INCLUSIVE KULLBACK INDEX - A MACROSCOPIC MEASURE IN ECOLOGICAL-SYSTEMS

The expression for energy in ecosystems given by Jorgensen and Mejer includes two information-theoretical measures, that is, Kullback information (K) and Wiener entropy (L); the energy is written as proportional to (K + L). Instead of L which is scale-dependent, we introduce, as a more adequate quantity, an index M which is a scale-independent quantity. The quantity K is a measure showing the degree of departure (''distance'') of distribution of a matter among compartments in a system from that in a reference system; the quantity M is the degree of departure (''distance'') of concentration of a matter in a system from that in a reference system; and (K + M) is the degree of departure of the state (distribution and concentration of a matter) of a system from that of a reference system. The index I = (K + M) is a kind of extension of the concept of Kullback information K. Let I = (K + M) be called '' inclusive Kullback index''. We adopt these indices (K, M, I) as useful macroscopic measures characterizing ecological systems. Model-calculation of these indices is made for Lake Mendota and for Lake Suwa by adopting Lake Biwa as a reference system. Hypotheses on tendency of change of these indices accompanying ecological succession are presented.