STEVENSON and CARRANZA: MAXIMUM YIELD ESTIMATES FOR OPISTHONEMA SPP. 



Ys and fs were estimated from linear and expo- 

 nential regressions of CPUE vs. effort when the 

 effort corresponding to a given year's catch was set 

 equal to effort applied during the same year (ft), or 

 an average of the effort applied buring the same 

 year and the previous year if). For the purposes of 

 calculating average effort, it was assumed that 

 thread herring exploited in Costa Rican waters 

 were recruited to the fishery at age 1 and remained 

 in the exploitable size range for 3 yr. Effort was 

 therefore averaged for a 2-yr period according to 

 the procedure described by GuUand (1969) on the 

 presumption that the mean duration of life in the 

 exploitable size range was 2 yr. This assumption 

 was generally supported by age and growth obser- 

 vations for species of this genus (Houde 1976; 

 Sokolov and Wong footnote 5; Paez Barrera foot- 

 note 3; Reintjes footnote 4) but needs to be con- 

 firmed by specific growth studies. 



A total of eight pairs of Ys and fs estimates were 

 obtained from both the original and standardized 

 data sets (Table 7). Analysis of the variance due to 

 random error after regression was evaluated by 

 calculating F-statistics. All regressions were per- 

 formed for 1969-79 data since the 1968 catch was 

 extremely low relative to the amount of effort ex- 

 pended (Table 3), suggesting that the single vessel 

 which was in operation that year was not perform- 

 ing to its full capacity For each model, predicted 

 yield values for/s = average observed effort and^ 

 = average standardized effort were plotted and 

 compared with actual annual 1969-79 yields. Val- 

 ues of equilibrium yield {Ye) predicted by each 

 model for given values of equilibrium effort (/e) 

 were calculated according to 



for the linear model, and 



(22) 



Ye = af^e-'^fE (23) 



for the exponential model. 



RESULTS AND DISCUSSION 



The results (Table 7) indicated a range of Y, and 

 fs estimates depending on the model, the form of 

 the independent variable if orf), and whether or 

 not effort was standardized. For all cases, Ys 

 ranged from 6,290 to 7,890 t. A wider range ofYs 

 estimates was predicted by the linear model 

 (6,700-7,890 t) as compared with the exponential 

 model (6,290-6,730 t). Observed fs estimates 

 ranged from 888 to 1,067 d and standardized fs 

 estimates ranged from 1,041 to 1,117 standard 

 days. Given the range of options which were 

 tested, these ranges were not extreme. All regres- 

 sions were statistically significant at >99% confi- 

 dence levels. 



Based on the "goodness of fit" as evaluated by 

 the F-statistic, /^produced a better fit than /J in all 

 cases, as did the exponential model as opposed to 

 the linear model and the standardization of effort. 

 The improved fit of the exponential model to 

 CPUE vs. average observed and average standard- 

 ized effort graphically was quite obvious (Figures 

 5, 6). Examining the independent effects on 

 maximum equilibrium yield estimates produced 

 by the standardization of effort data and the use of 

 two different models, it was apparent that within 

 each model standardization of the 1974-79 data 

 increased Ys, especially in the case of the linear 

 model whereas use of the exponential model de- 

 creased Ys estimates for both the standardized and 

 observed data, but more significantly with the 

 standardized data. Furthermore, the choice of ft or 

 fas the independent variable had very little effect 

 on the magnitude of these changes. Looking at the 



Table 7. — Summary of maximum equilibrium yield (Vj), the amount of fishing effort which produces maximum equilibrium yield (fs), 

 and Ys/fs estimates for the Costa Rican thread herring fishery as derived from linear and exponential surplus production models applied 

 to 1969-79 catch per unit effort and effort data. Linear and exponential regressions were repeated using effort data collected during the 

 same year (/"() and average effort over a 2-3t period if) as well as observed and adjusted effort estimates (see Tables 2, 6). Analyses of 

 variance (F-tests) indicated that all regressions were statistically significant at 99% confidence levels. 



'Rounded off to ttie nearest 10 t. 



^Effort expressed in standard days at sea 



697 



