FISHERY BULLETIN: VOL. 70. NO. 2 



specific conditions. He graphed the relationship 

 between a prey and a predator as shown in Fig- 

 ure 2(a). For simplicity, all the vertices (cap- 

 ital letters) can be standardized in energy units 

 (or energy per unit time). The lower case co- 

 efficients are dimensionless constants or have a 

 dimension of reciprocal time with values between 

 zero and 1.0. Vertices and coefficients are listed 

 in Table 1. Subscript 1 refers to the prey and 

 subscript 2 refers to the predator. When an- 

 other trophic level is added later, use of these 

 subscripts can be easily extrapolated. For ex- 

 ample, Di2 in Figure 2(a) is the amount of Prey 1 

 accessible to Predator 2; D24 in a later graph is 

 the amount of Prey 2 accessible to Predator 4. 



The symbols used in Figure 2 are further de- 

 fined in the following manner. 



Table 1. — Description of the vertices and coefficients 

 utilized in model development. 



^-© 



(a) 



q,(-1)(1) 1-m2-f2 



di2(1)bi2 



hi2(-1)bi2 



di2bi2 



hi2(ai2-bi2) 



(b) 



(c) 



Figure 2. — Trophic graphs of Species 2 preying on Species 1. Part (a) illustrates Menshutkin's (1969) 

 original formulation, and parts (b) and (c) represent the successive application of network analysis 

 to obtain the basic trophic unit. 



386 



