Age and growth of Zapteryx brevirostris (Elasmobranchii: Rhinobatidae) in southern Brazil

Wanessa P. D. Carmo Luís Fernando Fávaro Rui Coelho About the authors

ABSTRACT

Age and growth studies are fundamental to successful fisheries management. Zapteryx brevirostris (Müller & Henle, 1841) is distributed off the Brazilian continental shelf and this species is assessed as “Vulnerable” in the Red List of the International Union for the Conservation of Nature (IUCN). Thus, the objective of this study was to present previously unknown information about the age and growth of Z. brevirostris that can be used for its management, conservation, and fisheries. A total of 162 specimens were sampled, with total lengths (TL) varying between 35.7 cm and 56 cm. The vertebrae were embedded in resin, sectioned in cuts with 0.5 mm thickness and the growth bands of the vertebrae were read under a light microscope. In the studied area, Z. brevirostris ages were estimated from 4 to 10 years according to vertebrae patterns. The species reaches its maximum asymptotic size (Linf) around 56 cm (56 cm for females and 50.37 cm for males). This is the first estimate of age and growth for a species of the Zapteryx genus, and the results support the hypothesis that this ray requires future management conservation, particularly due to its slow growth rate and consequent susceptibility to overexploitation.

Keywords:
Back-calculation; Conservation; Growth rate; k value; Von Bertalanffy curves (VBGF)

RESUMO

Estudos de idade e crescimento são fundamentais para o sucesso da gestão pesqueira. Zapteryx brevirostris (Müller & Henle, 1841) distribui-se pela plataforma continental brasileira, sendo classificada como “Vulnerável” no livro vermelho da IUCN (International Union for the Conservation of Nature). Assim, o objetivo deste estudo foi apresentar informações previamente desconhecidas sobre a idade e o crescimento de Z. brevirostris que podem ser utilizados para sua gestão, conservação e pescas. No total foram amostrados 162 espécimes, com comprimento total (CT) variando de 35.7 cm a 56 cm. As vértebras foram incluídas em resina e seccionadas num corte com cerca de 0.5 mm de espessura, e as bandas de crescimento das vértebras foram lidas com microscópio de luz transmitida branca. Na área estudada, Z. brevirostris possui idades estimadas entre os 4 a 10 anos de idade, de acordo com seu padrão de vértebras. A espécie atinge seu Linf (comprimento máximo assintótico) em torno dos 56 cm (56 cm para fêmeas e 50.37 cm para machos). Essa é a primeira estimativa dos parâmetros de idade e crescimento para uma espécie do gênero Zapteryx, e os resultados obtidos corroboram a hipótese de que a espécie requer uma gestão de conservação adequada, devido sobretudo à sua lenta taxa de crescimento e consequente suscetibilidade à sobre-exploração.

Palavras-chave:
Conservação; Curva de von Bertalanffy (VBGF); k value; Retrocálculo; Taxa de crescimento

Introduction

Age and growth studies are fundamental to successful fishery management, since they act as a base to estimate important biological variables (Vazzoler, 1981Vazzoler AEAM. Manual de métodos para estudos biológicos de populações de peixes. Reprodução e Crescimento. Brasília: CNPq; 1981.; Campana, 2001Campana SE. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol. 2001; 59(2):197-242.; Goldman, 2004Goldman KJ. Age and growth of elasmobranch fishes. In: Bonfil R, Musick JA, editors. Elasmobranch fisheries management techniques. Singapore: Asia Pacific Economic Cooperation; 2004. p.97-132.). Most of the analytical methods of stock evaluation deal mainly with age composition data (Sparre, Venema, 1997Sparre P, Venema SC. Introduction to tropical fish stock assessment. Rome: Food and Agriculture Organization of the United Nations ; 1997. pt 1: Manual. (FAO Fisheries Technical Paper; 306/1).), where precise, exact and quality information are the key to obtaining growth estimates and other vital rates, such as natural mortality and longevity.

The determination of the age of a fish is usually conducted by counting seasonal growth marks present in several hard calcified structures. Most age and growth studies use otoliths or scales for teleosts. Regarding elasmobranchs, due to the lack of these structures, vertebrae and dorsal spines are most widely used to determine age (Campana, 2001Campana SE. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol. 2001; 59(2):197-242.; Goldman, 2004Goldman KJ. Age and growth of elasmobranch fishes. In: Bonfil R, Musick JA, editors. Elasmobranch fisheries management techniques. Singapore: Asia Pacific Economic Cooperation; 2004. p.97-132.).

Elasmobranchs have become important fishery resources in recent years (Barker, Schluessel, 2005Barker MJ, Schluessel V. Managing global shark fisheries: suggestions for prioritizing management strategies. Aquat Conserv. 2005; 15(4):325-47.), whether through directed fishing or as bycatch (Shotton, 1999Shotton R, editor. Case studies of the management of elasmobranch fisheries. Rome: Food and Agriculture Organization of the United Nations; 1999. pt. 1. (FAO Fisheries Technical Paper; No. 378).; Stevens et al., 2000Stevens JD, Bonfil R, Dulvy NK, Walker PA. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES J Mar Sci . 2000; 57(3):476-94.). However, this increase in elasmobranchs’ fisheries has not often been accompanied by information about the biology and ecology of these species (Stevens et al., 2000Stevens JD, Bonfil R, Dulvy NK, Walker PA. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES J Mar Sci . 2000; 57(3):476-94.). Elasmobranchs generally possess a K-style life strategy, with life cycles characterized by low growth rates and low reproductive potential (Cortes, 2000Cortés E. Life history patterns and correlations in sharks. Rev Fish Sci. 2000; 8(4):299-344.; Coelho, Erzini, 2002Coelho R, Erzini K. Age and growth of the undulate ray, Raja undulata,in the Algarve (Southern Portugal). J Mar Biolog Assoc U.K . 2002; 94:987-90., 2006Coelho R, Erzini K. Reproductive aspects of the undulate ray, Raja undulata, from the south coast of Portugal. Fish Res. 2006; 81(1):80-85.). These characteristics make this group extremely vulnerable to fishery pressure, and overexploitation can often occur even at relatively low levels of fishing mortality (Smith et al., 1998Smith SE, Au DW, Show C. Intrinsic rebound potentials of 26 species of Pacific sharks. Mar Freshw Res. 1998; 49:663-78.). Hoff, Musick (1990Hoff TB, Musick JA. Western North Atlantic shark-fishery management problems and informational requirements. In: Pratt HL, Gruber SH, Taniuchi T, editors. Elasmobranchs as living resources: advances in the biology, ecology, systematics and the status of the fisheries. Proceedings of the second United States-Japan Workshop East-West Center, Honolulu: U.S. Department of Commerce; 1990. p.455-72. (NOAA Technical Report; 90).) pointed out the lack of information regarding the age and growth of elasmobranchs as a limiting factor in the development of management plans, and Gomes et al. (2010Gomes UL, Signori CN, Gadig OBF, Santos HRS. Guia para identificação de tubarões e raias do Rio de Janeiro. Rio de Janeiro: Technical Books; 2010.) and Natanson et al. (2014Natanson LJ, Gervelis BJ, Winton MV, Hamady LL, Gulak SJB, Carlson JK. Validated age and growth estimates for Carcharhinus obscurus in the northwestern Atlantic Ocean, with pre- and post management growth comparisons. Environ Biol Fishes . 2014; 97(8):881-96.) corroborates this assertion stating that data about age, growth, and maturity in elasmobranches are generally limited.

