440 RiLElY [chap. 20 



surface, and a is a constant growth coefficient during the flowering period ; b is 

 the initial grazing coefficient ; the zooplankton is postulated to increase linearly, 

 so that grazing increases at a constant rate, c, per unit of time t. Using values for 

 the coefficients that had been estimated by Harvey et al., Fleming integrated 

 equation (3) and obtained a bell-shaped, symmetrical curve that approximated 

 observed conditions in nature. 



Riley (1941) obtained a series of observations on Georges Bank, including 

 measurements of phytoplankton, zooplankton, certain environmental charac- 

 teristics of the water and experimental determinations of phytoplankton 

 photosynthesis. These later (Riley, 1946) provided the basis for a theoretical 

 evaluation, again based on equation (1). A general equation was stated, 



dP 



a -L = P(P h -R-G) (4) 



in which P again is the total phytoplankton population per unit area of sea 

 surface, P h is a photosynthetic coefficient, R is the coefficient of phytoplankton 

 respiration, and G is a grazing coefficient. P h — R is analogous to b\ in equation 

 (1) and to a in (3), except that these terms are now to be regarded as ecological 

 variables rather than constants. 



Photosynthetic experiments in winter and early spring indicated a more or 

 less linear relationship between photosynthesis and incident radiation. Later 

 in the season there was a reduction in the rate that was correlated with phos- 

 phate depletion. The experiments were carried out on surface water, but it 

 was reasonable to suppose that the depth of the euphotic zone, as indicated by 

 transparency measurements, would affect the mean photosynthetic rate of the 

 total population. This mean rate was roughly computed by integrating the 

 illumination from the surface to a depth where the light intensity had a value 

 of 0.0015 g cal cm -2 min -1 and dividing by the depth of the layer. In winter 

 the depth of the mixed layer exceeded that of the euphotic zone, so that part 

 of the population was mixed downward to a depth where photosynthesis was 

 negligible. It was assumed in such cases that the photosynthetic coefficient was 

 reduced in proportion to the ratio of the depths of the two layers. In short, 

 photosynthesis was postulated to depend upon incident radiation, trans- 

 parency of the water, depth of the mixed layer, and phosphate. The equation 

 was 



P h = (pIoJkzJil-e-teiNV), (5) 



where p is an experimentally derived photosynthetic coefficient, Iq is incident 

 radiation, k is the extinction coefficient of visible light, and z\ is the arbitrarily 

 denned depth of the euphotic zone. N is a nutrient factor, here designated as 

 phosphate in [xg atoms P/l., and 



ug atoms P/l. . _, n „„ 

 N = ^ L — l — - — — i when P< 0.55. (6) 



0.55 



