PARRISH: MARINE TROPHIC INTERACTIONS BY DYNAMIC SIMULATION 



FiGURE 8. -Effects of age class structure and condition of 

 recruits on the response of a single species to an initial over- 

 population. (Curve A - 4-age class model with recruitment at 

 standard recruit weight; curve B - 4-age class model with Kj 

 recruitment; curve C - representative individual model.) The 

 three upper curves represent total species population, N; the 

 three lower curves represent total species biomass, B. 



values. In curve A, the system was represented by 

 an explicit 4-age class model in which recruitment 

 occurred at "standard recruit weight" (standard 

 equilibrium weight for recruitment age). In cur\'e 

 B the model was identical except that recruitment 

 occurred at K^ times "standard recruit weight." 

 The coefficient, K^ , is the ratio of the weight of the 

 class ending its first recruited year to its standard 

 equilibrium weight. Its use makes recruitment 

 weight more consistent with current conditions. In 

 curve C the system was represented by the 

 corresponding representative individual model. 

 Because of the way weight at recruitment is 

 expressed, curves B and C are most directly com- 

 parable. 



It is clear that there are some real differences in 

 dynamics among all three models. These simula- 

 tions and others indicate that for some detailed 

 studies of the dynamics of trophic systems, age 

 class models can provide additional information 

 not available through representative individual 

 models. However, much of the information of basic 

 interest is contained in the representative in- 

 dividual solution. The final stable state is predicted 



accurately. Because of its lower damping, this 

 model gives a conservative (maximum) estimate 

 of the time required for the system to return to 

 within any given range of this state, and this 

 maximum is close enough to the actual time to be 

 useful. For most variables and most perturbations, 

 the maximum amplitudes of the age class model 

 tend to be less than those of the representative 

 individual model, so that the latter tends to predict 

 an envelope of reasonable size within which the 

 actual values will lie. These characteristics make 

 the representative individual model especially 

 useful for predicting stability. 



The results shown and others suggest that the 

 representative individual model can be used to 

 approximate the behavior of the much more 

 difficult and expensive age class model sufficiently 

 well to justify use of the simpler model for many 

 purposes. However, the quality of the approxima- 

 tion depends upon the characteristics of the par- 

 ticular system to be simulated. Where species are 

 included that display a large range of sizes and 

 ecological differences among the age classes of the 

 recruited population, the representative in- 

 dividual approximation is likely to be less accept- 

 able. 



(D) Competition and Predation in 

 More Complex Webs 



A major purpose of the model developed here is 

 to serve as a tool for study of more complex trophic 

 systems. A few examples of particular interest are 

 presented below. 



In Figure 9 the trophic chain is extended by one 

 link in the simplest possible manner to make a 

 PlllOO web. Species C preys on species A which 

 preys on a constant input food base. Both interac- 

 tions employ Holling feeding functions. The 

 populations of all three trophic levels oscillated as 

 the system returned from the initial perturbation 

 of low food base biomass. Within about 3V2 to 4 

 cycles (»35 to 40 yr), all variables were within 

 about 1% of standard equilibrium values again. 

 The phase sequence of population and biomass 

 rapidly became level 1, level 2, level 3 as would be 

 expected. The population phase displacement was 

 complicated by the 2V2-yr reproductive lags and 

 the effect of predation on the species A population 

 (as species A lost weight, species C ate more 

 species A individuals to meet its energy demands). 



Such an extremely simple trophic web would be 



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