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

Theor Popul Biol. 2008 Feb;73(1):24-46. doi: 10.1016/j.tpb.2007.10.004. Epub 2007 Oct 22.


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.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Adaptation, Physiological / genetics*
  • Animals
  • Biological Evolution*
  • Genetics, Population*
  • Models, Statistical
  • Models, Theoretical
  • Plants / genetics
  • Population Dynamics
  • Reproduction, Asexual / genetics*
  • Selection, Genetic
  • Stochastic Processes
  • Viruses / genetics