SECT. 4] 



THEORY OF FOOD-CHAIN RELATIONS IN THE OCEAN 



451 



Equation (24) was derived empirically but has the sense that carnivores vary 

 in proportion to the square of the herbivore population. 



Steele's equations retain the framework of equations (12) to (14) and pre- 

 serve the interdependence of different food-chain levels but in a more tractable 

 form. They are solved numerically by stepwise integration. 



A sample of the results is shown in Fig. 5. Here seasonal cycles of three food 



0.4 



Fig. 5. Simulated seasonal cycle of phytoplankton, herbivore zooplankton anil phosphate 

 computed by means of equations (22) to (24), using four different values for the mixing 

 coefficient m. 



chain elements are calculated, using four different values for the mixing co- 

 efficient m, ranging from 5% to 0.5% interchange of water between the two 

 layers per day. The well known situation of a diatom flowering accompanied 

 by nutrient decrease and followed by zooplankton increase is faithfully de- 

 picted. According to Steele, the tendency to approach a summer steady state 

 by a series of damped oscillations may be a mathematical artifact. Although 

 phosphorus is strongly limiting in summer, the spring flowering is terminated 



