Smith and Kostlan: Growth of Etelis carbunculus from sagittal otolith radius 



465 



Results 





k-3 



SI 40 



Number of otoliths, fish size range, 

 and locations of collections are sum- 

 marized in Table 1. For comparison, 

 the maximum length registered in 

 fisheries landings (MLR) and mean of 

 available estimates of asymptotic 

 length (ML^) for each region and 

 their sources are also included. Inter- 

 mediate sizes were represented in the 

 data from most regions, but extreme- 

 ly large or small fish were under- 

 represented or lacking. The sample 

 from Vanuatu was very small, but 

 encompassed a wider range of fish 

 lengths than was sampled from any 

 other location. The limitations of the 

 data must be kept in mind in inter- 

 preting and comparing results. 



Nonlinear regressions of otolith 

 growth rate versus otolith radius in 

 microns (Table 2 ) produced estimates 

 of the parameters a, b, and c of the 

 rate equation, with asymptotic 95% confidence inter- 

 vals. Multiple correlation coefficients were calculated 

 for each regression as an additional index of fit. Data 

 were pooled for all locations to estimate a global rate 

 for otolith growth. The multiple correlation coefficients 

 are low for these curves, due to the wide range of varia- 

 tion in recorded increment density near the focus (high 

 residual variance). Predicted curves and recorded 

 microincrement densities for each region were com- 

 pared (Fig. 1). The function chosen mimics the behavior 

 of the rate curve fairly well; however, the fit could be 

 improved in the descending portion of the curve be- 

 tween 500 and 1500^m of otolith radius. Few readings 

 were made close to the otolith focus (<246/^m) for NMI 

 and Vanuatu samples (Fig. 1). Fitting the data to the 

 rate curve assumes that these otoliths grew similarly 

 to those for which the ascending portion of the curve 

 was sampled. The fit for the descending portion of the 

 curve is supportive of this assumption. However, since 

 the widest range of variation in recorded microincre- 

 ment densities was always found close to the focus, 

 these results should be interpreted cautiously. 



Predicted ages at equal otolith radius, using the 

 parameters in Table 2, were calculated for each region 

 (Table 3a). Although there were differences between 

 the estimated regional otolith growth parameters, 

 predicted ages as a function of otolith radius were 

 generally similar. The relationship between the shape 

 parameters a and b is such that differences between 

 them can be compensatory, one (a) controlling the 



HAWAII (N=1680) 



'HSflWsSKftSS'Wi*: '"J 



FRENCH POLYNESIA 

 (N = 3877) 



>WS3S£i*r.*i»^ I 



NORTHERN MARIANAS (NMI) 

 (N = 252) 



■(■•iS'i 



VANUATU (N=141) 



1000 2000 3000 4000 5000 6000 7000 8000 9000 1000 2000 3000 4000 5000 6000 7000 8000 9000 

 Focus Focus 



POSTROSTRAL RADIUS (microns) 



Figure 1 



Estimated otolith growth rate and recorded microincrement densities for red snap- 

 per Etelis carbunculus. 



amplitude of the rate curve and the other (b) the rate 

 of dampening. The radius at which peak otolith growth 

 rate is estimated (the maximum of the otolith growth- 

 rate function) was similar regardless of region or 

 weighting. Peak growth rate occurs where the deriva- 

 tive of axe _bx + c is equal to zero, or at x = 1/b. Esti- 

 mated ages for this radial distance are included in Table 

 3a, where it can be seen that the otoliths of ehu from 

 all regions reach their maximal growth rate between 

 1 and 2 months of age. Otoliths reach a constant growth 

 rate before fish are 1.5 years old, or between 3000 and 

 3500/mi of otolith radius. 



For comparison, the age estimates made by Ralston 

 and Williams for comparable 500-^m intervals of otolith 

 radius are given in Table 3b. The values are similar in 

 many respects for Hawaii and French Polynesia (where 

 more microincrement density estimates were made), 

 but there are observable differences for all regions. 

 Ralston and Williams' age estimates were lower close 

 to the otolith focus, the two estimates were equivalent 

 at intermediate radius, and their estimates were again 

 lower at greater otolith radius. The exception to this 

 pattern was seen for Vanuatu, for which our estimates 

 were substantially lower at maximum radius. The 

 radius at which the two estimates were equivalent and 

 the magnitude of the difference between them varies 

 from one region to another and is a function of the 

 amount and variability of microincrement density read- 

 ings and their effects on both estimates. The best check 

 of which method gave more accurate results would be 



