SAILA and PARRISH: EXPLOITATION EFFECTS 



1-1X12-012-^2 



hi2(ai2-bi2) 



hi3(ai3-bi3) 



1-m3-q3-f3 



Figure 4.- 



-Trophic graph of Species 2 and Species 3 

 preying on Species 1. 



and solving them simultaneously in the classical 

 manner. For competitor Species 2, Ri2 was writ- 

 ten as the sum of its inputs in the graph, and B2 

 was written as the sum of its own inputs. In 

 this case there are two equations in the three 

 variables B2, Bi, and Rn. R12 was eliminated 



to give B2/B1 in terms of coefficients. B^/Bi 

 was derived in a similar manner, and division 

 gave the ratio of the biomass of the two com- 

 peting species B2/B3 as follows: 



where: 



Inspection of Equation (18) reveals that if the 

 two species compete exactly equally, or are ex- 

 ploited equally, the ratio is unity. This is en- 

 tirely the expected result. By giving one species 

 or the other a competitive edge in one or an- 

 other of the coefficients, it is apparent that the 

 B2/B3 ratio can be changed. 



The simplest subweb involving predation on 

 two competing species is shown in Figure 5. 

 In this subweb Species 4 preys on Species 2 and 

 Species 3, and Species 2 and Species 3 prey on 

 Species 1. The procedure for deriving the ra- 

 tios B2/B1 and B3/B1 was exactly as described 

 above. That is, an equation was written for each 



l-mj-qj-fj 



l-m.-q.-f. 



l-rtij-qj-fs 



Figure 5. — Trophic graph of a 4-species subweb. In 

 this case Species 4 preys on Species 2 and Species 3, 

 and Species 2 and Species 3 prey on Species 1. 



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