Carrillo-Colin et al.: Bayesian estimation of the age and growth of Rhinoptera steindachneri 11 
The von Bertalanffy growth function (VBGF) has been 
used conventionally to describe growth in elasmobranchs 
(Cailliet et al., 2006) and involves the assumption that 
variation in growth rate is determined by an individual’s 
metabolic state, diet, and reproduction and by environ- 
mental factors (Pitcher and Hart, 1982). However, the 
VBGF does not always reflect the growth of elasmo- 
branchs. Therefore, it is necessary to explore alternative 
models (Smart et al., 2016). Neer and Thompson (2005) 
evaluated various models for estimating the growth of 
the cownose ray (R. bonasus) in the Gulf of Mexico, and 
they found that the Gompertz model (GM) described its 
growth convincingly. 
In our study, we estimated age by using counts of 
growth bands on vertebrae of golden cownose rays col- 
lected in the artisanal ray fishery of the GOC. We evalu- 
ated the ability of 2 models (VBGF and GM) to describe 
growth. We used a Bayesian approach to estimate the 
posterior probability of the growth parameters (mar- 
ginal posteriors). The availability of marginal posteriors 
of growth parameters allows the explicit incorporation 
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200 km 
of the uncertainty of parameters into further demo- 
graphic or stock assessment studies to obtain more real- 
istic estimates. 
Materials and methods 
Samples of golden cownose rays were collected in 2008— 
2014 from landings of the artisanal fishery and from 
bycatch of the commercial shrimp traw!] fishery in the 
southern GOC (Fig. 1). We recorded the sex of each 
sampled ray and measured the DW (in centimeters), 
avoiding the curvature of the body. A section of 8—10 
cervical vertebrae was extracted from each specimen 
(Natanson et al., 2018). Excess tissue and neural arches 
were excised from the vertebral segments, and verte- 
brae were exposed to sodium hypochlorite (5%) to 
remove the remaining fascial tissue (Anislado-Tolentino 
et al., 2008). 
A single vertebra was removed from each section by 
using a blade to expose the surface of the centrum and 
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Sinaloa 
Celestino 
Figure 1 
Map showing the primary locations (black circles) where golden cownose rays (Rhinoptera stein- 
dachneri) were sampled from landings of the artisanal fishery and from bycatch of the shrimp 
trawl fishery in the southern Gulf of California in Mexico between 2008 and 2014. The area with 
the diagonal lines indicates the Gulf of California. 
