458 KILEY LCHAP. 20 



T. If the population exists in a steady state in a particular locality, equation 

 (26) reduces to 



F\8{aph-y)-cT] = 0, 



cT = 8(a^h-y), 

 and 



a@ 8 /, 8y 



T 



»-?■ < 27 > 



We must recognize that although zooplankton can be stated in terms of 

 biomass, the available tuna data represent catch per unit of effort, which is 

 presumed to be a function of biomass but cannot be translated easily into 

 absolute terms. Thus equation (27) may be written 



,<*>'_ /(3|«.A-£), (28) 



where f(T) is the tuna catch per 100 hooks, and /is a conversion factor relating 

 tuna biomass to catch. 



Statistical analysis of zooplankton volumes and tuna catches can be used to 

 derive empirical constants for (28). Pairs of values were read from Sette (1955, 

 fig. 7). The correlation for observations north of the equator was 0.80 (0.01 > 

 P> 0.001). Inclusion of data from south latitudes lowered the correlation to a 

 relatively insignificant level. The regression equation for north latitudes is 



f(T) = 0.282/^-3.2, (29) 



so that the statistically computed constants are 



/(aj8S/c) = 0.282 (30) 



f(8y/c) = 3.2. (31) 



These will be applied to a further consideration of north equatorial waters. 

 They are obviously unsuitable for regional extrapolation. 



Although the constants in these equations are a cumbersome conglomeration 

 of terms, they have been kept intact rather than substituting a simpler notation 

 to emphasize the fact that they have biological meaning and are not merely 

 empiricisms. It would be desirable sooner or later to evaluate them in quantita- 

 tive terms. /3, y and 8 have been measured in experiments with various fishes 

 and presumably could be determined for some of the forage species, a and c are 

 more difficult in that predatory habits are so much a part of the natural environ- 

 ment in which they occur that one would hardly expect to get realistic results 

 under controlled observation. However, equations (27), (29) and (30) provide 

 an indirect method of dealing with these constants provided we know the other 

 physiological coefficients. Let us assume for purposes of discussion that jS = 0.8, 

 y = 0.02 (on a daily basis) and S = 0.3. These are reasonable values for some of 

 the fishes that have been examined and presumably are at least of the right 

 order of magnitude for present purposes. 



