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2018 A stochastic model for the evolution of species with random fitness
Daniela Bertacchi, Jüri Lember, Fabio Zucca
Electron. Commun. Probab. 23: 1-13 (2018). DOI: 10.1214/18-ECP190

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.

Citation

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Daniela Bertacchi. Jüri Lember. Fabio Zucca. "A stochastic model for the evolution of species with random fitness." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP190

Information

Received: 19 April 2018; Accepted: 7 November 2018; Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 07023474
MathSciNet: MR3882229
Digital Object Identifier: 10.1214/18-ECP190

Subjects:
Primary: 60J20
Secondary: 60J15, 60J80

JOURNAL ARTICLE
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