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

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

Publication Type | Journal Article |

Year of Publication | 2008 |

Authors | IM Rouzine, Brunet, E, Wilke, CO |

Journal | Theor Popul Biol |

Volume | 73 |

Issue | 1 |

Pagination | 24-46 |

Date Published | 2008 Feb |

ISSN | 0040-5809 |

Keywords | Adaptation, Physiological, Animals, Biological Evolution, Genetics, Population, Models, Statistical, Models, Theoretical, Plants, Population Dynamics, Reproduction, Asexual, Selection, Genetic, Stochastic Processes, Viruses |

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. |

DOI | 10.1016/j.tpb.2007.10.004 |

Alternate Journal | Theor Popul Biol |

PubMed ID | 18023832 |

PubMed Central ID | PMC2246079 |

Grant List | R01 AI063926-02 / AI / NIAID NIH HHS / United States R01 AI065960 / AI / NIAID NIH HHS / United States R01AI065960 / AI / NIAID NIH HHS / United States R01 AI0639236 / AI / NIAID NIH HHS / United States |