SECT. 4] THEORY OF FOOD-CHAIN RELATIONS IN THE OCEAN 455 



seasonal cycle in a given locus or a steady-state model of a vertical profile. 

 More than two dimensions would be extremely awkward to handle. 



Four of the five independent factors previously employed are acceptable for 

 further use in analyses of open ocean conditions, namely light, temperature, 

 vertical eddy diffusivity and the deep-water concentration of a limiting nutrient. 

 Transparency should be treated in part as a biological variable. Riley (1956) 

 found that a satisfactory equation for use in the open sea is 



k = 0.04 + 0.0088(7 + 0.054C%, (25) 



where k is the extinction coefficient of visible light, and C is [ig of chlorophyll 

 per liter. In shallow water additional terms would have to be added for ex- 

 tinction due to suspended silt and bottom sediment. 



Some types of problems would require inclusion of horizontal diffusion, 

 currents and, perhaps, upwelling as primary factors. Coastal waters present a 

 special problem in that the nutrient supply is influenced by runoff and by 

 transport along the bottom from offshore. This could be handled as a steady- 

 state profile extending from shore to deep water. However, a seasonal cycle in 

 a particular area would require some rather arbitrary coefficients of external 

 enrichment. 



5. Higher Elements of the Food Chain 



All of the models thus far constructed have dealt almost exclusively with 

 plankton. There are serious difficulties in attempting to extend the analysis to 

 higher food-chain levels. The multiplicity of species with individual food habits 

 does not lend itself to division into broad ecological groups. The alternative of 

 dealing with individual species not only would be impossibly laborious but 

 also would create some theoretical problems for which there are no clear 

 solutions in sight. Above the plankton level, food chains tend to become 

 intermeshed and often are more properly called food webs. A realistic treatment 

 must permit organisms to feed at more than one level of the food chain and 

 must make allowance for varying degrees of competition between species that 

 have an overlapping diet. There must also be provision for detritus feeders. 



The prey-predator equations are ideal for working with a simple, linear food 

 chain but obviously are ill-suited for a food web. It would be necessary to set 

 up a series of partial feeding coefficients corresponding to the various sources 

 of supply. Competition for the same food supply would be an even more difficult 

 problem. In the present state of our knowledge, any attempt to deal theoreti- 

 cally with these problems would probably be artificial and trivial. 



Thus there seems to be little point in trying to create realistic models of 

 higher food-chain elements until we possess better descriptive knowledge. 

 However, deliberately oversimplified models might be instructive, since the 

 problem of overall food-chain efficiency is not well understood. Riley (1956a) 

 has noted that there is not a close relationship between plankton productivity 

 and commercial fish yields in coastal and bank waters. Even in the clear 



