  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 Radon's decay in the
lungs in breathing.
