454 RILEY |"CHAP. 20 



maximum limit would be imposed on production by the rate of nutrient supply, 

 but wide variation would be possible below this limit. Their theory, reduced to 

 its simplest terms, is expressed by Volterra's equations for prey and predators, 

 modified only to the extent that a maximum limit is postulated for the con 

 centration of prey. At lower concentrations there would be prey-predator 

 oscillations. 



Moreover, if nutrient limitation is removed from (14), the zooplankton 

 population will depend only on light and temperature. This leads to unaccept- 

 able results. For example, there would be little difference in zooplankton 

 concentrations in up welling and non-up welling areas in the' tropics, or between 

 temperate and subtropical waters in summer. 



If the 14 C method essentially measures net production, as claimed by Ryther 

 (1956), these difficulties could be avoided by devising an ecological equation for 

 14 C uptake. It is too early to decide what factors would need to be used, but 

 presumably light intensity would be involved and probably a nutrient factor. 

 Holmes, Schaeffer and Shimada (1957) have clearly shown that high net 

 production coefficients are associated with nutrient enrichment in the equatorial 

 dome of the eastern Pacific. King, Austin and Doty (1957) obtained similar 

 results in the equatorial belt of up welling in the central and eastern Pacific. 

 These authors kindly put their data in the hands of the writer for a comparison 

 of 14 C uptake per unit of chlorophyll and the initial phosphate concentration 

 in the experiments. There was a large amount of scatter, but the correlation 

 coefficient of 0.32 was significant (P < 0.001). This is a promising result, es- 

 pecially since phosphate levels in the Pacific are so high that probably phosphate 

 is merely serving as a crude index of variation of some other element that is 

 more important as a limiting factor. 



However, in contrast with these results, Ryther and Yentsch found no 

 correlation between 14 C production coefficients and nutrients in New England 

 waters, a result later confirmed by Steele and Baird (unpublished MS) in the 

 North Sea. But the latter authors found that the chlorophyll content of the 

 phytoplankton declined, relative to total carbon, when phosphate was deficient. 

 Thus a production coefficient stated in terms of 14 C uptake per unit of phyto- 

 plankton carbon would be nutrient dependent. These results tend to invalidate 

 the use of chlorophyll in production coefficients that are to be applied to model 

 work unless there is thorough knowledge of chlorophyll : carbon ratios. 

 And unfortunately there are many circumstances in which measurement 

 of phytoplankton carbon is difficult or impossible because of associated 

 detritus. 



Some of the other physiological coefficients, as well as sinking rates, exist in 

 a similar state of flux and uncertainty. Thus it is premature to attempt to make 

 models more realistic until some of the immediate problems have been solved. 

 However, it seems worthwhile to discuss briefly some of the elements that might 

 be embodied in any future attempt. 



Although the main concern thus far has been with one-dimensional, steady- 

 state models, two-dimensional models are possible. These could be either a 



