The long-tail distribution function of mutations in bacteria

The Long Time Evolution Experiment. I recall the extremely interesting experiment with E. Coli, conducted by Prof. R. Lenski and his group [1, 2], and running already for more than 27 years. Among the reported results, I use the following [3]: 1. In a culture of bacteria, after 20,000 generations, around 3 × 10 single point mutations in the DNA are registered. These are local modifications of the DNA chain. I notice that the number of bacteria undergoing continuous evolution is around 5× 10. 2. They measure also the frequency of mutations involving rearrangements in segments of the DNA. In particular, mutations in which the repair mechanisms are damaged and the mutation rate increases 100 times. This mutator phenotype becomes dominant in two of twelve cultures (probability 1/6) after 2500 3000 generations, in a third culture (cumulative probability 1/4) after 8,500 generations, and in a fourth culture (cumulative probability 1/3) after 15,000 generations. The purpose of my paper is to present a model for mutations in bacteria and to adjust the model parameters in order to qualitatively fit these data. The accumulative character of mutations. In my model, the time evolution of cells defines trajectories, as schematically represented in Fig. 1, where two of these trajectories are drawn in red.