158 



Fishery Bulletin 102(1) 



last band for each vertebra that was measured, and we then 

 calculated the mean of this number for the entire sample: 



IK*. 



,)-i?„)//2=0.13(SE = 0.0009). 



The expected distance between the last (R n ) and the pen- 

 ultimate (i? n _! ) bands was estimated as a function of the 

 distance between the vertebral nucleus and the last band 

 (MI). The percent marginal increment (PMI) was calcu- 

 lated as 



PMI = [MI I (0. 13 x R n )] x 100. 



Analysis of variance to test for differences in PMI by 

 month was used. Post-hoc tests (Tukey honest significant 

 differences ( [HSD] ) were performed to indicate which 

 months were different. 



Characterization of the vertebral edge was used to de- 

 termine the time period of band formation (Carlson et al., 

 1999). Under reflected light, a narrow dark zone (MI 0), a 

 narrow light zone ( MI 0. 1 to 0.5 ), and a broad light zone ( MI 

 0.6 to 1 ) were observed. Absolute marginal increments ( MI ) 

 were also analyzed by trimester for juveniles aged four and 

 five years, and for adults ( more than eight years ) to confirm 

 the time of translucent zone formation. 



The relationship between VR and TL was calculated 

 by sex, tested for normality, and compared by ANCOVA 

 (Zar, 1996). The final regression in both sexes did not pass 

 through the origin, thus suggesting that the Fraser-Lee 

 method was the most appropriate for back-calculation 

 (Ricker, 1969). 



[TL]„ = (RJVR)({TL\-a) + a, 



where [TL] 

 R 



= the back-calculated length at age n; 



- vertebral radius at the time of the ring n\ 

 VR = the vertebral radius at capture; 

 TL = the length at capture; and 

 a = the intercept on the length axis. 



A von Bertalanffy growth function (VBGF) (von Berta- 

 lanffy, 1938) was fitted to back-calculated and observed 

 length-at-age data with the following equation. 



L . 1- 



kit („)i 



where L t = predicted length at age t; 



L r = mean asymptotic total length; 



K = growth rate constant; and 



t = the age when length is theoretically zero. 



To obtain parameters of VBGF, data were analyzed by 

 using FISHPARM (Prager et al., 1987) for nonlinear least- 

 squares parameter estimation. The Kappenman's method 

 (1981), based on the sum of squares of the differences 

 between observed and predicted lengths from a growth 

 model, was used for comparing male and female growth 

 curves. In addition, likelihood-ratio tests were used to com- 

 pare parameter estimates of the von Bertalanffy equation 

 between sexes (Cerrato, 1990). 



Von Bertalanffy parameters (L x , K) were also estimated 

 by the method of Fabens ( 1965 ) usually employed for recap- 

 ture data and which takes into account the size at birth (L (l ) 

 instead of t . This method reconfigures VBGF and forces the 

 regression through a known size at birth: 



L, =Ljl-be- 



where b = (L., 



-L )/L x 



We used Fabens routine for growth increment data 

 analysis of the FAO-ICLARM stock assessment tools (FI- 

 SAT) program (Gayanilo et al., 1996), assuming that the 

 time intervals (=At) for each size-at-age class were equal 

 and had a periodicity identical to that obtained from the 

 vertebral analysis. 



The lengths of 1055 individuals were divided into 5-cm 

 intervals and analyzed by the Shepherd method ( 1987 ) with 

 the length-frequency data analysis program ( LFDA ). Initial 

 values of L v were based on results from maximal lengths 

 in the sample and from literature (Compagno. 1984). K 

 values ranging from 0.05 to 1.8 were used as input into the 

 program, which was run repeatedly until the highest score 

 function was obtained. The L x and /f values were then used 

 to calculate t (Sparre et al., 1989): 



t Q = t + {l/K)(\nlL. -lt])/LJ. 



Using an age-length key, based on 317 individuals for 

 which vertebrae were read, we evaluated the age composi- 

 tion of the sample (Bartoo and Parker, 1983). Maximal ages 

 in the sample were calculated by employing the inverted 

 VBGF (Sparre et al.. 1989). Further, the formula by Fa- 

 bens (1965) [5(ln2)/AT for longevity estimation was used. 

 All statistical inferences were made at a significance level 

 of 0.05. 



Results 



The total sample size consisted of 1055 individuals: (551 

 males [93-248 cm], 499 females [110-252 cm], and 5 

 individuals of undetermined sex [169-260 cm]) (Fig. 2). Of 

 these, vertebrae were removed from 317 specimens (182 

 males [113-215 cm], 132 females [111.5-234.9 cm], and 

 3 individuals of undetermined sex [169-242 cm]). 



Differences in the relationship between VR and TL 

 between sexes were not found to be significant (P=0.81D. 

 The regression for the overall sample showed a linear 

 relationship: TL = 13.523V/? + 41.824 <rM).89: n=317>, 

 indicating that vertebrae are suitable structures for age 

 determination, and methods based on direct proportion are 

 appropriate for back-calculation. 



The average percentage error, calculated between two 

 readings, ranged from 098 to 4.5^ in vertebrae with 2 to 

 17 bands and the average IAPE for the overall sample was 

 2.4'-. Coefficient of variation (CV) between readings for 

 total sample was 6.88' < . 



Monthly PMI analysis, for the entire sample, indicated 

 that bands were formed from June to October, when high- 



