14 ULANOWICZ 



who has the field representation of Newton's laws of motion from 

 which to deduce the behavior of particular flows, most classically 

 trained ecologists explain various species behavior in terms of 

 Darwinian selection. Ecosystem models do not derive from any 

 fundamental principle, however; they are a patchwork of empirical 

 analogies and educated guesses. 



No finished solutions are readily forthcoming, but I would like to 

 speculate that all these questions can be addressed by a variational or 

 optimizational statement. The clues that this might be so are found 

 in the language of both the modeler and the evolutionist. Attractors 

 can be described as points or surfaces of maximal properties. The 

 evolutionist, in turn, is forever speaking in the superlative. 



Others have hinted at an ecosystem variational principle 

 (Glansdorf and Prigogine, 1971; Kemer, 1964; Ulanowicz, 1972). As 

 early as 1925, Lotka suggested that living systems act to maximize 

 the rate of energy capture. Odum and Pinkerton (1955) elaborated 

 on this theme, and H. T. Odum treated the Lotka principle as 

 axiomatic in many of his analyses. Energy is used in a very loose 

 sense in these discussions. It is likely that one of the later definitions 

 [e.g., exergy (Rant, 1956), the energetic measure of the departure of 

 a system from the thermodynamic equilibrium state] is more suited 

 to the descriptional task. 



Thus we can envision a surface H(X, X) in phase hyperspace such 

 that any spontaneous movement along the surface maximizes the 

 rate of energy storage (or some other suitable property). Domains of 

 attraction are delimited by relative minimums. Attractors are points 

 or surfaces of relative maximums. Strain in the ecosystem is defined 

 as the distance between H and H*. Presumably H would have its zero 

 level at thermodynamic equilibrium so that the values of the relative 

 maximums would indicate the maturity of each domain of attrac- 

 tion, allowing us to compare different ecosystem structures. Like 

 Liapunov functions, H would be a system property defined from the 

 components. 



The requisite variational principle would be an extension of 

 evolutionary theory. That is, current evolutionary dogma would be 

 necessary but not sufficient to explain all the phenomena the new 

 principle would presumably encompass. Surely such extension would 

 be objected to by many as unnecessary. Some might even complain 

 that an ecosystem variational principle smacks of teleology, but a 

 glance at the application of variational principles in inanimate 

 physics shows this fear to be groundless. Ultimately, however, the 

 burden of proof is upon the proponents of the new principle to 

 demonstrate the unifying powers alluded to. 



