Frazier et al.: Growth rates of Sphyrna tiburo estimated from tag-recapture data 
— GOM GROTAG 
--- Atlantic GROTAG 
—— GOM age based 
-—-- Atlantic age based 
Fork length (mm) 
— GOM GROTAG 
- - - Atlantic GROTAG 
—— GOM age based 
-—-- Atlantic age based 
10 12 
Age (years) 
Figure 5 
Comparison of growth curves from GROTAG models, which are based on tag- 
recapture data, and from age-based von Bertalanffy growth functions based 
on data from Lombardi et al. (2007) and Frazier et al. (2014) for (A) female 
and (B) male bonnetheads (Sphyrna tiburo) tagged in the northeastern Gulf of 
Mexico (GOM) during 1993-2006 and off the Atlantic coast of the southeastern 
United States (Atlantic) during 1998-2019. Age-based models were generated 
by using original length-at-age data from Lombardi et al. (2007) for sharks in 
the GOM because published models used total length and band count. 
341 
model for females in the GOM may be an 
artifact of sample size, although the 
model produced much greater variation 
in growth estimates at gg3), contrary to 
the estimates from other models indicat- 
ing a source of variation other than sam- 
ple size. These results indicate that there 
may be significant underestimation of 
ages of bonnetheads in the GOM with 
the age-based models. 
Sampling, fishing pressure, or gear 
bias could have affected results of the 
age-based models; however, estimates of 
age at 50% maturity calculated by using 
age-independent, length-based growth 
estimates also point to significant dif- 
ferences in maturity. These estimates of 
age at 50% maturity indicate that female 
bonnetheads mature at an average of 
1.5 years and males mature at an average 
of 3.2 years later than females and males 
do according to age-based estimates, 
providing further evidence of age under- 
estimation in the GOM data set. The GRO- 
TAG model does not produce comparable 
estimates of average age at length; how- 
ever, data from long-term tag-recapture 
studies were available. When these data 
were combined with results from growth 
models, calculated longevity for female 
and male bonnetheads in the GOM are 
8.9 and 11.4 years from the GROTAG 
models and 6.5 and 10.8 years from the 
age-based models; these ages are con- 
siderably older than the maximum age 
estimates of 5.5+ and 7.5+ reported by 
Lombardi-Carlson et al. (2003). 
Data from long-term tag-recapture 
efforts and longevity estimates calcu- 
lated from GROTAG models confirm the 
report of age underestimation for bon- 
netheads in the Atlantic region by Fra- 
zier et al. (2014). However, for females, 
length-based estimates of age at 50% 
maturity are not significantly different 
from age-based estimates. If age under- 
estimation was common in the age-based 
study for sharks in the Atlantic region, it 
and faster rates at which k is reached compared with esti- 
mates from age-based models. Plots of bootstrapped 
growth estimates for females from the GOM age-based 
model indicate large uncertainty in growth estimates at 
the upper reference length. Comparatively, results from 
GROTAG models for bonnetheads in the Atlantic region 
and in the GOM and from the age-based model for bonnet- 
heads in the Atlantic region indicate less uncertainty at 
the upper reference length compared with the lower refer- 
ence length at which growth is expected to be more vari- 
able (Erzini, 1994). The large uncertainty in the age-based 
may be rare or only in individuals at or near L,, given the 
agreement between growth models and life history param- 
eters for females. 
Although age and growth studies are not necessarily 
expected to encounter the oldest individuals in a popula- 
tion because of their relative scarcity (Bishop et al., 2006), 
there is increasing evidence that age is frequently under- 
estimated in many studies of age and growth of elasmo- 
branch species, especially in those of long-lived species 
(e.g., Kalish and Johnston, 2001; Francis et al., 2007; 
Frazier et al., 2015; Harry, 2018; Natanson et al., 2018b). 
