SciELO - Scientific Electronic Library Online

 
vol.90Historia de la vegetación, ambiente y evidencia de actividad humana de los últimos 6,000 años en el lago alpino La Luna, Nevado de TolucaEcología térmica de dos especies de lagartijas del género Xenosaurus (Squamata: Xenosauridae) en México índice de autoresíndice de assuntospesquisa de artigos
Home Pagelista alfabética de periódicos  

Serviços Personalizados

Journal

Artigo

Indicadores

Links relacionados

  • Não possue artigos similaresSimilares em SciELO

Compartilhar


Revista mexicana de biodiversidad

versão On-line ISSN 2007-8706versão impressa ISSN 1870-3453

Rev. Mex. Biodiv. vol.90  México Jan. 2019  Epub 12-Fev-2019

http://dx.doi.org/10.22201/ib.20078706e.2019.90.1969 

Ecology

New records of crustaceans infesting Phractocephalus hemioliopterus (Siluriformes: Pimelodidae), the large catfish from the Amazon

Nuevos registros de crustáceos que infestan Phractocephalus hemioliopterus (Siluriformes: Pimelodidae), el gran bagre del Amazonas

Marcos Sidney B. Oliveiraa  * 

Lincoln L. Corrêaa  b 

Raissa A. Gonçalvesc 

Lígia R. Nevesd 

Luiza Prestese 

Drielly O. Ferreiraf 

Marcos Tavares-Diasd  f 

a Programa de Pós-graduação em Recursos Aquáticos Continentais Amazônicos, Universidade Federal do Oeste do Pará, CEP 68040-470, Santarém, PA, Brazil.

b Instituto de Ciências e Tecnologia das Águas, Universidade Federal do Oeste do Pará, CEP 68040-470, Santarém, PA, Brazil.

c Programa de Pós-graduação em Aquicultura, Universidade Nilton Lins, CEP 69058-030, Manaus, AM, Brazil.

d Programa em Biodiversidade e Biotecnologia da Amazônia, Universidade Federal do Amapá, CEP 68903-419, Macapá, AP, Brazil.

e Universidade do Estado do Amapá, CEP 66077-830, Macapá, AP, Brazil, Programa em Ecologia Aquática e Pesca, Universidade Federal Rural da Amazônia, CEP 66077-830, Belém, PA, Brazil

f Embrapa Amapá, Rodovia Juscelino Kubitschek, Km 5, No. 2600, Universidade, CEP 68903-419, Macapá, AP, Brazil

Abstract

The aim of the present study was to investigate the infracommunities of ectoparasitic crustaceans in Phractocephalus hemioliopterus Bloch and Schneider, 1801, a catfish from the lower Amazon River, in the state of Pará, eastern Amazon region, Brazil. From 12 hosts examined, a total of 45 specimens of crustacean ectoparasites from 5 species were found in the tegument, oral cavity or dorsal fins. The species were: Argulus multicolor, Argulus violaceus, Dolops nana, Dolops discoidalis, and Braga patagonica. Dolops discoidalis was the dominant ectoparasite, while D. nana had the highest mean intensity in the tegument, which was the most infested host site. This is the first record of A. multicolor, A. violaceus, D. nana and B. patagonica parasiting P. hemioliopterus.

Keywords: Amazon; Freshwater fish; Parasites; Pimelodidae

Resumen

El objetivo del presente estudio fue investigar las infracomunidades de crustáceos ectoparásitos en Phractocephalus hemioliopterus Bloch y Schneider, 1801, un bagre de la parte baja del río Amazonas, en el estado de Pará, en la Amazonía oriental, Brasil. A partir de 12 hospederos examinados, se encontraron un total de 45 ejemplares de crustáceos ectoparásitos de 5 especies en el tegumento, cavidad o aletas dorsales orales. Las especies fueron: Argulus multicolor, Argulus violaceus, Dolops nana, Dolops discoidalis y Braga patagonica. Dolops discoidalis fue el ectoparásito dominante, mientras que D. nana tuvo la intensidad media más alta en el tegumento, que fue el sitio más infestado. Este es el primer registro de A. multicolor, A. violaceus, D. nana y B. patagonica parasitando P. hemioliopterus.

