title: Probability and time to fixation of an evolving sequence.
abstract: The propagation of a sequence in a population is traced using a branching process model of Poisson distributions. The sequence, initially inserted in a location of the genome of a single individual, is under selective pressure and can undergo detrimental, beneficial or even neutral mutations that allow for adaptive possibilities in the future. The exact solution for the ultimate probability of fixation (u) of the sequence in this model is a Lambert W function of mutation rates and selective values: [Formula: see text] where γ = 1 + s-μd-μb, β = 2αμb, s is the intrinsic coefficient of selection of the sequence (selective advantage is set by s > 0), μd and μb are the deleterious and beneficial rates of mutations that occur in the sequence and α is the effect of beneficial mutations. Predictions are adaptable to a wide range of situations, e.g., fixation of favourable mutations, local mutators or gene duplicates. The equation for the probability of fixation can be recursively nested, which leads to a non-obvious conclusion: the ultimate probability of fixation of the favourable combination of a number of rare events occurring in the sequence is not the product of the individual probabilities of the events but tends to be approximately proportional to the product of their square roots, which results in a remarkably high chance of fixation. This conclusion has implications in several topics of evolutionary genetics. The analysis also gives the distribution of the times of occurrence of the beneficial mutations that will lead to sequence fixation.
authors.affiliation: Departamento de Biología Funcional, Universidad de Oviedo, 33071 Oviedo, Spain. Electronic address: esr@uniovi.es.
authors.forename: Enrique
authors.initials: E
authors.lastname: Santiago
mesh_terms: D005075:Biological Evolution; D006801:Humans; D008957:Models, Genetic; D009154:Mutation; D016012:Poisson Distribution; D011336:Probability; D012641:Selection, Genetic; D013997:Time Factors
keywords: Fixation probability; Genome evolution; Mutation