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Article Dans Une Revue Journal of Applied Probability Année : 2016

Distribution of the quasispecies for a Galton–Watson process on the sharp peak landscape

Résumé

Abstract We study a classical multitype Galton–Watson process with mutation and selection. The individuals are sequences of fixed length over a finite alphabet. On the sharp peak fitness landscape together with independent mutations per locus, we show that, as the length of the sequences goes to ∞ and the mutation probability goes to 0, the asymptotic relative frequency of the sequences differing on k digits from the master sequence approaches (σe - a - 1)( a k / k !)∑ i ≥ 1 i k /σ i , where σ is the selective advantage of the master sequence and a is the product of the length of the chains with the mutation probability. The probability distribution Q (σ, a ) on the nonnegative integers given by the above equation is the quasispecies distribution with parameters σ and a .
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Dates et versions

hal-03852262 , version 1 (14-11-2022)

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Joseba Dalmau. Distribution of the quasispecies for a Galton–Watson process on the sharp peak landscape. Journal of Applied Probability, 2016, 53 (2), pp.606-613. ⟨10.1017/jpr.2016.25⟩. ⟨hal-03852262⟩
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