Molina et al.: Age and growth of Mustelus schmitti 
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Table 1 
Equations of the 7 growth models fitted to the length-at-age data of nar- 
rownose smooth-hound ( Mustelus schmitti) collected in 2008 in Anegada Bay, 
Argentina, where VBGF=the von Bertalanffy growth function; L t =length at 
age t ; L 0 = length at age 0; L 0 *=the fixed length at age 0; ti=age 1; t 3= the 
maximum age recorded;, t 2 =&n age between t\ and t 3 , Lx=length at age 
L 2 =length at age L 3 =length at age t 3 ; L„=asymptotic length; and K, g, 
G, and G init =the growth coefficients of the different models. In the Francis 
model, r=(L 3 -L 2 ) / (Z^-Lj). In the Gompertz model, a=the instantaneous 
growth rate at the inflection point of the curve. 
Model 
Growth function 
Original VBGF 
Traditional VBGF 
Fixed-Lo VBGF 
Francis 
Mooij 
Logistic 
Gompertz 
L t = L 0 + (L m - L 0 ) x (1 - expl- K x *>) 
L t = L„ x(l - eX pl- K(t - t0 M) 
L t = L 0 * + (L„ - L 0 *) x (1 - exp (_K « «) 
L t = Lj + (L 3 - Lj) x ([1 - r 2 « l - ‘D ' I 43 - “»] / [1 - r 2 ]) 
L t = (G init x [L«, - L 0 *] /LJ exp (Ginit/L “ ,t 
L t = (L 0 * LJ/ (L 0 + [L m - L 0 ]) exp (_g x 
L t = L 0 X (ex pGll-expl-gxt))) 
The longevity was assumed to be the age at 95% of 
! L„ by using Fabens (1965) equation. Natural mortality 
1 (M) was calculated, by following Booth et al. (2011), 
1 as the median of the empirical model of Pauly (1980), 
Hoenig (1983), and Jensen (1996): 
^(Pauiy) = exp(-0.0152 - 0.2791nL oo 
+ 0.6543111# + 0.4631nT), (2) 
•^(Hoenig) = exp(1.44 - 0.9821n£ max )), and (3) 
M (Jensen) = 1.6#, (4) 
where L„ and # = the VGBF model parameters; 
T = the mean water temperature (12. 7°C); and 
f max = the age of the oldest fish sampled (Hoenig, 
1983). 
Results 
A total of 1577 narrownose smooth-hound, with sizes 
ranging from 300 to 810 mm TL (mean: 460 mm TL 
[standard error (SE) 90 mm]; mode: 390 mm TL), were 
; collected. Of these sharks, 245 were subsampled. Siz- 
es of subsampled fish ranged from 320 to 810 mm TL 
(mean: 490 mm [SE 90 mm TL]; mode: 400 mm TL) (Fig. 
3). Of the fish examined, 52.46% were females, ranging 
in size between 331 and 810 mm TL, and 47.54% were 
males, with a size range of 320-791 mm TL. 
In the vertebrae of narrownose smooth-hound, we 
observed a pattern of alternating opaque and translu- 
cent bands and an annual cycle in the seasonal evo- 
! lution of the proportion of translucent edges (Fig. 4). 
Vertebrae with translucent margins increased in Feb- 
ruary (summer), reached a 76% peak in May (autumn), 
and decreased to a value of approximately 11% from 
j August (winter) to November (spring). These data indi- 
| cate a yearly periodicity in translucent band formation. 
; The total number of individuals used for this analysis 
was slightly smaller than the total subsample number 
because of illegibility of the edge of the vertebra of 23 
individuals. This illegibility was the result of an error 
in the concentration of hypochlorite used for cleaning. 
The outer layer of these 23 vertebrae was corroded by 
hypochlorite and, therefore, was illegible. 
The ages determined for the total population ranged 
from 0 to 11 years. A pattern of increase in length with 
age was observed (Table 2); however, this pattern was 
not consistent at some ages, particularly at ages of 
0-1 years and above 6-7 years, where the number of 
individuals was proportionally low. Results for back- 
calculated length at age indicated a more consistent 
pattern of increase in length with age but also abrupt 
leaps in length at older ages. The age bias plot shows 
no systematic bias between the 2 readers (Fig. 5), with 
a range of error from -2 to 1 band, and a percent- 
age of agreement of 82.45%. Estimation of ages was 
highly precise, according to the average percent error 
and average coefficient of variation (4.54% and 3.23%, 
respectively). Band counts by reader 1 had a range of 
error of -3 to 3 bands and a percentage of agreement of 
87.82%. Obtained values of average percent error and 
average coefficient of variation for reader 1 indicate a 
precise age estimation (3.94% and 2.79%, respectively). 
Band counts by reader 2 had a range of error from -4 
to 3 bands and a percentage of agreement of 82.88%. 
Average percent error and average coefficient of varia- 
tion for reader 2 indicate precise age estimation (3.05% 
and 2.15%, respectively). 
Age 1 was the most predominant age for both sexes, 
representing 19.54% of all females and 19.64% of all 
males, followed by age 2 for females with 18.04% and 
age 3 for males with 17.85% (see Table 2). 
Our back calculation of length-at-age data produced 
2162 observations. Back-calculated mean and SE val- 
ues are presented in Table 2. Although within the SE 