The species Zapteryx brevirostris (Müller, Henle, 1841) is distributed from the Brazilian continental shelf in Rio de Janeiro to the south of the province of Buenos Aires (Argentina) (Castello, 1971Castello HP. Contribución al conocimento sistemático y biológico de Zapteryx brevirostris (Müller & Henle, 1841) de la costa atlántica marplatense (Chondrichthyes, Rhinobatidae). Physis. 1971; 30(80):619-29.; Figueiredo, 1977Figueiredo JL. Manual de Peixes Marinhos do Sudeste do Brasil. São Paulo: Museu de Zoologia da Universidade de São Paulo; 1977. pt. 1, Introdução - Cações, Raias e Quimeras.; Menni, Stehmann, 2000Menni RC, Stehmann MFW. Distribution, environment and biology of batoid fishes off Argentina, Uruguay and Brazil. A review. Rev Mus Argent Cienc Nat. 2000; 2(1):69-109.). It is described as preferring cold waters (Gomes et al., 2010Gomes UL, Signori CN, Gadig OBF, Santos HRS. Guia para identificação de tubarões e raias do Rio de Janeiro. Rio de Janeiro: Technical Books; 2010.) and is the only species of the Zapteryx genus in the Atlantic Ocean (Batista, 1991Batista VS. Aspectos quantitativos da fecundidade e do desenvolvimento embrionário da raia Zapteryx brevirostris Müller & Hendle, 1841 (Pisces, Rhinobatidae) da enseada de Itaipu, Niterói, Rio de Janeiro. Rev Bras Biol . 1991; 51(3):495-501.). This species is frequently found in coastal waters (Figueiredo, 1977Figueiredo JL. Manual de Peixes Marinhos do Sudeste do Brasil. São Paulo: Museu de Zoologia da Universidade de São Paulo; 1977. pt. 1, Introdução - Cações, Raias e Quimeras.), reaches a maximum size of 59 cm TL (total length) for males and 65 cm TL for females (Colonello et al., 2011Colonello JC, García ML, Menni RC. Reproductive biology of the lesser guitarfish Zapteryx brevirostris from the south-western Atlantic Ocean. J Fish Biol . 2011; 78(1):287-302. Available from: http://www.ncbi.nlm.nih.gov/pubmed/21235561
http://www.ncbi.nlm.nih.gov/pubmed/21235...
) and attains maturity between 42 and 43 cm TL (Batista, 1991Batista VS. Aspectos quantitativos da fecundidade e do desenvolvimento embrionário da raia Zapteryx brevirostris Müller & Hendle, 1841 (Pisces, Rhinobatidae) da enseada de Itaipu, Niterói, Rio de Janeiro. Rev Bras Biol . 1991; 51(3):495-501.; Santos et al., 2006Santos C, Cortellete GM, Araújo KCB, Spach HL. Estrutura populacional da raia-viola Zapteryx brevirostris (Chondrichthyes, Rhinobatidae), na plataforma adjacente à baía de Paranaguá, PR. Acta Biologica Leopondensia. 2006; 28(1):32-37.). The species is commercially exploited by small-scale fishing on the coast of the state of Paraná (southern Brazil) (Santos et al., 2006Santos C, Cortellete GM, Araújo KCB, Spach HL. Estrutura populacional da raia-viola Zapteryx brevirostris (Chondrichthyes, Rhinobatidae), na plataforma adjacente à baía de Paranaguá, PR. Acta Biologica Leopondensia. 2006; 28(1):32-37.; Bornatowski et al., 2009Bornatowski H, Abilhoa V, Charvet-Almeida P. Elasmobranchs of the Paraná Coast, southern Brazil, south-western Atlantic. Mar Biodivers Rec. 2009; 2:e158. Available from: http://www.journals.cambridge.org/abstract_S1755267209990868
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) and it is described as “vulnerable” in the red list of the International Union for the Conservation of Nature (IUCN) (Vooren et al., 2006Vooren CM, Lamónaca AF, Massa A, Hozbor N, editors. Zapteryx brevirostris: The IUCN Red List of Threatened Species. Version 2014.2. 2006. Available from: http://www.iucnredlist.org
http://www.iucnredlist.org...
).

In Brazil the small-scale fisheries are growing, increasing the pressure on this species and enlarging the gaps in the biological knowledge of the elasmobranchs species. The increase in studies about this species life cycle is very necessary to enable a more efficient and sustainable management plan. Thus, the objective of this study was to present previously unknown information about the age and growth of Z. brevirostris that can be used for its management, conservation, and fisheries.

Material and Methods

Sampling. The collection of biological material was carried out in collaboration with the small-scale fishery on the coast of the state of Paraná, and occurred between May 2012 and November 2013. The small-scale fishers on this coast work in estuarine environments and open sea. The practices carried out in open sea by these communities consist especially of fishing using bottom otter trawls (with boards or doors), set nets and “caceio” nets. The set nets usually use 16 to 22 cm mesh sizes (the type used for data collection in this paper) and generally catch a greater diversity and a larger number of elasmobranchs than with other mesh sizes, with Z. brevirostris being the most abundant elasmobranch species (Robert, 2012Robert MC. A captura de elasmobrânquios na costa paranaense. In: Bornatowski H, Abilhoa V, editores. Tubarões e raias capturados pela pesca artesanal no Paraná: guia de identificação. Curitiba: Hori Consultoria Ambiental ; 2012. p.27-34. (Hori Cadernos Técnicos; No. 4).).

As soon as the specimens were collected by a fisherman, they had their total length (TL - measurement in centimeters from the nose to the tail) measured and their sex determined by the presence or absence of claspers in males. The specimens were then anesthetized by medullary section and a section of 3 to 5 vertebrae were extracted from the region below the dorsal fin. The vertebrae were duly labeled and frozen until laboratory processing.

Preparation of the samples. In the laboratory, all organic residues from the vertebrae were extracted using scalpel and tweezers, after having individualized each vertebra. The vertebrae were then cleaned based on the following protocol: 5 minutes in bleach (commercial sodium hypochlorite), rinsed in water, manual cleaning of the organic remains using tweezers, 3 minutes in bleach and, lastly, tap water to eliminate bleach residues. The vertebrae were then placed and stored in 70% ethanol.

In order to facilitate the sectioning, and given their small size, the vertebrae were embedded in polyester resin. To accomplish this, the vertebrae were dried under a paper towel at room temperature about one hour before embedding in the resin. After being embedded in the resin, the vertebrae were sagitally sectioned using a low speed Buehler IsoMet cutter (with two saws spaced 0.5 mm apart), resulting in a cut similar to a “bowtie”. These cuts were stained using a saturated solution of crystal violet for 3 minutes. They were then left to dry between absorbent papers and pressed by two microscope slides for 24 hours to keep the cut from rolling up. Once dry, the cuts were placed on microscope slides using Cytoseal 60.

The growth bands of the vertebrae were read using dissecting microscope with transmitted white light. Following the Cailliet et al. (2006Cailliet GM, Smith WD, Mollet HF, Goldman KJ. Age and growth studies of chondrichthyan fishes: the need for consistency in terminology, verification, validation, and growth function fitting. Environ Biol Fishes . 2006; 77(3-4):211-28. Available from: http://link.springer.com/10.1007/s10641-006-9105-5
http://link.springer.com/10.1007/s10641-...
) methodology, two types of growth bands were considered in the cuts, a wider opaque band and a narrower translucent band. Each pair of bands was considered a ring. Three independent readings were carried out for each vertebra, without previous knowledge of the TL, sex or the number of rings of each individual, estimated in earlier readings. In order to calculate the precision of age estimates, the techniques of index of average percent error (APE), defined by Beamish, Fournier (1981Beamish RJ, Fournier DA. A method for comparing the precision of a set of age determinations. Can J Fish Aquat Sci. 1981; 38(8):982-83.), and the coefficient of variation (CV), defined by Chang (1982Chang WYB. A statistical method for evaluating the reproducibility of age determinations. Can J Fish Aquat Sci . 1982; 39(8):1208-10.), were used.

Age and growth. In this study, the back-calculation techniques of body proportional hypothesis (BPH), Dahl-Lea, Fraser-Lee and scale proportional hypothesis (SPH) (Francis, 1990Francis RICC. Back-calculation of fish length: a critical review. J Fish Biol . 1990; 36(6):883-902.) were used to obtain the lengths of individuals at previous ages, since in the analyzed samples, length classes under 35 cm TL were not obtained. Back-calculation established linear regressions between the total length of the animals and the radius of the vertebrae and between the radius of the vertebrae and the total length for the sexes together and separately. These values obtained through back-calculation were used to produce the von Bertalanffy growth curves (VBGF).

In order to determine the size of the specimens at age zero (birth), ten embryos with near birth size (14 cm TL) (Carmo, Fávaro in prep.) had their vertebrae removed, cleaned and digitally microphotographed. The open-source Image J software (Abramoff et al., 2004Abràmoff MD, Magalhães PJ, Ram SJ. Image Processing with ImageJ. Biophotonics International, 2004; 11(7):36-42.) was used to take measurements that were then used to define as the birth band (age 0) in the remaining sample.

