SECT. 4] THEORY OF FOOD-CHAIN RELATIONS IN THE OCEAN 441 



V is a correction for vertical turbulence given by 



V = 21/22, wheii2i<22, 



in which 22, the depth of the mixed layer, is defined as the maximum depth at 

 which the density is no more than 0.02o t units more than the surface value. 



Phytoplankton respiration was assessed statistically from experimental data. 

 The respiratory coefficient R increased with increasing temperature. The data 

 were not accurate enough to assess the form of the curve reliably, but it was 

 assumed to be a logarithmic relationship. The equation was 



R = 0.0175e°-°69?\ (7) 



where T is the temperature in °C. The grazing rate was postulated to be 



= gH, (8) 



where g is a grazing coefficient and H is the observed herbivore zooplankton 

 population. 



Equations (5), (7) and (8) restate equation (4) in terms of the six environ- 

 mental factors that have been listed. Average numerical values were derived 

 from Georges Bank data and were plotted on a seasonal basis. An approximate 

 integration was then obtained over successive short intervals of time, assuming 

 for each variable a constant average value during that time. In the time 

 interval to t, 



In P t -\n P = Pl-R-G, (9) 



and by a series of such integrations a relative curve of seasonal change was 

 obtained. This was arbitrarily transformed into absolute terms by statistically 

 determining the best fit of the curve for all of the cruise averages for phyto- 

 plankton. Results are shown in Fig. la. 



Subsequently other seasonal cycles were examined (Riley, 1947; Riley and 

 Von Arx, 1949). The first of these was based on observations in southern New 

 England waters off Woods Hole by Lillick (1937), Clarke and Zinn (1937) and 

 Clarke (1938). The second was an analysis of Kokubo's (1940) study of Husan 

 Harbor, Korea. Subsidiary data obtained by the Imperial Fisheries Experiment 

 Station of Korea were also utilized. The theoretical equations were similar to 

 those described above except for minor alterations that were introduced in an 

 attempt to improve the accuracy, such as the use of a photosynthetic tempera- 

 ture coefficient and a nitrate depletion factor in the Husan analysis. Results are 

 shown in Figs, lb and c. 



Although the agreement between observed and calculated values was by no 

 means perfect, the models succeeded in depicting recognizably observed 

 regional differences in seasonal cycles and, in the case of Husan Harbor, 

 differences from one year to the next. In the latter case, the large autumn 

 flowering of 1932 was due to a complex of favorable factors including light, 

 nutrients and a sparse zooplankton crop, whereas in 1933 all three factors were 

 less advantageous. Indeed, these analyses indicated that few major events in 



