Mutators, population size, adaptive landscape and the adaptation of asexual populations of bacteria

Selection of mutator alleles, increasing the mutation rate up to 10,000- fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second- order selection can optimize population fitness when few favorable mutations are required for adaptation.