MODELING ENVIRONMENTAL STRESS 13 



stationary state closely. Analysis of local systems is quite well 

 developed, but application of the analytical results to real ecosystems 

 is not free from ambiguities. Some of the models exhibit consider- 

 able realism and can be used as management tools to identify 

 exogenous stresses that might jeopardize ecosystem integrity. 



The observation that ecosystems undergo sudden, radical struc- 

 tural changes makes a nonlinear analysis of finite amplitude stress 

 imperative. This endeavor is bound to be wrought with analytical 

 difficulties. Even the simplest nonlinear model can exhibit bizzare 

 behavior (May, 1974), To analyze finite amplitude stress, the 

 mathematical ecologist may have to enlarge his skills to include such 

 subjects as statistical mechanics, topology, nonlinear optimization 

 theory, and variational calculus. The progress in this field treats the 

 feasibility of alternate stable states. 



The need for a holistic approach to ecosystem response has long 

 been recognized (Odum, 1977), but the development of a macro- 

 scopic theory remains in its preliminary stages. Some correlation of 

 total system variables to imposed stress has been noted, but much 

 more empiricism seems necessary before the inductive leap to 

 fundamental principles can be made. 



Despite the remoteness of holistic principles, this review brings 

 up several questions that may indicate a fruitful approach to 

 macroscopic laws. 



First, the language used in discussing nonlinear ecosystem 

 response [e.g., "domain of attraction," "adsorbing set" (Botkin and 

 Sobel, 1975), "strange attractor" (May and Oster, 1976)] is intrigu- 

 ing. If much of the experimentation with dynamic systems leads to 

 the recognition of attractor surfaces, why not make an effort to 

 describe the attractor surface, both mathematically and biologically? 



Second, Kerr's (1974) emphasis on reconciling microscopic and 

 macroscopic approaches to ecosystem research deserves considera- 

 tion. Is it necessary to wait until theories at both levels are well 

 developed before the two can be related, or can a single principle 

 bridge the gap between them? 



Third, Harte and Levy's (1975) speculation on the ordination of 

 various stable states is appealing. What ecosystems manager would 

 not rejoice at a quantitative comparison between two ecosystem 

 states which distinguishes the more mature? 



Fourth, and most relevant to this discussion, what is a definition 

 of total system strain, H, which can be closely related to the 

 dynamics of the system? 



Finally, how might the gulf between the systems ecologists and 

 the evolutionary biologists be bridged? Like the fluid dynamicist 



