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.

Bertacchi, D., Lember, J., Zucca, F. (2018). A stochastic model for the evolution of species with random fitness. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 23(0) [10.1214/18-ECP190].

A stochastic model for the evolution of species with random fitness

Bertacchi, Daniela
;
2018

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.
Articolo in rivista - Articolo scientifico
Birth and death process; Fitness; Generalized GMS model; Limit distribution; Queuing process; Survival;
generalized GMS model; birth and death process; survival; fitness; queuing process; limit distribution
English
24-nov-2018
2018
23
0
88
open
Bertacchi, D., Lember, J., Zucca, F. (2018). A stochastic model for the evolution of species with random fitness. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 23(0) [10.1214/18-ECP190].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/213759
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