Different hierarchy of avalanches observed in the Bak-Sneppen evolution model

Abstract

A quantity $\overline{f}$ denoting the average fitness of an ecosystem is introduced in the Bak-Sneppen model. Through this quantity, a different hierarchy of avalanches, $f_0$ avalanche, is observed in the evolution of Bak-Sneppen model. An exact gap equation, governing the self-organization of the model, is presented in terms of $\overline{f}.$ It is found that self-organized threshold $f_c$ can be exactly obtained. Two basic exponents of the new avalanche $\tau ,$ avalanche distribution, and D, avalanche dimension are given through simulations of one- and two-dimensional Bak-Sneppen models. It is suggested that $\overline{f}$ may be a good quantity in determining the emergence of criticality.