472 
Fishery Bulletin 113(4) 
well and Casey, 1976; 159 cm TL, Gruber 
and Compagno, 1981; 156 cm TL, Moreno 
and Moron, 1992). The mean value of this 
range (135 to 140 cm TL) was converted 
to FL (84 cm FL) by using this equation 
(n=390; coefficient of multiple determi- 
nation [/? 2 ] =0.92; standard error of the 
intercepts. 41; standard error of the 
slope=0.01; regression analysis of vari- 
ance: F=4675; PcO.Ol) (see Fernandez- 
Carvalho et ah, 2011): 
FL = 0.58 TL + 4.83. (4) 
The generalized VBGF with 4 parame- 
ters was defined by Richards (1959) with 
the following equation: 
L t - Li n f((l-e(-^(l-m)(t-to))) <1/1_m (5) 
where to = the theoretical age at zero 
length; and 
m is the fitted fourth function para- 
meter. 
Two versions of the GGF (Ricker, 1975) 
were fitted, one with 3 parameters and 
the other with 2 parameters and a fixed 
Lq. The same value of Lq that was used in 
the 2-parameter VBGF model (84 cm FL) 
was used in the second GGF model: 
L t = L 0 e G[1 - e( -*«), (6) 
where G = the instantaneous rate of 
growth at time t\ 
L t = the mean length at age t\ 
k - the rate of decrease in G; and 
Lq = length at birth. 
The size distribution of the sample was plotted and 
analyzed in R with ggplot2 (Wickham, 2009). All but 1 
of the 5 growth models were fitted in R, by using non- 
linear least squares with the Gauss-Newton algorithm 
(nls function in R). The generalized VBGF model was 
fitted through the use of nonlinear least squares with 
a grid-search technique (package nls2; Grothendieck, 
2013). For each model, the mean values of parameters 
were estimated, and the standard errors and 95% CIs 
of those estimates were calculated. Furthermore, model 
goodness-of-fit was assessed with the Akaike informa- 
tion criterion (AIC) and the Bayesian information cri- 
terion values. A likelihood ratio test (LRT), as defined 
by Kimura (1980) and recommended by Cerrato (1990), 
was used to test the null hypothesis that there is no 
difference in growth parameters between males and fe- 
males for the bigeye thresher. The growth parameters of 
the samples from the North and South Atlantic Ocean 
were also compared. For the purposes of this analysis, 
the samples from the 2 hemispheres were separated on 
the basis of the 5°N parallel, as recommended in the 
ICCAT manual for shark species (ICCAT 6 ). 
6 ICCAT (International Commission for the Conservation of 
Results 
Samples 
Of the 546 vertebrae of bigeye thresher, 501 were used 
for the age and growth analysis because they had at 
least 2 identical readings. From these samples, 258 
vertebrae were from females (52%) and 241 vertebrae 
were from males (48%); the sex of 2 specimens could 
not be determined. The size distribution used in this 
study ranged from 102 to 265 cm FL for females (mean: 
165.7 cm FL [standard deviation ( SD )] 32.8) and from 
94 to 260 cm FL for males (mean: 170.2 cm FL [SD 
30.9]) (Fig. 3). 
The sample size for vertebrae of bigeye thresher 
that were collected in the North Atlantic Ocean was 
358 (200 from females and 158 from males), and the 
size distribution ranged from 94 to 242 cm FL (mean: 
159.3 cm FL [SD 29.9]). The sample size for vertebrae 
that were collected in the South Atlantic Ocean was 
141 (58 from females and 83 from males), and size dis- 
tribution ranged from 128 to 260 cm FL (mean: 189.5 
cm FL [SD 26.2]). 
Atlantic Tunas). 2013. ICCAT Manual. [Online publica- 
tion under development]. [Available at website, accessed 
January 2014.] 