The von Bertalanffy growth model is the most commonly used equation in studies of age and growth of fish in general, including the Chondrichthyes (Cailliet et al., 2006Cailliet GM, Smith WD, Mollet HF, Goldman KJ. Age and growth studies of chondrichthyan fishes: the need for consistency in terminology, verification, validation, and growth function fitting. Environ Biol Fishes . 2006; 77(3-4):211-28. Available from: http://link.springer.com/10.1007/s10641-006-9105-5
http://link.springer.com/10.1007/s10641-...
). The growth curve to be studied for the species Z. brevirostris followed the traditional von Bertalanffy growth model and a modified version of the VBGF model with fixed size at birth (VBGF with fixed L 0 ), where: Von Bertalanffy growth model (VBGF):

L t = L i n f ( 1 - e - k ( t - t 0 )

Modified VBGF model with fixed size at birth (VBGF with fixed L 0 ):

L t = L i n f 1 - b e - k t

where: b = (LinfL 0 )/Linf. Lt: size (TL, cm) at age t (year); Linf: maximum asymptotic size (TL); L 0: size (TL, cm) at birth; k: growth coefficient (year−1); t 0: theoretical age (year) at size zero.

Fixed size at birth was determined based on Carmo, Fávaro (in prep.) as being 14 cm TL, and confirmed by Gomes et al. (2010Gomes UL, Signori CN, Gadig OBF, Santos HRS. Guia para identificação de tubarões e raias do Rio de Janeiro. Rio de Janeiro: Technical Books; 2010.) who verified neonates between about 13 and 16 cm long.

All of the growth models were created in the open-source software R (R core team, 2014R Development Core Team. R: A language and environment for statistical computing [Computer software manual - Internet]. Vienna: R Foundation for Statistical Computing; 2014. Available from: http://www.r-project.org
http://www.r-project.org...
) using nonlinear least squares (NLS). The parameters were calculated for each growth model, with the respective standard errors (SE) and confidence intervals (CI, 95%). The plots were created in R, in some cases using the package ggplot2 (Wickham, 2009Wickham H. ggplot2: elegant graphics for data analysis. New York: Springer; 2009.).

The results of the sizes-at-age obtained by the VBGF growth curve and produced from the results of the different back-calculation techniques, were tested for normality using the Lilliefords test (Lilliefors, 1967Lilliefors HW. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc.1967; 62(318):399-402.), and tested for homogeneity of the variances using Levene tests (Levene, 1960Levene H. Robust tests for equality of variances. In: Olkin I, Ghurye SG, Hoeffding W, Madow WG, Mann HB, editors. Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press; 1960. p.278-92.). The back-calculation method is used to fill the gaps of a sample with reduced size in certain classes (e.g. young individuals), when the sample size is small or if the samples were not obtained every month, thus obtaining a reliable value (Goldman, 2004Goldman KJ. Age and growth of elasmobranch fishes. In: Bonfil R, Musick JA, editors. Elasmobranch fisheries management techniques. Singapore: Asia Pacific Economic Cooperation; 2004. p.97-132.). Additionally, it is a robust method that increases the quantity of information of the sample and also allows the monitoring of mean growth rates of distinct age groups (Smith, 1983Smith CL. Summary of round table discussions on back calculation. In: Prince ED, Pulos LM, editors. Proceedings of the international workshop on age determination in oceanic pelagic fishes: tunas, billfishes, and sharks; 1983. p.45-47. (NOAA Technical Reports NMFS; 8).), using the proportionality between the size of the fish and the radius of the structure (Whitney, Carlander, 1956Whitney RR, Carlander KD. Interpretation of body-scale regression for computing body length of fish. J Wildl Manage. 1956; 20(1):21-27.; Goldman, 2004Goldman KJ. Age and growth of elasmobranch fishes. In: Bonfil R, Musick JA, editors. Elasmobranch fisheries management techniques. Singapore: Asia Pacific Economic Cooperation; 2004. p.97-132.). Since the assumption of normality was not verified for all age classes, nonparametric (Kruskal-Wallis) tests were used to verify significant statistical differences between the mean lengths at each age. The difference between the sexes was also tested using these hypothesis tests.

In order to evaluate the adequacy of the model to the data and the quality of the fit, the Akaike information criterion (AIC) (Akaike, 1974Akaike HAI. A new look at the Statistical Model Identification. IEEE Trans Automat Contr. 1974; 19(6):716-23.) was calculated for each of the models created, including the VBGF growth curves and VBGF with fixed L 0 . The model with the best fit was defined as that which presented the lowest AIC value (Katsanevakis, 2006Katsanevakis S. Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fish Res . 2006; 81(2-3):229-35.).

The likelihood ratio test (LRT), as defined by Kimura (1980Kimura DK. Likelihood methods for the von Bertalanffy growth curve. Fish Bull. 1980; 77(4):765-76.) and recommended by Cerrato (1990Cerrato RM. Interpretable statistical tests for growth comparisons using parameters in the von Bertalanffy equation. Can J Fish Aquat Sci . 1990; 47(7):1416-26.), was used to compare the growth curves of males and females. It tested the null hypothesis that there are no differences in growth parameters of males and females. This test was also used among the four back-calculation techniques, grouped two by two, to observe if they presented significant differences.

Results

A total of 162 specimens of Z. brevirostris, 71 females (44%) and 91 males (56%), were sampled. The length of the sampled individuals varied from 35.7 cm to 56 cm TL (the largest female: 56 cm; the largest male: 50.37 cm), with mean size in females reaching 46.15 ± 2.86 cm (mean + SD) and in males 44.81 ± 2.70 (mean + SD). The frequency of occurrence of the specimens was greater in the intermediate size classes, with few individuals in the maximum and minimum size classes (Fig. 1).

Fig. 1
Distribution of length frequencies (1cm TL size classes) of the sample of Zapteryx brevirostris collected in the southern coast of Brazil and used in this study. M refers to males and F to females.

The graph obtained between TL and size of the radius of the vertebra for the grouped sexes suggests a direct relationship between the growth of the animal and the growth of the vertebra (Fig. 2). In the sample that was obtained, the analyzed specimens presented ages varying from 4 to 10 years, for both males and females. In terms of precision indexes in the age estimates, the APE was estimated to be 9.71 and the CV was estimated to be 13.7.

Fig. 2
Relationship between total length (TL, cm) and radius of the vertebra (cm) for Zapteryx brevirostris with the sexes grouped, using free-swimming adult individuals. The line represents a linear regression (R2 = 0.75).

The values of the mean sizes at each age, obtained through the several back-calculation techniques showed that these sizes did not differ statistically except at ages 9 and 10 for the grouped data, and at ages 8 to 10 for the sexes separately (Tab. 1).

Tab. 1
Result of the Kruskal-Wallis test for mean sizes at ages obtained by the different back-calculation techniques. The ages that did not present statistical differences with α = 0.05 are represented in bold.

In the VBGF curves for the values directly observed from the samples (vertebrae), there were some convergence problems in the models, with the values estimated to present elevated standard errors and unreasonable values. Therefore, the study accepted only the values obtained through back-calculation using the four techniques described above (Tab. 2). The Kimura test, carried out among the four back-calculation techniques used, revealed a P ≤ 0.05, showing that its results presented significant differences in relation to the VBGF curves obtained.

Tab. 2
Growth parameters estimated for Zapteryx brevirostris (grouped sexes, and females and males separately), obtained with the VBGF growth curve and the VBGF with fixed size at birth (L0 = 14 cm TL). The parameters are given for each model, with their respective standard errors (SE) and 95% confidence intervals (CI).

