FISHERY BULLETIN: VOL. 84, NO. 3 



Table 2.— Estimated values of the sardine ecosystem model parameters (from Atkinson 1980). 



population data during the simulation period (Fig. 

 3). The estimates are uncoupled from these data and, 

 hence, reflect strictly a priori knowledge as would 

 exist in applications where predictions are required. 

 Furthermore, the parameter values are not pro- 

 posed as best estimates of these parameters, but 

 simply provide a consistent set of values for use in 

 the simulation demonstration. The nonlinear pro- 

 gramming approach of mine is structured in general 

 to bound future ecosystem response characteristics 

 given only a priori population data. 



Ecosystem Simulations 



The simulated sardine ecosystem histories are 

 presented and compared with estimated sardine and 

 anchovy population data in Figure 7. The adult sar- 

 dine population simulation is in reasonably good 

 agreement with the data of Murphy (1966) giving 

 the many approximations and simplifying assump- 

 tions used in the modeling. The major dynamic 

 features of the adult sardines decline are consistent, 

 including the sharp rebounds associated with the 

 favorable conditions for sardine larvae survival in 

 1938 and 1939 and again in 1947 (Fig. 6). 



The simulated anchovy response in Figure 7, 

 which ignores any fluctuating larvae survival com- 

 ponent, appears to track the 3-yr averaged estimates 

 of Murphy (1966). The anchovy population increases 

 along with the competitor group to fill the ecological 

 void in this trophic level. The predator biomass 

 decreased slightly because the decline of the sardine 



results in a less desirable food supply, at least ac- 

 cording to estimated input parameters. Unfortun- 

 ately, there are no available data for comparing with 

 the predicted competitor and predator group 

 responses. 



Another simulation run was made to investigate 

 the speculation that fluctuating larval survival rates, 

 by themselves, might have caused the sardine col- 

 lapse. The sardine fishing rate was held at the 

 relatively low levels that existed before 1932 (d 3 = 

 0.10), and the fluctuating larvae survival model in 

 Figure 6 was applied. The resulting simulation run 

 is presented in Figure 8 and shows the predicted 

 history of the adult sardine population, along with 

 that of the anchovy, competitor, and predator 

 groups. The adult sardine population again fluc- 

 tuates markedly but now remains at relatively high 

 levels, in no apparent danger of collapsing. It would 

 appear from these runs that the added fishing 

 pressure is necessary to explain the actual event dur- 

 ing this period. 



CONCLUSIONS 



A general set of discrete-time difference equations 

 have been developed for use in simulating the im- 

 portant dynamic processes effecting fish popula- 

 tions, including 



• interactions between competors, predators, and 

 prey 



• birth, growth, and aging processes within a 



546 



