## Electronic Communications in Probability

### A stochastic model for the evolution of species with random fitness

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 88, 13 pp.

Dates
Accepted: 7 November 2018
First available in Project Euclid: 24 November 2018

https://projecteuclid.org/euclid.ecp/1543028983

Digital Object Identifier
doi:10.1214/18-ECP190

#### Citation

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

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