444 KILEY [CHAP. 20 



a whole — plants, animals and their component chemical elements — forms a vast 

 and intricately related system. The short cuts that have been discussed accom- 

 plish the immediate purpose of describing seasonal changes in plankton but 

 fail to elucidate the broader principles of ecological relations. 



Ordinary ecological reasoning supplies the principles for a broader quantita- 

 tive theory. Every environment possesses certain distinctive physical features 

 — properties of geography and climate — that determine what kind of population 

 can invade it and which continue to exercise a control of the population by 

 influencing the rates of all life processes. These are independent factors ; they 

 exist whether there is a population or not, although the way they operate 

 depends upon the physiological behavior of all organisms in the community. 

 In addition, the population brings with it a mass of interdependent biological 

 relationships. But a sound analysis must recognize that only the physical 

 factors are basically causal, and the biological relations must be resolved by 

 simultaneous solutions of a series of inter-related equations. 



Riley, Stommel and Bumpus (1949) made preliminary tests of this type of 

 analysis, using data from five areas in the western North Atlantic, ranging 

 from temperate coastal waters to an oceanic region in the subtropics. An 

 abbreviated food chain was postulated consisting of phytoplankton, herbivores, 

 their predators and phosphate. Equations were written for each group and the 

 necessary physiological coefficients were inserted. A review of ecological and 

 physiological data provided a basis for developing relationships between these 

 coefficients and their environment ; however, lack of sufficient knowledge of 

 some processes necessitated the use of arbitrary assumptions. 



Five independent environmental factors were used in the analysis. They 

 were incident radiation, temperature, vertical eddy diffusivity, transparency of 

 the water, and the deep-water concentration of phosphate. Only the first 

 three were fully justified as basic factors. The phosphate in deep water is 

 admittedly affected by biological processes, but the concentration remains 

 sensibly constant so that its effect on the surface layer through the agency of 

 vertical turbulence is both fundamental and predictable. Transparency can 

 hardly be regarded as a basic factor because it is affected by phytoplankton. 

 The relationship could have been included in the analysis, but for the time 

 being it seemed desirable to avoid this added complication. The problem was 

 further simplified by assuming the existence of a steady state. In other words, 

 the calculation determined the quantity of each ecological group that could 

 exist as an equilibrium population with any particular array of primary 

 environmental factors. The steady-state assumption required application to 

 situations in which one could expect a reasonably stable population. 



The mathematical treatment consisted of equations for phytoplankton and 

 phosphate at a series of about twenty depths, extending from the surface to 

 well below the euphotic zone. Herbivores and carnivores were treated simply 

 as a mean concentration in the vertical column. Simultaneous solution was 

 effected by the "relaxation" method of Southwell (1946), an arithmetic pro- 

 cedure of successive approximation. 



