Frazier et al.: Growth rates of Sphyrna tiburo estimated from tag-recapture data 335 
Table 2 
Summary of data collected for bonnetheads (Sphyrna tiburo) tagged and recaptured in the 
northeastern Gulf of Mexico (GOM) during 1993-2006 and in the Atlantic Ocean off the 
southeastern United States (Atlantic region) during 1998-2019. The number of individuals 
recaptured (7), the range of fork lengths (FLs) of fish at initial capture and recapture, and 
the range, mean, and standard deviation (given in parentheses) of times at liberty for recap- 
tured sharks are provided by region and sex. 
Mean time at 
liberty (d) 
Time at 
liberty (d) 
Initial Recapture 
Region n FL (mm) FL (mm) 
450-958 
520-780 
642-1014 
543-805 
1—2028 
1-1639 
10-3263 
13-2659 
GOM 99 430-930 
40 400-750 
Atlantic region 172 550-1013 
18 532-767 
308 (366) 
259 (319) 
458 (518) 
401 (823) 
(u=1.0, w=0.58), indicating that growth likely ceases at 
some point during the year and that it peaks in June. The 
SD of the measurement error for the model for females in 
the GOM (s=11.9 mm FL) is more than double that of the 
model for females in the Atlantic region (s=4.8 mm FL) 
with 95% CIs that do not overlap, indicating significant 
differences in measurement error between the 2 regions. 
The model for females in the Atlantic region had a negli- 
gible mean measurement error of —0.5 mm FL. The con- 
tamination probability parameter was not included in 3 
of the 4 models and is very low (p<0.001) in the model for 
females in the Atlantic region; therefore, the occurrence of 
outliers is scarce in all data sets. 
Age-based growth model and regional comparisons 
The Francis (1988a) age-based model produced nearly 
identical estimates of VBGF parameters to those produced 
by using the Beverton and Holt (1957) modeling method 
reported in Frazier et al. (2014). 
For both regions, the age-based models for males pre- 
dicted faster mean annual growth at smaller lengths and 
slower growth than the length-based models as bonneth- 
eads approached estimated L,, (Fig. 3). For males in the 
Atlantic region, 95% CIs for age-based estimates of growth 
rates overlap at GROTAG-predicted rates for both g¢1. 
and £75 (Fig. 3). For males in the GOM, 95% CIs overlap 
at GROTAG-predicted rates for 479; however, at 737, 95% 
CIs do not overlap and rates are significantly different 
from those from the age-based model, with the age-based 
model predicting near zero growth by an FL of 708 mm 
(Fig. 3). 
For females from the Atlantic region, the age-based 
model predicted a faster growth rate at smaller lengths 
but very similar growth rates at larger lengths compared 
with predicted rates from the GROTAG model (Fig. 4), 
and 95% CIs overlap at both g;,, and gj 999. For females 
in the GOM, the age-based model predicted nearly iden- 
tical growth rates at the smaller GROTAG reference 
length (g4¢5); however, the age-based model predicted a 
much smaller L,, than the estimate from the GROTAG 
model (Fig. 4). The predicted growth rate at the larger ref- 
erence length (go,;) is significantly higher than the esti- 
mate from the age-based model, with no overlap in 95% 
Cls. The significant differences in estimated growth rates 
for both males and females at g737 and go,;, between the 
GROTAG and age-based models indicate sampling bias or 
age underestimation in the GOM age-based model. 
Plots of growth rates and 95% CIs estimated for males 
with the GROTAG model do not indicate significant dif- 
ferences in growth between populations in the Atlantic 
region and the GOM (Fig. 3); however, results from like- 
lihood-ratio tests (x7=40.8, df=3, P<0.001) indicate signifi- 
cant differences in growth between regions. 
Plots of growth rates with 95% CIs estimated for 
females as well as results from likelihood-ratio tests 
(y7=31.2, df=3, P<0.001) for the best-fit GROTAG models 
indicate that growth was significantly different between 
regions, with a significant difference in average growth 
rates occurring in individuals larger than ~850 mm FL 
(Fig. 4). Plots of von Bertalanffy growth curves by sex, 
region, and model further illustrate the difference in pre- 
dicted lengths at age (Fig. 5); however, caution should be 
used when comparing curves between the GROTAG and 
age-based models because of different definitions of L 
(Francis, 1988a). 
To allow comparisons of growth within and between 
models and regions, growth rates were calculated for 2 ref- 
erence lengths (g;;,, 839) by using the GROTAG and age- 
based models. Plots of bootstrap parameter estimates 
from the GROTAG model indicate clear differences in g39 
between regions with no overlap in 95% Cls (Fig. 6). Plots 
of GROTAG bootstrap parameter estimates indicate less 
variation in growth with greater length for both regions. 
Overall, given the estimates from both models, the varia- 
tion in predicted growth is much higher for the population 
in the GOM than for the population in the Atlantic region. 
At the set reference lengths, growth rates do not signifi- 
cantly differ between the age-based and GROTAG models; 
however, as presented in Figure 3, estimated growth rates 
co 
