2009/09/11 by Hervé Guiol, Herve Guiol, Fabio P. Machado +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · Social Sciences · #60K35 #82B26 #92D15 #Complex Systems and Time Series Analysis #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K35 #msc:82B26 #msc:92D15 #q-bio.PE
paper · pdf · doi:10.48550/arxiv.0909.2108
6 pages, 1 figure, TeX, Added references, To appear in Markov Processes and Related Fields
openalex publication_date 2009/09/11 · arxiv created 2010/11/08 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.