In terms of goodness of fit of the models (using the AIC), regarding the estimated growth curves, the three-parameter VBGF curve (in the grouped data and for males and females) presented the lowest AIC, and therefore the best quality of fit of the model, justifying the preference for discussing the results obtained with the three-parameter VBGF curve (Tab. 2). The Kimura test was carried out in the four back-calculation techniques used, and significant differences were found between the VBGF growth curves and between the sexes (P ≤ 0.05). In turn, the VBGF curve obtained by the Fraser-Lee technique also presented lower AIC values and in general biological parameters that are more feasibly observed in nature (for grouped data, and for males and females separately) and was thus chosen as the most feasible and final growth curve for the species. Note that the AIC can be used only to compare different models within the observed values or within the different back-calculation techniques due to different sample sizes using each technique. Similarly, the AIC can only be used to compare models only within each sex (or for the sexes combined) as the sample size is different for each sex.

Analyzing this final VBGF curve for the species Z. brevirostris, Linf presented 56.4 cm of TL for grouped data, 59.5 cm TL for females, and 54.9 cm TL for males. The value of k was 0.12 for the grouped sexes, 0.11 for females and 0.13 for males. The final VBGF curves are presented in Fig. 3.

Fig. 3
Von Bertalanffy growth curves (VBGF) according to the Fraser-Lee back-calculation technique. Data for females and males separately: VBGF and VBGF with fixed L0 at 14 cm.

Discussion

The age and growth parameters for a species of the genus Zapteryx were estimated for the first time in this study. Taking this into account, the results were compared to studies of another species of the same family (Rhinobatidae) and elasmobranchs in general, given the absence of more specific information for this species from the southern Atlantic Ocean.

The maximum size obtained (56 cm for females and 50.37 cm for males) was found within the maximum length described for the species by Colonello et al. (2011Colonello JC, García ML, Menni RC. Reproductive biology of the lesser guitarfish Zapteryx brevirostris from the south-western Atlantic Ocean. J Fish Biol . 2011; 78(1):287-302. Available from: http://www.ncbi.nlm.nih.gov/pubmed/21235561
http://www.ncbi.nlm.nih.gov/pubmed/21235...
) and Bornatowski, Abilhoa (2012Bornatowski H, Abilhoa V. Tubarões e raias capturados pela pesca artesanal no Paraná: guia de identificação. Curitiba: Hori Consultoria Ambiental; 2012. (Hori Cadernos Técnicos; No. 4).): 59 cm of TL for males and 65 cm of TL for females.

The growth difference between the sexes that was presented in this study is well-documented among elasmobranchs, with generally larger females than males, including Z. brevirostris (Casey et al., 1985Casey JG, Pratt HL Jr, Stillwell CE. Age and growth of the sandbar shark (Carcharinus plumbeus) from the western North Atlantic. Can J Fish Aquat Sci . 1985; 42(5):963-75.; Ismen, 2003Ismen A. Age, growth, reproduction and food of common stingray (Dasyatis pastinaca L., 1758) in Iskenderun Bay, the eastern Mediterranean. Fish Res . 2003; 60(1):169-76.; Skomal, Natanson, 2003Skomal G, Natanson L. Age and growth of the blue shark (Prionace glauca) in the North Atlantic Ocean. Fish Bull . 2003; 101(3):627-39.; Yamaguchi et al., 2005Yamaguchi A, Kawahara I, Ito S. Occurrence, growth and food of long headed eagle ray, Aetobatus flagellum, in Ariake Sound, Kyushu, Japan. Environ Biol Fishes . 2005; 74(2):229-38.; Santos et al., 2006Santos C, Cortellete GM, Araújo KCB, Spach HL. Estrutura populacional da raia-viola Zapteryx brevirostris (Chondrichthyes, Rhinobatidae), na plataforma adjacente à baía de Paranaguá, PR. Acta Biologica Leopondensia. 2006; 28(1):32-37.). As typical in elasmobranchs, females reach the larger size because it is necessary to support embryonic young, so the body size required for female gestation is greater than that for male, because male does not need to support embryos (Klimley, 1987Klimley AP. The determinants of sexual segregation in the scalloped hammerhead shark, Sphyrna lewini. Environ Biol Fishes , 1987; 18(1):27-40.)

Estimates of growth models are strongly affected by the absence of very young and/or old individuals (Campana, 2001Campana SE. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol. 2001; 59(2):197-242.; Cailliet, Goldman, 2004Cailliet GM, Goldman KJ. Age determination and validation in chondrichthyan fishes. In: Carrier JC, Musick JA, Heithaus MR, editors. Biology of sharks and their relatives. Boca Raton (FL): CRC Press; 2004. p.399-448.). Therefore, it is probable that the factor that most influenced the discrepancy between the values obtained in the sample (observed values) and the values obtained by back-calculation is the composition of the sample, where there is a lack of individuals with ages less than 4 (smaller than 35 cm of TL). The lack of these individuals is the result of a common problem in elasmobranch collections: the fishing gear is not selective for every length class, as observed by Branstetter (1987Branstetter S. Age, growth and reproductive biology of the silky shark, Carcharhinus falciformis, and the scalloped hammerhead, Sphyrna lewini, from the northwestern Gulf of Mexico. Environ Biol Fishes. 1987; 19(3):161-73. Available from: http://link.springer.com/10.1007/BF00005346
http://link.springer.com/10.1007/BF00005...
), and Thorson, Simpfendorfer (2009Thorson JT, Simpfendorfer CA. Gear selectivity and sample size effects on growth curve selection in shark age and growth studies. Fish Res . 2009; 98(1-3):75-84.) also considered fishing gear to be a factor that greatly influences sample composition. However, it could also be a natural behavior of the species to not occur at the collection site when smaller than 35 cm, searching for another habitat during its initial phases of development, since, according to Espinoza et al. (2011Espinoza M, Farrugia TJ, Lowe CG. Habitat use, movements and site fidelity of the gray smooth-hound shark (Mustelus californicus Gill 1863) in a newly restored southern California estuary. J Exp Mar Biol Ecol. 2011; 401(1-2):63-74. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0022098111001018
http://linkinghub.elsevier.com/retrieve/...
), the patterns of fidelity to a certain site and its inter-annual use remain uncertain for many coastal elasmobranchs, due to the lack of quantitative behavioral data, including for this species.

The lack of convergence that the VBGF curve presented for the observed data was likely due to this absence of young individuals in the samples, which represented ages less than 4 (TL less than 35 cm). This led to the choice of using back-calculated data, which, according to Smith (1983Smith CL. Summary of round table discussions on back calculation. In: Prince ED, Pulos LM, editors. Proceedings of the international workshop on age determination in oceanic pelagic fishes: tunas, billfishes, and sharks; 1983. p.45-47. (NOAA Technical Reports NMFS; 8).), is a robust method to use. Thorson, Simpfendorfer (2009Thorson JT, Simpfendorfer CA. Gear selectivity and sample size effects on growth curve selection in shark age and growth studies. Fish Res . 2009; 98(1-3):75-84.) suggested that in order to produce a reliable curve in age and growth studies, the minimum sample size would be 200 individuals. In several cases where the number of samples was less than the suggested number, the use of back-calculation has been observed. Several authors (e.g. Bonfil et al., 1993Bonfil R, Mena R, Anda D. Biological parameters of commercially exploited silky sharks, Carcharhinus falciformis, from the Campeche Bank, Mexico. NOAA Tech Rep NMFS. 1993; 115:73-86.; Natanson et al., 1995Natanson LJ, Casey JG, Kohler NE. Age and growth estimates for the dusky shark, Carcharhinus obscurus, in the western North Atlantic Ocean. Fish Bull . 1995; 93:116-26.; Sminkey, Musick, 1995Sminkey TR, Musick JA. Age and growth of the sandbar shark, Carcharhinus plumbeus, before and after population depletion. Copeia. 1995; (4):871-83.; Lessa et al., 1999Lessa R, Santana FM, Paglerani R. Age, growth and stock structure of the oceanic whitetip shark, Carcharhinus longimanus, from the southwestern equatorial Atlantic. Fish Res .1999; 42(1-2):21-30. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0165783699000454
http://linkinghub.elsevier.com/retrieve/...
; Lessa et al., 2004Lessa R, Santana FM, Hazin FH. Age and growth of the blue shark Prionace glauca (Linnaeus, 1758) off northeastern Brazil. Fish Res . 2004; 66(1):19-30. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0165783603001930
http://linkinghub.elsevier.com/retrieve/...
; Başusta et al., 2008Başusta N, Demirhan SA, Çiçek E, Başusta A, Kuleli T. Age and growth of the common guitarfish, Rhinobatos rhinobatos, in Iskenderun Bay (north-eastern Mediterranean, Turkey). J Mar Biolog Assoc U.K. 2008; 88(4):837-42. Available from: http://www.journals.cambridge.org/abstract_S0025315408001124
http://www.journals.cambridge.org/abstra...
; Santana, Lessa, 2004Santana FM, Lessa R. Age determination and growth of the night shark (Carcharhinus signatus) off the northeastern Brazilian coast. Fish Bull . 2004; 102(1):156-67.; Natanson et al., 2007Natanson LJ, Sulikowski JA, Kneebone JR, Tsang PC. Age and growth estimates for the smooth skate, Malacoraja senta, in the Gulf of Maine. Environ Biol Fishes . 2007; 80(2-3):293-308.) have presented back-calculated growth curves to describe the growth of elasmobranchs.

