164 Information Storage and Neural Control 



this particular grapii is rotated 90° clockwise around the vertical 

 axis (compared to previous figures of this type) to improve the 

 perspective in which the surface is viewed. Studying the surface 

 from back to front first, we see that cost increases in a generally 

 hyperbolic or logarithmic fashion with depth of collection; the 

 surface is saddle-shaped, being convex upward from back to front. 

 The fact that it rises toward the viewer supports the previous 

 conclusion that the deeper populations are less viable than those 

 nearer the surface — their cost of operation is higher. The ribbon- 

 shaped segment in the figure denotes the loci on the surface and 

 on the horizontal plane where the ratio p7r~^ is unity, i.e., where 

 an exact balance between energy inputs and expenditures is 

 achieved. For any specified collection depth, this ribbon indicates 

 the depth at which the sample must be suspended to achieve a 

 steady state between inputs and losses. This depth is seen to become 

 shallower as the collection depth increases — another indication of the 

 intrinsically higher vitality of populations found nearer the surface. 



Viewing the surface of Figuie 12 from right to left, cost is shown 

 to increase as suspension depth is increased. In this direction the 

 surface is concave upward. Thus, despite the measure of dark- 

 adaptability demonstrated earlier, the price to a population of 

 inhabiting deeper layers in the water mass is unequivocally in- 

 creased cost of operation. This datum appears to provide an 

 economically logical reason for stratification. A well-known doc- 

 trine from marginal analysis in economics (39) states that the 

 scale of an activity should be expanded so long as marginal 

 profitability (increase in net utility gain) is a positive value, and 

 carried to a point where marginal yield is zero. This corresponds 

 to the procedure in calculus of maximizing a function by setting 

 its first derivative to vanish. Applied to the plankton, this law 

 demands, in view of observed depth-cost relationships, that the 

 community should invest biomass energy to concentrate its com- 

 ponent organisms near the surface up to the point where additional 

 return becomes zero. It would appear that the stratification 

 behavioi of the York River plankton is consistent with sound 

 economic policy. 



The converse of the marginal profitability law would be: If 

 marginal gains are negative, the scale of an activity should be 



