Molina et al.: Age and growth of Mustelus schmitti 
373 
Table 3 
Mean estimates, observed and back calculated (BC) with standard errors (SEs), of growth parameters for the narrownose 
smooth-hound ( Mustelus schmitti) ca'ptured in Anegada Bay, Argentina, in 2008, determined with the 7 growth models. 
VBGF=the von Bertalanfy growth function; L^length at age 1; L 2 =the length at an age between 1 and the maximum age 
recorded; L 3 =length at maximum age recorded, L M = the asymptotic length; and K, g, G, and G init =the growth coefficients of 
the different models. Lengths are given as total lengths in centimeters. 
Females Males Sexes combined 
Growth model 
Observed 
estimate 
SE 
BC 
estimate 
BC 
SE 
Observed 
estimate 
SE 
BC 
estimate 
BC 
SE 
Observed 
estimate 
SE 
BC 
estimate 
BC 
SE 
Original VBGF 
893.71 
109.23 
864.89 
33.01 
762.56 
72.15 
786.43 
62.55 
855.14 
77.52 
878.81 
13.80 
L 0 
365.96 
13.34 
387.78 
9.14 
334.58 
16.21 
390.35 
9.53 
342.89 
10.53 
370.63 
2.97 
K 
0.061 
0.036 
0.166 
0.028 
0.151 
0.047 
0.137 
0.036 
0.104 
0.026 
0.150 
0.014 
Traditional VBGF 
L„ 
893.73 
109.23 
864.88 
33.01 
762.56 
72.16 
786.43 
62.55 
855.14 
77.52 
878.81 
13.80 
K 
0.061 
0.036 
0.166 
0.028 
0.151 
0.047 
0.137 
0.036 
0.104 
0.026 
0.150 
0.014 
h 
-6.95 
1.93 
-4.26 
0.60 
-3.82 
0.92 
-5.02 
0.92 
-4.93 
0.83 
-4.60 
0.19 
Fixed-Lo VBGF 
765.81 
34.80 
718.31 
13.51 
710.39 
33.45 
702.44 
18.66 
745.20 
24.04 
758.38 
6.36 
K 
0.160 
0.024 
0.217 
0.019 
0.190 
0.030 
0.340 
0.025 
0.169 
0.016 
0.174 
0.016 
Francis 
365.96 
13.34 
387.78 
9.14 
334.58 
16.21 
390.35 
9.53 
342.89 
10.53 
373.36 
6.58 
l 2 
564.92 
7.17 
613.59 
3.28 
578.09 
6.89 
599.62 
4.06 
573.34 
4.70 
608.32 
2.55 
l 3 
706.33 
15.43 
704.18 
10.79 
683.05 
21.78 
698.32 
16.49 
700.12 
12.12 
704.26 
9.09 
Mooij 
L„ 
765.81 
34.80 
718.31 
13.51 
710.39 
33.45 
702.44 
18.66 
745.20 
24.04 
758.38 
6.36 
Ginit 
119.31 
10.72 
162.80 
8.47 
137.22 
13.65 
155.10 
10.48 
125.62 
8.16 
146.45 
7.70 
Gompertz 
L„ 
862.53 
102.37 
840.93 
24.81 
742.70 
43.51 
751.05 
44.11 
788.81 
47.01 
749.33 
22.76 
G 
-0.13 
0.11 
-0.46 
0.04 
-0.28 
0.06 
-0.44 
0.07 
-0.20 
0.06 
-0.44 
0.04 
t 
0.13 
0.04 
0.22 
0.03 
0.22 
0.05 
0.19 
0.04 
0.16 
0.03 
0.21 
0.02 
Logistic 
L„ 
815.52 
51.93 
777.30 
8.38 
758.68 
51.94 
757.36 
11.37 
753.75 
34.22 
730.46 
18.14 
L 0 
362.80 
11.73 
382.14 
8.86 
340.32 
13.24 
398.74 
7.87 
354.13 
8.64 
398.88 
5.36 
g 
0.182 
0.020 
0.406 
0.018 
0.208 
0.027 
0.402 
0.023 
0.223 
0.028 
0.260 
0.023 
curves fitted to the growth data can be observed in Fig- 
ure 6A for females and 6B for males. Note that the 
original and traditional VBGF variants and the model 
with the Francis parameterization of the VBGF have 
the exact same AIC and BIG values because they are 
algorithmic modifications of the same model; hence, 
AIC and BIG values will not change. The same is true 
for the fixed-L 0 variant and the model with the Mooij 
parameterization of the VBGF. 
We chose to use the original VBGF model in our 
comparisons of growth between sexes for narrownose 
smooth-hound. The likelihood ratio test for the origi- 
nal VBGF model revealed no significant differences in 
growth between sexes for each parameter (mean 
1.94 [SE 0.22]; P>0.15). Extra sum-of-squares tests 
produced a similar result, failing to identify any differ- 
ences in the growth parameters between sexes (mean 
F=1.28 [SE 0.51]; P>0.15). The AIC, BIC, and w values 
presented in Table 5 also indicate that there were no 
differences between sexes in growth parameters. For 
females and males combined, estimates of the growth 
parameters from the 7 growth models are shown in 
Table 3, with the corresponding fitted growth curve 
shown in Figure 6C. 
The overall <|), calculated by using the parameters 
of the original VBGF model, was 4.69 for females and 
4.94 for males. 
Longevity was 20.87 years and 12.24 years for fe- 
males and males, respectively. Total natural mortal- 
ity rates were 0.19/year and 0.26/year for females and 
males, respectively. 
Discussion 
Age and growth estimates for fish have been shown to 
be highly dependent on the size range of collected sam- 
ples (Campana, 2001). For example, Lessa et al. (2016) 
in their study of the crocodile shark ( Pseudocarcharias 
kamoharai) did not capture small individuals, and the 
lack of small fish introduced a bias in their estimates 
of the growth parameters. This bias makes their re- 
sults applicable to only the study area or appropriate 
for extrapolation only for populations with a similar 
size composition. In long-lived species >30 years, e.g. 
Lamniformes like the white shark ( Carcharodon car- 
charias ), or the shortfin mako ( Isurus oxyrinchus), 
the lack of larger individuals in a sample can result 
in an underestimation of maximum age (Ardizzone et 
al., 2006; Natanson et al., 2006; Hamady et al., 2014; 
Andrews and Kerr, 2015). In our study of narrownose 
smooth-hound, the size of individuals captured ranged 
from 300 mm TL up to 810 mm TL; in other studies, 
individuals >850 mm TL, when present, have not been 
