PARRISH: MARINE TROPHIC INTERACTIONS BY DYNAMIC SIMULATION 



I 



20 



30 

 TIME, 



40 

 YEARS 



50 



60 



70 



Figure 11.— Course of competition between two fish species with 

 unequal metabolic demands, competing for a common food base. 

 Species B is favored, since ttg = 0.7 cCf^- N ^ = population of 

 species A; N p = population of species B; W^ = body weight of 

 species A; Wg = body weight of species B. 



2-level P12000 web started without initial pertur- 

 bation, with identical body weights and popula- 

 tions of the two species. This situation is 

 somewhat analogous to the simultaneous entry of 

 the two competitors into an environment where 

 the prey biomass and input are fairly close to the 

 standard equilibrium values. The system moved 

 away from the even start with oscillations which 

 were firmly damped toward an apparent new 

 steady state. In this state, the population and 

 weight of the more capable competitor were 

 increased relative to those of the less able con- 

 tender. Their final relative positions might be 

 characterized by the biomass ratio B^/B^ = 1.30. 

 It is interesting to compare this prediction with 

 that derived from the simpler graph theory 

 analysis (Saila and Parrish 1972). This was ac- 

 complished by using the variable values from the 

 present model for Q, B, and M to calculate the 

 parameters q, h, a, b, and m for the graph theory 

 model. These parameter values were then used in 

 Equation (18) of Saila and Parrish (1972) to com- 

 pute the biomass ratio B2/B2, = 1.56 of the compe- 

 titors. This ratio is directly comparable with the 

 ratio B^/B^ = 1.30 from Figure 11. In view of the 

 considerable differences in the two approaches, 

 the agreement seems too good to be entirely for- 

 tuitous. 



The above simulation represents simple unequal 

 competition with the competitors' populations 

 controlled by natural mortality and fecundity. 

 Considerable theoretical and practical interest at- 

 taches to the influence of predatory mortality on 

 such a system. Questions arise concerning whether 

 more competing species can coexist, or whether 

 competitors can coexist on a more even basis, 

 where they are utilized by a common predator than 

 in an otherwise similar environment without such 

 top predation. Paine (1966) dealt with these ques- 

 tions by observation and field experiment and 

 suggested that some intertidal systems seemed 

 able to support more competing species when a top 

 predator was present. Parrish and Saila (1970) 

 explored a small number of cases by dynamic 

 simulation of systems using Lotka-Volterra type 

 interactions. Some competitive situations were 

 found in which two unequally competing species 

 persisted longer in more equal numbers when 

 utilized by a top predator. Subsequently, May 

 (1971) did a neighborhood stability analysis of the 

 same systems and determined stability criteria in 

 terms of competitive and predatory coefficients. 

 Using coefficient values picked on this basis, 

 Cramer and May (1972) used the Parrish and Saila 

 model to demonstrate a case where an unstable 

 two-species competition became stable when a 

 common top predator was added to the system. 



Figure 12 illustrates the behavior of a system 

 with species C added as a top predator on the 

 P12000 web of Figure 11. After some oscillation, 

 the system moved to a new stable state with 

 species C reduced to a level such that the competi- 

 tors could support the total mortality. The stable 

 relative biomasses of the competitors still reflect 

 the competitive advantage of species B, but the 

 ratio Bg /B^ = 1.23 is less than in the comparable 

 2-level system; i.e., the competitors occur in more 

 nearly equal numbers. The result obtained by us- 

 ing the graph theory parameter values in Equa- 

 tion (19) of Saila and Parrish (1972) is B^ /B^ = 

 1.39. When compared with the B2 /B^ = 1.56 for 

 the P12000 web, this also represents a more even 

 standing among the competitors. Table 3 sum- 

 marizes the B^/B^ values obtained by dynamic 

 simulation and by graph theory. 



The same trend toward more equal biomasses of 

 two species competing in the q coefficient when a 

 common predator was present was found (Saila 

 and Parrish 1972) using an independent set of 

 "rough coefficients" provided by Menshutkin 

 (1969). These comparisons of biomass ratios are 



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