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Bak-Sneppen-type models and rank-driven processes

Grinfeld, Michael and Knight, Philip A. and Wade, Andrew R. (2011) Bak-Sneppen-type models and rank-driven processes. Physical Review E, 84 (4). ISSN 1539-3755

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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.