Dynamics of an interacting Bak-Sneppen model system

Abstract

The Bak-Sneppen model is one of the simplest models for evolution and has found its popularity among physicists, mathematicians and biologists for its ability to model, among others, punctuated equilibria and self-organized criticality. With few assumptions, it encapsulates the basic dynamical properties of biological evolution. However, due to the coarse-grained approach of the Bak-Sneppen model to modelling species evolution, there is no information that can be said about their subspecies. Here, two new models are formulated which instead of the treating the Bak-Sneppen model as a collection of species, the entire model is treated as a single species with many subspecies variants and this set of subspecies is allowed to interact with a separate set of subspecies, that is, a separate Bak-Sneppen model. Despite creating two new interacting models, their dynamics are similar to that of the original. The dynamical properties of the original Bak-Sneppen model is seen to be independent of simultaneous updates caused between the interacting models.