A stochastic model of evolution
Probability
2010-11-09 v2 Populations and Evolution
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 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.
Cite
@article{arxiv.0909.2108,
title = {A stochastic model of evolution},
author = {Herve Guiol and Fabio P. Machado and Rinaldo B. Schinazi},
journal= {arXiv preprint arXiv:0909.2108},
year = {2010}
}
Comments
6 pages, 1 figure, TeX, Added references, To appear in Markov Processes and Related Fields