wan Yi Chan & Peter Pak Hang Cheung & Hong Zheng & Caiqi Liu & Qi Li & Marc Ka Chun Chong & Yexian Zhang & Eng-kiong , 2024. "Predictive evolutionary modelling for influenza virus by site-based dynamics of mutations," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    20. 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.

    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:82:y:2012:i:1:p:66-76. 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.