SECT. 4] 



where 



THEORY OF FOOD -CHAIN RELATIONS IN THE OCEAN 



1-I5[1*+1*E» 



447 



(18) 



P r is production below z meters during the time interval At ; pi, p 2 are the 

 phytoplankton populations at the beginning and end of the interval ; 8p/8z, 

 8T/8z are mean gradients of population and temperature at depth z ; hi, h% are 

 the concentrations of zooplankton. 



The left-hand side of equation (17) contains only p-i. The right-hand side, in 

 addition to p\, also contains pz as is apparent in equation (18). However, the 

 third term on the right is much smaller than the others, so that equation (17) 

 can be used to predict p 2 by successive approximation. 



Plont pigment units/I 

 2 3 4 



a 100 - 



150^ 



200 



fxq atoms P/l. 



Fig. 3. Dots are mean values for phytoplankton (Harvey plant pigment units) at four 

 stations in the slope water off southern New England in May, 1939 (Riley, Stommel 

 and Bumpus, 1949). Smooth curves are theoretical vertical distributions of phyto- 

 plankton and phosphate calculated from equations (12) and (13). 



The mean value for the upper 20 m was computed. This was used to deter- 

 mine the 30-m value, and so on to 50 m or more. Calculations were first made 

 with the derived values for g and v, but in some cases these were altered later 

 in order to see if more realistic results could be obtained. In general there was 

 good agreement between the model and observations. 



Steele's method of calculating g and v is a useful biproduct of mathematical 

 models. In both processes, laboratory experiments have given highly variable 

 and sometimes conflicting results, and the sinking rate in particular cannot be 

 predicted even to the nearest order of magnitude. But if most of the terms in 

 the equation are known with some degree of confidence, one or two unknowns 

 can be evaluated. In the present case there was evidence of a seasonal change 

 in the sinking rate, which could hardly have been discovered in any other way. 



