Different hierarchy of avalanches observed in the bak-sneppen evolution model

A quantity &fmacr; denoting the average fitness of an ecosystem is introduced in the Bak-Sneppen model. Through this quantity, a different hierarchy of avalanches, &fmacr;(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 &fmacr;. It is found that self-organized threshold &fmacr;(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 &fmacr; may be a good quantity in determining the emergence of criticality.