FOX: FITTING THE GENERALIZED STOCK PRODUCTION MODEL 



(Table 1). The catchability coefficient, q, was as- 

 sumed to be 1.0. Figure 2 presents the equilib- 

 rium values of catch per unit effort and yield at 

 fishing effort values ranging from 0.0 to 1.3 for the 

 simulated shrimp population. Above/" =1.3 the 

 population level did not stabilize in 25 yr of simu- 

 lation and aif = 2.0 the population was definitely 

 extinguished. The equilibrium data for/" =0.0 to 

 1.3 were fit to the generalized stock production 

 model with PRODFIT to illustrate the obtainable 

 degree of correspondence. The generalized stock 

 production model very closely approximates the 

 equilibrium values for the simulated pandalid 



Table 1. — Empirical management implications for the simu- 

 lated pandalid shrimp population and those estimated for the 

 generalized stock production model with PRODFIT. 



0.2 0.4 0.6 08 1.0 1.2 14 16 1.8 

 FISHING EFFORT 



2.0 



6 r 



0.2 04 0.6 0.8 1.0 12 14 

 FISHING EFFORT 



1.6 



1.8 20 



Figure 2. — Fit of the generalized stock production model (line) 

 to simulated equilibrium values (circles) of (A) catch per unit 

 effort and (B) yield by computer program PRODFIT. Shaded 

 areas represent nonequilibrium. 



shrimp population being slightly low in the range 

 off = 0.7 to 1.1 and slightly high beyond/" = 1.1 

 (Figure 2). The estimated parameters are also 

 very close (Table 1). 



The problem which confronts a fishery scientist 

 is to estimate the parameters of Table 1, hence 

 the equilibrium relationship of Figure 2, from 

 catch and fishing effort data representing transi- 

 tional rather than equilibrium states. To illus- 

 trate the efficacy of the equilibrium approxi- 

 mation approach and to provide a comparison 

 between the two fishing effort averaging methods, 

 a 12-yr fishing effort history was selected which 

 approximates the rapid expansion of fishing for 

 Pandalus borealis in Ugak Bay, Alaska. Exploit- 

 ing the simulated shrimp population with the 

 fishing effort history produced the catch and catch 

 per unit effort history in Figure 3. Two compari- 

 sons were made, the first using the deterministic 

 data shown in Figure 3 and the second introducing 

 some random error. 



Deterministic Comparison 



The appropriate averaging time, k, for the 

 weighted average method is four since the fishable 

 part of the simulated shrimp population consists 

 of four significant year classes. The appropriate 

 averaging time, T, for the unweighted average 

 method is 2 since the average duration of the 

 fishable phase is 2 yr. The results of fitting the 



YEAR 



Figure 3. — Catch (dots) and catch per unit effort (circles) cal- 

 culated with a fishing effort history (triangles) from the simu- 

 lated pandalid shrimp population. 



29 



