2 ULANOWICZ 



tensile stress) was presumed linear. Twice the stress resulted in twice 

 the strain. 



The modulus of elasticity (the ratio of strain to stress) as a 

 property of a solid is useful if we are designing a structure such as a 

 bridge, but it is often necessary to know also the behavior of a solid 

 system under extreme stresses. In fact, as the stress on a metal rod 

 increases, a point is reached where the strain becomes dispropor- 

 tionately larger than the applied force. Not long thereafter the rod 

 reaches the critical point; i.e., the strain is such that the rod will no 

 longer return to its original state. Still further stress leads to 

 increasingly disproportionate strain, culminating in a catastrophe 

 when the rod loses its identity (yield point). 



The behavior of a simple mechanical system under heavy stress 

 differs markedly from its corresponding response to low stress. It is 

 significantly nonlinear, and it culminates in loss of system structure. 

 It is this response to heavy stress that is important to psychologists 

 and physiologists, for whom stress has come to mean a "response to 

 external or internal processes which reach those threshold levels that 

 strain its physiological and psychological integrative capacities close 

 to or beyond their limits" (Basowitz et al., 1955). 



Stress, therefore, takes on different connotations for the engineer 

 and the psychologist. Although it may not be obvious, this dual 

 meaning of stress is found in ecological research. Ecologists have 

 been slow to define and accept a useful measure of the response of 

 the ecosystem to stress, i.e., ecological strain. Just as it is impossible 

 to discuss mechanical stress without considering its conjugate, strain, 

 the discussion of stress in ecological systems is fragmentary without 

 some hypothetical measure of system strain. Before attempting a 

 working definition of strain, however, we should consider how stress 

 arises in ecosystem models. 



Although ecosystem models may be stochastic, discrete, spatially 

 heterogeneous, etc., much of systems analysis, following the lead of 

 the early modelers, has concentrated on deterministic, first-order, 

 ordinary differential equations, such as (see Lotka, 1957), 



X = f(X,P,t) (1) 



where X is a vector of state variables, t is time, and P is a vector of 

 parameters. Parameters of a model include initial conditions, fluxes 

 into and out of the system, and characteristics of the functional form 

 of f (such as exponents or multiplicative constants). 



The external world may impinge on the ecosystem (exogenous 

 stress) through arbitrary variations in P and X; X may change 



