Abstract: We propose a simple model, based on Monte Carlo simulations, for studying the effects of changes in the environment on the adaptation and extinction of evolving species. We show that the geological data of climatic changes are well described by Lévy-stable distributions. This leads, in our model, to a fairly good reproduction of the known data on species extinctions. We have also found that the dependence of the probability that a given number of species becomes extinct in one time step, on the number of extinct species shows a cross-over from a
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