STEVENSON and CARRANZA: MAXIMUM YIELD ESTIMATES FOR OPISTHONEMA SPP 



"1 — T — I — I — r 



200 400 600 



1 I — \ — I — \ — I — I — \ — r . . 



800 1000 1200 1400 1600 1800 2000 

 AVERAGE EFFORT (STANDARD DAYS AT SEA) 



Figure 8. — Costa Rican thread herring yield curves predicted 

 by the exponential and linear surplus production models and 

 annual 1968-79 catch and average standardized effort data. 



years. Catches in 1972, 1974, and 1975 were con- 

 siderably greater than Ye values estimated by the 

 exponential model. The linear model predicted ac- 

 tual yields more accurately through 1975, espe- 

 cially when effort data were standardized, but de- 

 viated substantially in 1976 and 1977. 



The general tendency toward increasing effort 

 ceased in 1978 and 1979 when substantially lower 

 catches were taken with less effort (Figures 7,8). 

 Linear and exponential models were fit to 1969-77 

 data, using average effort only, since it appeared 

 that a closer agreement between observed and 

 predicted yields might be obtained if data for the 

 last 2 yr were eliminated. This was not the case. Ys 

 estimates increased by 280-360 t and /!• estimates 

 by about 50 d (Table 8), corresponding to a slight 



Table 8. — Estimates of maximum equilibrium yield iYsK the 

 corresponding amount of fishing effort (/g) and Yg/fs estimates 

 for the Costa Rican thread herring fishery as derived from linear 

 and exponential surplus production models for 1969-76. Only 

 average observed and adjusted effort data were used. 



'Rounded off to tfie nearest 10 t. 



^Effort expressed in standard days at sea 



shift upwards and to the right in the predicted 

 yield curves, but no statistical improvement in fit 

 could be demonstrated. Yield analyses therefore 



were quite robust since approximately the same 

 results were obtained from the two data sets. 



Evaluation of the Model 



A fundamental assumption of the surplus pro- 

 duction yield model is that surplus population 

 growth that is harvested by the fishery is at any 

 point in time a function of population biomass. 

 Under the assumption that fishing mortality is 

 directly related to fishing effort by a constant pro- 

 portionality factor, changes in the rate of popula- 

 tion growth can also be related to fishing effort. 

 Thus, the model assumes equilibrium conditions, 

 i.e., that changes in population size — as estimated 

 by CPUE — will remain in equilibrium with a 

 given fishing effort. For developing fisheries in 

 which effort is continually increasing, this 

 equilibrium seldom has an opportunity to become 

 established. Even in cases where effort does stabi- 

 lize, variations in population size (and therefore, 

 yields) can be expected, especially if recruitment 

 is highly variable and bears little relation to 

 spawning stock size. The problem is further 

 exacerbated if there is a significant delay between 

 spawning and recruitment since the model as- 

 sumes that the response of equilibrium yield to 

 changes in population size is immediate. In fact, 

 yield in any given year will seldom be related to 

 population size during the same year. 



For the Pacific thread herring, the presumed lag 

 time between spawning and recruitment was 

 small (1 yr?) and correction procedures were not 

 employed. The relationship between recruitment 

 and stock size for Opisthonema spp. was not 

 known, but the fact that the Costa Rican thread 

 herring population declined without major inter- 

 ruptions once the fishery began suggests that re- 

 cruitment fluctuations were not extreme. If re- 

 cruitment had varied significantly as stock size 

 declined, the reduction in CPUE with increasing 

 effort (Figures 5, 6) would not have been so uni- 

 form and the model would not have fit the data 

 nearly so well. 



A major problem which is common to all surplus 

 production yield analyses is the nonindependence 

 of X and Y variables when CPUE is plotted as a 

 function of effort. As pointed out by Sissenwine 

 (1978), the relationship between X and its recip- 

 rocal is hyperbolic. Therefore, CPUE vs. effort re- 

 lationships are inherently biased. Following Gul- 

 land's (1969) procedure for averaging effort in the 

 independent variable, not only does the model 



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