FISHERY BULLETIN: VOL. 69, NO. 3 



with a random number generator by the multi- 

 plicative congruential method (subroutine 

 RAND, University of Washington Computer 

 Center) . The variances and means of residuals 

 and log-residuals were calculated at each fishing 

 effort level. 



The results of the simulation trials are given 

 in Table 1. It was obvious from the formulation 

 of equation (23) that Model — assuming con- 

 stant residual variance — was inappropriate, the 

 simulation trials add confirmation. Model 1 — 

 assuming residual standard deviation propor- 

 tional to fishing efl'ort — is also rejected over any 

 moderate range of fishing effort. A close approx- 

 imation, however, is obtained for / ^ 22,000. 



Model 2 — assuming constant log-residual var- 

 iance — appears to be valid up to .58,000 ^ / < 

 65,000, where a trend of increasing variance be- 

 gins. The hypothesis of common log-residual 

 variance for / ^ 65,000 was tested by Bartlett's 

 f-test (Snedecor and Cochran, 1967) . The result 

 is not significant (uncorrected x' = 7.72, 9 df, 

 Pr >0.50). Including the log-residual variance 

 for / = 70,000, however, significance is ap- 

 proached (corrected x^ = 16.35, 10 df, 

 Pr <0.10). 



Model 3 — assuming residual standard devia- 

 tion proportional to catch — fulfills the assump- 

 tion about as well as Model 2. The proportional 

 relationship between the residuals standard de- 

 viations and deterministic catch (Figure 1) ap- 

 pears to be different between catches given by 

 fishing effort below and above that which pro- 



■o 4 



50 100 150 



Deterministic Cotch (x lO') 



200 



Figure 1. — Standard deviation of the^ residuals, €3, 

 plotted against the deterministic catch, C, for statistical 

 Model 3. • = fishing effort below maximum sustainable 

 yield (MSY) level. A = fishing effort above MSY level. 

 ® = fishing effort at MSY level. 



duces the maximum sustainable yield (MSY) 

 (C = 196 X 10*). Regression analysis reveals 

 that variance about regression, Sy^^, is highly 

 significantly different between below and above 

 MSY levels (F r= 9.90; 4, J df; Pr <0.01), but 

 the regression coefficients, b, are not significantly 

 diff-erent (t = 1.47; 5 df; Pr >0.20)-Table 2. 

 The "above MSY" regression has a i/-intercept, 

 which must be zero, significantly different from 

 zero {t = 3.30; 4 df ; Pr <0.05). It appears 

 that Model 3, like Model 2, is valid up to 

 58,000 ^ / < 65,000 (Figure 1). 



Table 1. — Results of the stochastic catch simulation trials of the generalized production model. 



574 



