Length-weight relationships of the ichthyofauna from a coastal subtropical system: a tool for biomass estimates and ecosystem modelling

Relações comprimento-peso da ictiofauna de um sistema costeiro subtropical: uma ferramenta para estimativas de biomassa e modelagem de ecossistemas

Abstract

Aiming to analyse the growth pattern, to allow biomass estimates and consequently to subsidize the ecosystem modelling, the length-weight relationships (LWR) of 39 fish species from the Araçá Bay, a subtropical coastal area chosen as model for a holistic study comprising environmental, social and economic aspects have been estimated. The objective of this study was to provide LWR for the fishes from the area itself, accurately based on the life stages of fish populations present there. Particularly for Albula vulpes, Trachinotus carolinus, T. falcatus, Archosargus rhomboidalis and Kyphosus sectatrix these are the first records of LWR in Brazil.

Keywords
Araçá Bay; relative growth; Huxley model; Brazil

Resumo

Com o objetivo de analisar o padrão de crescimento e viabilizar estimativas de biomassas e, consequentemente, subsidiar a modelagem ecossistêmica, foram estimadas as relações comprimento-peso (RCP) de 39 espécies de peixes da baía do Araçá, uma área costeira subtropical escolhida como modelo para um estudo holístico compreendendo aspectos ambientais, sociais e econômicos. O objetivo deste estudo foi fornecer RCP para os peixes da própria área, baseadas nas estágios de vida das populações ictiícas ali presentes. Especialmente para Albula vulpes, Trachinotus carolinus, T. falcatus, Archosargus rhomboidalis e Kyphosus sectatrix estas são as primeiras estimativas de RCP no Brasil.

Palavras-chave
baía do Araçá; crescimento relativo; modelo de Huxley; Brasil

Introduction

In the current ichthyology, it is noteworthy that biodiversity conservation and sustainability are not dissociable. Socio-ecosystem approach for fishery management is a fact (Baigun et al. 2012). In the Southwestern Atlantic Ocean comprising the Brazilian coast, there are many marine environments with different levels of impact (Lana et al. 2001, Meniconi et al. 2012), consequence of global changes in local, medium and high scales (Ray & McCormick-Ray 2014). The Araçá Bay (23º48'47,3"S 45º24'22,1"W) (Figure 1) is one of them, and it was chosen as a model for a holistic and integrated study comprising biology, ecology, oceanography, economy, sociology and policy (BIOTA FAPESP Araçá 2015).

Figure 1
Map locating the Araçá Bay in the Brazilian coast, a coastal subtropical ecosystem.

Araçá Bay is an area of approximately 1 Km² subjected to daily tides, showing tidal pools, mangroves, rocky substrates, sandy beaches and the typical pelagic and benthic habitats. It shelters three beaches and two small islands. The Mãe Isabel stream flows in its north portion. In addition, it is directly affected by pollution and by the São Sebastião Port, which is close to the area. Fishermen live surrounding the bay using it and its adjacent areas for survival. Biodiversity and species richness in Araçá Bay are surprisingly high, playing an important role in the productivity of the adjacent areas (Amaral et al. 2010, 2015).

Concerning the fish population dynamics and the community structure, length-weight relationships (LWR) are one of the most useful tools in applied ichthyology and fishery management (Pauly 1984, Froese 2006). Among their several applications (Vianna et al. 2004, Macieira & Joeux 2009, Joeux et al. 2009, Silveira & Vaz-dos-Santos 2015), LWR are used to estimate fish biomass, the basis for the ecosystem modelling (Pope et al. 2006, Gasalla et al. 2007, Maury et al. 2007, Froese et al. 2008), one of the main purposes of the Araçá Bay study (BIOTA FAPESP Araçá 2015). In Brazil, these contributions have been used to estimate the biomass and to subsidize the modelling, as it is the case of demersal (Haimovici & Velasco 2000, Nascimento et al. 2012) and small pelagic ichthyofauna (Cergole & Dias Neto 2011, Vaz-dos-Santos & Rossi-Wongtschowski 2013). In order to assess the growth pattern of the fish species and to provide an essential tool to estimate the biomass with data from the area itself, the present study aimed to estimate the length-weight relationships (LWR) of the ichthyofauna in the Araçá Bay.

