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August 2013 Upper bound on the rate of adaptation in an asexual population
Michael Kelly
Ann. Appl. Probab. 23(4): 1377-1408 (August 2013). DOI: 10.1214/12-AAP873

Abstract

We consider a model of asexually reproducing individuals. The birth and death rates of the individuals are affected by a fitness parameter. The rate of mutations that cause the fitnesses to change is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu, Etheridge and Cuthbertson [Ann. Appl. Probab. 20 (2010) 978–1004] it was shown that the average rate at which the mean fitness increases in this model is bounded below by $\log^{1-\delta}N$ for any $\delta>0$. We achieve an upper bound on the average rate at which the mean fitness increases of $O(\log N/(\log\log N)^{2})$.

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Michael Kelly. "Upper bound on the rate of adaptation in an asexual population." Ann. Appl. Probab. 23 (4) 1377 - 1408, August 2013. https://doi.org/10.1214/12-AAP873

Information

Published: August 2013
First available in Project Euclid: 21 June 2013

zbMATH: 1271.92023
MathSciNet: MR3098436
Digital Object Identifier: 10.1214/12-AAP873

Subjects:
Primary: 92D15
Secondary: 60J27 , 82C22 , 92D10

Keywords: Adaptation rate , Evolutionary process , Moran model , selection

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.23 • No. 4 • August 2013
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