SECT. 4] 



THEORY OF FOOD-CHAIN RELATIONS IN THE OCEAN 



449 



where v and A are the phytoplankton sinking rate and vertical eddy coefficient 

 as before. 



The analysis shows that there must be an exact balance of processes in order 

 to maintain a steady state, which must satisfy the equation 



Pi(a + b 2 )l(Pi 2 -ab 2 ) = tan fal (21) 



Furthermore, a steady state is not possible if v 2 > 4Aoj 1 , and the depth of the 



Phytoplankton (arbitrary units) 

 4 6 8 10 I? 



20 40 



Eddy diffusivity (4) 



60 



Fig. 4. (a) Vertical distribution of phytoplankton calculated from equations (19) and (20), 

 using four different values for vertical eddy diffusivity. (b) Relationship between 

 eddy diffusivity and phytoplankton sinking rate that is required for maintenance of 

 a steady state according to equation (21). 



productive layer must fall within the limits of < / < 77^81. 



Fig. 4a is a family of curves computed from equations (19) and (20). E, coi 

 and o»2 are the same throughout. a>\ is equivalent to a daily increase of 10% in 

 the upper layer, and o»2 is a 7% decrease below the depth /, which is set at 50 m. 

 Only A and v vary, and their relationship, which must satisfy equation (21), is 