Material and Methods

Five samples (October 2012, March 2013, July 2013, October 2013 and January 2014) were attained by using nine different fishing gears, ensuring ontogenetic representativeness of the ichthyofauna. Fish species were identified, measured (total length, L_T, 0.1 mm) and weighed (total weight, W_T, 0.001 g). Nomenclature followed Eschmeyer (2015). Data from samples were pooled and the potential model W_T=aL_T^b (Huxley 1993) was fitted through the non-linear iterative least squares method (Zar 2010). Fits were assessed through residual analysis and the coefficient of determination values, calculated as r²=[Σ(y_p-y_a)²/Σ(y_o-y_a)²], where y_p is the predicting weight for the individual i, y_a is the average weight and y_o is the observed weight for the individual i (Vieira 2006). Growth pattern (whether isometric or allometric in relation to the referential value 3) was verified through t confidence intervals (CI) of b estimates: every value inside the CI is statistically similar to the estimate. The proportion of young and adult fishes in the sampling was informed, thus allowing checking the life stage represented by the regressions. The young fish were those assigned as immature (never spawned) and those ones in the other phases as adults, in accordance to Brown-Peterson et al. (2011).

Results and Discussion

A total of 12,362 specimens belonging to 39 species, 21 families and 11 orders were analysed (Table 1). The allometric coefficient (b) varied between 2.55 and 3.97 (mean = 3.086, median = 3.096). The variation of the coefficient of determination (between 0.759 and 0.999, mean = 0.956, median = 0.978) and residual analysis ensured the acuity of regressions even in the cases in which r² values were reduced by the biological variability. Especially in these cases, it is important to highlight that these models represent the portion of the population and their condition in the Araçá Bay and they should be used for biomass estimates in this particular situation. Although almost all length ranges were represented in the sampling, the proportional contribution of small and young fishes (59% of species) was higher than that in adults and longer fishes (31% of species). The Sardinella brasiliensis, Trachinotus spp., Caranx latus and Umbrina coroides sampling were constituted only by young fishes, while for Archosargus rhomboidalis, Menticirrhus americanus, Eugerres brasilianus, Cynoscion jamaicensis and Gymnothorax ocellatus adults dominated the sampling. The remaining 10% corresponded to 3 species in which it was not possible to evaluate the life stage and one in which the proportion was exactly 1:1 (Diapterus rhombeus).

Table 1
Number of fishes (n), total length range, parameters and t confidence intervals (CI) of the potential model (W_T=aL_T^b), coefficient of determination, relative growth pattern (i = isometric; a = allometric; + = positive; - = negative) and percentage of individuals by life stage.

