Punctuated equilibrium and ‘‘history-dependent’’ percolation

Abstract

We study the Bak-Sneppen (BS) punctuated equilibrium model of biological evolution and calculate its critical exponents. We show that this model can be mapped onto a two-dimensional model of the invasion percolation type, which is ‘‘history dependent,’’ in that the exponents depend on the order in which the sites of the system are updated. We find that the critical exponents γ, ${\nu }_{\mathrm{\perp }}$, σ, and ω for the BS model are different from those of the directed percolation model, but the combination σ${\nu }_{\mathrm{\perp }}$ is the same.