On the Generalization of the GMS Evolutionary Model

#### S. Michael, S.E. Volkov

2012, v.18, №2, 311-322

ABSTRACT

We study a generalization of the evolution model proposed by Guiol, Machado and Schinazi [A stochastic model of evolution. Markov Processes and Relat. Fields, 2011, v.17, N2, 253-258]. In our model, at each moment of time a random number of species is either born or removed from the system; the species to be removed are those with the lower fitnesses, fitnesses being some numbers in $[0,1]$. We show that under appropriate conditions, a set of species approaches (in some sense) a sample from a uniform distribution on $[f,1]$, where $f\in [0,1)$, and that the total number of species forms a recurrent process in most other cases.

Keywords: Bak - Sneppen evolution model,interacting particle systems,random walk