FREQUENCY RESPONSE OF A MARINE ECOSYSTEM 21 



Shugart (1972) to estimate ecosystem stability and merged with 

 them ideas about two aspects of ecosystem stability discussed by 

 Holling (1973). These ideas concern the ability of an ecosystem to 

 resist displacement from a stable point and its speed of return to the 

 stable point after perturbation. 



Holling viewed ecosystems as nonlinear entities capable of 

 reorganizing structurally and of assuming different stable states in 

 response to perturbation. A system displaced far beyond changes 

 caused by normal environmental fluctuations can adapt by modifying 

 its structure or function. It may move, perhaps irreversibly, into the 

 attractive domain of a new stable point. 



In contrast, Webster, Waide, and Patten (1975) considered 

 ecosystem stability in a more restricted sense. They viewed normal 

 ecosystem behavior as a linear response to normally occurring 

 environmental fluctuations (Patten, 1975). A perturbation large 

 enough to cause a structural change as an adaptation replaces the 

 original ecosystem with a new one, whose dynamics should be linear 

 about a new stable point. 



In this sense, Webster, Waide, and Patten (1975) redefined 

 Rolling's two aspects of stability and used two parameters from 

 linear frequency -response analysis as estimators of normal ecosystem 

 stability: (1) Resistance is the ability of an ecosystem to withstand 

 displacement by an input and is estimated, inversely, by the 

 undamped natural frequency, cOp, of the system. (2) Resihence is the 

 ability of the ecosystem to return to equilibrium once displaced and 

 can be estimated by the system damping ratio, ^. Both these 

 parameters can be estimated numerically from Bode amplitude and 

 phase plots calculated from linear models (see Child and Shugart, 

 1972; Waide et al., 1974). Webster, Waide, and Patten derived these 

 frequency response parameters for eight different ecosystem models 

 by analytical solution of the linear systems of equations. 



Harwell, Cropper, and Ragsdale (1977), using digital and analog 

 simulations of the same eight linear models, generated stability 

 rankings for the ecosystems which differed from those of Webster, 

 Waide, and Patten (1975). The discrepancies may be partially 

 explained by the presence of nonlinearities in ecosystem response to 

 normal fluctuations. An alternate method for quantifying ecosystem 

 stability, one that can verify stability estimates independently of 

 assumptions in a linear model, would be useful. 



In this paper we apply a method well known in the physical 

 sciences to evaluate the linearity of response to seasonal environ- 

 mental fluctuations of one compartment in a natural ecosystem, 

 Narragansett Bay, Rhode Island. This method, which is based on 

 spectral analysis of time series of input— response data, does not 



