Bounding The Rate of Adaptation In A Large Asexually Reproducing Population With Fast Mutation Rates

Details Bounding The Rate of Adaptation In A Large Asexually Reproducing Population With Fast Mutation Rates Bounding The Rate of Adaptation In A Large Asexually Reproducing Population With Fast Mutation Rates

2011-08-01

arxiv.org/abs/1108.0440v1

Mathematics

Probability

26 pages

Scientific paper

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 (2009) 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 $O(\log N/\log \log N)$.

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