The lowest AIC value indicates the greatest goodness-of-fit (Burnham, Anderson, 2002Burnham KP, Anderson DR. Model selection and multimodel inference: a practical information-theoretic approach. New York (NY): Springer-Verlag; 2002.; Katsanevakis, 2006Katsanevakis S. Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fish Res . 2006; 81(2-3):229-35.). The AIC was carried out using the three and two-parameter VBGF curves, always with the three-parameter curve presenting the lowest AIC, whether in the observed data or in the data obtained by back-calculation. Therefore, in the two tested models, the three-parameter VBGF curves better represent the growth model of the species Z. brevirostris.

The Linf obtained for the data presented 56.4 cm TL for grouped data, 59.5 cm TL for females and 54.9 cm of TL for males, which corroborates the values obtained in the sampling, where the largest TL was 56 cm for females and 50.37 cm for males. Therefore, the Linf derived from back-calculation is in conformity with maximum lengths observed in the region, corroborating the choice of the three-parameter VBGF curve obtained with back-calculated data by the Fraser-Lee technique, as the best to describe the growth of the species Z. brevirostris.

The value of k for males (0.13) was a little larger than the value for females (0.11). This type of dimorphism, with females growing at smaller rates than males has been described for other batoids species, such as Leucoraja ocellata (Sulikowski et al., 2003Sulikowski JA, Morin MD, Suk SH, Howell WH. Age and growth estimates of the winter skate ( Leucoraja ocellata ) in the western Gulf of Maine. Fish Bull . 2003; 101(2):405-13.), Amblyraja radiata (Mcphie, Campana, 2009Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.) and Malacoraja senta (Mcphie, Campana, 2009Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.). The growth difference between sexes, verified by the Kimura test, coincides with the fact that females are larger than males and grow at lower growth rates. Here the females of Z. brevirostris showed larger size than males, a situation also reported by Batista (1987Batista VS. Desenvolvimento sexual de Zapteryx brevirostris (Müller & Henle, 1841), no litoral do Rio de Janeiro, Brasil. Rev Bras Biol. 1987; 47(3):301-07.; 1991Batista VS. Aspectos quantitativos da fecundidade e do desenvolvimento embrionário da raia Zapteryx brevirostris Müller & Hendle, 1841 (Pisces, Rhinobatidae) da enseada de Itaipu, Niterói, Rio de Janeiro. Rev Bras Biol . 1991; 51(3):495-501.), Santos et al. (2006Santos C, Cortellete GM, Araújo KCB, Spach HL. Estrutura populacional da raia-viola Zapteryx brevirostris (Chondrichthyes, Rhinobatidae), na plataforma adjacente à baía de Paranaguá, PR. Acta Biologica Leopondensia. 2006; 28(1):32-37.), Abilhoa et al. (2007Abilhoa V, Bornatowski H, Oliveira Freitas M. Some information on reproduction and embryonic development of the lesser guitarfish Zapteryx brevirostris in Southern Brazil. Acta Adriat. 2007; 48(2):185-90.) and Carmo, Fávaro (in prep). According to Bornatowski, Abilhoa (2012Bornatowski H, Abilhoa V. Tubarões e raias capturados pela pesca artesanal no Paraná: guia de identificação. Curitiba: Hori Consultoria Ambiental; 2012. (Hori Cadernos Técnicos; No. 4).) this is an expected occurrence for viviparous species, characteristic of the species, with the largest length for females being a reflection of the bodily need to promote embryonic development during the gestation period (Santos et al., 2006Santos C, Cortellete GM, Araújo KCB, Spach HL. Estrutura populacional da raia-viola Zapteryx brevirostris (Chondrichthyes, Rhinobatidae), na plataforma adjacente à baía de Paranaguá, PR. Acta Biologica Leopondensia. 2006; 28(1):32-37.). The value of k for the grouped data was 0.12, which is similar to the values found for a few other batoids such as Aetobatus flagellum (0.11; Yamaguchi et al., 2005Yamaguchi A, Kawahara I, Ito S. Occurrence, growth and food of long headed eagle ray, Aetobatus flagellum, in Ariake Sound, Kyushu, Japan. Environ Biol Fishes . 2005; 74(2):229-38.), Malacoraja senta (0.12; Natanson et al., 2007Natanson LJ, Sulikowski JA, Kneebone JR, Tsang PC. Age and growth estimates for the smooth skate, Malacoraja senta, in the Gulf of Maine. Environ Biol Fishes . 2007; 80(2-3):293-308.; Mcphie, Campana, 2009Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.) and Raja undulata (0.11; Coelho, Erzini, 2002Coelho R, Erzini K. Age and growth of the undulate ray, Raja undulata,in the Algarve (Southern Portugal). J Mar Biolog Assoc U.K . 2002; 94:987-90.). Comparing the value of k obtained for the growth of Z. brevirostris with other species of the same family, Rhinobatos rhinobatos (Başusta et al., 2008Başusta N, Demirhan SA, Çiçek E, Başusta A, Kuleli T. Age and growth of the common guitarfish, Rhinobatos rhinobatos, in Iskenderun Bay (north-eastern Mediterranean, Turkey). J Mar Biolog Assoc U.K. 2008; 88(4):837-42. Available from: http://www.journals.cambridge.org/abstract_S0025315408001124
http://www.journals.cambridge.org/abstra...
) the value of k of Z. brevirostris is smaller than the value obtained for R. rhinobatos (0.15). However, both present a high k compared with the value of k of other species of rays: 0.02 for Bathyraja minispinosa (Ainsley et al., 2011Ainsley SM, Ebert DA, Cailliet GM. Age, growth, and maturity of the whitebrow skate, Bathyraja minispinosa, from the eastern Bering Sea. ICES J Mar Sci. 2011; 68(7):1426-34. Available from: http://icesjms.oxfordjournals.org/cgi/doi/10.1093/icesjms/fsr072
http://icesjms.oxfordjournals.org/cgi/do...
), 0.04 for Raja binoculata (McFarlane, King, 2006McFarlane GA, King JR. Age and growth of big skate (Raja binoculata) and longnose skate (Raja rhina) in British Columbia waters. Fish Res . 2006; 78(2-3):169-78. Available from: http://dx.doi.org/10.1016/j.fishres.2006.01.00
http://dx.doi.org/10.1016/j.fishres.2006...
), 0.07 for Amblyraja radiata (Mcphie, Campana, 2009Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.) and Raja rhina (McFarlane, King, 2006McFarlane GA, King JR. Age and growth of big skate (Raja binoculata) and longnose skate (Raja rhina) in British Columbia waters. Fish Res . 2006; 78(2-3):169-78. Available from: http://dx.doi.org/10.1016/j.fishres.2006.01.00
http://dx.doi.org/10.1016/j.fishres.2006...
), and 0.08 for Dasyatis pastinaca (Ismen, 2003Ismen A. Age, growth, reproduction and food of common stingray (Dasyatis pastinaca L., 1758) in Iskenderun Bay, the eastern Mediterranean. Fish Res . 2003; 60(1):169-76.). The rays of the family Rhinobatidae present lower values of k than L. ocellata (0.18; McPhie, Campana, 2009Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.) and Leucoraja erinacea (0.19; McPhie, Campana, 2009Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.), for examples. With these results, the species Z. brevirostris can be considered to have a relatively high growth rate compared with most other species of rays.

