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

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.

arXiv comment50 pages, 8 figures

References in corpus (1)

• Evolution on a smooth landscape

Cited by in corpus (36)

• Genetic progression and the waiting time to cancer
• The noisy edge of traveling waves
• The speed of evolution in large asexual populations
• The contribution of statistical physics to evolutionary biology
• Optimality of mutation and selection in germinal centers
• Quasispecies theory for finite populations
• Asexual Evolution Waves: Fluctuations and Universality
• Evolutionary branching via replicator-mutator equations
• Explicit solutions for replicator-mutator equations: extinction vs. acceleration
• Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution
• Evolution of molecular phenotypes under stabilizing selection
• Survival of the simplest: the cost of complexity in microbial evolution
• Muller's ratchet with overlapping generations
• Traveling waves of selective sweeps
• Clonal interference and Muller's ratchet in spatial habitats
• A new approach to computing the asymptotics of the position of Fisher-KPP fronts
• Genealogies in simple models of evolution
• Asymptotic behavior of the rate of adaptation
• Finite population size effects in quasispecies models with single-peak fitness landscape
• Diffusion approximations in population genetics and the rate of Muller's ratchet
• Upper bound on the rate of adaptation in an asexual population
• The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus
• Rare beneficial mutations cannot halt Muller's ratchet in spatial populations
• A model with Darwinian dynamics on a rugged landscape
• The equivalence between weak and strong purifying selection
• Rare beneficial mutations can halt Muller's ratchet
• Extending the applicability of Thermal Dynamics to Evolutionary Biology
• Deleterious passengers in adapting populations
• Lethal Mutagenesis in Viruses and Bacteria
• The Dynamics of Genetic Draft in Rapidly Adapting Populations
• Statistical Physics of Biological Evolution
• Fluctuations of fitness distributions and the rate of Muller's ratchet
• Collective Fluctuations in models of adaptation
• The stochastic edge in adaptive evolution
• Absolute negative mobility in evolution
• The rate of adaptation in large sexual populations with linear chromosomes