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 $\delta$ 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.

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

References in corpus (3)

• The traveling wave approach to asexual evolution: Muller's ratchet and speed of adaptation
• Noisy traveling waves: effect of selection on genealogies
• Fixation Probability for Competing Selective Sweeps

Cited by in corpus (8)

• The speed of evolution in large asexual populations
• Asexual Evolution Waves: Fluctuations and Universality
• Traveling waves of selective sweeps
• Clonal interference and Muller's ratchet in spatial habitats
• Muller's ratchet with compensatory mutations
• Upper bound on the rate of adaptation in an asexual population
• Rare beneficial mutations cannot halt Muller's ratchet in spatial populations
• Branching with selection and mutation I: Mutant fitness of Fréchet type