FISHERY BULLETIN; VOL. 73, NO. 4 



TIME, YEARS 



Figure 9.-Response of a simple 3-level trophic web (PUIOO) to 



an initial low prey abundance. ( food base; 2nd level 



fish species; — 3rd level fish species.) 



rare indeed in nature, but it is interesting for at 

 least two reasons. The various species might be 

 thought of as representing in some sense v^hole 

 trophic levels of more extensive natural systems, 

 each level consisting of a rather homogeneous 

 group of species. If all the species at a single level 

 have identical trophic parameters, this simple web 

 in fact represents them exactly. This follows 

 logically and has also been verified in simulation. 

 Thus, the PlllOO web model provides a base line 

 for comparison for later unequal competition runs 

 in a 3-level system. It represents the behavior of 

 any n equally competing species at a trophic level, 

 each with a population of \/nth the total popula- 

 tion. The PllOOO web model provides the same 

 kind of base line for competition in 2-level sys- 

 tems. 



Figure 10 illustrates the simplest web, PUllO, 

 with four trophic levels: the food base and three 

 fully modeled fish species. It consists of the PlllOO 

 web with species D added as a top predator. Again, 

 an initial perturbation of low food base biomass 

 caused oscillation of trophic variables of all 

 species. After about 8 to 9 cycles (»70 yr), all were 

 within a very few percent of standard equilibrium 

 values again. The same population and biomass 

 phase sequence appears. Predation by species D 

 caused quicker response of the species C popula- 



tion, reducing the phase displacement between 

 species A and species C. The large phase 

 displacement now occurred between species C and 

 species D. The basic period of oscillation was also 

 shortened from about 10 yr to about 8 yr. In all the 

 above cases, maximum oscillation amplitudes of 

 variables were less than the initial perturbation, 

 and they rapidly became substantially less. 



Effects produced on the system by feeding 

 competition between species were of particular 

 interest in these studies. No attempt was made to 

 formulate explicit (interference) competition. 

 Implicit competition was studied by constructing 

 models with two predator species utilizing a com- 

 mon prey species. The PllOOO and PlllOO models 

 above represent exactly equal competition at the 

 second level in 2- and 3-level webs respectively. 



The abstraction of exactly equal competition is 

 not likely nor very interesting ecologically. A 

 simple type of unequal competition is modeled by 

 replacing one of the two species A-type competi- 

 tors with species B, which is identical except that 

 it has the advantage that its a^^^.^. anda^iax are 70% 

 of the species A values. Thus it has lower metabolic 

 requirements and grows more for a given food 

 intake. Figure 11 illustrates a simulation of this 



10 



20 30 40 



TIME, YEARS 



50 



70 



Figure lO.-Responseof a simple 4-level trophic web (PI 11 10) to 



an initial low prey abundance. ( food base; 2nd level 



fish species; 3rd level fish species; 4th level fish species.) 



710 



