MODELING ENVIRONMENTAL STRESS 



ROBERT E. ULANOWICZ 



University of Maryland, Center for Environmental and Estuarine Studies, 



Solomons, Maryland 



ABSTRACT 



The word stress when applied to ecosystems is ambiguous. Stress may be 

 low-level, with accompanying near-linear strain, or it may be of finite magnitude, 

 with nonlinear response and possible disintegration of the system. Since there 

 are practically no widely accepted definitions of ecosystem strain, classification 

 of models of stressed systems is tenuous. Despite appearances, most ecosystem 

 models seem to fall into the low-level linear response category. Although they 

 sometimes simulate systems behavior well, they do not provide necessary and 

 sufficient information about sudden structural changes nor structure after 

 transition. Dynamic models of finite-amplitude response to stress are rare 

 because of analytical difficulties. Some idea as to future transition states can be 

 obtained by regarding the behavior of unperturbed functions under limiting 

 strain conditions. Preliminary work shows that, since community variables do 

 respond in a coherent manner to stress, macroscopic analyses of stressed 

 ecosystems offer possible alternatives to compartmental models. 



Unfortunately, the term stress is not used uniformly in ecological 

 discussions. It comes to our discipline from mechanics, physiology, 

 and psychology and brings different shades of meaning from each 

 source. In clarifying what is meant by stress and its consequences, it 

 is useful to refer to the meaning given to the word by nineteenth 

 century engineers. 



Stress represented "the forces or pressures exerted upon a 

 material" (Meier, 1972). In mechanics, stress had no utility without 

 its conjugate, strain, "a measure of the deformation brought about 

 by the action of the stresses." The relationship between applied 

 stress and observed strain (e.g., the elongation of a metal rod under 



