20 DWYER, NIXON, OVIATT, PEREZ, AND SMAYDA 



purposes, to describe mechanisms regulating the behavior of the 

 ecosystem and to predict the effects of disturbances to the system 

 (Wiegert, 1975). Debate concerning optimal methods for achieving 

 these goals continues. In particular, the level of detail included in the 

 model (e.g., the number of state variables or compartments, the form 

 of the interaction equations, the possible inclusion of uncertainty in 

 model structure and function, the importance of spatial and 

 temporal heterogeneity, and methods for model validation and 

 sensitivity analysis) has been a topic for lively discussion (Wiegert, 

 1975). 



We have focused this study on one controversial aspect of 

 modeling philosophy — the usefulness of limiting ecosystem models 

 exclusively to systems of linear equations. We show^ that an adequate 

 description of ecosystem stability properties cannot always be 

 derived from a linearized model of the ecosystem. 



The advantages and drawbacks of linear modeling methods were 

 discussed in detail by Wiegert (1975), O'Neill (1975), and Bledsoe 

 (1976). They agree that a variety of techniques exist for dealing with 

 systems of linear equations and that linear analysis may be valuable 

 for the range of behavior over which an ecosystem is known to 

 respond linearly. All conclude, however, that there is little a priori 

 justification for applying linear methods to all ecosystem studies and 

 that the convenience of linear methods is one major reason for their 

 use in many ecosystem studies. 



One technique frequently employed is linear frequency response 

 analysis. In this paper we evaluate the usefulness of this methodology 

 in an instance when the linearity of ecosystem behavior is not 

 apparent. 



Child and Shugart (1972) estimated the frequency response of 

 their linear model of magnesium cycling in a tropical forest by 

 perturbing it with a spectrum of sinusoidal inputs. They used plots of 

 response amplitude, normalized with respect to input amplitude, vs. 

 frequency and of phase shift vs. frequency to provide information 

 about linear system properties. These are the Bode plots familiar to 

 engineers [see Fig. 7(a)] and can be used to write a transfer function 

 for the system, which is a Laplace-transformed, linear differential- 

 equation model. Child and Shugart (1972), Shinners (1972), Brewer 

 (1974), or any elementeiry systems text will provide a more thorough 

 discussion of Bode plots and frequency-response techniques. 



Waide et al. (1974) used similar frequency domain methods to 

 evaluate the stability and sensitivity to perturbations of a linear 

 model of calcium cycling in the Hubbard Brook, New Hampshire, 

 watersheds, a temperate forest. Webster, Waide, and Patten (1975) 

 extended the linear frequency response methods used by Child and 