Palabras clave: Amazonía; Peces de agua dulce; Parásitos; Pimelodidae

Introduction

The Siluriformes genus Phractocephalus Agassiz described by Spix and Agassiz (1829) (Pimelodidae) has 3 species, but only 1 remains alive, the Phractocephalus hemioliopterus Bloch and Schneider, 1801, the larger catfish from the Amazon. The 2 extinct species are: Phractocephalus nassi Lundberg and Aguilera, 2003, and Phractocephalus acreornatus Aguilera, Bocquentin, Branco, Lundberg and Maciente, 2008. In Venezuela and Colombia, P. hemioliopterus is known as “cajaro” while in Brazil it is known as “pirarara” tailed catfish.

Phractocephalus hemioliopterus is widely distributed throughout the Amazon River and its major tributaries in white, clear and black water. This Siluriformes can be found on beaches and river channels, rapids and flooded forests, and can grow up to 1.3 m in length (Barbarino Duque & Winemiller, 2003; Goulding, 1980; Santos et al., 2006). This catfish supports large commercial fisheries in the Amazon River system (Barbarino-Duque & Winemiller, 2003). This catfish is omnivorous, with carnivorous tendencies, and feeds on several species of fish including other Pimelodidae, Prochilodontidae, Cetopicidae, Synbranchidae, Serrasalmidae species, as well as reptiles, amphibians, some vegetables (Barbarino Duque & Winemiller, 2003), crabs, fruits and seeds (Goulding, 1980; Maia & Chalco, 2002). Its reproduction occurs during the seasonal floodings of the Amazon (Ferreira et al., 1998).

Among the crustacean parasites of fish, there are species of Branchiura Thorell, 1818; Copepoda Milne Edwards, 1940, and Isopoda Latreille, 1871 (Luque et al., 2013). Species of these crustaceans infest freshwater, saltwater and brackish water fish around the world and can be found in the integument, fins, mouth, lid, nostrils, gills, anus and abdominal cavity (Luque et al., 2013; Mamani et al., 2004; Oda et al., 2015; Tavares-Dias et al., 2015; Thatcher, 2006). In the Brazilian Amazon, branchiurans, copepods and isopods infest fish of the Characiformes, Perciformes, Siluriformes, Osteoglossiformes, and Rajiformes orders (Luque et al., 2013; Tavares-Dias et al., 2015; Oliveira et al., 2017). Characiform fish of the Serrasalmidae family have been the most infested, mainly by species of Argulus and Dolops (Tavares-Dias et al., 2015). Yet little is known about the parasitic fauna of P. hemioliopterus, especially crustacean speciesis known to infest this host, being recorded only Dolops discoidalis Bouvier, 1899 of the Solimões River (central Amazon) (Malta, 1984) and Jari River (easten Amazon) (Oliveira et al., 2017).

The present study aimed to investigate the parasitic crustacean fauna infesting P. hemioliopterus in the lower Amazon River, state of Pará, northern Brazil, to contribute to the knowledge of the host-parasite relationship and increase knowledge about the biodiversity in the region.

Materials and methods

Twelve specimens of P. hemioliopterus were collected in October 2012, during the dry season, off the left bank of the Amazon River, in the state of Pará, Brazil (Fig. 1). The Amazon River system and its tributaries are responsible for the formation of large areas that are periodically flooded due to high rainfall and tidal surges. In the rainy season, the waters invade the plains, creating favorable conditions that allow the majority of fish species to reproduce. According to the Macapá-AP Meteorology rainfall volume was 23.17 mm, with a maximum temperature of 45 ºC and a minimum of 32 °C and relative humidity 45.48%, at the time of collection. This is the main period for feeding, growth and energy accumulation for several species of fish, especially during the dry season (Braga et al., 2011; Maia & Chalco, 2002).

Figure 1 Geographic localization of area of collection of Phractocephalus hemioliopterus in the lower Amazon River, state of Pará, Brazil. 

The fish were caught using hooks and lines during 9 hours, with the freshwater prawn Macrobrachium amazonicum Heller, 1862, used as bait. Immediately after collection, the integument, fins, mouth, anus, operculum, eyes and nostrils of each P. hemioliopterus were examined in search of crustacean parasites. When found, the parasites were collected and quantified. Then, each fish was measured for total weight (g) and standard length (cm). The present study was carried out according to the principles adopted by the Brazilian College of Animal Experimentation - COBEA.

