Fernandez-Carvalho et a!.: Age and growth of Alopias superciliosus in the Atlantic Ocean 
471 
Figure 2 
Image of a vertebral section of a vertebra from 
a female bigeye thresher (Alopias superciliosus ) 
with a fork length of 170 cm and with 8 visible 
growth bands (B=birth mark). The specimen was 
collected in 2008 as part of this study to estimate 
the age and growth of this species in the Atlantic 
Ocean. 
Carvalho et ah, 2011). To prevent bias in counting 
bands, the 2 readers had no knowledge of the length 
or sex of each shark. After that step, the remaining 
samples (n- 429) were then read 3 times by the pri- 
mary reader (J. Fernandez-Carvalho), and only those 
vertebrae with band counts that were the same for at 
least 2 of the 3 readings were accepted for the age and 
growth analysis. To prevent reader familiarity with any 
particular vertebrae, each reader completed the first or 
second readings of each set of vertebrae (n=117 or 429 
before starting the second or third readings. The tem- 
poral periodicity of band formation was assumed to be 
annual, although this notion was not validated (see the 
Discussion section). 
To compare the aging precision between the 3 read- 
ings, both the coefficient of variation (CV) (Chang, 
1982) and the average percent error (APE) (Beamish 
and Fournier, 1981) were calculated and compared. The 
percentage of agreement (PA) and percentage of agree- 
ment within one growth band (PA ±1 year) among the 
readings were also calculated. Age-bias plots, where 
the mean (with 95% confidence interval [Cl]) of the 
reading thought to be less accurate is plotted for each 
distinct age from the reading thought to be more ac- 
curate (reading 3), were used to graphically assess the 
precision of aging between the 3 readings (Campana, 
2001 ). 
Furthermore, contingency tables and 2 chi-square 
tests of symmetry (McNemar and Evans and Hoenig 
tests) were used to test the null hypothesis that the 
readings are interchangeable versus the alternative 
that there are systematic differences between the read- 
ings (Hoening et ah, 1995; Evans and Hoenig, 1998). 
The McNemar test is a “maximally pooled” test of sym- 
metry where all squared differences of the values of 
the contingency table on each size of the diagonal are 
added and that result is divided by the sum of the val- 
ues on each size of the diagonal; the Evans and Hoenig 
method is a diagonally projected test of symmetry, in 
which the values are summed along a series of diago- 
nal cells that project outward from the central diago- 
nal (Hoening et al., 1995; Evans and Hoenig, 1998). In 
addition, the symmetry of all 3 readings was tested 
simultaneously by plotting triplets of readings on a 
hexagon plot (Evans and Hoenig, 1998). All symmetry 
analysis was carried out by using R statistical soft- 
ware, vers. 3.0.1 (R Core Team, 2013), with the package 
“fishmethods” (Nelson, 2013). The hexagon plots for the 
triplets of readings were created and interpreted with 
R code provided by J. Hoenig (Hoenig 5 ). 
Growth modeling 
Five growth models were used and compared in order 
to describe the growth of this species: 3 variations of 
the von Bertalanffy growth function (VBGF) and 2 
versions of the Gompertz growth function (GGF). The 
VBGF variations were 1) a reparameterisation of the 
3-parameter VBGF to estimate size at birth (Lq) in- 
stead of theoretical length at age 0 Uq) as suggested by 
Cailliet et al. (2006), 2) a modified 2-parameter VBGF 
that used a known and fixed Lq, and 3) a generalized 
VBGF with 4 parameters. 
For the 3-parameter VBGF model derived to esti- 
mate Lq, the following equation was used: 
L t = L; n f - (A in f - L 0 )e~ kt , ( 1 ) 
where L t = mean length at age t\ 
L [ n f = asymptotic maximum length; 
k = the growth coefficient; and 
Lq = length at birth. 
For the modified 2-parameter VBGF model with a 
fixed Lq, the following equation was used: 
L t = Li n f(l - be~ kt ), (2) 
where b was calculated with the equation immediately 
below: 
b = (A in f - L 0 )/L in f , (3) 
For the latter model, a fixed value of 84 cm FL was 
used for Lq. This value was chosen to be equivalent to 
a range of total lengths (TL) of 135-140 cm, the size es- 
timated for this species at birth by Chen et al. (1997). 
This value is comparable with the smallest sizes of 
free-swimming bigeye thresher reported to date (130 
cm TL, Bigelow and Shroeder, 1948; 155 cm TL, Still- 
5 Hoenig, J. M. 2014. Personal commun. Dep. Fish. Sci., 
Virginia Inst. Mar. Sci., Gloucester Point, VA 23062 
