474 
Fishery Bulletin 1 13(4) 
Table 1 
Results from the 2 forms of chi-square <x 2 ) tests of symmetry used to compare and detect 
nonrandom differences between the 3 sets of age readings of bigeye thresher (Alopias 
superciliosus), the McNemar maximally pooled method and the Evans and Hoenig method 
that pools along diagonals (Hoening et al., 1995; Evans and Hoenig, 1998). The vertebrae 
were collected in the Atlantic Ocean between September 2007 and December 2009. 
McNemar Evans and Hoenig 
Readings 
X 2 
P 
X 2 
df 
P 
Reading 1 vs. reading 2 
0.03 
0.85 
3.18 
7 
0.87 
Reading 1 vs. reading 3 
0.51 
0.47 
3.98 
7 
0.78 
Reading 2 vs. reading 3 
4.00 
0.05 
8.49 
5 
0.13 
varying between a range of possible values) was used. 
The growth parameters obtained from the regular 
3-parameter VBGF model were considered best for de- 
scribing the growth of this species for both sexes. This 
designation was decided on the basis of both the statis- 
tical goodness-of-fit of this model and because the esti- 
mated biological parameters obtained seemed realistic. 
When this VBGF model was used, the estimated L; n f 
values were always higher and the k values were lower 
than those values obtained from the VBGF model with 
a fixed Lq for both females (Li n f=284.2 cm FL, £=0.06/ 
B /\— - 
/ \ 
{ \ 
/ 1 \ 
/ 
\ / 
/\ 
/ \ 
/ \ 
/ \ 
/ \ 
1 
\ 
/ 2 l\/l 1 1 \a 
( 1 - 2 - 4 - 9 - 28 - 761 9768 - 34 - 7 — 2-3 
\ 2 A 02 1 v / 
\ 1 | 3 \ 1 / 
\ y \ / 
\ / 
\ / 
\ / 
c v — 
\ / 
\ / 
\ / 
V 
Figure 5 
Hexagon plot used to test the symmetry of the 
3 readings of growth bands in vertebrae taken 
from bigeye thresher ( Alopias superciliosus ) 
collected between 2007 and 2009 and used to 
estimate the age and growth of this species in 
the Atlantic Ocean. The 3 axes correspond to 
the first reading (A), second reading (B), and 
third reading (C). The numbers refer to the 
number of triplets at each location on the plot, 
and all possible locations are represented as 
gray circles. 
year) and males (Li n f=245.6 cm FL, k= 0.09/year) (Ta- 
ble 2; Fig. 6). When the GGF models were used, a simi- 
lar pattern was found, with the GGF producing lower 
k values for both sexes than the values obtained from 
the GGF model with a fixed Lq 
With the LRT tests (Kirnura, 1980), significant dif- 
ferences were found between sexes in all the esti- 
mated VBGF parameters, except for the Lq (Lj n f LRT; 
X 2 =6.08, df=l, P<0.05; k LRT: x 2 =4.13, df=l, P< 0.05; L 0 
LRT: x 2 =1.66, df=l, P>0.05; combined parameters LRT: 
X 2 =9.69, df=3, P<0.05). For all models, k values were 
lower and Li n f values were higher for females than for 
males. 
When we compared the growth of bigeye thresher 
between the 2 hemispheres (North and South Atlan- 
tic Ocean), only the 2-parameter VBGF model with a 
fixed Lq converged for the separate sexes in each hemi- 
sphere and the traditional VBGF model converged for 
the North Atlantic Ocean but not for the South Atlan- 
tic Ocean. Therefore, the VBGF model with a fixed Lo 
was used to obtain and compare the growth parameters 
for the 2 hemispheres (Table 3). The overlaps in the 
95% CIs of the parameters were used for this compari- 
son. There was no overlapping of the 95% CIs between 
the North and South Atlantic Ocean, with the excep- 
tion of a slight overlap in the Lj n f for males. For both 
sexes, the Lj n f was higher for the South Atlantic Ocean 
than for the North Atlantic Ocean and the estimated k 
values were higher for the North Atlantic Ocean (£f e _ 
males=0.16 [95% Cl 0.14, 0.18]; £ ma i es =0.18 [Cl 0.15, 
0.21]) than for the South Atlantic Ocean (£f e males = 0-09 
[Cl 0.07, 0.11]; £ males =0.13 [Cl 0.11, 0.15]). 
Discussion 
Several approaches were used in this study to evaluate 
the precision of age estimates and to test for bias in 
the age determinations of bigeye thresher, as suggested 
by Goldman et al. (2012): PA, PA ±1 year, APE, CV, 
age-bias plots, and tests of symmetry. To our knowl- 
edge, this study is the first to test the symmetry of 3 
