The Annals of Applied Probability

Asymptotic behavior of the rate of adaptation

Feng Yu, Alison Etheridge, and Charles Cuthbertson

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We consider the accumulation of beneficial and deleterious mutations in large asexual populations. The rate of adaptation is affected by the total mutation rate, proportion of beneficial mutations and population size N. We show that regardless of mutation rates, as long as the proportion of beneficial mutations is strictly positive, the adaptation rate is at least $\mathcal{O}(\log^{1-\delta}N)$ where δ can be any small positive number, if the population size is sufficiently large. This shows that if the genome is modeled as continuous, there is no limit to natural selection, that is, the rate of adaptation grows in N without bound.

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Ann. Appl. Probab., Volume 20, Number 3 (2010), 978-1004.

First available in Project Euclid: 18 June 2010

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Zentralblatt MATH identifier

Primary: 92D15: Problems related to evolution
Secondary: 82C22: Interacting particle systems [See also 60K35] 60J05: Discrete-time Markov processes on general state spaces 92D10: Genetics {For genetic algebras, see 17D92}

Adaptation rate natural selection evolutionary biology Moran particle systems


Yu, Feng; Etheridge, Alison; Cuthbertson, Charles. Asymptotic behavior of the rate of adaptation. Ann. Appl. Probab. 20 (2010), no. 3, 978--1004. doi:10.1214/09-AAP645.

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