The speed of evolution in large asexual populations

TL;DR

This paper reviews models of evolutionary speed in large asexual populations, providing exact solutions for infinite populations and approximate methods for finite populations, supported by numerical simulations.

Contribution

It offers a comprehensive analysis of the speed of evolution, including an exact solution for infinite populations and new estimates for finite populations with various mutation effects.

Findings

Exact solution for infinite population speed

Estimates for finite population size effects

Comparison of analytic estimates with simulations

Abstract

We consider an asexual biological population of constant size $N$ evolving in discrete time under the influence of selection and mutation. Beneficial mutations appear at rate $U$ and their selective effects $s$ are drawn from a distribution $g(s)$. After introducing the required models and concepts of mathematical population genetics, we review different approaches to computing the speed of logarithmic fitness increase as a function of $N$, $U$ and $g(s)$. We present an exact solution of the infinite population size limit and provide an estimate of the population size beyond which it is valid. We then discuss approximate approaches to the finite population problem, distinguishing between the case of a single selection coefficient, $g(s) = \delta(s - s_b)$, and a continuous distribution of selection coefficients. Analytic estimates for the speed are compared to numerical simulations up to population sizes of order $10^{300}$.