The crustacean collection procedures were performed at the site of fish collection, with crustaceans being collected from one fish at a time. This procedure lasted around 3.5 minutes for each fish, and the fish were immediately returned to the Amazon River.

All the crustaceans collected were fixed in 70% alcohol for 24 hours and then stored in 70% ethanol containing 10% glycerin and processed for identification. The identification of the crustacean species followed Lemos de Castro (1959, 1986) and Thatcher (2006). The ecological descriptors used were those proposed by Bush et al. (1997) and Rohde et al. (1995).

The length-weight relationship was calculated using the equation W = aLb, where W is the total weight in grams, L is the standard length in cm, and a and b are constants (Le-Cren, 1951). The type of growth was verified using the t-test where: H0: b = 3 (isometric growth) and H1: b ≠ 3 (allometric growth) (p = 0.05). Spearman’s correlation coefficient (rs) was used to determine possible correlations between the abundance of parasitic crustaceans and the standard length and body weight of the host (Zar, 1996).

Results

A total of 12 specimens of P. hemioliopterus measuring 39.0 ± 13.2 cm and weighing 1,830 ± 1,974.5 g were collected and examined for the collection of parasitic crustaceans. A total of 91.7% of the fish examined were parasitized by 1 or more species of crustaceans. From the integument, dorsal fin or mouth of the hosts, 45 parasites were collected, such as: Argulus multicolor Stekhoven, 1937, Argulus violaceus Thomsen, 1925, Dolops nana Lemos de Castro, 1950, D. discoidalis (Branchiura: Argulidae), and Braga patagonica Schiödte and Meinert, 1884 (Isopoda: Cymothoidae). Dolops discoidalis was the dominant parasite, while D. nana had the greatest intensity of infestation. The tegument was the most infested host site (Table 1).

Table 1 Crustacean parasites of Phractocephalus hemioliopterus (N = 12) from the lower Amazon River, state of Pará, Brazil. P: Prevalence, MI: mean intensity, MA: mean abundance, FD: frequency of dominance, IS: infestation site, TNP: total number of parasites. 

Parasite species P (%) MI MA FD (%) IS TNP
Argulus multicolor 8.3 6.0 0.50 0.133 Oral cavity 6
Argulus violaceus 8.3 4.0 0.33 0.089 Oral cavity 4
Braga patagonica 8.3 1.0 0.08 0.022 Dorsal fin 1
Dolops nana 8.3 16.0 1.33 0.356 Integument 16
Dolops discoidalis 58.3 2.5 1.50 0.40 Integument 18

A positive correlation was observed between the abundance of D. discoidalis and the length and body weight of the hosts (Table 2). For P. hemioliopterus, the equation that described the length-weight relationship was: W = 0.041x2.8369; r² = 0.985, which demonstrated an isometric type growth (t < t2 (0.05) 11; p < 0.05), indicating proportional growth of both the body weight and length of the hosts.

Table 2 Spearman’s correlation coefficient (rs) between abundance of parasites and standard length and body weight for infracommunities of parasite crustaceans of Phractocephalus hemioliopterus (N = 12) from the lower Amazon River, state of Pará, Brazil. 

Length Weight
Parasites rs p rs p
Argulus multicolor -0.2191 0.493 -0.219 0.492
Argulus violaceus -0.438 0.154 -0.395 0.202
Dolops discoidalis 0.767 0.003* 0.744 0.005*
Dolops nana - - 0.131 0.682
Braga patagonica - - -0.004 0.892

Discussion

Dolops discoidalis was the dominant parasitic species in P. hemioliopterus, while D. nana exhibited the highest average intensity. Other studies related to the occurrence of these crustaceans parasitize P. hemiolioptera of Solimões River (central Amazon) (Malta, 1982) and Jari River (eastern Amazon) (Oliveira et al., 2017), however, it is not possible to compare infection levels because of the low number of fish examined in these other studies. However, infestation levels were higher than those of Pseudoplatystoma fasciatum (Linnaeus, 1766) and Pseudoplatystoma tigrinum (Valenciennes, 1840) from the Ichilo and Beni River basins in Bolivia (Mamani et al., 2004). Argulus multicolor and A. violaceus occurred only in the oral cavity of P. hemioliopterus, while D. nana and D. discoidalis, and B. patagonica were found in the tegument and fins, respectively. Species of Argulus fixed themselves to the hosts via suction cups, a method that appears to be less efficient than the modified jaws terminating in strong claws of species of Dolops, as well as B. patagonica, which fixes to its host using its legs with strong claws, which also seem to be effective for fixing. Furthermore, the choice of fixation site of the crustaceans may be mainly related to food availability (Thatcher, 2006).

