Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 88, 13 pp.
A stochastic model for the evolution of species with random fitness
We generalize the evolution model introduced by Guiol, Machado and Schinazi (2010). In our model at odd times a random number $X$ of species is created. Each species is endowed with a random fitness with arbitrary distribution on $[0,1]$. At even times a random number $Y$ of species is removed, killing the species with lower fitness. We show that there is a critical fitness $f_c$ below which the number of species hits zero i.o. and above of which this number goes to infinity. We prove uniform convergence for the fitness distribution of surviving species and describe the phenomena which could not be observed in previous works with uniformly distributed fitness.
Electron. Commun. Probab., Volume 23 (2018), paper no. 88, 13 pp.
Received: 19 April 2018
Accepted: 7 November 2018
First available in Project Euclid: 24 November 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J15
Bertacchi, Daniela; Lember, Jüri; Zucca, Fabio. A stochastic model for the evolution of species with random fitness. Electron. Commun. Probab. 23 (2018), paper no. 88, 13 pp. doi:10.1214/18-ECP190. https://projecteuclid.org/euclid.ecp/1543028983