FISHERY BULLETIN: VOL. 69, NO. 3 



well described by a production model — good re- 

 lationships are observed in Figure 2. These data 

 were used by Pella and Tomlinson in exempli- 

 fying their technique ; for comparative purposes 

 the same data are utilized here. The results of 

 this section, however, should be considered as 

 just an example and not a recommendation on 

 management. 



The parameters of the generalized production 

 model for the tuna fishery were estimated by the 

 Pella-Tomlinson computer program, GENPROD, 

 replacing the fitting criterion, S, with those of 

 each alternative statistical model [equations 

 (11), (15), and (18)]. Each parameter was 

 searched to five digits or until the improvement 

 in S was less than 0.01 Cr at three levels of nu- 

 merical approximation in equation (5) — 

 M= 1,3,5- — (Table4). Increasing the precision 

 of numerical approximation greatly changed the 

 parameter estimates between N = 1 and 3, but 

 only slightly between N = S and 5. The most 

 sensitive parameter is H, followed in order by 

 K, q, m, and r. Consequently, the estimates 

 of the average environmentally limited maxi- 

 mum population _size, P„ , and average optimum 

 population size Poi,t, vary with the level of pre- 



cision. Pella and Tomlinson indicated that un- 

 reasonable estimates were obtained for the 

 catchability coefficient, q, (presumably with 

 A'' = 1) and made an arbitrary selection of a 

 "reasonable" estimate. "Reasonable" catcha- 

 bility coefficients are obtained here with N = B, 

 making unnecessary the arbitrary selection of 

 a reasonable estimate. The management impli- 

 cations of maximum equilibrium catch, Cunx, and 

 optimum fishing efl'ort, /opt, are surprisingly 

 robust to the degree of precision of the numerical 

 approximation. Schaefer (1957) mentioned 

 previously, however, that these two management 

 implications are robust to changes in the esti- 

 mate of q in his estimating method; Pella and 

 Tomlinson also mentioned the phenomenon for 

 their technique. The S criteria values were re- 

 duced about Tyi- or less by choosing A'^ = 3, as 

 against A'' = 1 and reduced a negligible 0.2% 

 or less by choosing N = 5 (Si and S2 increased 

 minutely due to the level of precision chosen for 

 S) . Obviously, the error due to approximation 

 in equation (5), as previously stated, is negli- 

 gible for these data with A'' ^ 3. 



Turning to the eff'ects of the alternative sta- 

 tistical models (with N = 5), it may be seen 



Table 4. — Parameters and management implications of the generalized production model for the eastern tropical 

 Pacific yellowfin tuna fishery, 1934-67, estimated with the Pella-Tomlinson technique (GENPROD) using four dif- 

 ferent statistical models and three levels of precision, A^, in equation (5). 



H 

 (10-5) 



(10- 



Management implications 



Pounds 

 (10«) 



Pounds 

 (10») 



/opt 



Boat 

 days 



Pounds 

 (10«) 



Criterion 



' Pella and Tomlinson (1969; Table 5). 



576 



