466 



Fishery Bulletin 89(3). 1991 



to count all microincrements to a specific radius for the 

 same otoliths. This was beyond the scope of the pres- 

 ent study. 



Fork lengths and age estimates, obtained by integrat- 

 ing the rate curve over the corresponding otolith radius 

 (Appendix 1), were fit to a von Bertalanffy growth 

 curve (Table 4). Both unconstrained regression and 

 regressions with constraints on asymptotic length 

 (L^) or age at zero length (t = 0) were tested. Regres- 

 sions with the highest indices of correlation were 

 generally obtained by forcing the curve through an 

 estimate of asymptotic length obtained from the 

 literature or from regional fisheries statistics. The 

 greatest value of MLR or ML^ from Table 1 for each 

 region was used as an approximation of an appropriate 

 forcing value. The criterion for convergence was based 

 on a minimum level of improvement in the ratio of 

 subsequent sum of squares errors (SSE): 



(SSEj - SSE i _ 1 )/(SSE 1 + 10" 6 )< lO" 8 . 



Regressions which didn't converge after 200 iterations 

 were eliminated. NMI was the only region for which 

 the regression was able to converge with the constraint 

 that to = 0. Two fish from French Polynesia were 

 omitted from the data, because their otolith radial 

 lengths were not recorded. 



Log-linear regressions using the Gaschiitz et al. 

 (1988) BASIC program were also done for comparison. 

 These are weighted regressions of average age-at- 

 length for NMI and French Polynesia, which had more 

 than 50 observations. Figure 2 shows the best four 

 growth curves (from Table 4). For all regions except 

 NMI, these were the nonlinear regressions constrained 

 in L^ . The nonlinear method of fitting was preferred 

 because it involved no artificial reduction of the 

 variance observed in the data. For NMI the nonlinear 

 regression constrained only to t = was used, 

 because it had a higher r 2 value and lower residual 

 variance. None of the curves for NMI showed a good 

 fit; these results are included for comparison. 



The scatterplot of age-at-length data (Fig. 2) illus- 

 trates the limitation on regression estimates imposed 

 by the size range and number of fish sampled for each 

 region. The most significant constraints on fitting a 

 growth curve to the data were the high variance of 

 estimated age (otolith radius) as a function of fork 

 length, particularly for NMI and French Polynesia, and 

 the limited range of fish sizes sampled. It was necessary 

 to constrain most of the growth curves to an in- 

 dependently estimated value of L M , since there were 

 few data points to represent extremely large or small 

 fish. Although unconstrained curves could be fit to the 



