MODELING ENVIRONMENTAL STRESS 7 



stress have been local in nature; i.e., the system closely tracks the 

 normal state, H*. Locally there is little difference between linear and 

 nonlinear representations. Nonlinear representations tend to be more 

 sensitive to parameter changes, however, and sensitivity and stability 

 are closely related (Estberg and Patten, 1975). Thus a higher 

 percentage of linear attempts at modeling are likely to survive into 

 the final stages of an investigation. 



Although they have served ecosystem science well, local models 

 of stress response still leave much to be desired. The instability of a 

 system to small stress serves as nothing more than a warning signal to 

 the ecosystem manager. Local instability is neither necessary nor 

 sufficient to cause a system to switch to a different configuration 

 when subjected to a finite stress. Furthermore, the analysis reveals 

 nothing about the future structure of the system if it should change 

 character. Finally, in most local considerations little emphasis can be 

 placed on endogenous strain, which may arise from finite excursions 

 from the normal state. 



FAR-FIELD STRESS ANALYSIS 



The deficiencies of low-stress models are the cause of many 

 ecological managers' suspicions of the modeling process. This point 

 was underscored at a recent symposium on ecological modeling in a 

 resource-management framework when three investigators — Schaaf 

 (1975), O'Neill (1975), and Orlob (1975) — independently cited 

 Rolling's multiple steady-state hypothesis and the burning desire of 

 ecologist and manager alike to understand more about the "collaps- 

 ing" ecosystem syndrome. Managers are necessarily concerned with 

 species changes within the systems in their charge. The conditions 

 leading to structural changes in the system and the configuration of a 

 collapsed or new ecosystem are matters of utmost importance in 

 their eyes. 



At the time of the symposium (1975), practically no research on 

 the problem of switching between domains of attraction caused by 

 finite amplitude stress was widely known. All investigators agreed on 

 the need for theoretical research. In addition, Orlob called for 

 controlled experimentation on collapsing ecosystems and systems 

 subjected to low-level chronic stress. 



The problem of mapping domains of attraction for an ecosystem 

 is a formidable task. It is enough to cause a theoretical ecologist like 

 May (1975) to remark: "I find it difficult to envision any simple 

 number, or handful of numbers, which will quantify the resilience of 

 a complicated natural ecosystem." There have been no major break- 



