The Quasispecies for the Wright–Fisher Model
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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.
KeywordsQuasispecies 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.
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Conflict of interest
The authors declare that they have no competing interest.
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