A positive correlation was observed between the abundance of D. discoidalis with host size, due to the larger area available in the integument for these ectoparasites (Malta, 1984; Mamani et al., 2004; Walker et al., 2008). As D. discoidalis infests fish from different families, it shows no host specificity (Luque et al., 2013; Tavares-Dias et al., 2014; Thatcher, 2006). Dolops nana has been described as mainly parasitizing fish from the family Anostomidae such as Leporinus spp. from the Paraná River basin (Luque et al., 2013), but has not been recorded for Pimelodidae species from the Amazon basin. Therefore, this is the first report of D. nana for P. hemioliopterus.

Argulus violaceus, a parasite of Hoplias malabaricus, Hypostomus commersonii, Loricaria anus, Basilichthy bonariensis, Pimelodus albicans, Rhamdia quelen, and Rhamdia sapo from South America (Thatcher, 2006), exhibited low levels of infestation for P. hemioliopterus. However, there have been no reports of this crustacean infesting fish in Brazil until now. As such, this is the first record of A. violaceus both for a host in Brazil and for P. hemioliopterus.

The infestation of A. multicolor in P. hemioliopterus was low, similar to a report for P. tigrinum, but inferior to the infestation documented for Pseudoplatystoma punctifer (Castelnau, 1855) in the central Amazon (Lopes et al., 2009). In Brazil, A. multicolor infests fish from the Amazon River (Bittencourt et al., 2014; Lopes et al., 2009; Malta, 1984; Thatcher, 2006), Pantanal basin (Fontana et al., 2012), and Tocantins River (Yamada & Takemoto, 2013) and Jari River (Oliveira et al., 2017). However, this is the first record of A. multicolor for P. hemioliopterus.

Only one specimen of B. patagonica was found in the dorsal fin of P. hemioliopterus. This species of isopod with no host specificity was found causing severe lesions in a region near the dorsal fin of Colossoma macropomum (Cuvier 1816), due to the strong claws used for attachment (Tavares-Dias et al., 2014). However, no macroscopic lesions in P. hemioliopterus were found in the present study. Among isopod parasites of fish, B. patagonica has been recorded in fish in the Brazilian Amazon, infesting species in the Acestrorhynchidae, Erythrinidae, Cichlid, Curimatidae, Characidae, Cynodontidae, Loricaridae, Serrasalmidae and Sciaenidae (Luque et al., 2013; Tavares Dias et al., 2014; Tavares-Dias et al., 2015; Oliveira et al., 2017). However, this is the first record of B. patagonica for P. hemioliopterus.

The length-weight relationship is used to estimate the weight of fish when their length is known, and provides relevant information for fisheries (Ruffino & Isaac, 1995). In the present study, this relationship is representative of the growth of young and adult fish, which may have influenced isometric growth (b = 2.8369), which was within the range expected for fish (Froese, 2006). However, there are no other growth records for P. hemioliopterus. Isometric growth is the most desirable for fish cultivation and has also been recorded for other Pimelodidae such as P. fasciatum and P. tigrinum from a natural environment (Mateus & Penha, 2007). This seems to be characteristic for species whose feeding occurs at higher trophic levels (Barbieri, 1989). Moreover, such growth is an indication that the environment provides suitable food conditions for the development of P. hemioliopterus, which exhibited proportional weight and body length growth.

Finally, the diversity of parasitic crustacean species was high in P. hemioliopterus, with 5 species from 2 families and 3 genera. In general, the community of parasitic crustaceans was characterized by mixed infestation, low prevalence and low abundance, but with dominance of D. discoidalis.

Acknowledgements

To the Coordination for the Improvement of Higher Education Personnel (CAPES) for the Masters Scholarship awarded to Oliveira, M. S. B., and the Brazilian Council for Scientific Development (CNPq) for the productivity scholarship awarded to Dr. Tavares-Dias, M.