Order	Family	Species		n	Total lenght (mm)			a	±	CI	b	±	CI	r2	growth pattern	% of life stage
					minimun	average	maximum									youngs	adults
Albuliformes	Albulidae	Albula vulpes	(Linnaeus, 1758)	60	32	78	210	6.571.10-6	±	2,201.10-6	3,05	±	0,063	0,984	i	78	22
Anguiliformes	Muraenidae	Gymnothorax ocellatus	Agassiz, 1831	38	332	402	522	4.169.10-9	±	0,100.10-10	3,97	±	0,419	0,933	a+	16	84
Clupeiformes	Engraulidae	Anchoa tricolor	(Spix & Agassiz, 1829)	111	35	73	103	7.670.10-6	±	4,756.10-6	2,99	±	0,142	0,931	i	71	29
	Clupeidae	Harengula clupeola	(Cuvier, 1829)	654	39	74	212	6.331.10-6	±	7,854.10-7	3,12	±	0,025	0,983	a+	97	3
		Sardinella brasiliensis	(Steindachner, 1879)	538	43	78	116	1.306.10-6	±	3,929.10-7	3,41	±	0,057	0,990	a+	100	---
Aulopiformes	Synodontidae	Synodus foetens	(Linnaeus, 1766)	77	56	169	238	2.990.10-6	±	2,191.10-6	3,13	±	0,137	0,990	i	66	34
Mugiliformes	Mugilidae	Mugil curema	Valenciennes, 1836	1272	25	129	452	1.672.10-5	±	3,335.10-6	2,90	±	0,033	0,986	a-	73	27
Atheriniformes	Atherinopsidae	Atherinella brasiliensis	(Quoy & Gaimard, 1825)	1760	22	89	151	4.542.10-6	±	3,923.10-7	3,10	±	0,021	0,986	a+	42	58
Beloniformes	Hemiramphidae	Hyporhamphus unifasciatus	(Ranzani, 1841)	63	116	199	322	2.562.10-7	±	1,999.10-7	3,45	±	0,099	0,959	a+	34	66
Scorpaeniformes	Triglidae	Prionotus punctatus	(Bloch, 1793)	155	22	104	220	1.394.10-5	±	2,568.10-6	2,98	±	0,034	0,986	i	64	36
Perciformes	Centropomidae	Centropomus parallelus	Poey, 1860	24	200	318	403	1.307.10-4	±	2,610.10-4	2,55	±	0,342	0,896	a-	---	---
	Serranidae	Diplectrum radiale	(Quoy & Gaimard, 1824)	110	55	148	246	2.645.10-6	±	1,189.10-6	3,32	±	0,089	0,978	a+	49	51
	Carangidae	Caranx latus	Agassiz, 1831	37	59	171	225	3.765.10-5	±	4,056.10-5	2,82	±	0,208	0,956	i	100	---
		Chloroscombrus chrysurus	(Linnaeus, 1766)	50	38	118	210	2.070.10-5	±	1,166.10-5	2,85	±	0,108	0,999	a-	57	43
		Oligoplites saurus	(Bloch & Schneider, 1801)	211	20	54	254	3.194.10-6	±	3,943.10-7	3,17	±	0,022	0,999	a+	94	6
		Trachinotus carolinus	(Linnaeus, 1766)	91	18	34	62	1.488.10-5	±	6,755.10-6	2,99	±	0,112	0,999	i	94	6
		Trachinotus falcatus	(Linnaeus, 1758)	115	18	37	65	3.511.10-5	±	1,347.10-5	2,87	±	0,100	0,865	a-	100	---
		Trachinotus goodei	Jordan & Evermann, 1896	31	62	97	125	1.139.10-5	±	1,634.10-5	3,01	±	0,294	0,968	i	100	---
	Lutjanidae	Lutjanus analis	(Cuvier, 1828)	31	39	203	410	1.296.10-5	±	7,750.10-6	3,01	±	0,101	0,999	i	64	36
		Lutjanus synagris	(Linnaeus, 1758)	38	54	120	316	3.779.10-5	±	1,054.10-5	2,81	±	0,049	0,999	a-	77	23
	Gerreidae	Diapterus rhombeus	(Cuvier, 1829)	1038	14	124	258	3.999.10-6	±	5,887.10-7	3,27	±	0,033	0,971	a+	50	50
		Eucinostomus argenteus	Baird & Girard, 1855	2552	17	76	189	1.049.10-5	±	2,157.10-6	3,03	±	0,045	0,982	i	60	40
		Eucinostomus gula	(Quoy & Gaimard, 1824)	163	73	137	205	6.515.10-6	±	3,159.10-6	3,16	±	0,093	0,967	a+	51	49
		Eucinostomus melanopterus	(Bleeker, 1863)	87	28	174	230	1.177.10-5	±	1,392.10-5	3,02	±	0,231	0,951	i	36	64
		Eugerres brasilianus	(Cuvier, 1830)	35	152	194	269	8.614.10-6	±	1,016.10-5	3,10	±	0,226	0,991	i	11	89
	Haemulidae	Haemulon steindachneri	(Jordan & Gilbert, 1882)	56	99	154	258	1.573.10-5	±	8,818.10-6	2,99	±	0,105	0,968	i	71	29
		Orthopristis ruber	(Cuvier, 1830)	256	54	84	148	1.953.10-5	±	5,317.10-6	2,94	±	0,058	0,978	i	70	30
		Haemulopsis corvinaeformis	(Steindachner, 1868)	1477	46	120	178	8.432.10-6	±	1,177.10-6	3,11	±	0,028	0,973	a+	34	66
	Sparidae	Archosargus rhomboidalis	(Linnaeus, 1758)	46	16	135	191	9.168.10-6	±	5,438.10-6	3,14	±	0,120	0,999	a+	---	100
	Sciaenidae	Ctenosciaena gracilicirrhus	(Metzelaar, 1919)	187	42	107	145	3.765.10-6	±	1,973.10-6	3,26	±	0,104	0,892	a+	59	41
		Cynoscion jamaicensis	(Vaillant & Bocourt, 1883)	109	124	192	269	6.382.10-6	±	6,343.10-6	3,13	±	0,188	0,829	i	14	86
		Menticirrhus americanus	(Linnaeus, 1758)	61	28	234	425	5.671.10-6	±	5,201.10-6	3,13	±	0,156	0,984	i	5	95
		Umbrina coroides	Cuvier, 1830	38	70	111	185	1.871.10-6	±	1,418.10-6	3,38	±	0,145	0,999	a+	100	---
	Gobiidae	Ctenogobius boleosoma	(Jordan & Gilbert, 1882)	145	20	39	55	1.706.10-5	±	1,384.10-5	2,81	±	0,213	0,860	i	---	---
	Kyphosidae	Kyphosus sectatrix	(Linnaeus, 1758)	30	23	237	462	5.829.10-6	±	5,522.10-6	3,20	±	0,156	0,993	a+	---	---
Pleuronectiformes	Paralichthyidae	Citharichthys spilopterus	Günther, 1862	101	40	112	199	2.704.10-6	±	7,936.10-7	3,26	±	0,061	0,969	a+	63	37
		Etropus crossotus	Jordan & Gilbert, 1882	387	30	89	143	2.907.10-6	±	7,864.10-7	3,28	±	0,054	0,759	a+	28	72
		Syacium papillosum	(Linnaeus, 1758)	38	52	112	155	1.104.10-5	±	1,216.10-6	3,01	±	0,216	0,972	i	79	21
Tetraodontiformes	Tetraodontidae	Sphoeroides greeleyi	Gilbert, 1900	90	43	87	174	1.126.10-4	±	5,921.10-5	2,64	±	0,109	0,869	a-	46	54

