June 2016 Distribution of the quasispecies for a Galton–Watson process on the sharp peak landscape
Joseba Dalmau
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J. Appl. Probab. 53(2): 606-613 (June 2016).

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 $\infty$ and the mutation probability goes to 0, the asymptotic relative frequency of the sequences differing on $k$ digits from the master sequence approaches $(\sigma{\rm e}^{-a}-1)({a^k}/{k!})\sum_{i\geq1}{i^k}/{\sigma^i},$ where $\sigma$ 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 $\mathcal{Q}(\sigma,a)$ on the nonnegative integers given by the above equation is the quasispecies distribution with parameters $\sigma$ and $a$.

Citation

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Joseba Dalmau. "Distribution of the quasispecies for a Galton–Watson process on the sharp peak landscape." J. Appl. Probab. 53 (2) 606 - 613, June 2016.

Information

Published: June 2016
First available in Project Euclid: 17 June 2016

zbMATH: 1344.60081
MathSciNet: MR3514303

Subjects:
Primary: 60J80
Secondary: 92D25

Keywords: Galton–Watson process , Quasispecies

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 2 • June 2016
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