A Stochastic Model of Evolution

H. Guiol, F.P. Machado, R.B. Schinazi

2011, v.17, №2, 253-258

ABSTRACT

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, 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 a uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.

Keywords: Bak - Sneppen model,evolution,stochastic model,cut-off phenomenon

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