References

Barbarino-Duque, A., & Winemiller, K. O. (2003). Dietary segregation among large catfishes of the Apure and Arauca Rivers, Venezuela. Journal of Fish Biology, 63, 410-427. https://doi.org/10.1046/j.1095-8649.2003.00163 [ Links ]

Barbieri, G. (1989). Dinâmica da reprodução e crescimento de Hoplias malabaricus (Bloch, 1794) (Osteichthyes, Erythrinidae) da represa do Monjolinho, São Carlos/SP. Revista Brasileira de Zoologia, 6, 225-233. https://doi.org/10.1590/s0101-81751989000200006 [ Links ]

Bittencourt, L. S., Pinheiro, D. A., Cárdenas, M. Q., Fernandes, B. M., & Tavares-Dias, M. (2014). Parasites of native Cichlidae populations and invasive Oreochromis niloticus (Linnaeus, 1758) in tributary of Amazonas River (Brazil). Brazilian Journal of Veterinary Parasitology, 23, 44-54. https://doi.org/10.1590/s1984-29612014006 [ Links ]

Braga, B., Varella, P., & Gonçalves, H. (2011). Transboundary Water Management of the Amazon Basin. Water Resources Development, 27, 477-496. https://doi.org/10.1080/07900627.2011.595382 [ Links ]

Bush, A. O., Lafferty, K. D., Lotz, J. M., & Shostak, A. W. (1997). Parasitology meets ecology on its own terms: Margolis et al. Revisited. Journal of Parasitology, 83, 575-583. https://doi.org/10.2307/3284227 [ Links ]

Ferreira, E. J. G., Zuanon, J. A. S., & Santos, G. M. (1998). Peixes comerciais do médio Amazonas: Região de Santarém - PA. IBAMA, Brasília: Coleção Meio Ambiente, Série Estudos de Pesca. [ Links ]

Fontana, M., Takemoto, R. M., Malta, J. C. O., & Mateus, L. A. F. (2012). Parasitism by argulids (Crustacea: Branchiura) in piranhas (Osteichthyes: Serrasalmidae) captured in the Caiçara bays, upper Paraguay River, Pantanal, Mato Grosso State, Brazil. Neotropical Ichthyology, 10, 653-659. https://doi.org/10.1590/s1679-62252012005000019 [ Links ]

Froese, R. (2006). Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations. Journal of Applied Ichthyology, 22, 241-253. https://doi.org/10.1111/j.1439-0426.2006.00805.x [ Links ]

Goulding, M. (1980). The fishes and the forest. Explorations in Amazonian natural history. Berkeley: University of California Press. [ Links ]

Le-Cren, E. D. (1951). The length-weight relationship and seasonal cycle in gonad weight and condition in the perch (Perca fluviatilis). Journal of Animal Ecology, 20, 201-219. https://doi.org/10.2307/1540 [ Links ]

Lemos de Castro, A. (1959). Sobre as espécies Sul-Americanas do gênero Braga Schioedte and Meinert, 1881. (Isopoda, Cymothoidea). Arquivos do Museu Nacional do Rio de Janeiro, 49, 69-77. [ Links ]

Lemos de Castro, A. (1986). 30. Branchiura. In T. T. Schaden (Ed.), Manual de identificação de invertebrados límnicos do Brasil (pp. 1-23). Brasília: CNPq. [ Links ]

Lopes, L. P. C., Varella, A. M. B., & Malta, J. C. O. (2009). Metazoan parasites of Pseudoplatystoma punctifer (Linnaeus, 1766) and Pseudoplatystoma tigrinum (Spix and Agassiz, 1829) (Siluriformes: Pimelodidae) of the Cent. al Amazon Basin, Brazil. Biologia Geral e Experimental, 9, 3-15. [ Links ]

Luque, J. L., Vieira, F. M., Takemoto, R. M., Pavanelli, G. C., & Eiras, J. C. (2013). Checklist of Crustacea parasitizing fishes from Brazil. Check List, 9, 1449-1470. https://doi.org/10.15560/9.6.1449 [ Links ]

Maia, L. A., & Chalco, F. P. (2002). Produção de frutos de espécies da floresta de várzea da Amazônia central importantes na alimentação de peixes. Acta Amazonica, 32, 45-54. https://doi.org/10.1590/1809-43922002321054 [ Links ]

Malta, J. C. O. (1984). Os peixes de um lago de várzea da Amazônia central (Lago Janauacá, Rio Solimões) e suas relações com os crustáceos parasitos (Branchiura: Argulidae). Acta Amazonica , 14, 355-372. https://doi.org/10.1590/1809-43921984143372 [ Links ]

