MODELING ENVIRONMENTAL STRESS 3 



through cropping or mass infusion of a species; and P may change in 

 a number of ways. For example, the multiphers and exponents are 

 often strongly dependent on abiotic variables, such as temperature, 

 salinity, light, etc. These forcing functions, in turn, may possess both 

 regular and stochastic components. The input fluxes, necessary to 

 every living system, vary similarly. 



Occasionally complex systems will exhibit the characteristics of 

 strain without any apparent imposed stress. The term endogenous 

 stress has been coined to describe such phenomena, but the previous 

 discussion reveals this to be a misnomer. Nonlinear systems some- 

 times produce an output without any corresponding input. "Endoge- 

 nous strain" would, therefore, be a more accurate descriptor for such 

 behavior. 



Attempting to provide a workable definition for strain in an 

 ecosystem, Innis (1975) found it useful to invoke an arbitrary 

 function of the state of the system, 



H = h(X, X) (2) 



to measure the deviation from some prescribed state, H*, character- 

 ized as unstressed. For example, H* might be taken to be a 

 stationary state, i.e., 



H* = h(X*,0) (3) 



where X* is the solution of f(X*, P, t) = 0. Any suitably defined 

 metric could be used to describe the distance between H and H*, i.e., 

 the ecological strain: 



S= ||H-H*|| (4) 



As Innis remarked, whether any particular deviation is indicative 

 of a stressed system is somewhat arbitrary and depends largely on the 

 context of the discussion. Woodwell (1975), for example, argued 

 against the threshold concept in ecology. In his view, any chronic 

 stress takes its toll on the ecosystem in the form of a chronic, albeit 

 sometimes small, deviation. The linear view of stress would be quite 

 useful for his purposes. 



In contrast, HoUing (1973) cited the possibility of multiple 

 stationary states for a given ecosystem — several H*, each with its 

 own "domain of attraction" characterized by a finite deviation, 

 Scrit- Deviations in excess of the critical strain can lead to transition 

 into another domain. Furthermore, such transition may incur a 



