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