32 DWYER, NIXON, OVIATT, PEREZ, AND SMAYDA 



runoff and wind-driven water turbulence being probably the most 

 important, have not been analyzed quantitatively. River flow varies 

 seasonally, however, with an apparently random storm-runoff com- 

 ponent superimposed on the yearly sinusoid. 



These higher frequency processes appear to be harmonics of the 

 fundamental driving frequency of 1 cycle/year. The presence of 

 significant oscillations in the phytoplankton data at frequencies not 

 found in any of the major environmental inputs indicates the 

 existence of a nonlinearity in the primary production of the 

 ecosystem. These even harmonics are commonly observed in systems 

 where the response is proportional to the square of an input or to a 

 cross product of two inputs. We have not as yet found a specific 

 mechanism in Narragansett Bay which might generate these harmon- 

 ics. 



Sampling of sewage input and phytoplankton response in the 

 6-month microcosm experiment was not designed with spectral 

 analysis in mind. A square-wave sewage input of 3-month 's duration 

 (between arrows. Fig. 2) was attempted. One microcosm receiving 

 sewage and one control (representing many replicates) are shown. 

 The Fourier transformation used in spectral analysis treats this single 

 square wave as a repeating process occurring twice per year; this is 

 the primary spectral peak in both ammonia input and chlorophyll 

 response (Fig. 6). Although theoretically an impulse or step input to 

 a system can yield all the information necessary to calculate system 

 frequency response, the actual generation of the infinite slope 

 characteristic of impulses and step inputs is virtually impossible in 

 the real world. Spectra for both ammonia input and chlorophyll 

 response show secondary peaks at even multiples of 2 cycles/year 

 and a large variance (caused by lack of stationarity) at zero 

 frequency. These tend to mask the possible presence of true 

 harmonics caused by ecosystem nonlinearities. 



Despite our inability to ascertain through this experiment the 

 degree of linearity in our microcosm models, we feel that input of a 

 true sinusoid that repeats many times in the course of an experiment, 

 combined with regular high-frequency sampling, will yield time-series 

 data adequate for estimating ecosystem stability and linearity. 



In another attempt to find linear behavior, cross-spectral 

 analysis for the bay and microcosm time series were performed for 

 all possible single inputs to the phytoplankton compartment. Three 

 examples, representative of the other results, are presented here. 



First, portions of the ammonia and phytoplankton time series 

 which overlap (1972—1974) were used to compute spectra. Cross- 

 spectral analysis of these two spectra generated estimates of 



