54 
Fishery Bulletin 11 7(1-2) 
5 10 15 21 
Years at liberty 
Figure 2 
Relationship of time at liberty to count of vertebral band pairs 
past the mark from oxytetracycline (OTC) injection for the 8 
recaptured sandbar sharks (Carcharhinus plumbeus) used in 
growth analysis for this study. These sharks were tagged from 
1986 through 2009 in the western North Atlantic Ocean. The 
dashed line indicates the 1:1 relationship. 
the OTC mark was seen in 2 of the 3 smallest sharks 
(CM1031 and CM 1027), and the age of the third shark 
(CM945) was underestimated by 23.5% (Table 1). Con¬ 
versely, the degree of underestimation was greater 
for sharks that were larger (>129 cm FL) at tagging 
(CM1025, CM1029, and CM1024). On the basis of bomb 
radiocarbon validation (Andrews 2011), we would ex¬ 
pect annual periodicity to be approximately 12 years; 
the amount of time at liberty past 12 years would de¬ 
termine the amount of age underestimation. Therefore, 
a lower amount of age underestimation is expected be¬ 
cause of the limited time of growth beyond 12 years 
in 2 sharks (CM1031 and CM1027), which were small 
at tagging compared with the sharks at liberty for 
the same period of time but tagged at a larger size 
(CM1025 and CM 1029). For example, for 1 of these 
small sharks (CM1027), 13 total band pairs were 
counted and validated as annual, but for 2 of the large 
sharks (CM1025 and CM1029) counts of 14 band pairs 
underestimated times at liberty by 9.1 and 5.5 years, 
respectively (Table 1). 
Growth analysis with tag-recapture data 
Tag-recapture data for 149 sandbar sharks were used 
in the Gulland and Holt (1959) and GROTAG (Fran¬ 
cis, 1988) models for growth analysis. Time at liber¬ 
ty ranged from 1.0 to 25.0 years, and size at tagging 
ranged from 48.0 to 172.8 cm FL (Suppl. Table) (on¬ 
line only). Tagging was conducted in all months except 
December, with most tags deployed from May through 
August (/z=101). These sharks were recaptured in all 
months of the year, with the most sharks taken in 
June, July, and August (/? = 22 each) and the 
lowest numbers of sharks taken in September, 
November, and December (zz=5, 4, 2, respec¬ 
tively). The results of the log-likelihood ratio 
tests using the GROTAG model (Francis, 1988) 
indicate that the more complex nonlinear mod¬ 
el with all 6 of the parameters included was 
the best fit for these data (see estimates for 
Model 4 in Table 2). The mean annual growth 
rates were calculated at 60 cm FL (10.65 cm/ 
year) and 160 cm FL (1.67 cm/year; Table 2). 
The fits failed for Models 1 and 5 (Table 2). 
We compared results for parameters of the 
von Bertalanffy growth function: estimates of 
L„ were higher and estimates of k were lower 
from the Gulland and Holt (1959) model than 
from the GROTAG model (Francis, 1988). In 
addition, although the growth curves from 
these 2 models look similar up to approximate¬ 
ly age 20, the Gulland and Holt (1965) model 
produces a curve with slightly higher length- 
at-age estimates past this age (Table 3, Fig. 
2). The ages validated with bomb radiocarbon 
dating for sharks in Andrews et al. (2011) and 
the known ages for OTC-injected sharks in this 
study follow the updated growth curves based 
on current tag-recapture data, rather than the 
growth curve based on previously published vertebral 
band-pair count data (Fig. 3). 
Discussion 
In view of current knowledge that using vertebral cen¬ 
tra age estimates in larger sharks is not correct (Harry, 
2018; Natanson et al., 2018), it is clear that growth 
models when used with extensive tag-recapture data 
can provide more accurate age estimates. As shown in 
this study, sharks with validated ages, such as those 
from OTC marking in this study and bomb radiocar¬ 
bon dating (Andrews et al., 2011), are more closely 
aligned with tag-recapture-based growth curves than 
growth curves derived from vertebral band-pair counts. 
Sharks with validated ages started to deviate from the 
growth curves based on vertebral band-pair counts and 
followed the growth curves based on tag-recapture data 
by 12-16 years, indicating that, by this range of ages, 
variation among individual sharks in rate of band-pair 
deposition was possibly related to growth rate during 
the maturation process (Fig. 3). 
Determination of age in elasmobranchs from band- 
pair counts on vertebral centra has relied on the ca¬ 
veat that each band pair represents a year. However, 
in 75% of the vertebrae from specimens in this study, 
it has been shown that the band pairs are not annual 
throughout life; band-pair counts underestimate age in 
these specimens. The 2 sharks that exhibited annual 
band-pair deposition were both tagged at smaller sizes; 
on the sample from the smallest individual, the OTC 
mark was seen just past the birth band, but, on the 
