  We investigate, using mean-field theory and simulation, the effect of
asymmetry on the critical behavior and probability density of Bak-Sneppen
models. Two kinds of anisotropy are investigated: (i) different numbers of
sites to the left and right of the central (minimum) site are updated and (ii)
sites to the left and right of the central site are renewed in different ways.
Of particular interest is the crossover from symmetric to asymmetric scaling
for weakly asymmetric dynamics, and the collapse of data with different numbers
of updated sites but the same degree of asymmetry. All non-symmetric rules
studied fall, independent of the degree of asymmetry, in the same universality
class. Conversely, symmetric variants reproduce the exponents of the original
model. Our results confirm the existence of two symmetry-based universality
classes for extremal dynamics.
