PREDATION AND EFFICIENCY IN LABORATORY POPULATIONS 237 



in which P' is the steady state population standing crop in calories maintain- 

 able under the given predation system, and P is the standing crop in the 

 absence of predation. If / is independent of predation, it can be shown that 



y _ Y 

 FY ~ FAc (4) 



in which Ac is the increase in maintenance cost per calorie day of standing 

 crop that is attributable to predation. Population efficiency is the yield to 

 the predator per maintenance cost increase associated with predation. 



Equation (4) is derived from the following argument : 



In order to maintain hving protoplasm, energy must be expended. The 

 greater the necessary expenditure per calorie day of standing crop the smaller 

 the standing crop that can be maintained by a given energy income per day. 



In general, increase of I will imply increase of P, but the precise form of 

 the relation between P and I is not obvious a priori. For Daphnia, since it has 

 been experimentally demonstrated that P is a linear function of /, we can 

 write: 



I=Pc (5) 



and if J is not altered by predation we can write: 



I = P' (c + Ac), (6) 



which permits us to establish the identity : 



P'Ac = I (.-'-), 



The population efficiency, Ep^, associated with a predation procedure that 

 removed only one kind of yield animal, /, can be evaluated from the equation 



i=p'c+i^ (7) 



^pi 



when data from a sufficient number of populations, each subjected to 

 different predation procedures, are available. 



This equation was solved using three categories of yield and steady state 

 data from twenty-two experimental D. pulex populations (Slobodkin, I959)- 

 A least squares solution for c and the three population efficiencies indicated 

 that a predation system which took only adult animals as yield, would have 

 a population efficiency of 48 per cent, while removal of only young animals 

 would have a population efficiency of 4 per cent. If it were possible to take 

 only eggs as yield the population efficiency would be 6 per cent. 



