Carrillo-Colin et al.: Bayesian estimation of the age and growth of Rhinoptera steindachneri 15 
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Mean marginal increment 
Oo 
T 
M-J J-A 
Bimester 
100 
80 
60 
40 | 
Edge percentage 
20 5 
ih 
M-A  M-J J-A 
Bimester 
B 
J-F 
S-O N-D 
Figure 4 
The periodicity of band formation was assessed by using (A) relative marginal increment analysis and (B) edge per- 
centage analysis for golden cownose rays (Rhinoptera steindachneri) sampled during 2008-2014 in the southern Gulf of 
California in Mexico. In panel A, the black circles represent the mean marginal increments, the error bars indicate the 
95% credible intervals, and the numerals above the error bars indicate sample sizes by bimester. In panel B, the black 
and white bars represent percentages of edges that were opaque and translucent, respectively. Results of analyses are 
shown for 2-month periods or bimesters: January—February, March—April, May—June, July-August, September—October, 
and November—December. 
ranged from 0 to 13 years for both sexes com- 
bined, with 69.1% of individuals assigned ages 
of 0-1 years (Fig. 5). The oldest individuals were 
13 years old for both females (92.9 cm DW) and 
males (96.6 cm DW). 
Growth estimation 
The results of the process in which the WAIC 
was used for model selection indicate that the 
GM was better at explaining the growth of 
golden cownose rays, given the reduction of 
2.44 units of WAIC from the WAIC of the VBGF 
(Table 1). Similarly, there was no gain in the 
model fitting from the inclusion of sex varia- 
tion in the GM. When sex was included in the 
GM, the WAIC increased by 7.85 units (from 
1459.82 to 1467.67). Therefore, we selected the 
model for both sexes combined. 
Results from use of the GM indicate that the 
golden cownose ray grows rapidly during its 
first 4 years of life, and its growth rate decreases 
after age 4 as it approaches its asymptotic size 
at the age of 13 years (Fig. 6). After the burn-in 
period, the simulations generated the marginal poste- 
rior probability distributions of the GM (Fig. 7, A—C). 
The predicted mean values of growth parameters of the 
GM were more realistic than those predicted with the 
VBGF (Table 1), which were considerably higher than 
the actual maximum lengths observed for the golden 
cownose ray and seemed to be overestimated. 
Frequency (no. of fish) 
BS ¢ 8 12 13 14 
Age (years) 
WW V1 
Figure 5 
Age-frequency distributions indicating the estimated age structure 
of female (black bars) and male (white bars) golden cownose rays 
(Rhinoptera steindachneri) sampled during 2008-2014 in the south- 
ern Gulf of California in Mexico (number of rays=249). 
Discussion 
Our results indicate that the golden cownose ray lives up to 
13 years, an age that is similar to the ages reported for the 
cownose ray (ft. bonasus) in the Chesapeake Bay (13 years 
for females and 8 years for males; Smith and Merriner, 
1987). However, the maximum reported age for the 
