Asymptotic behavior of the rate of adaptation

TL;DR

This paper analyzes how the rate of adaptation in large asexual populations increases with population size, showing it grows unboundedly if beneficial mutations are present, regardless of mutation rates.

Contribution

It demonstrates that the adaptation rate grows at least logarithmically with population size in large asexual populations with beneficial mutations.

Findings

Adaptation rate is at least logarithmic in population size for large populations.

Presence of beneficial mutations ensures unbounded growth of adaptation rate.

Rate of adaptation grows without bound as population size increases.

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.