Isometric growth pattern was detected in 17 species, positive allometry in 16 and negative allometry in 6 species (Figure 2). While the coefficient a is the condition factor varying due to many factors related to the fish biology, physiology and body shape (Braga 1986, Froese 2006), the coefficient b represents mainly the growth pattern usually varying between 2.5 and 3.5 (Froese 2006). In G. ocellatus such upper limit was exceeded, and this was due both to the anguilliform body (Moyle & Cech 2004) and the narrow amplitude of lengths (Froese 2006).

Figure 2
Frequency distribution of b values for 39 species caught in the Araçá Bay, a coastal subtropical ecosystem.

Consulting the FishBase (Froese & Pauly 2015), for Albula vulpes, Trachinotus carolinus, T. falcatus, Archosargus rhomboidalis and Kyphosus sectatrix, these are the first records of LWR in Brazil. In spite of the availability of LWR parameters for the other species (Froese & Pauly 2015), only Muto et al. (2000) studied the ichthyofauna in the same area, but outside the coastal environments. These authors used mm-g and comparisons with other studies in cm-g can be done after the conversion using the equation of Froese (2006). Muto et al. (2000) provided LWR for 57 species based on samples attained from the continental shelf adjacent to Araçá Bay between 1993 and 1997, but only 18 species (Gerreidae, Haemulidae, Sciaenidae, flounders and some others) were the same ones. In comparison to this study, differences in the LWR were found mainly for the Gerreidae family with lower b amounts. Such heterogeneity in the species composition and growth pattern (mainly isometry and positive allometry) ensure that Araçá Bay is a growth ground for the ichthyofauna of the area revealed by the high amounts of b coefficients. Only Ctenogobius boleosoma and Etropus crossotus are resident species; the others go to the Araçá Bay to feed and grow (Vaz-dos-Santos et al. 2015).

In comparison with other LWR studies of the Southwestern Atlantic, it is possible to verify that Araçá Bay is shared by the ichthyofauna from different habitats. The continental shelf is dominated by the demersal sciaenids (Vianna et al. 2004), pelagic clupeiforms and carangids (Vaz-dos-Santos & Rossi-Wongtschowski 2013). In coastal environments (mangroves, rockpools), gerreids, gobiids and Atherinella brasiliensis usually predominate (Macieira & Joyeux 2009, Costa et al. 2014). Differences among LWR of these studies were expected due to different fishing gears, areas and periods, especially when it is considered the space (and time) scale of the present study. In such context, aiming the biomass estimates and ecosystem modelling, the present results are the most suitable: they are from the area itself and the use of nine fishing gears reduces (almost cancelled) selectivity. Data and results are representing properly and along a cycle (year) the different development phases of fishes using the Araçá Bay.

