452 1ULEY [CHAP. 20 



by grazing before phosphate declines to the point that is postulated as limiting 

 in the model. In this respect the model agrees with the conclusions of other 

 investigators cited above as to the importance of the grazing effect in British 

 waters. Steele also calculated other cycles, examining the effects of variations 

 in sinking, grazing and photosynthetic rates. 



In a later paper (Steele, 1961), equations (22) and (24) were slightly modified 

 to analyze a situation in which light intensity varied from day to day in 

 accordance with observed radiation at Aberdeen, Scotland, in May and June. 

 1957. In essence this is a simple stochastic treatment. Large random fluctua- 

 tions from day to day during the early part of the period had only a slight 

 effect on the phytoplankton population. Later there was a week of bright 

 weather followed by a slightly longer period of low radiation. These systematic 

 variations resulted in the growth and subsequent decay of a phytoplankton 

 flowering of considerable size. Changes in phosphate and zooplankton were less 

 pronounced. 



Steele also presented a theoretical analysis of the effects of zooplankton 

 patchiness on the distribution of phytoplankton and phosphate. His model 

 demonstrated that zooplankton patches produced a significant reduction of 

 phytoplankton if they remained in contact with the same plant population for 

 about a week. Changes in phosphate were relatively small. 



Steele's models of time series represent a simple and orderly series of events. 

 But if pairs of values for phytoplankton and zooplankton or any other two 

 biological variables are taken from the graph and plotted together, the correla- 

 tion is distinctly non-linear, because of time lags and other non-linearities in 

 the relationships that are involved. In the case of phytoplankton and zoo- 

 plankton, the curve is roughly elliptical. Steele pointed out that with sufficient 

 random scatter the elliptical form would not be obvious, and the relationship 

 would simply appear to be a poor correlation. This was demonstrated in the 

 analysis of the effect of stochastic fluctuations of zooplankton. 



The importance of this concept lies in the fact that relationships observed in 

 a time series are essentially analogous to horizontal variations found in nature. 

 In certain cases this is clearly demonstrable, as when a spring flowering begins 

 in shallow water and gradually spreads to deeper water, so that the time series 

 can be equated with onshore-offshore distance. Similarly, in a tropical area of 

 upwelling, time is synonymous with distance along the path of movement 

 away from the area of upwelling. Commonly, horizontal variations are more 

 randomized, but the existence of a variety of stages of development at successive 

 sampling points tends to be supported by horizontal variations in the quantity 

 of plankton, species composition and photosynthetic coefficients. Thus the 

 anatysis demonstrates that, with conventional sampling, apparent randomness 

 and poor correlations between different biological variables can result from well 

 defined processes. Steele further points out that lines or grids of stations per- 

 haps are not well suited for the study of plankton problems and that detailed 

 sampling of small and unusually homogeneous areas may be necessary in order 

 to reveal the biological patterns of the growth process. 



