458 W- T. Edmondson 



the standard error of estimate (S.E.E.) which, following Snedecor (1946, p. 117), 

 can be used as a measure of dispersion of the points from the line of best fit, entirely 

 analagous to the standard deviation in a frequency distribution. 



It will be of interest to compare the standard errors of estimate of the regression 

 equations with the standard deviation of the rate of photosynthesis, 0-545. 



When photosynthesis is taken as a function of chlorophyll concentration alone 

 (Fig. 2), the standard error of estimate is 0-420. When surface Hght intensity is added 

 as a second independent variable, the standard error of estimate is reduced to 0-382 

 (Fig. 3). The equation relating these variables is P = 0-0172C — 0-0056L - 0-273. 

 Taking further account of the volume of plankton does not decrease variability, but 

 taking account of phosphate concentration reduces the standard error of estimate 

 still further to 0-283. In this analysis, phosphate concentration gives better results 

 than does the rate of phosphate assimilation. 



Thus, a large fraction of the deviation from the regression line can be accounted 

 for statistically by variations in chlorophyll, light, and phosphate concentration. 

 (Compare with Riley, Stommel and Bumpus, 1949.) The regression equation which 

 relates these four variables is : 



P = 0-0304C + 0-0052L + 0-0275F - 0-239 (S.E.E. 0-28). This equation des- 

 cribes the relationships which existed among the variables during the course of the 

 experiment; but, on the basis of the known physical mechanisms involved, we can 

 regard it additionally as a statement of relative effect of controlUng factors. 



The massive doses of phosphate which were added to the tanks do not represent 

 usual concentrations available in natural conditions. Examination of the data shows 

 that a positive relation with phosphate concentration existed only when the entire 

 range of concentration was considered. Within the small range of variation of phos- 

 phate concentration usually met in natural waters, no correlation existed. Each tank 

 behaved somewhat differently from the rest, and the relationships with phosphate 

 concentration in the water are too complex for further discussion in this paper. 



The hght intensity to which reference has been made above is that at the surface 

 of the water. Since the transparency of the water changed with the size of the popula- 

 tion, the intensity to which the bottles were exposed is different, and not by a constant 

 ratio. The intensity at a depth of 50 cm was calculated from measurements of trans- 

 parency made by Mr. C. M. Weiss, and used in computing the points shown in Fig. 

 4, derived from Fig. 3. It is seen that, by taking account of the transparency of the 

 water, the field of points is made more nearly linear and the regression line comes 

 closer to the origin than in Fig. 3. The correlation coefficient r^^c is 0-86. While 

 the difference from rp-^ is not significant statistically, it is distinctly larger. The 

 equation shown in the figure is: 



P" = 0-735C + 3-057 (S.E.E. 10-72) 



This treatment of the light data is something of an over-simplification, since it 

 implies that there is a direct and hnear correlation between rate of photosynthesis 

 and hght intensity. While the tanks were shaded to prevent inhibition by bright 

 hght, the sun was able to shine in during a small part of the day, and a simple pro- 

 portionahty is not to be expected. However, deviation is not serious, and a more 

 detailed analysis of the available data is not justified. Nevertheless it should be reahzed 

 that a more elaborate treatment of light might result in considerable reduction in 



