52 
Fishery Bulletin 11 7(1-2) 
Table 1 
Tag-recapture data and vertebral band-pair counts for 12 recaptured sandbar sharks (Carcharhinus plumbeus) injected with 
oxytetracycline (OTC) and tagged between 1983 and 2009 in the western North Atlantic Ocean. The relationship between 
years at liberty (YAL) and counts of vertebral band pairs (BP) is included (BP-YAL). An asterisk (*) indicates an estimated 
length. The last 4 sharks were either at liberty for less than 1 year or had no visible OTC mark and were not included in 
analysis. TFL=fork length at tagging; RFL=fork length at recapture; VR=vertebral radius; M=mature; and UNK=unknown 
sex. 
No. of Underestimation 
Specimen 
ID code 
Sex 
TFL 
(cm) 
RFL 
(cm) 
Date 
tagged 
Date 
recaptured 
YAL 
Growth 
(cm) 
BPs past 
OTC mark 
Total no. 
of BPs 
BP-YAL 
Maturity 
between BP 
and YAL (%) 
CM1025 
F 
119 
159 
5/16/2001 
6/28/2017 
16.12 
40 
7.0 
14.0 
-9.12 
M 
56.58 
CM1029 
F 
136 
156 
11/14/2000 
5/26/2010 
9.53 
20 
4.0 
14.0 
-5.53 
UNK 
58.03 
CM1024 
M 
129 
154 
5/2/2009 
5/29/2017 
8.10 
25 
4.0 
13.0 
-4.1 
M 
50.62 
CM945 
F 
68 
150 
10/25/1996 
8/8/2002 
11.77 
82 
9.0 
11.0 
-2.77 
UNK 
23.53 
CM1026 
F 
114 
132 
8/6/1986 
7/29/1993 
6.98 
18 
5.0 
13.0 
-1.98 
UNK 
28.37 
CM867 
M 
115 
134 
5/19/1989 
2/22/1993 
3.76 
19 
2.5 
10.0 
-1.26 
UNK 
33.51 
CM1031 
M 
56 
156 
9/21/1998 
6/4/2014 
15.70 
100 
15.5 
16.0 
-0.20 
M 
CM1027 
F 
85 
147 
8/3/1996 
7/27/2006 
9.98 
62 
10.0 
13.0 
0.02 
UNK 
CM751 
M 
56 
59 
7/31/1983 
9/7/1983 
0.10 
3 
<1 
CM932 
F 
150 
153 
11/14/2000 
3/1/2001 
0.29 
3 
<1 
CM1028 
F 
160 
165* 
4/22/2009 
8/25/2010 
1.34 
5 
No OTC 
CM 1030 
M 
130* 
153 
5/4/2009 
6/6/2011 
2.01 
23 
No OTC 
agreed on a final count, a layer with the OTC mark 
was superimposed on the consensus layer. The trans¬ 
parency of the OTC layer was decreased until the 
marks on the consensus layer were visible. 
g a = the mean annual growth rate at arbitrary 
length a; and 
gp = the mean annual growth rate at the arbi¬ 
trary length p. 
Growth analysis with tag-recapture data 
Data from only those sharks at liberty for >1 year and 
with a reliably measured body length at both tagging 
and recapture were used in growth curve analysis 
(n = 149). Parameters for the von Bertalanffy growth 
function from the tag-recapture data were generated 
by using both the Gulland and Holt (1959) and GRO- 
TAG (Francis, 1988) models in R, vers. 3.5.1 (R Core 
Team, 2018). 
The Francis (1988) method (GROTAG) uses maxi¬ 
mum likelihood techniques to estimate growth param¬ 
eters and variability from tagging data. A coefficient 
of variation of growth variability ( v ), the mean and 
standard deviation of measurement errors (s=standard 
deviation of measurement error), and outlier contami¬ 
nation ip) are estimated as well as growth rates at 2 
user-selected lengths (a and P). The reference lengths, 
a and P, were chosen to lie within the range of tagged 
individuals. The form of the von Bertalanffy equation 
becomes 
fig«-qg P 
S a ~ § p 
1 + 
a-P 
\AT 
where L x = the length at tagging; 
A L = the increment in length; 
AT = the increment in time; 
( 2 ) 
Mean annual growth rates for the GROTAG model 
were estimated at 60 and 160 cm FL to represent the 
size ranges of the sandbar shark. The simplest model, 
a linear fit with minimal parameters (a and s), was 
used initially, with additional parameters added to 
successively increase model complexity. Significant im¬ 
provement in the model results was achieved by using 
log-likelihood ratio tests (Francis, 1988). The model 
searches for the set of parameters that maximize the 
log-likelihood ratio (X). The introduction of additional 
parameters must increase X by 1.92 to be significant 
(P<0.05) (Francis, 1988). 
The value of the theoretical age at which a fish 
would have zero length (f 0 ) cannot be estimated from 
tagging data alone; rather, it requires an estimate of 
absolute size at age, such as size at birth. We calcu¬ 
lated t 0 with the von Bertalanffy growth function (von 
Bertalanffy, 1939) by using the following equation: 
to — t + (l/^iflnlCZ/oo — )], (3) 
where L t = known length at age (size at birth); 
L«, = mean asymptotic fork length; 
t = age; and 
k = a growth constant (per year). 
The t 0 values were calculated on the basis of an aver¬ 
age size at birth of 47.7 cm FL (Casey et al., 1985) 
with t= 0. Values for and k were calculated in the 
tag-recapture models. 
