FISHERY BULLETIN: VOL. 73, NO. 4 



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20 



30 40 



TIME, YEARS 



50 



60 



70 



Figure 12. -Course of competition between two fish species, A 

 and B, with unequal metabolic demands, competing for a com- 

 mon food base and utilized equally by a common predator, C. {a^ 

 = 0.7 ttA)- 



Table 3.-Biomass ratios for competing species. 



related to the concept of equitability diversity 

 (Lloyd and Ghelardi 1964). 



Some effects of human exploitation on systems 

 of this kind have been briefly examined. Human 

 exploitation on any species in any trophic web is 

 expressed by the addition of Equation (18) to 

 Equation (11) for that species (see MODEL sec- 

 tion). Exploitation has been applied to two iden- 

 tical competitors in simple P12000 webs which 

 were initially at standard equilibrium. It has 

 produced the expected result of reducing both 

 populations. Since the system is energy-controlled, 

 there is always an accompanying increase in the 

 competitors' body weights (which are always 

 equal), and an increase in food base biomass, B^ . 

 The total biomass of the competitor trophic level 

 remains essentially constant. Differential exploi- 

 tation of the two competitors affects the ratio of 



Figure 13.-Effect of differential exploitation on the biomass 

 ratio, B2/B3, of two equally competing fish species: dynamic 

 simulation prediction. The coefficient of instantaneous fishing 

 mortality for species 3 is always F3 = 0.3. 



their numbers, and therefore also their biomass 

 ratio. Figure 13 shows an example, using identical 

 species A-type competitors that have arbitrarily 

 been designated species 2 and species 3. This is the 

 kind of curve produced by graph theory analysis 

 for exploitation situations by Saila and Parrish 

 (1972); e.g., their Figure 6, curve B. Parameter 

 relationships are considerably different in the two 

 papers. Natural mortality, M, in the present case is 

 about 10 times its value in the Saila and Parrish 

 paper. For another set of parameter values and a 

 particular series of values of the exploitation 

 coefficient, F, the stable i?2 ^^3 ratio was predicted 

 by both the dynamic simulation and the linear 

 graph theory technique, as shown in Figure 14. 



Exploitation of a comparable 3- level trophic web 

 has also been simulated. A common predator, 

 similar to species C except smaller, was added 

 preying equally on two competitors almost iden- 

 tical with species A. A stable state for this 

 unexploited system was found. Exploitation was 

 applied to the competitors at various /' values that 

 had been used previously with the P12000 web. At 

 sufficiently low values of F (in the range of Figure 

 14), in the new exploited steady state, the food 

 base biomass, i?, , increased with exploitation of 

 the competitors. The competitor with the lower F 

 value increased in absolute population and 

 biomass, while the more heavily exploited compe- 

 titor decreased in both. Again, total biomass at the 

 second trophic level remained essentially constant. 

 In all cases, population and body weight of the 

 predator decreased markedly when the competi- 



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