Evolutionary Biology

, Volume 45, Issue 3, pp 318–323 | Cite as

The Quasispecies for the Wright–Fisher Model

  • Raphaël Cerf
  • Joseba Dalmau
Research Article


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.


Quasispecies Error threshold Wright–Fsher: population threshold 



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.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no competing interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département de mathématiques et applicationsÉcole normale supérieure, CNRS, PSL Research UniversityParisFrance
  2. 2.Laboratoire de Mathématiques d’OrsayUniv. Paris-Sud, CNRS, Université Paris-SaclayOrsayFrance
  3. 3.Centre de Mathématiques et ApplicationsÉcole PolytechniquePalaiseauFrance

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