FISHERY BULLETIN: VOL. 79, NO. 4 



more closely approximate equilibrium conditions, 

 but the replacement of ^^ by /^reduces the inter- 

 dependence of the two variables. However, as dem- 

 onstrated by Roff and Fairbairn (1980), temporal 

 trends in effort such as those observed for the 

 Costa Rican thread herring fishery produce corre- 

 lations between ft and /^since both are increasing 

 (or decreasing). This autocorrelation in the inde- 

 pendent variable in turn indicates a spurious cor- 

 relation between CPUE and average effort. In the 

 examples examined by those authors, the degree 

 of autocorrelation between f and f increased 

 when shorter time periods were used to calculate 

 f. Furthermore, for periods of 2 or 3 yr, there was a 

 significant correlation between /J and/^even in the 

 absence of trends in ft over time. 



In the present assessment, since there were 

 definite trends in both standardized and unstan- 

 dardized effort and since effort was averaged over 

 only a 2-yr period, the nonindependence of the 

 variables in the regression analyses could not 

 have been significantly reduced. In fact, an 

 examination of the deviations between observed 

 and predicted CPUE for both models as applied to 

 average observed and standardized effort (Figure 

 9) revealed considerable time trends. These trends 

 were more obvious after effort standardization. 

 Clearly, the variables in the regression analyses 

 were not independent. Strictly speaking, there- 

 fore, the F-test used to evaluate the degree of fit 

 was not valid since it assumes that Y observations 

 are independent and normally distributed with 

 common variance. Residual mean squares for the 

 individual regression analyses, however, assume 

 nothing about the distributive properties of the 

 error term in the regression model. Although they 

 cannot be used to evaluate the statistical signifi- 

 cance of fit, they did confirm that better fits were 

 obtained with average effort, the exponential 

 model and standardized effort. 



A second problem which was not addressed was 

 the assumption that fishing mortality remained 

 directly proportional to fishing effort (Equation 

 (3)) as population size diminished. Thread herring 

 may remain vulnerable to capture even at low 

 stock sizes since they congregate in schools at the 

 surface, i.e., the same fishing mortality may be 

 exerted even with reduced effort. If fishing mortal- 

 ity and effort do not remain directly proportional, 

 the surplus production model is not appropriate 

 for predicting maximum equilibrium yields. 

 There was no way to evaluate this possible source 

 of error. 



Linear Model 

 Observed effort 



>- 

 < 



Q 

 Q 



< 



Q 



en 

 \ 



if) 



o 



CO 



o 



UJ 

 13 

 CL 

 CJ 



_) 

 < 



9 

 in 



UJ 



a: 



Lineor Model 

 Standardized effort 



Exponential Model 

 Observed effort 



2.0 — 



1.0 — 



-1,0 

 •2.0—1 



Exponential Model 

 Standardized effort 



10 



n — 7 — 1 1 1 — \-i 1 T'^ — I 1 — Xi 1 



1/2 3 4\5 6/7 8 9 



Y E ARS 



\' 



FIGURE 9. — Residual ( observed-predicted I 1969-79 catch per 

 unit effort values for the linear and exponential yield models 

 arranged in chronological sequence. 



Despite these problems, the surplus production 

 model provided a clear analytical interpretation of 

 the data. The range of Ys and/s estimates was not 

 extreme, although the linear model applied to 

 standardized data produced higher Ys estimates 

 than the other analyses. While there was no basis 

 for assessing how "correct" the standardization 

 procedure was, it did result in higher Ys and fs 

 estimates for both the linear and exponential 

 models and improved the least squares fit to the 

 data, especially for the exponential model. Clearly, 

 some adjustment in observed effort was called for. 

 Acceptable estimates of Ys and fs were obtained 

 from a fairly short time series of catch and effort 

 data (11 yr). The success of this assessment was 

 due in part to the reliability of the catch and effort 

 data provided by the canning companies to the 

 Ministry of Agriculture, and the fact that data 



700 



