SECT. 4J 



THEORY OK FOOD-CHAIN RELATIONS IN THE OCEAN 



443 



sary to assume a maximum limit for assimilation, which was set at 8% of the 

 animals' weight per day, otherwise the rate of increase would have been too 

 rapid during the spring flowering. The limitation was qualitatively realistic 

 although empirically derived, because it is well known that herbivores at such 

 times eat more than they can digest. Carnivorous predation was attributed to 

 Sagittae and was proportional to their number, although they were not the sole 

 predators. A predation coefficient and the death rate were determined statisti- 

 cally. The results, shown in Fig. 2, were moderately realistic, but the empirical 

 elements made the analysis less acceptable than the phytoplankton treatment. 



Assimilation 



Fig. 2. Seasonal cycle of zooplankton on Georges Bank, (a) Summation of growth pro- 

 cesses. Upper curve is the postulated seasonal cycle of the coefficient of assimilation. 

 From it the coefficients of respiration, predation and natural death are successively 

 subtracted. The remainder, the lowest curve, is the estimated rate of change of the 

 zooplankton population, (b) Dots represent observed zooplankton population; the 

 smooth curve is a theoretical seasonal cycle obtained by approximate integration of 

 the rate curve in (a). 



The equations that have been described transformed the Volterra theory 

 into a promising ecological tool, but an important aspect of the theory was lost, 

 namely the mutual dependence of equations (1) and (2). Fleming postulated an 

 arbitrary rate of zooplankton increase, and the writer used observational data. 

 Ecologists recognize the existence of this mutual dependence in nature. Zoo- 

 plankton growth depends on the quantity of phytoplankton available, and 

 conversely, grazing affects the phytoplankton concentration. Also, the animals 

 and bacteria release inorganic nutrients that influence phytoplankton growth, 

 which in turn reduces the nutrient concentration. The biological association as 



