The traveling wave approach to asexual evolution: Muller's ratchet and speed of adaptation

TL;DR

This paper applies traveling-wave theory to model asexual evolution, providing analytical expressions for mutation accumulation and adaptation speed, with improved methods for stochastic edge treatment and broad predictive accuracy.

Contribution

It introduces enhanced traveling-wave models for Muller's ratchet and adaptation, including correction terms for discrete fitness classes and broad applicability.

Findings

Accurately predicts mutation accumulation rate in Muller's ratchet

Predicts adaptation speed grows logarithmically with population size

Traveling-wave theory aligns well with empirical data across parameters

Abstract

We use traveling-wave theory to derive expressions for the rate of accumulation of deleterious mutations under Muller's ratchet and the speed of adaptation under positive selection in asexual populations. Traveling-wave theory is a semi-deterministic description of an evolving population, where the bulk of the population is modeled using deterministic equations, but the class of the highest-fitness genotypes, whose evolution over time determines loss or gain of fitness in the population, is given proper stochastic treatment. We derive improved methods to model the highest-fitness class (the stochastic edge) for both Muller's ratchet and adaptive evolution, and calculate analytic correction terms that compensate for inaccuracies which arise when treating discrete fitness classes as a continuum. We show that traveling wave theory makes excellent predictions for the rate of mutation accumulation in the case of Muller's ratchet, and makes good predictions for the speed of adaptation in a very broad parameter range. We predict the adaptation rate to grow logarithmically in the population size until the population size is extremely large.