NOTE
Nature is Not Uniform ROBERT E. ULANOWICZ AND WILFRIED CEES, Solomons, Maryland 20688
F. WOLFF
Receiued 21 May 1992; revised 23 May 1992
Our suggestion that the measure D might be useful as a criterion for aggregation was made as a peripheral speculation. In light of the calculations by Dr. Pahl-Wostl, we would no longer recommend that D replace the average mutual information as the benchmark for component aggregation. We further recognize that it is possible for ecosystem parsing to influence the magnitude of D, and we support Dr. Pahl-Wostl’s call for further study into the ramifications of trophic aggregation. We caution the reader, however, that Dr. Pahl-Wostl’s argument was couched ad txtremum to make this particular point and will work only when the underlying (preaggregation) distribution of real transfers is uniformly distributed, as in her example. Given the very strong probability that nature is more irregular than uniform, one would have to be extremely clever to invent an aggregation that would move a real system back toward the diagonal, as in her example d. (Unless, of course, one aggregates down to a very small number of compartments. Then the statistics of small numbers would force it back to the diagonal, as happened with the small systems we plotted.) We believe that to attribute the considerable magnitudes of D we calculated for systems with 20-50 compartments entirely (or even mostly) to unintentional bias on the part of those collecting the data would therefore be unwarranted.
MA THEM TICAL BIOSCIENCES 112: 185 ( 1992) OElsevier Science Publishing Co., Inc., 1992 655 Avenue of the Americas, New York, NY 10010
185 0025-5564/92/$5.00
Nature is Not Uniform ROBERT E. ULANOWICZ AND WILFRIED CEES, Solomons, Maryland 20688
F. WOLFF
Receiued 21 May 1992; revised 23 May 1992
Our suggestion that the measure D might be useful as a criterion for aggregation was made as a peripheral speculation. In light of the calculations by Dr. Pahl-Wostl, we would no longer recommend that D replace the average mutual information as the benchmark for component aggregation. We further recognize that it is possible for ecosystem parsing to influence the magnitude of D, and we support Dr. Pahl-Wostl’s call for further study into the ramifications of trophic aggregation. We caution the reader, however, that Dr. Pahl-Wostl’s argument was couched ad txtremum to make this particular point and will work only when the underlying (preaggregation) distribution of real transfers is uniformly distributed, as in her example. Given the very strong probability that nature is more irregular than uniform, one would have to be extremely clever to invent an aggregation that would move a real system back toward the diagonal, as in her example d. (Unless, of course, one aggregates down to a very small number of compartments. Then the statistics of small numbers would force it back to the diagonal, as happened with the small systems we plotted.) We believe that to attribute the considerable magnitudes of D we calculated for systems with 20-50 compartments entirely (or even mostly) to unintentional bias on the part of those collecting the data would therefore be unwarranted.
MA THEM TICAL BIOSCIENCES 112: 185 ( 1992) OElsevier Science Publishing Co., Inc., 1992 655 Avenue of the Americas, New York, NY 10010
185 0025-5564/92/$5.00
