ATK1NSUN: 1-1SH i'Ui'ULAilUIN DflNAMlOS 



1.0 



ESTIMATED FISHING RATE 



DERIVED FROM MURPHY'S (1966) DATA 



FISHING RATE MODEL 



1930 



34 



38 



42 



46 



50 



YEAR 



Figure 5.— Model of sardine fishing rate, 6 3 (t), used in the sardine ecosystem simulations. 



SURVIVAL FACTOR MODEL 



YEAR CLASS SURVIVAL 

 ESTIMATE BY SETTE (1969) 





24 « 

 (A 



Z 



o 



20 



16 



1930 



34 



38 



42 

 YEAR 



46 



50 



S 



o 



t 



8) 



< 



< 



W 

 </> 



O 



a. 



>■ 



at 



z 



i 



< 



(0 



Figure 6.— Model of sardine larvae survival, E^t), used in the sardine ecosystem simulations. 



defined by the assumed equilibrium condition prior 

 to 1932-52. Setting the time-varying fishing rate at 

 its pre-1932 value (d 3 = 0.10) and fixing the time- 

 varying larval survival factor at its reference value 

 (E 1 = 1.0), a set of seven equality constraints were 

 specified corresponding to the seven population 

 equations in Table 1 with P(t + 1) = P(t) = P. 

 While there is still significant degrees-of -freedom 

 in the model (i.e., more parameters than equality 

 constraints), I was able to greatly resolve their 

 values based on my nonlinear programming pro- 

 cedures. 



The parameters in Table 2 represent the "nom- 

 inal" estimates presented by me (1980) based on my 



NLP analyses. In searching for minimum and max- 

 imum population response levels throughout 

 bounded parameter space, a series of intermediate 

 search steps were taken that produced suites of 

 interdependent parameter values satisfying the 

 pre-1932 equilibrium condition. Population response 

 levels were equated to the average sardine popula- 

 tion during the 1932-52 simulation period in this 

 analysis. The selected nominal parameter suite in 

 Table 2 gives response levels approximately midway 

 between the determination of minimum and max- 

 imum levels. 



Note that the parameter values in Table 2 were 

 not derived from statistical procedures using the 



545 



