A stochastic model of evolution

Details A stochastic model of evolution A stochastic model of evolution

2009-09-11

arxiv.org/abs/0909.2108v2

Mathematics

Probability

6 pages, 1 figure, TeX, Added references, To appear in Markov Processes and Related Fields

Scientific paper

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.

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