SECT. 4] THEORY OF FOOD -CHAIN RELATIONS IN THE OCEAN 453 



4. Prognosis for Mathematical Models 



Simple models of the type developed by Steele are invaluable in improving 

 our insight into plankton problems, and the results generally are sufficiently 

 realistic to fulfill most of the functions of a quantitative analysis. 



The more complicated models which attempt to be faithful to nature are 

 limited by the state of our physiological knowledge. In recent years some 

 interesting new techniques have been developed for measuring physiological 

 processes in nature and in the laboratory. However, these are too new to be 

 thoroughly trustworthy, and in some cases there are unresolved conflicts 

 between new and old methods. The future is promising, but at the moment it 

 must be admitted that little progress is being made in the development of 

 complex models. 



The study of phytoplankton production is a typical example of an un- 

 resolved physiological problem. Riley, Stommel and Bumpus (1949) developed 

 an empirically realistic equation for surface photosynthesis in which the 

 ecological variables were light, temperature and phosphate. The equation 

 provided an adequate expression for some 215 experiments on surface popula- 

 tions in temperate and subtropical waters of the western North Atlantic. 

 However, there was not enough information available to devise a realistic 

 treatment of subsurface production. The models used the same equation for all 

 depths, so that photosynthesis declined with depth in proportion to the decrease 

 in light intensity. Admittedly this was a lame device, and the method needs to 

 be overhauled. 



Ryther and Yentsch (1957) proposed a simpler method involving only light, 

 which was applied later (Ryther and Yentsch, 1958) with a fair degree of 

 success to southern New England coastal waters. According to these authors, 

 there appears to be an adjustment of the population to any particular light 

 intensity such that the rate of production and the nutrient supply are in 

 balance. Therefore nutrients do not need to be specifically represented in the 

 formula. The validity of this concept appears to be supported by data in 

 the paper cited, but it remains to be determined how generally applicable the 

 method will be to the varying degrees of non-steady states that sometimes are 

 found in nature. It is not applicable to Georges Bank data obtained by Riley 

 (1941) except in experiments with an initial phosphate concentration of 

 0.4 Ltg atom P/l. or less. At the highest concentrations encountered, the average 

 observed photosynthesis was twice the predicted value. 



Ryther and Yentsch handled the problem of subsurface photosynthesis 

 more realistically than Riley, Stommel and Bumpus, and the overall accuracy 

 of their method may be superior. However, it is not suitable for mathematical 

 models. The interplay between nutrients and phytoplankton that is found in 

 (12) and (13) and in (22) and (23) is the only guarantee of stability in the 

 system. If phytoplankton production is limited by the supply of nutrients but 

 is independent of nutrient concentrations, as postulated by Ryther and Yentsch, 

 there is no theoretical reason for the system to achieve a steady state. A 



