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The Quasispecies for the Wright–Fisher Model

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Abstract

We consider the classical Wright–Fisher model of population genetics. We prove the existence of an error threshold for the mutation probability per nucleotide, below which a quasispecies is formed. We show a new phenomenon, specific to a finite population model, namely the existence of a population threshold: to ensure the stability of the quasispecies, the population size has to be at least of the same order as the genome length. We derive an explicit formula describing the quasispecies.

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Funding

The second author acknowledges that this work was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.

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Authors and Affiliations

  1. Département de mathématiques et applications, École normale supérieure, CNRS, PSL Research University, 75005, Paris, France

    Raphaël Cerf

  2. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405, Orsay, France

    Raphaël Cerf

  3. Centre de Mathématiques et Applications, École Polytechnique, 91128, Palaiseau, France

    Joseba Dalmau

Authors
  1. Raphaël Cerf
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  2. Joseba Dalmau
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Correspondence to Joseba Dalmau.

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The authors declare that they have no competing interest.

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Cerf, R., Dalmau, J. The Quasispecies for the Wright–Fisher Model. Evol Biol 45, 318–323 (2018). https://doi.org/10.1007/s11692-018-9452-0

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  • DOI: https://doi.org/10.1007/s11692-018-9452-0

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