title: 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.
authors.affiliation: Department of Molecular Biology and Microbiology, Tufts University, 136 Harrison Avenue, Boston, MA 02111, USA. igor.rouzine@tufts.edu
authors.forename: Igor M
authors.initials: IM
authors.lastname: Rouzine
authors.forename: Eric
authors.initials: E
authors.lastname: Brunet
authors.forename: Claus O
authors.initials: CO
authors.lastname: Wilke
mesh_terms: D000222:Adaptation, Physiological / Q000235:genetics*; D000818:Animals; D005075:Biological Evolution; D005828:Genetics, Population; D015233:Models, Statistical; D008962:Models, Theoretical; D010944:Plants / Q000235:genetics; D011157:Population Dynamics; D012100:Reproduction, Asexual / Q000235:genetics*; D012641:Selection, Genetic; D013269:Stochastic Processes; D014780:Viruses / Q000235:genetics