Marginal increment analysis as a verification technique for the periodicity of growth band deposition did not present significant data in this study, since there were months with no sampling. This corroborates with Cailliet (1990Cailliet GM. Elasmobranch age determination and verification: an update review. In: Pratt HL, Jr., Gruber SH, Taniuchi T, editors. Elasmobranchs as living resources: advances in the biology, ecology, systematics and the status of the fisheries. Proceedings of the second United States-Japan Workshop East-West Center, Honolulu: U.S. Department of Commerce; 1990. p.57-165. (NOAA Techical Report NMFS; 90).) and Campana (2001Campana SE. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol. 2001; 59(2):197-242.), who cited the factor sampling size as an error related to marginal increment analysis. Validation or verification of age is important in age and growth studies, through, for example, marginal increment analysis (Cailliet et al., 1986Cailliet GM, Radtke RL,Welden BA. Elasmobranch age determination and verification: a review. In: Uyeno T, Arai R, Taniuchi T, Matsuura K, editors. Indo-Pacific fish biology. Proceedings of the second international conference on Indo Pacific fishes Tokyo: Ichthyological Society of Japan, Tokyo National Museum; 1986. p.345-60., 2006Cailliet GM, Smith WD, Mollet HF, Goldman KJ. Age and growth studies of chondrichthyan fishes: the need for consistency in terminology, verification, validation, and growth function fitting. Environ Biol Fishes . 2006; 77(3-4):211-28. Available from: http://link.springer.com/10.1007/s10641-006-9105-5
http://link.springer.com/10.1007/s10641-...
; Cailliet, 1990Cailliet GM. Elasmobranch age determination and verification: an update review. In: Pratt HL, Jr., Gruber SH, Taniuchi T, editors. Elasmobranchs as living resources: advances in the biology, ecology, systematics and the status of the fisheries. Proceedings of the second United States-Japan Workshop East-West Center, Honolulu: U.S. Department of Commerce; 1990. p.57-165. (NOAA Techical Report NMFS; 90).; Campana, 2001Campana SE. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol. 2001; 59(2):197-242.). However, the lack of marginal increment analysis, for several reasons, can also be found in other studies related to elasmobranchs (e.g. Wintner, Cliff, 1999Wintner SP, Cliff G. Age and growth determination of thewhite shark, Carcharodon carcharias from the east coast of South Africa. Fish Bull . 1999; 97(1):153-69.; Başusta et al., 2008Başusta N, Demirhan SA, Çiçek E, Başusta A, Kuleli T. Age and growth of the common guitarfish, Rhinobatos rhinobatos, in Iskenderun Bay (north-eastern Mediterranean, Turkey). J Mar Biolog Assoc U.K. 2008; 88(4):837-42. Available from: http://www.journals.cambridge.org/abstract_S0025315408001124
http://www.journals.cambridge.org/abstra...
; Fernandez-Carvalho et al., 2011Fernandez-Carvalho J, Coelho R, Erzini K, Santos MN. Age and growth of the bigeye thresher shark, Alopias superciliosus, from the pelagic longline fisheries in the tropical northeastern Atlantic Ocean, determined by vertebral band counts. Aquat Living Resour. 2011; 24(4):359-68. Available from: http://www.alr-journal.org/10.1051/alr/2011046
http://www.alr-journal.org/10.1051/alr/2...
). Up to now, verification of the annual periodicity of vertebral bands has not been done for species of the family Rhinobatidae. It is assumed, therefore, that a pair of growth bands, constituted by a hyaline ring and an opaque ring, is deposited in this species each year, as verified for other elasmobranchs (Bonfil et al., 1993Bonfil R, Mena R, Anda D. Biological parameters of commercially exploited silky sharks, Carcharhinus falciformis, from the Campeche Bank, Mexico. NOAA Tech Rep NMFS. 1993; 115:73-86.; Cailliet et al., 1983Cailliet GM, Martin LK, Kusher D, Wolf P, Welden BA. Techniques for enhancing vertebral bands in age estimation of California elasmobranchs. In: Prince ED, Pulos LM, editors. Proceedings of the International Workshop on age determination of Oceanic Pelagic Fishes: Tunas, Billfishes, and Sharks; 1983. p.157-165. (NOAA Technical Reports NMFS); Lessa et al., 1999Lessa R, Santana FM, Paglerani R. Age, growth and stock structure of the oceanic whitetip shark, Carcharhinus longimanus, from the southwestern equatorial Atlantic. Fish Res .1999; 42(1-2):21-30. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0165783699000454
http://linkinghub.elsevier.com/retrieve/...
; Oshitani et al., 2003Oshitani S, Nakano S, Tanaka S. Age and growth of the silky shark Carcharhinus falciformis from the Pacific Ocean. Fish Sci. 2003; 69(3):456-64.; Santana, Lessa, 2004Santana FM, Lessa R. Age determination and growth of the night shark (Carcharhinus signatus) off the northeastern Brazilian coast. Fish Bull . 2004; 102(1):156-67.; Romine et al., 2006Romine J, Grubbs R, Musick J. Age and growth of the sandbar shark, Carcharhinus plumbeus, in Hawaiian waters through vertebral analysis. Environ Biol Fishes . 2006; 77(3-4):229-39). However, this is a question that should be dealt with and studied in the future for this species.

The ray Z. brevirostris was found from 4 to 10 years of age in the study area. The species reaches its Linf at about 59.5 cm for females and 54.9 cm for males. The age and growth parameters for this species, presented in this study, corroborate the hypothesis that this ray requires future management conservation due to its slow growth rate and susceptibility to overexploitation, as f other elasmobranchs (Sulikowski et al., 2003Sulikowski JA, Morin MD, Suk SH, Howell WH. Age and growth estimates of the winter skate ( Leucoraja ocellata ) in the western Gulf of Maine. Fish Bull . 2003; 101(2):405-13.; Natanson et al., 2007Natanson LJ, Sulikowski JA, Kneebone JR, Tsang PC. Age and growth estimates for the smooth skate, Malacoraja senta, in the Gulf of Maine. Environ Biol Fishes . 2007; 80(2-3):293-308.). This group should have its fisheries closely monitored in order to conserve its members as important components of the marine ecosystem (Vooren, 2012Vooren CM. Prefacio. In Bornatowski H, Abilhoa V, editores. Tubarões e raias capturados pela pesca artesanal no Paraná - guia de identificação. Curitiba: Hori Consultoria Ambiental ; 2012. p.1-3. (Hori Cadernos Técnicos; No. 4)). In a review of the life history characteristics of long-life marine species, Musick (1999Musick JA. Ecology and conservation of long-lived marine animals. In: Life in the slow lane: ecology and conservation of long-lived marine animals. Musick JA, editor. American Fisheries Society Symposium; 1999.p.1-10. vol. 23.) concluded that species with k coefficients ≤ 0.10 year-1 are extremely susceptible to decline due to overexploitation, a value that is near to the one obtained for Z. brevirostris. As such, the current population status and fishing effort for this species should be monitored and assessed in future stock assessments.

Acknowledgments

We are thankful to Zé do Zuca, the fisherman who collected the specimens. To Diego Zanlorenzi and Bianca Possamai for lab work help. WPDC is thankful to the people of CCMAR-Universidade do Algarve (Jorge Gonçalves, “Camané”, Luis, Pedro Monteiro, Pedro Veiga, Frederico, Mafalda, Isidoro, Inês e Nuno), and especially grateful to Joana Carvalho and Nour Salam for the support in the preparation of samples. WPDC was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). RC is supported by an Investigador-FCT contract (Ref: IF/00253/2014) from the Portuguese Foundation for Science and Technology (FCT, Fundação para a Ciência e Tecnologia).

