%0 Journal Article
%T A stochastic model of evolution
%A Herve Guiol
%A Fabio P. Machado
%A Rinaldo B. Schinazi
%J Mathematics
%D 2009
%I arXiv
%X We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type that is killed is the one with the smallest fitness. We show that there is a sharp phase transition when the birth probability is larger than the death probability. The set of species with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.
%U http://arxiv.org/abs/0909.2108v2