Upper bound on the rate of adaptation in an asexual population

TL;DR

This paper establishes an upper bound on the rate of fitness increase in an asexual population model, complementing previous lower bounds and providing insights into the limits of adaptation speed.

Contribution

The paper derives a new upper bound on the average rate of fitness increase in an asexual population, refining understanding of adaptation limits.

Findings

Upper bound on fitness increase rate is O(log N / (log log N)^2)

Previous lower bound was log^{1-δ} N for any δ>0

Results improve theoretical understanding of adaptation speed limits

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 $O(\log N/(\log\log N)^2)$.