References

  • Abilhoa V, Bornatowski H, Oliveira Freitas M. Some information on reproduction and embryonic development of the lesser guitarfish Zapteryx brevirostris in Southern Brazil. Acta Adriat. 2007; 48(2):185-90.
  • Abràmoff MD, Magalhães PJ, Ram SJ. Image Processing with ImageJ. Biophotonics International, 2004; 11(7):36-42.
  • Ainsley SM, Ebert DA, Cailliet GM. Age, growth, and maturity of the whitebrow skate, Bathyraja minispinosa, from the eastern Bering Sea. ICES J Mar Sci. 2011; 68(7):1426-34. Available from: http://icesjms.oxfordjournals.org/cgi/doi/10.1093/icesjms/fsr072
    » http://icesjms.oxfordjournals.org/cgi/doi/10.1093/icesjms/fsr072
  • Akaike HAI. A new look at the Statistical Model Identification. IEEE Trans Automat Contr. 1974; 19(6):716-23.
  • Barker MJ, Schluessel V. Managing global shark fisheries: suggestions for prioritizing management strategies. Aquat Conserv. 2005; 15(4):325-47.
  • Başusta N, Demirhan SA, Çiçek E, Başusta A, Kuleli T. Age and growth of the common guitarfish, Rhinobatos rhinobatos, in Iskenderun Bay (north-eastern Mediterranean, Turkey). J Mar Biolog Assoc U.K. 2008; 88(4):837-42. Available from: http://www.journals.cambridge.org/abstract_S0025315408001124
    » http://www.journals.cambridge.org/abstract_S0025315408001124
  • Batista VS. Desenvolvimento sexual de Zapteryx brevirostris (Müller & Henle, 1841), no litoral do Rio de Janeiro, Brasil. Rev Bras Biol. 1987; 47(3):301-07.
  • Batista VS. Aspectos quantitativos da fecundidade e do desenvolvimento embrionário da raia Zapteryx brevirostris Müller & Hendle, 1841 (Pisces, Rhinobatidae) da enseada de Itaipu, Niterói, Rio de Janeiro. Rev Bras Biol . 1991; 51(3):495-501.
  • Beamish RJ, Fournier DA. A method for comparing the precision of a set of age determinations. Can J Fish Aquat Sci. 1981; 38(8):982-83.
  • Bonfil R, Mena R, Anda D. Biological parameters of commercially exploited silky sharks, Carcharhinus falciformis, from the Campeche Bank, Mexico. NOAA Tech Rep NMFS. 1993; 115:73-86.
  • Bornatowski H, Abilhoa V. Tubarões e raias capturados pela pesca artesanal no Paraná: guia de identificação. Curitiba: Hori Consultoria Ambiental; 2012. (Hori Cadernos Técnicos; No. 4).
  • Bornatowski H, Abilhoa V, Charvet-Almeida P. Elasmobranchs of the Paraná Coast, southern Brazil, south-western Atlantic. Mar Biodivers Rec. 2009; 2:e158. Available from: http://www.journals.cambridge.org/abstract_S1755267209990868
    » http://www.journals.cambridge.org/abstract_S1755267209990868
  • Branstetter S. Age, growth and reproductive biology of the silky shark, Carcharhinus falciformis, and the scalloped hammerhead, Sphyrna lewini, from the northwestern Gulf of Mexico. Environ Biol Fishes. 1987; 19(3):161-73. Available from: http://link.springer.com/10.1007/BF00005346
    » http://link.springer.com/10.1007/BF00005346
  • Burnham KP, Anderson DR. Model selection and multimodel inference: a practical information-theoretic approach. New York (NY): Springer-Verlag; 2002.
  • Cailliet GM, Smith WD, Mollet HF, Goldman KJ. Age and growth studies of chondrichthyan fishes: the need for consistency in terminology, verification, validation, and growth function fitting. Environ Biol Fishes . 2006; 77(3-4):211-28. Available from: http://link.springer.com/10.1007/s10641-006-9105-5
    » http://link.springer.com/10.1007/s10641-006-9105-5
  • Cailliet GM. Elasmobranch age determination and verification: an update review. In: Pratt HL, Jr., Gruber SH, Taniuchi T, editors. Elasmobranchs as living resources: advances in the biology, ecology, systematics and the status of the fisheries. Proceedings of the second United States-Japan Workshop East-West Center, Honolulu: U.S. Department of Commerce; 1990. p.57-165. (NOAA Techical Report NMFS; 90).
  • Cailliet GM, Goldman KJ. Age determination and validation in chondrichthyan fishes. In: Carrier JC, Musick JA, Heithaus MR, editors. Biology of sharks and their relatives. Boca Raton (FL): CRC Press; 2004. p.399-448.
  • Cailliet GM, Martin LK, Kusher D, Wolf P, Welden BA. Techniques for enhancing vertebral bands in age estimation of California elasmobranchs. In: Prince ED, Pulos LM, editors. Proceedings of the International Workshop on age determination of Oceanic Pelagic Fishes: Tunas, Billfishes, and Sharks; 1983. p.157-165. (NOAA Technical Reports NMFS)
  • Cailliet GM, Radtke RL,Welden BA. Elasmobranch age determination and verification: a review. In: Uyeno T, Arai R, Taniuchi T, Matsuura K, editors. Indo-Pacific fish biology. Proceedings of the second international conference on Indo Pacific fishes Tokyo: Ichthyological Society of Japan, Tokyo National Museum; 1986. p.345-60.
  • Campana SE. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol. 2001; 59(2):197-242.
  • Casey JG, Pratt HL Jr, Stillwell CE. Age and growth of the sandbar shark (Carcharinus plumbeus) from the western North Atlantic. Can J Fish Aquat Sci . 1985; 42(5):963-75.
  • Castello HP. Contribución al conocimento sistemático y biológico de Zapteryx brevirostris (Müller & Henle, 1841) de la costa atlántica marplatense (Chondrichthyes, Rhinobatidae). Physis. 1971; 30(80):619-29.
  • Cerrato RM. Interpretable statistical tests for growth comparisons using parameters in the von Bertalanffy equation. Can J Fish Aquat Sci . 1990; 47(7):1416-26.
  • Chang WYB. A statistical method for evaluating the reproducibility of age determinations. Can J Fish Aquat Sci . 1982; 39(8):1208-10.
  • Coelho R, Erzini K. Age and growth of the undulate ray, Raja undulata,in the Algarve (Southern Portugal). J Mar Biolog Assoc U.K . 2002; 94:987-90.
  • Coelho R, Erzini K. Reproductive aspects of the undulate ray, Raja undulata, from the south coast of Portugal. Fish Res. 2006; 81(1):80-85.
  • Colonello JC, García ML, Menni RC. Reproductive biology of the lesser guitarfish Zapteryx brevirostris from the south-western Atlantic Ocean. J Fish Biol . 2011; 78(1):287-302. Available from: http://www.ncbi.nlm.nih.gov/pubmed/21235561
    » http://www.ncbi.nlm.nih.gov/pubmed/21235561
  • Cortés E. Life history patterns and correlations in sharks. Rev Fish Sci. 2000; 8(4):299-344.
  • Espinoza M, Farrugia TJ, Lowe CG. Habitat use, movements and site fidelity of the gray smooth-hound shark (Mustelus californicus Gill 1863) in a newly restored southern California estuary. J Exp Mar Biol Ecol. 2011; 401(1-2):63-74. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0022098111001018
    » http://linkinghub.elsevier.com/retrieve/pii/S0022098111001018
  • Fernandez-Carvalho J, Coelho R, Erzini K, Santos MN. Age and growth of the bigeye thresher shark, Alopias superciliosus, from the pelagic longline fisheries in the tropical northeastern Atlantic Ocean, determined by vertebral band counts. Aquat Living Resour. 2011; 24(4):359-68. Available from: http://www.alr-journal.org/10.1051/alr/2011046
    » http://www.alr-journal.org/10.1051/alr/2011046
  • Figueiredo JL. Manual de Peixes Marinhos do Sudeste do Brasil. São Paulo: Museu de Zoologia da Universidade de São Paulo; 1977. pt. 1, Introdução - Cações, Raias e Quimeras.
  • Francis RICC. Back-calculation of fish length: a critical review. J Fish Biol . 1990; 36(6):883-902.
  • Goldman KJ. Age and growth of elasmobranch fishes. In: Bonfil R, Musick JA, editors. Elasmobranch fisheries management techniques. Singapore: Asia Pacific Economic Cooperation; 2004. p.97-132.
  • Gomes UL, Signori CN, Gadig OBF, Santos HRS. Guia para identificação de tubarões e raias do Rio de Janeiro. Rio de Janeiro: Technical Books; 2010.
