36 DWYER, NIXON, OVIATT, PEREZ, AND SMAYDA 



microcosms alleviates most problems by permitting complete envi- 

 ronmental control and making frequent sampling easy. Replicated 

 laboratory microcosms subjected to broad-band white-noise inputs 

 produce flatter response spectra than those produced by natural 

 narrow-band inputs [Fig. 5(d)]. The flatter input and response 

 spectra tend to show more coherence and, thus, are more amenable 

 to cross-spectral frequency response analysis. 



Since there is evidence of a nonlinearity in the Narragansett Bay 

 ecosystem, we investigated the possible use of some nonlinear 

 frequency response methods. The most promising appeared to be the 

 describing function (Shinners, 1972; Brewer, 1974), but its applica- 

 tion produced no useful results. 



Patten (1975), in describing natural ecosystems as linear because 

 frequencies present in the inputs are always present in the output, 

 ignored the possible presence of additional variance at other 

 frequencies in the response spectrum. Another example of the 

 presence of additional variance was recently described by Ollason 

 (1977), who performed a frequency-domain analysis of three 

 freshwater microcosms, each subjected to a different amplitude of an 

 incident-light sinusoid with a period of 4 days. Variance spectra were 

 calculated for time series of the phytoplankton component and three 

 protozoan taxa for each microcosm. The spectrum for phyto- 

 plankton in the microcosm receiving the lowest amplitude sinusoid 

 showed variance only at the input frequency (1 cycle/4 days). 

 Spectra for the other three components of that microcosm and all 

 spectra for the other two microcosms showed substantial variance at 

 frequencies other than the input frequency. Thus the characteristics 

 of the response spectra appear to be functions of the frequency of 

 the input sinusoid, as well as of the system compartment being 

 monitored. We concluded that linearity of response is not a universal 

 ecosystem property and that we must test for it with data from the 

 natural ecosystem before we attempt to model its near-equilibrium 

 dynamics linearly or to estimate its stability properties. 



Spectral analysis is a valuable testing method. Its major drawback 

 is the number and frequency of samples needed to resolve significant 

 peaks in variance spectra. Many studies have already been done, 

 however, in which useful spectra have been computed from 

 ecological time-series data (see Piatt and Denman, 1975). Rapid 

 technological development of automated sampling equipment and 

 phenomenal price decreases for minicomputer systems capable of 

 automated data acquisition will make good environmental time series 

 available to most researchers. As physical scientists have already 

 learned, frequency-domain analyses provide versatile tools for reduc- 

 ing and interpreting these data. 



