A quantitative study of the dynamics of adaptive mutation appearance

We present two dynamical models for the appearance of adaptive mutations, which permit a quantitative comparison with experimental observations. The models quantify two alternative pictures: The hyper-mutating sub-population picture, and the population-wide mutation picture. We find that both models are equally successful in reproducing the results of experiments in which a single mutation is required. They also enable us to estimate the values of key biological parameters, such as successful mutation rates. We then analyze the multiple mutations experiment of Rosche and Foster (Proc. Natl. Acad. Sci. 96 (1999) 6862) using a combined model, again obtaining quantitative agreement between theory and experiment. We conclude that additional experimental tests concentrating on the dynamics of mutation appearance, and especially the ones involving double mutations, are required in order to determine the relative contribution of the two mechanisms to adaptive mutations appearance.