  • Hoff TB, Musick JA. Western North Atlantic shark-fishery management problems and informational requirements. In: Pratt HL, Gruber SH, Taniuchi T, editors. Elasmobranchs as living resources: advances in the biology, ecology, systematics and the status of the fisheries. Proceedings of the second United States-Japan Workshop East-West Center, Honolulu: U.S. Department of Commerce; 1990. p.455-72. (NOAA Technical Report; 90).
  • Ismen A. Age, growth, reproduction and food of common stingray (Dasyatis pastinaca L., 1758) in Iskenderun Bay, the eastern Mediterranean. Fish Res . 2003; 60(1):169-76.
  • Katsanevakis S. Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fish Res . 2006; 81(2-3):229-35.
  • Kimura DK. Likelihood methods for the von Bertalanffy growth curve. Fish Bull. 1980; 77(4):765-76.
  • Klimley AP. The determinants of sexual segregation in the scalloped hammerhead shark, Sphyrna lewini Environ Biol Fishes , 1987; 18(1):27-40.
  • Lessa R, Santana FM, Hazin FH. Age and growth of the blue shark Prionace glauca (Linnaeus, 1758) off northeastern Brazil. Fish Res . 2004; 66(1):19-30. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0165783603001930
    » http://linkinghub.elsevier.com/retrieve/pii/S0165783603001930
  • Lessa R, Santana FM, Paglerani R. Age, growth and stock structure of the oceanic whitetip shark, Carcharhinus longimanus, from the southwestern equatorial Atlantic. Fish Res .1999; 42(1-2):21-30. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0165783699000454
    » http://linkinghub.elsevier.com/retrieve/pii/S0165783699000454
  • Levene H. Robust tests for equality of variances. In: Olkin I, Ghurye SG, Hoeffding W, Madow WG, Mann HB, editors. Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press; 1960. p.278-92.
  • Lilliefors HW. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc.1967; 62(318):399-402.
  • McFarlane GA, King JR. Age and growth of big skate (Raja binoculata) and longnose skate (Raja rhina) in British Columbia waters. Fish Res . 2006; 78(2-3):169-78. Available from: http://dx.doi.org/10.1016/j.fishres.2006.01.00
    » http://dx.doi.org/10.1016/j.fishres.2006.01.00
  • Mcphie RP, Campana SE. Bomb dating and age determination of skates (family Rajidae) off the eastern coast of Canada. ICES J Mar Sci . 2009; 66:546-60.
  • Menni RC, Stehmann MFW. Distribution, environment and biology of batoid fishes off Argentina, Uruguay and Brazil. A review. Rev Mus Argent Cienc Nat. 2000; 2(1):69-109.
  • Musick JA. Ecology and conservation of long-lived marine animals. In: Life in the slow lane: ecology and conservation of long-lived marine animals. Musick JA, editor. American Fisheries Society Symposium; 1999.p.1-10. vol. 23.
  • Natanson LJ, Casey JG, Kohler NE. Age and growth estimates for the dusky shark, Carcharhinus obscurus, in the western North Atlantic Ocean. Fish Bull . 1995; 93:116-26.
  • Natanson LJ, Gervelis BJ, Winton MV, Hamady LL, Gulak SJB, Carlson JK. Validated age and growth estimates for Carcharhinus obscurus in the northwestern Atlantic Ocean, with pre- and post management growth comparisons. Environ Biol Fishes . 2014; 97(8):881-96.
  • Natanson LJ, Sulikowski JA, Kneebone JR, Tsang PC. Age and growth estimates for the smooth skate, Malacoraja senta, in the Gulf of Maine. Environ Biol Fishes . 2007; 80(2-3):293-308.
  • Oshitani S, Nakano S, Tanaka S. Age and growth of the silky shark Carcharhinus falciformis from the Pacific Ocean. Fish Sci. 2003; 69(3):456-64.
  • R Development Core Team. R: A language and environment for statistical computing [Computer software manual - Internet]. Vienna: R Foundation for Statistical Computing; 2014. Available from: http://www.r-project.org
    » http://www.r-project.org
  • Robert MC. A captura de elasmobrânquios na costa paranaense. In: Bornatowski H, Abilhoa V, editores. Tubarões e raias capturados pela pesca artesanal no Paraná: guia de identificação. Curitiba: Hori Consultoria Ambiental ; 2012. p.27-34. (Hori Cadernos Técnicos; No. 4).
  • Romine J, Grubbs R, Musick J. Age and growth of the sandbar shark, Carcharhinus plumbeus, in Hawaiian waters through vertebral analysis. Environ Biol Fishes . 2006; 77(3-4):229-39
  • Santana FM, Lessa R. Age determination and growth of the night shark (Carcharhinus signatus) off the northeastern Brazilian coast. Fish Bull . 2004; 102(1):156-67.
  • Santos C, Cortellete GM, Araújo KCB, Spach HL. Estrutura populacional da raia-viola Zapteryx brevirostris (Chondrichthyes, Rhinobatidae), na plataforma adjacente à baía de Paranaguá, PR. Acta Biologica Leopondensia. 2006; 28(1):32-37.
  • Shotton R, editor. Case studies of the management of elasmobranch fisheries. Rome: Food and Agriculture Organization of the United Nations; 1999. pt. 1. (FAO Fisheries Technical Paper; No. 378).
  • Skomal G, Natanson L. Age and growth of the blue shark (Prionace glauca) in the North Atlantic Ocean. Fish Bull . 2003; 101(3):627-39.
  • Sminkey TR, Musick JA. Age and growth of the sandbar shark, Carcharhinus plumbeus, before and after population depletion. Copeia. 1995; (4):871-83.
  • Smith CL. Summary of round table discussions on back calculation. In: Prince ED, Pulos LM, editors. Proceedings of the international workshop on age determination in oceanic pelagic fishes: tunas, billfishes, and sharks; 1983. p.45-47. (NOAA Technical Reports NMFS; 8).
  • Smith SE, Au DW, Show C. Intrinsic rebound potentials of 26 species of Pacific sharks. Mar Freshw Res. 1998; 49:663-78.
  • Sparre P, Venema SC. Introduction to tropical fish stock assessment. Rome: Food and Agriculture Organization of the United Nations ; 1997. pt 1: Manual. (FAO Fisheries Technical Paper; 306/1).
  • Stevens JD, Bonfil R, Dulvy NK, Walker PA. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES J Mar Sci . 2000; 57(3):476-94.
  • Sulikowski JA, Morin MD, Suk SH, Howell WH. Age and growth estimates of the winter skate ( Leucoraja ocellata ) in the western Gulf of Maine. Fish Bull . 2003; 101(2):405-13.
  • Thorson JT, Simpfendorfer CA. Gear selectivity and sample size effects on growth curve selection in shark age and growth studies. Fish Res . 2009; 98(1-3):75-84.
  • Vazzoler AEAM. Manual de métodos para estudos biológicos de populações de peixes. Reprodução e Crescimento. Brasília: CNPq; 1981.
  • Vooren CM. Prefacio. In Bornatowski H, Abilhoa V, editores. Tubarões e raias capturados pela pesca artesanal no Paraná - guia de identificação. Curitiba: Hori Consultoria Ambiental ; 2012. p.1-3. (Hori Cadernos Técnicos; No. 4)
  • Vooren CM, Lamónaca AF, Massa A, Hozbor N, editors. Zapteryx brevirostris: The IUCN Red List of Threatened Species. Version 2014.2. 2006. Available from: http://www.iucnredlist.org
    » http://www.iucnredlist.org
  • Whitney RR, Carlander KD. Interpretation of body-scale regression for computing body length of fish. J Wildl Manage. 1956; 20(1):21-27.
  • Wickham H. ggplot2: elegant graphics for data analysis. New York: Springer; 2009.
  • Wintner SP, Cliff G. Age and growth determination of thewhite shark, Carcharodon carcharias from the east coast of South Africa. Fish Bull . 1999; 97(1):153-69.
  • Yamaguchi A, Kawahara I, Ito S. Occurrence, growth and food of long headed eagle ray, Aetobatus flagellum, in Ariake Sound, Kyushu, Japan. Environ Biol Fishes . 2005; 74(2):229-38.

Publication Dates

  • Publication in this collection
    2018

History

  • Received
    24 Jan 2017
  • Accepted
    06 Dec 2017
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