FISHERY BULLETIN: VOL. 73, NO. 1 



course, reveal that there is no equilibrium yield 

 in the range of f = 1.6 to 2.0 for the simulated 

 shrimp population (Figure 2). 



Table 6 provides a comparison of the catchabil- 

 ity coefficient estimates by three techniques for 

 each fishing effort averaging method. Clearly the 

 best estimates were produced by the geometric 

 mean for the integral method, with the mean es- 

 timate by the weighted average fishing effort pro- 

 cedure being slightly better than that of the un- 

 weighted average procedure. 



COMPARATIVE EXAMPLES OF THE 



EQUILIBRIUM APPROXIMATION 



AND TRANSITION PREDICTION 



APPROACHES 



Computer program GENPROD (Pella and Tom- 

 linson 1969) was employed to fit the deterministic 

 and stochastic catch and effort histories of the 

 simulated shrimp to compare the results of the 

 transition prediction and equilibrium approxima- 

 tion approaches. The reader is cautioned, as in the 

 previous section, that these results are largely 

 illustrative and should not be misconstrued as 

 being valid for all cases in which a production 

 model may be employed. 



Deterministic Comparison 



The comparison of equilibrium parameters in 

 Table 7 reveals that the equilibrium approxima- 

 tion approach provided estimates that were closer 

 to all the empirical values except m , where the two 

 approaches estimated the same value as the em- 

 pirical equilibrium fit. GENPROD estimated 

 parameters which predicted the simulated catch 

 history (Figure 3) extremely well— the largest 

 error was only 0.05, the sum of squared errors was 

 0.00659, and the R statistic, a measure of im- 

 provement in the fit over simply using the mean 

 catch as a predictor (Pella and Tomlinson 1969), 

 was 0.99994. Utilizing the empirical equilibrium 

 parameters in the generalized production model, 

 however, resulted in a poorer, but still good, pre- 

 diction of the transition state catches — the max- 

 imum error was 0.50, the sum of squared errors 

 was 0.48515, and the R statistic was 0.99544. Ap- 

 parently due to failure of the assumptions regard- 

 ing population lag and age structure shifts or 

 problems with precision in the numerical integra- 

 tion, the accuracy of some equilibrium parameter 

 estimates by the transition prediction approach 



Table 6.— Estimates of the catchability coefficient, q, from the 

 five replicated stochastic catch histories by three methods for the 

 weighted and unweighted fishing effort averaging procedures. 

 Actual value of q is 1.0. 



were sacrificed in order to reduce the sum of 

 squared errors by nearly 99%. 



Stochastic Comparison 



The results of fitting the five replicate stochastic 

 catch histories by the equihbrium approximation 

 and transition prediction approaches are given in 

 Table 8. Of the four common parameters (m, Y max, 

 C/max > and g), the equilibrium approximation ap- 

 proach estimates were closer to the empirical val- 

 ues of m , y^ax > and q , both on the average and for 

 most of the replicates. The transition prediction 

 approach estimates were closer, on the average, to 

 the empirical value for L^'max- The transition pre- 

 diction approach provided one extremely poor es- 

 timate ofq (replicate 3) and all replicate estimates 

 are above the empirical value — the latter phe- 

 nomenon could be related to the accuracy of the 

 numerical integration scheme in GENPROD (Fox 

 1971). The additional parameter required by 

 GENPROD, the ratio of the initial to unexploited 

 population size (Po/Pmax), was estimated very 

 well. 



There is considerable variability in the esti- 

 mates of the most frequently desired parameter, 

 ^max, by either approach (Table 8) in spite of as- 

 suming an ideal error structure (independent, 



Table 7.— Empirical and estimated parameters for the simu- 

 lated pandalid shrimp catch history using the equilibrium ap- 

 proximation and transition prediction approaches. 



Approach 



m 



0, 



Empirical '060 5.60 



Equilibrium approximation^ 0.60 5.67 

 Transition prediction^ 0,60 5.92 



17.96 

 17.97 

 17.69 



1.00 

 0.87 

 1.32 



1.00 



1.16 



'Estimated, Table 1. 



^Program PRODFIT, k = 4. unweighted estimates option. 



^Program GENPROD, KK = 3, DEL = 3, unweighted estimates. 



32 



