This thesis is aimed at studying mutations, understood as trajectories in the DNA configuration space. An evolutive model of mutations in terms of Levy flights is proposed. The parameters of the model are estimated by means of data from the Long-Term Evolution Experiment (LTEE) with {it E. Coli} bacteria. The results of simulations on competition of clones, mean fitness, etc are compared with experimental data. We discuss the qualitative analogy found between the bacterial mutator phenotype and the cancerous cells. The role of radiation as source of mutations is analyzed. We focus on the case of Radons decay in the lungs in breathing.
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