Torres-Palacios et al.: Age and growth parameters of Urotrygon aspidura 
175 
Table 2 
Parameters and statistical criteria for the von Bertalanffy growth model (VBGM), two-phase growth model (TPGM), 
Gompertz growth model (GGM), and logistic growth model (LGM) used to describe the growth of male Panamic stingrays 
(Urotrygon aspidura) (sample size [n]=180) collected in the central zone of the Pacific coast of Colombia in 2006-2009 and 
2015. Two data sets are presented; the adjusted data set considers the months with peaks of reproduction. The parameters 
and criteria are the asymptotic disc width (DW„, in centimeters), birth size (DW 0 , fixed to 7.5 cm for models with 2 and 
4 parameters), annual growth rate ( k ), age at transition between 2 phases or inflection point « h ), maximum difference in 
DW at age between the VBGM and TPGM at the t h (h), Akaike information criterion (AIC,). difference in AIC ; between 
models (Aj), and Akaike weight (»;). Weighted averages from the TPGM are given with standard errors of the mean (SEs). 
Numerals after the model abbreviation indicate the number of parameters used in that model. Dashes indicate that data 
were not available because variables were not included in a model. 
Model DW„ k t 0 t h h DW 0 AIC; A ; iC; 
Unadjusted data 
VBGM-3 
15.99 
0.79 
-1.47 
- 
- 
10.97 
736.08 
0.00 
0.27 
VBGM-2 
15.31 
1.65 
- 
- 
- 
7.50 
924.74 
188.65 
0.00 
GGM-3 
15.84 
0.93 
-1.08 
- 
- 
10.97 
736.42 
0.34 
0.22 
GGM-2 
15.22 
2.00 
- 
- 
- 
7.50 
924.88 
188.79 
0.00 
LGM-3 
15.72 
1.08 
-0.77 
- 
- 
10.97 
736.75 
0.67 
0.19 
LGM-2 
17.05 
0.72 
_ 
- 
- 
10.93 
737.38 
1.30 
0.14 
TPGM-5 
17.11 
0.81 
-1.33 
2.60 
0.40 
10.95 
736.83 
0.75 
0.18 
TPGM-4 
16.81 
1.45 
- 
2.56 
0.68 
7.50 
927.01 
190.92 
0.00 
Adjusted data 
VBGM-3 
15.08 
1.34 
-0.63 
- 
- 
8.59 
640.61 
4.10 
0.08 
VBGM-2 
14.85 
1.76 
- 
- 
- 
7.50 
646.70 
10.19 
0.00 
GGM-3 
14.82 
1.90 
-0.28 
- 
- 
8.20 
644.78 
8.27 
0.01 
GGM-2 
14.71 
2.26 
- 
- 
- 
7.50 
647.85 
11.35 
0.00 
LGM-3 
14.70 
2.38 
-0.10 
- 
- 
8.17 
646.05 
9.55 
0.01 
LGM-2 
14.65 
1.52 
- 
- 
- 
9.84 
674.94 
38.43 
0.00 
TPGM-5 
15.96 
1.63 
-0.48 
2.22 
0.54 
8.07 
636.51 
0.00 
0.64 
TPGM-4 
Weighted 
15.94 
1.81 
2.16 
0.67 
7.50 
638.30 
1.80 
0.26 
average from 
TPGM (SE) 
15.95 
(0.01) 
1.68 
(0.15) 
- 
2.20 
(0.05) 
0.58 
(0.11) 
- 
- 
- 
- 
older ages of 14 years for females and 12 years for males 
(Guzman-Castellanos, 2015). The Panamic stingray can be 
considered a short-lived species (<8 years), similar to other 
species belonging to Urotrygonidae (Hale and Lowe, 2008; 
Mejia-Falla et al., 2014; Santander-Neto, 2015), whereas 
in other ray families, such as Dasyatidae and Rajidae, 
maximum ages can exceed 17 years (Francis et al, 2001; 
Licandeo et al., 2006; Smith et al., 2007; Aversa et al., 2011; 
Ba§usta and Sulikowski, 2012; O’Shea et al., 2013). 
Traditionally, the most used model to describe elasmo- 
branch growth (Cailliet et al., 2006) has been the VBGM; 
however, numerous studies indicate that other models 
can be better adjusted (Araya and Cubillos, 2006; Smart 
et al., 2016). The Gompertz growth model has been used 
with batoid species (Neer and Cailliet, 2001; Neer and 
Thompson, 2005; Matta and Gunderson, 2007; Ainsley 
et al., 2011), and the TPGM, which incorporates changes 
in growth rates during the lives of organisms, usually 
has been related with changes in energy investment in 
reproductive processes (Araya and Cubillos, 2006; Aversa 
et al., 2011). 
Differences in the age parameters obtained between the 
adjusted and the unadjusted age data, the former being 
more similar to the biological data, demonstrate the impor¬ 
tance of considering the reproductive and size character¬ 
istics of each species, as well as the multi-model approach, 
to obtain more reliable growth parameters (Harry et al., 
2010; Mejia-Falla et al., 2014). However, most age studies 
do not include adjustment based on the reproductive cycle, 
ignoring the potential effects that lack of adjustment could 
have on the demographic analyses and, therefore, on the 
fishery management of these cartilaginous fish species 
(Cailliet, 2015). 
It has been suggested that the use of different mod¬ 
els (or a multi-model approach) in growth studies allows 
researchers to select the model that is best adjusted to the 
data (Katsanevakis, 2006; Smart et al., 2016). For demo¬ 
graphic modeling purposes, of the 8 models applied to 
describe the DW-age relationship in the Panamic stingray, 