Malta, J. S. (1982). Os argulídeos (Crustacea: Branchiura) da Amazônia brasileira. Aspectos da ecologia de Dolops discoidalis Bouvier, 1899 e Dolops bidentata Bouvier, 1899 (1). Acta Amazonica , 12, 521-528. https://doi.org/10.1590/1809-43921982123521 [ Links ]

Mamani, M., Hamel, C., & Van Damme, P. A. (2004). Ectoparasites (Crustacea: Branchiura) of Pseudoplatystoma fasciatum (surubí) and P. tigrinum (chuncuina) in Bolivian whitewater floodplains. Ecología en Bolivia, 39, 9-20. [ Links ]

Mateus, L. A., & Penha, J. M. (2007). Dinâmica populacional de quatro espécies de grandes bagres na bacia do Rio Cuiabá, Pantanal Norte, Brasil (Siluriformes, Pimelodidae). Revista Brasileira de Zoologia , 24, 87-98. https://doi.org/10.1590/s0101-81752007000100012 [ Links ]

Oda, F. H., da Graça, R. J., Tencatt, L. F. C., Tavares, L. E. R., Froehlich, O., & Takemoto, R. M. (2015). The Poorly Known Riggia acuticaudata (Crustacea: Isopoda) Parasitizing Ancistrus sp. (Siluriformes: Loricariidae) from the Paraguay River Basin, Brazil, with Comments on its Reproductive Biology. Comparative Parasitology, 82, 25-28. http://dx.doi.org/10.1654/4738.1 [ Links ]

Oliveira, M. S. B., Corrêa, L. L., Ferreira, D. O., Neves, L. R., & Tavares-Dias, M. (2017). Records of new localities and hosts for crustacean parasites in fish from the eastern Amazon in northern Brazil. Journal of Parasitic Diseases, 41, 565-570. [ Links ]

Rohde, K., Hayward, C., & Heap, M. (1995). Aspects of the ecology of metazoan ectoparasites of marine fishes. International Journal for Parasitology, 25, 945-970. https://doi.org/10.1016/0020-7519(95)00015-t [ Links ]

Ruffino, M. L., & Isaac, V. J. (1995). Life cycle and biological parameters of several Brazilian Amazon fish species. Naga, 18, 41-45. [ Links ]

Santos, G. M., Ferreira, E. J. G., & Zuanon, J. A. S. (2006). Peixes comerciais de Manaus. Ibama, Manaus: PróVárzea. [ Links ]

Tavares-Dias, M., Araújo, C. S. O., Barros, M. S., & Viana, G. M. (2014). New hosts and distribution records of Braga patagonica, a parasite Cymothoidae of fishes from the Amazon. Brazilian Journal of Aquatic Science and Technology, 18, 91-97. https://doi.org/10.14210/bjast.v18n1.p91-97 [ Links ]

Tavares-Dias, M., Dias-Júnior, M. B. F., Florentino, A. C., Silva, L. M. A., & Cunha, A. C. (2015). Distribution pattern of crustacean ectoparasites of freshwater fish from Brazil. Brazilian Journal of Veterinary Parasitology , 24, 136-147. http://dx.doi.org/10.1590/S1984-29612015036 [ Links ]

Thatcher, V. E. (2006). Amazon fish parasites. 2ª Ed. Sofia, Moscow: Pensoft Publishers. [ Links ]

Walker, P. D., Harris, J. E., Van Der Velde, G., & Wendelaar Bonga, S. E. (2008). Effect of host weight on the distribution of Argulus foliaceus (L.) (Crustacea, Branchiura) within a fish community. Acta Parasitologica, 53, 165-172. http://dx.doi.org/10.2478/s11686-008-0020-0 [ Links ]

Yamada, F. H., & Takemoto, R. M. (2013). Metazoan parasite fauna of two peacock-bass cichlid fish in Brazil. Check List , 9, 1371-1377. https://doi.org/10.15560/9.6.1371 [ Links ]

Zar, J. H. (1996). Biostatistical Analysis. New Jersey: Prentice-Hall. [ Links ]

Recebido: 17 de Outubro de 2016; Aceito: 14 de Agosto de 2019

*Corresponding author: marcosidney2012@hotmail.com (M.S.B. Oliveira)

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License