Frazier et al.: Growth rates of Sphyrna tiburo estimated from tag-recapture data 
Bootstrapping (with 5000 iterations) was used to develop 
95% confidence intervals (CIs) for VBGF parameter esti- 
mates. Model estimates and CIs were generated by using 
the FSA package (vers. 0.3.2; Ogle, 2012) in R (vers. 3.6.0; 
R Core Team, 2019). 
Comparisons of tag-recapture and age-based growth 
To compare growth rates between models, annual growth 
rates were estimated by using the parameters of the age 
and growth models to calculate mean length at estimated 
age. These values were used to create trend lines of the 
relationship between mean growth and FL, allowing 
comparison of the growth rates based on the GROTAG 
reference lengths. Parameter values from bootstrapping 
were used to calculate 95% CIs for the age-based growth 
rates. 
To allow statistical and visual comparison of growth 
rates between the populations in the Atlantic region and 
GOM, we calculated growth at 2 reference lengths corre- 
sponding to the mean of the 3 smallest L, of sharks from 
the Atlantic region and a length less than the smallest 
age-based bootstrap L., estimate (g,, gg). Region-specific 
bootstrap values (from the use of 5000 iterations) were 
used to calculate average growth and 95% CIs at the 
shared reference lengths. To allow comparisons of growth 
between age-based and length-based models, we calcu- 
lated mean growth rates for age-based models (g’,, g’3) 
corresponding to growth rates from length-based models 
(Sq. 8g). These were calculated by using bootstrapped esti- 
mates of parameters /», /x, and /y to solve for age-based 
growth rates (g’,, ’3). The resulting values equate to the 
expected annual growth rate of fish at the age when mean 
length is equal to reference length o or 8. The length-based 
(84, 8g) and age-based (g’,, g’3) growth rates were plot- 
ted with 95% CIs to allow comparisons of growth within 
and between regions and models. All GROTAG models 
were generated by using the fishmethods package (vers. 
1.4-0; Nelson, 2013) in R. 
For the GROTAG model, an additional parameter 
needed to produce von Bertalanffy growth curves, theoret- 
ical age at length zero (ty), was calculated by using mod- 
el-specific L., and k as well as observed mean size at birth 
(Lo) with age (t=0): 
1 (L,, — Ly) 
to = or Bu [a= (6) 
Region-specific mean Ly) was 263 mm FL for sharks from 
the Atlantic region (Frazier et al., 2014) and 252 mm FL 
for sharks from the GOM (R. Hueter, unpubl. data). 
Longevity and age at 50% maturity 
Estimated maximum ages from the region-specific age 
and growth studies provided initial values of maximum 
age; however, these values are likely underestimated in a 
fished population (Bishop et al., 2006). For the age-based 
and length-based models, longevity was estimated for 
each region and sex. The recaptured shark with the great- 
est time at liberty was assigned an age at initial capture 
by using L, and model-specific VBGF parameters recon- 
figured to solve for age where 
inf = 2 
L,, 
Age =| —— 
+ to. (7) 
This calculated age at initial capture was then added to 
time at liberty to estimate longevity. 
The GROTAG-derived VBGF parameters were used to 
solve for sex-specific age at 50% maturity by using equa- 
tion 7 with L, set to estimates of length at 50% maturity 
of sharks from the Atlantic Ocean (male: 617.8 mm FL; 
female: 818.5 mm FL; Frazier et al., 2014) and the GOM 
(male: 630.8 mm FL; female: 716.4 mm FL; Lombardi- 
Carlson‘), allowing calculation of age at 50% matu- 
rity without introducing bias from age _ estimation. 
Confidence intervals for longevity and age at 50% matu- 
rity were generated by using the 95% CIs for the VBGF 
parameters. For the published estimates of age at 
50% maturity, 95% Cls are recorded as published for the pop- 
ulation in the Atlantic region; however, no measurements of 
uncertainty were reported for the population in the GOM. 
Results 
Data collection 
A total of 139 and 190 recaptured bonnetheads were avail- 
able from the GOM and the Atlantic Ocean off the southeast- 
ern United States, respectively (Fig. 1). Ranges of lengths at 
capture and recapture and range and mean of time at liberty, 
by region and sex, are reported in Table 2. Sex- and region- 
specific recapture data sets did not encompass the range of 
lengths that have been reported as present in each region’s 
population (Ulrich et al., 2007; Bethea et al., 2015). Large 
females were lacking in the GOM data set (n=99, only 
2 females greater than 880 mm FL available; Suppl. Table 
[online only]), and there was no representation of small females 
in the Atlantic region data set (n=172, no females less than 
550 mm FL present; Table 2). Sample sizes for males from the 
GOM (n=40) and the Atlantic region (n=18) were relatively 
small, and lengths did not adequately represent the range of 
individuals found in the population, especially in the Atlantic 
region (Table 2, Suppl. Table [online only]). In comparison, the 
smallest and largest bonnetheads in the data used in the age- 
based models for fish in the Atlantic region are 245 and 
825 mm FL (males) and 262 and 1043 mm FL (females) 
(Frazier et al., 2014), and those in the data used in the GOM 
“ Lombardi-Carlson, L. A. 2007. Life history traits of bonneth- 
eads, Sphyrna tiburo, from the eastern Gulf of Mexico. South- 
east Data, Assessment, and Review SEDAR13-DW-24, 7 p. 
[Available from website.] 
