SECT. 4] THEORY OF FOOD -CHAIN RELATIONS IN THE OCEAN 457 



zooplankton which has been obtained either by theoretical methods or field 

 observations. Hence we shall be particularly concerned with feeding and growth 

 efficiency of forage fishes and tuna, and how this information might be used to 

 compute their biomass. The study will also show the kind of information that 

 needs to be acquired in order to understand the dynamics of the fish popula- 

 tion. 



Although not much is known about the production of forage animals, it 

 seems safe to assume that their growth processes qualitatively resemble those 

 of small temperate -water fishes which have been studied, so that it is only the 

 magnitude of the processes which is uncertain. Hence the general form of the 

 relationship between food and growth will be derived from some of the experi- 

 ments that have been reported. The work of Dawes (1930, 1931) is instructive. 

 Small plaice in their third year (20-120 g) were fed varying amounts of food, 

 from a maintenance ration, 31, which was just enough to hold the weight 

 approximately constant, to about five times this amount. A 2M ration was 

 sufficient to double the size during one summer growth season. There was a 

 further increase with maximal feeding but at reduced efficiency. The daily 

 maintenance ration was of the order of 1-2.4% of the weight of the fish, the 

 percentage decreasing with increasing size of the animals. Between M and 2M 

 the growth increment averaged about M/S. 



These relations can be put into a simple equation provided the available 

 food is relatively scarce, permitting the assumptions (a) that the fish eat all 

 prey encountered, and (b) that there is a constant efficiency of conversion. Then 

 for the forage fishes 



Total consumption = ah, 



where h is the concentration of herbivore zooplankton, and a is a predation 

 coefficient. 



Total assimilation == afih, 



where /3 represents the fraction of consumption that can be assimilated (0.8- 

 0.9 in most fishes according to Ricker, 1946). If y is defined as basal plus work 

 metabolism, 



Growth = 8(afih — y), 



where S is the fraction of the excess over maintenance that results in an increase 

 in weight (generally 0.3 or more in small fishes). 



The rate of change of the forage animals can now be given as 



^ = F[8(af3h-y)-cT], (26) 



where F is forage animals, and c is the coefficient of capture by potential tuna, 



