## The Annals of Applied Probability

### Asymptotic behavior of the rate of adaptation

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 18 June 2010

https://projecteuclid.org/euclid.aoap/1276867304

Digital Object Identifier
doi:10.1214/09-AAP645

Mathematical Reviews number (MathSciNet)
MR2680555

Zentralblatt MATH identifier
1193.92079

#### Citation

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. https://projecteuclid.org/euclid.aoap/1276867304

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