A different type of spatial-temporal correlation in the process approaching
the self-organized criticality is investigated for the two simple models f
or biological evolution. The changed behaviors of the position with minimum
barrier are shown to be quantitatively different in the two models. Differ
ent results of the correlation are given for the two models. We argue that
the correlation can be used, together with the power-law distributions, as
criteria for self-organized criticality.