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Bayesian Estimation of the Age and Growth of the Golden Cownose Ray

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Bayesian Estimation of the Age and Growth of the Golden Cownose Ray 10 National Marine Fisheries Service Fishery Bulletin First U.S. Commissioner established in 1881 of Fisheries and founder NOAA of Fishery Bulletin Abstract—The aim of this study was to Bayesian estimation of the age and growth of the use a Bayesian approach to estimate age and growth parameters for the golden golden cownose ray (Rhinoptera steindachneri) cownose ray (Rhinoptera steindachneri) in the southern Gulf of California in in the southern Gulf of California in Mexico Mexico. Age estimates were obtained through analysis of vertebrae of 249 Luis D. Carrillo-Colín1 individuals. The von Bertalanffy growth J. Fernando Márquez-Farías (contact author)2 function (VBGF) and Gompertz growth 3 model (GM) were fit to length-at- age Raúl E. Lara-Mendoza 4 data by using a Markov chain Monte Oscar G. Zamora-García Carlo algorithm for parameter estima- tion. Prior distributions of parameters Email address for contact author: [email protected] were included for an informative prior for disc width at birth (DW0) and unin- 1 Posgrado en Ciencias del Mar y Limnología 3 Dirección General Adjunta de Investigación formative priors for the theoretical Universidad Nacional Autónoma Pesquera en el Atlántico maximum disc width (DW∞) and growth de Mexico Instituto Nacional de Pesca y Acuacultura coefficients (k and g, for the VBGF and Avenida Ciudad Universitaria 3000 Secretaría de Agricultura y Desarrollo Rural GM, respectively). Our results indicate 04510 Coyoacán, Mexico City, Avenida Mexico 190 that the golden cownose ray lives up to Mexico Colonia del Carmen 13 years. The GM for combined sexes 04100 Coyoacán, Mexico City, Mexico was selected as the best model by using 2 Facultad de Ciencias del Mar the Watanabe–Akaike information cri- Universidad Autónoma de Sinaloa 4 Servicios Integrales de Recursos Biológicos, terion for model selection suitable for Paseo Claussen s/n Acuáticos y Ambientales Bayesian estimation. The mean values 82000 Mazatlán, Sinaloa, Mexico Calle Genaro Estrada 406 Centro of the GM parameters were as follows: 82000 Mazatlán, Sinaloa, Mexico DW∞=101.10 cm (95% credible inter- val [CI]: 94.19–110.43), g=0.15 year−1 (CI: 0.12–0.18), and DW0=40.00 cm (CI: 39.29–40.71). This study of the golden cownose ray contributes to the information available to develop better management and conservation strate- The golden cownose ray (Rhinoptera species (Bizzarro et al., 2007). Its dor- gies for this species. steindachneri) ranges from the Gulf of soventrally flattened and broad body California (GOC) to Peru, including the makes it susceptible to being caught in Galapagos Islands. Abundant in the gill- net fisheries and as bycatch by the GOC in summer, this species inhabits trawlers licensed to catch shrimp and coastal waters and migrates season- operate in the GOC (Márquez-Farías, ally (McEachran and Notarbartolo-di- 2002). Despite the importance of the Sciara, 1995). Bizzarro et al. (2007) golden cownose ray in the artisanal ray investigated the biology of the golden fishery of the GOC, detailed informa- cownose ray in the GOC and reported tion on the life history of this species a maximum length of 104 cm disc width and age estimates are scarce. Aging is (DW) and a median length at matu- necessary to determine age- specific sur- rity of around 70 cm DW. This species vival and reproduction rates, which are produces a single embryo at a size of useful for assessing species productivity 38–45 cm DW after 12 months of ges- (Cortés, 1998). However, determining tation. Low fecundity, typical of chon- age in chondrichthyans is challenging Manuscript submitted 30 June 2020. drichthyan species, is recognized as a because of the logistical problems of col- Manuscript accepted 3 March 2021. limiting factor for the sustainability lecting samples that result from their Fish. Bull. 119:10–20 (2021). Online publication date: 22 March 2021. of the fisheries that target them and seasonal migrations and because of the doi: 10.7755/FB.119.1.3 leads to the rapid overexploitation of difficulty of identifying growth bands in populations. hard parts (Cailliet, 2015). Growth is a The views and opinions expressed or The GOC supports the largest arti- fundamental component of life history, implied in this article are those of the sanal and multi- specific ray fishery in and the ability to model it is impera- author (or authors) and do not necessarily reflect the position of the National Mexico, and the golden cownose ray is tive for practical fishery assessments Marine Fisheries Service, NOAA. among the most commonly captured (Smart et al., 2016). Carrillo-Colín et al.: Bayesian estimation of the age and growth of Rhinoptera steindachneri 11 National Marine The von Bertalanffy growth function (VBGF) has been of the uncertainty of parameters into further demo- Fisheries Service Fishery Bulletin First U.S. Commissioner used conventionally to describe growth in elasmobranchs graphic or stock assessment studies to obtain more real- established in 1881 of Fisheries and founder NOAA of Fishery Bulletin (Cailliet et al., 2006) and involves the assumption that istic estimates. 