Fixation of clonal lineages under Muller's ratchet

For clonal lineages of finite size that differ in their deleterious mutatio nal effects, the probability of fixation is investigated by mathematical th eory and Monte Carlo simulations. If these fitness effects are sufficiently small in one or both lineages, then the lineage with the less deleterious effects will become fixed with high probability. If, however, in both linea ges the deleterious effects are larger than a thresholds, then the probabil ity of fixation is independent of the fitness effects and depends only on t he initial frequencies of the Lineages. This threshold decreases with decre asing genomic mutation rate U and increases with population size N. (For N = 10(5), we have s(c) approximate to 0.1 if U = 1, and s(c) approximate to 0.015 if U = 0.1). Above the threshold, the competition is not driven by th e ratio of mean fitnesses of the lineages, but by the relative sizes of the zero-mutation classes, which are independent of the fitness effects of the mutations. After the loss of the zero-mutation class of a lineage, the oth er lineage will spread to fixation with high probability and within a short time span. If the mutation rates of the lineages differ substantially, the lineage with the lower mutation rate is fixed with very high probability u nless the lineage with the larger mutation rate has very slightly deleterio us mutational effects. If the mutation rates differ by not more than a few percent, then the lineage with the higher mutation rate and the more delete rious effects can become fixed with appreciable probability for a certain r ange of parameters. The independence of the fixation probability on the fit ness effects in a single population leads to dramatic effects in metapopula tions: lineages with more deleterious effects have a much higher fixation p robability. The critical value s(c), above which this phenomenon occurs, de creases as the migration rate between the subpopulations decreases.