SECT. 4] THEORY OF FOOD-CHAIN RELATIONS IN THE OCEAN 459 



Equation (31) can be written in the form 



8y/c = 3.2T//(T), (32) 



where T is the biomass of potential tuna expressed in any convenient terms of 

 weight per unit volume of water. Substituting known and assumed values and 

 rearranging, 



0.3x0.02 _ 0.0019/(T) 

 C ~ 3.2T/f{T) ~ T (33) 



Similarly equation (30) can be written 



aj8 S/c = 0.282T/f(T). (34) 



If c is derived from equation (32) and substituted into (34), 



a = 0.0887/18 = 0.0022. (35) 



Calculated in this way, a and c each have the sense of the fraction of prey 

 consumed each day by a unit biomass of predator. 



The value for a seems small, and it remains to be seen whether it will prove 

 to be realistic. There is no frame of reference except temperate waters, which 

 might be quite different. Harvey (1950) found that the biomass of pelagic fish 

 in the English Channel was approximately equal to that of zooplankton. The 

 zooplankton was estimated to have a daily productivity of 10% of the bio- 

 mass. In the present case the biomass of forage animals would have to equal 

 that of zooplankton in order to utilize some 5-10% of the crop per day at the 

 calculated value of a. However, such data as are available (King, Austin and 

 Doty, 1957) suggest that the biomass of forage animals averages little more 

 than a tenth that of the zooplankton. 



It seems unlikely that the physiological coefficients used in deriving a in 

 equation (35) are in error by an order of magnitude, but there is a possibility 

 of a mathematical artifact due to oversimplification of the food chain. Suppose 

 that forage animals consist of two trophic levels instead of one and that F± 

 feeds upon herbivores and F 2 upon F\. The origin of the constant in (35) goes 

 back to the correlation between tuna catch and zooplankton, but this is now an 

 even more indirect relationship because F\ intervenes between h and F2. If 

 the biomass of Fi is less than that of A, a predation coefficient for F% that is 

 derived from the constant in the regression equation must be correspondingly 

 larger. Equation (29) may be rewritten 



f(T) = (0.2»2h/F!)Fi- 3.2, 



and (35) then becomes 



a 2 = 0.08873^2^1, (36) 



where the subscripts 2 denote that these are coefficients for the F<l group. 



A realistic treatment of the food chain would require thorough investigation 

 of such problems. It suffices for the moment to point out that they exist. The 