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 Materials and methods VBGF does not always reflect the growth of elasmo- branchs. Therefore, it is necessary to explore alternative Samples of golden cownose rays were collected in 2008– models (Smart et al., 2016). Neer and Thompson (2005) 2014 from landings of the artisanal fishery and from evaluated various models for estimating the growth of bycatch of the commercial shrimp trawl fishery in the the cownose ray (R. bonasus) in the Gulf of Mexico, and southern GOC (Fig. 1). We recorded the sex of each they found that the Gompertz model (GM) described its sampled ray and measured the DW (in centimeters), growth convincingly. avoiding the curvature of the body. A section of 8–10 In our study, we estimated age by using counts of cervical vertebrae was extracted from each specimen growth bands on vertebrae of golden cownose rays col- (Natanson et al., 2018). Excess tissue and neural arches lected in the artisanal ray fishery of the GOC. We evalu- were excised from the vertebral segments, and verte- ated the ability of 2 models (VBGF and GM) to describe brae were exposed to sodium hypochlorite (5%) to growth. We used a Bayesian approach to estimate the remove the remaining fascial tissue (Anislado- Tolentino posterior probability of the growth parameters (mar- et al., 2008). ginal posteriors). The availability of marginal posteriors A single vertebra was removed from each section by of growth parameters allows the explicit incorporation using a blade to expose the surface of the centrum and 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. 12 Fishery Bulletin 119(1) was fixed to a flat piece of wood with synthetic resin. Each vertebral centrum was sectioned in a sagittal (3) plane through the focus with an IsoMet Low Speed Saw1 (Buehler Ltd., Lake Bluff, IL) that had double blades where N = the number of vertebrae; separated by 0.24 mm. Each section was mounted on R = the number of readers; a slide and photographed with transmitted light on an xij = the age i determined for individual j; Olympus SZ61 stereomicroscope (Olympus Corp., Tokyo, = the mean age calculated for individual j; Japan) equipped with an OptixCam S7N digital camera A = the numbers of agreements; and (Microscope LLC, Roanoke, VA). We created a database B = the number of readings done. of section images for the interpretation and counting of growth bands. Periodicity of band formation Age estimation We performed and compared 2 methods to infer the period of band formation: edge percentage analysis and relative Opaque and translucent bands form annually, and under marginal increment (MI) analysis following Cailliet (2015). transmitted light, these bands appear dark and light, We categorized the edge type of each section of a vertebra respectively (Beamish, 1979). Age estimates were made by as opaque or translucent, and the relative frequency of each counting these band pairs (one dark and one light band) edge type was tabulated in bimesters (2- month intervals). along the corpus calcareum after identifying the birth- The MI analysis was conducted over bimesters by using mark, the first distinct band after the focus (Cailliet et al., vertebrae from rays at the ages of 1–3 years (number of 2006). The distance from the focus to the edge of a verte- rays=94) to reduce bias that can be caused by the inclu- bra and the thickness of each band were recorded by using sion of older individuals with many bands (Lessa et al., Image-Pro Plus image analysis software (vers. 6.0, Media 2006). Bimesters with mean MI values close to 1 were Cybernetics Inc., Rockville, MD). Images were projected interpreted to be the time of year when the growth cycle is onto a screen for the identification of growth bands. We about to be completed (Cailliet et al., 2006): used several vertebrae for defining reading criteria, and 3 independent readers counted the growth bands along the (4) corpus calcareum on each vertebral section. We considered only age estimates with which at least 2 readers coincided. where MI = the marginal increment; Otherwise, readings were discarded. We used a Bayesian VR = the vertebral radius; t- test by using reference (uninformative) priors for the r = the distance from the focus to the last band mean (µ) and standard deviation (σ) of DW (Suppl.
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