Before revision:  The lognormal pattern dominates when the total of the density independent processes obeys rotational invariance (symmetry) with respect to the summing up of the individual processes acting on abundance . Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches.
After revision:  The lognormal pattern dominates when the processes acting on net species growth rate obey rotational invariance (symmetry) with respect to the summing up of the individual processes acting on abundance . Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches.