title: Bak-Sneppen-type models and rank-driven processes.
abstract: The Bak-Sneppen model is a well-known stochastic model of evolution that exhibits self-organized criticality; only a few analytical results have been established for it so far. We report a surprising connection between Bak-Sneppen-type models and more tractable Markov processes that evolve without any reference to an underlying topology. Specifically, we show that in the case of a large number of species, the long time behavior of the fitness profile in the Bak-Sneppen model can be replicated by a model with a purely rank-based update rule whose asymptotics can be studied rigorously.
authors.affiliation: Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom. m.grinfeld@strath.ac.uk
authors.forename: Michael
authors.initials: M
authors.lastname: Grinfeld
authors.forename: Philip A
authors.initials: PA
authors.lastname: Knight
authors.forename: Andrew R
authors.initials: AR
authors.lastname: Wade