SECT. 4] THEORY OF FOOD-CHAIN RELATIONS IN THE OCEAN 461 



stants but vary with age and food supply. However, present information 

 indicates that all of the factors tend to vary together in a general slowing down 

 with increasing age and size, and the relation of the coefficients in the equations 

 is such that the variations tend in part to cancel. Thus they can be altered 

 considerably without having a profound effect on the final result. This is readily 

 demonstrated by postulating some more or less reasonable values and applying 

 them to the equations that have been developed. 



Table I 

 Hypothetical Tuna Physiological Coefficients 



Skipjack Yellowfin or other 



or other similarly large 



small tunas fish 



It will be noted in Table I that y and S' are smaller in the small tunas than 

 in forage animals, and there is a further reduction in the large tunas. This is 

 qualitatively typical of cases that have been examined, although the quantities 

 proposed are open to question. M is equal to the observed growth rate on a 

 daily basis of skipjack in the vicinity of Hawaii (Murphy et al., 1958), and the 

 use of this figure for M assumes a steady state in which growth is balanced 

 against total mortality. It seems reasonable to postulate a lower value for the 

 large tunas. 



As an average sort of equatorial situation, let us suppose that the zooplankton 

 population has a displacement volume of 25 ml/ 1000 m 3 and the tuna catch is 

 6/100 hooks. The forage fish population is assumed to be 3.5 ml/ 1000 m 3 , which 

 appears to be in accord with the trawl data that are available. 



If all of the tunas were of the smaller variety, and if they had no competitors 

 for the available food supply, their potential biomass according to equation (40) 

 would be 1.2 g wet weight/ 1000 m 3 . Putting the result into more familiar terms, 

 this would equal 1.6 lb/acre in a stratum 150 m thick. The estimated annual 

 production would be 1.9 lb/acre. Corresponding figures for large tuna would be 

 2.8 lb/acre for biomass and 1.0 for annual production. This is more or less in 

 accord with the usual concept of the large fishes having a larger total biomass 

 and a slower rate of growth. 



The figures given are small compared with estimated crops on some of the 

 temperate-water fishing banks. However, the annual production is within the 

 same range as commercial catches from some pelagic associations that have 

 been described, such as the cisco and lake trout fisheries in Canadian lakes, as 



