Asymptotic behavior of the rate of adaptation

Details Asymptotic behavior of the rate of adaptation Asymptotic behavior of the rate of adaptation

2007-08-25

arxiv.org/abs/0708.3453v4

Annals of Applied Probability 2010, Vol. 20, No. 3, 978-1004

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP645 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP645

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 $\delta$ 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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