456 RILEY [CHAP. 20 



correlations that were established by Sette (1955) for phosphate, zooplankton, 

 and tuna in the tropical Pacific, the relationship appeared to be non-linear. 

 Moderate regional variations in zooplankton were accompanied by larger 

 variations in tuna. 



Smith and Swingle (1939) demonstrated a similarly non-linear relation 

 between particulate organic matter in fertilized fish ponds and production of 

 blue gills. In this work the fish were introduced as fry and fingerlings, and the 

 ponds were drained at the end of the test period to recapture the product of a 

 season's growth. Thus the results were more accurate than is commonly the 

 case in fisheries work. 



This is a type of relationship that can be examined readily with the aid of 

 simple mathematical models. Certain other non-conformities between basic 

 productivity and fish production probably are the result of competition 

 between fishes and commercially unimportant species. For reasons given above, 

 such relations do not warrant theoretical investigation at the present time. 



Aside from its complexity, the upper end of the food chain presents certain 

 other problems. It is only in certain special cases that the true biomass of a 

 fish population can be assessed accurately. If the model is to be compared with 

 nature, a relationship generally must be established between theoretical bio- 

 mass and catch per unit of effort. Also physiological studies and feeding experi- 

 ments on fishes have been somewhat different from the zooplankton investiga- 

 tions, necessitating slight changes in model methods. Thus it seems desirable 

 to develop a simple model of the upper end of a food chain, perhaps more as an 

 investigation of methods than for any intrinsic merit. 



A pelagic food chain in tropical and subtropical waters is postulated, con- 

 sisting, as in earlier studies, of phytoplankton, herbivores and first-order 

 carnivores ; but in addition a second order of carnivores is proposed. The first 

 order carnivores are in actual fact a mixed group consisting of small fishes, 

 squids and Crustacea. The common collective term for this group is forage 

 animals. More than one level of the food chain may be included, and probably 

 the situation is more accurately characterized as a food web rather than a food 

 chain. However, in the first approximation, the forage animals are regarded 

 as a single level having the characteristics of small fish. 



The second order carnivores are a hypothetical entity called potential tuna. 

 This means that the model seeks to determine the quantity of tuna that could 

 be supported in a given area on the food that is available. This is expected to 

 be a maximal estimate because the tunas compete for food with other groups 

 such as sharks and marlin. Also any variations not associated with the food 

 supply of adult fish, such as migrations and year class fluctuations, are ignored. 

 Thus the actual quantity of tuna in a given area at any one time might be more 

 or less than the potential crop. Because of these simplifications the model has 

 little immediate value, but on the other hand it deals with one of the weakest 

 aspects of fisheries biology, namely an understanding of the supporting power 

 of a given area and the potential yield. 



The analysis presupposes that there is information on phytoplankton and 



