Fernandez-Carvalho et al.: Age and growth of Alopias superciliosus in the Atlantic Ocean 
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Age estimation and comparison of age readings 
Although the vertebrae of bigeye thresher were in gen- 
eral difficult to read, the birth band was easily identifi- 
able because it coincides with an angle change in the 
corpus calcareum of vertebrae (Goldman and Musick, 
2005). A high degree of agreement over time was ob- 
served between the 3 readings of the primary reader, 
with the PA between the first and second, first and 
third, and second and third readings being 46%, 43% 
and 87%, respectively. Of the vertebrae examined, 91.8% 
had at least 2 identical readings (94.4% within one 
growth band) and, therefore, were accepted for growth 
modeling. The CV between the 3 readings 
of the primary reader was 10%, and the 
APE was 7.7%. In a graphical compari- 
son with age-bias plots, a high agreement 
with no systematic bias was observed be- 
tween the first 2 readings and the last 
reading of the primary reader (Fig. 4). 
The chi-square tests of symmetry showed 
little evidence of systematic differences 
between these readings, and only one 
test indicated marginally significant dif- 
ferences (McNemar test of readings 2 and 
3: x 2 =4, df=l, P=0.046) (Table 1). 
In the hexagon plot (Fig. 5), 3 axes 
correspond with readings 1, 2, and 3. If 
all 3 readings are the same, the triplet 
is plotted in the center, regardless of the 
reading values (e.g., 1,1,1 or 3,3,3). If 2 
of the readings agree, the observation 
will fall along one of the axis lines; for 
example, a reading of 3,3,5 will fall along 
the line where readings 1 and 2 agree, 
and the point will be 2 units away from 
the center (because the observation that 
disagrees is 2 values higher than the 
readings that agree). Similarly, a read- 
ing of 6,6,8 will fall on top of the reading 
of 3,3,5. If all 3 readings are equivalent 
(i.e., interchangeable), then there would 
be an overall symmetry. That is, each tri- 
angle would have the same number of ob- 
servations, and the 6 rays from the cen- 
ter outward would have the same number 
of observations (except for discrepancies 
solely due to sampling error). 
The hexagon plot developed in this 
study shows that most of the observations 
fell on the A axis (the horizontal line) 
(Fig. 5). This placement of observations 
in the plot corresponds with the second 
reading (B) equaling the third reading 
(C) and with the first reading (A) being 
more variable than the other 2 readings. 
However, the tests of symmetry did not 
reveal significant differences that would 
have supported systematic changes in 
the readings over time toward higher or 
lower values (i.e., the aging criteria remained stable). 
As time passed, the primary reader’s readings showed 
less variability but did not change systematically be- 
cause there was little evidence of differences between 
the readings from causes other than random error. 
Growth modeling 
The ages estimated in this study ranged from 0 (young 
of the year) to 25 years for both sexes. Of the 5 growth 
models used, the generalized VBGF with 4 parameters 
was the only model that did not converge, even when 
the grid-search technique (with the starting values 