The presence of the young-of-the-year of the Brazilian sardine, Sardinella brasiliensis, in the Araçá Bay is noteworthy. This is the most important fishery resource in Brazil (MPA 2011), spawning along the continental shelf (Matsuura 1998). The displacement to a coastal ecosystem indicates the importance of Araçá Bay to the recruitment of the species.

Acknowledgements

We would like to thank A. C. Z. Amaral and C. L. D. B. Rossi Wongtschowski, coordinators of BIOTA FAPESP Araçá Project (2011/50317-5). We are also grateful to all team members who took part in sampling. Permanent licenses for sampling and transport: 36168 and 40132-1 (SISBIO/ICMBio) and we thank both of the referees and their valuable comments. The first author expresses his gratitude to CNPq due to the research grant 305403/2015-0.

References

• AMARAL, A.C.Z., MIGOTTO, A.E., TURRA, A. & SCHAEFFER-NOVELLI, Y. 2010. Araçá: biodiversity, impacts and threats. Biota Neotrop. 10(1):219-264. http://www.biotaneotropica.org.br/v10n1/en/abstract?inventory+bn01210012010
  » http://www.biotaneotropica.org.br/v10n1/en/abstract?inventory+bn01210012010
• AMARAL, A.C.Z., TURRA, A., CIOTTI, A.M., ROSSI-WONGTSCHOWSKI, C.L.D.B., SCHAEFFER-NOVELLI, T. 2015. Vida na Baía do Araçá: diversidade e importância. Lume, São Paulo.
• BAIGÚN, C.R.M., COLAUTTI, D., LÓPEZ, H.L., VAN DAMME, P.A. & REIS, R.E. 2012. Application of extinction risk and conservation criteria for assessing fish species in the lower La Plata River basin, South America. Aquatic Conserv: Mar. Freshw. Ecosyst. 22:181-197. DOI:10.1002/aqc.2223
  » https://doi.org/10.1002/aqc.2223
• BIOTA FAPESP Araçá 2015. Biodiversidade e funcionamento de um ecossistema costeiro subtropical: subsídios para a gestão integrada. Available at http://www.biota.oka-web.com/ (last accessed 23 March 2015).
  » http://www.biota.oka-web.com/
• BRAGA, F.M.S. 1986. Estudo entre fator de condição e relação peso/comprimento para alguns peixes marinhos. Braz. J. Biol. 46(2):339-346.
• BROWN-PETERSON, N.J., WYANSKI, D.M., SABORIDO-REY, F., MACEWICZ, B.J. & LOWERRE-BARBIERI, S.K. 2011. A standardized terminology for describing reproductive development in fishes. Mar. Coast. Fish. 3(1):52-70. DOI.org/10.1080/19425120.2011.555724
  » org/10.1080/19425120.2011.555724
• CERGOLE, M.C. & DIAS NETO, J. 2011. Plano de gestão para o uso sustentável de sardinha-verdadeira Sardinella brasiliensis no Brasil. Instituto Brasileiro do Meio Ambiente e dos Recursos Naturais Renováveis, Brasília.
• COSTA, M.R., PEREIRA, H.H., NEVES, L.M. & ARAÚJO, F.G. 2014. Length-weight relationships of 23 fish species from Southeastern Brazil. J. Appl. Ichthyol. 30(1):230-232. DOI:10.1111/jai.12275.
  » https://doi.org/10.1111/jai.12275
• ESCHMEYER, W.N. (ed.) 2015. Catalog of fishes: genera, species, references. Available at http://researcharchive.calacademy.org/research/ichthyology/catalog/fishcatmain.asp (last accessed 23 March 2015).
  » http://researcharchive.calacademy.org/research/ichthyology/catalog/fishcatmain.asp
• FROESE, R. & PAULY, D. 2015. FishBase. World Wide Web electronic publication, version (02/2015). Available at http://www.fishbase.org (last accessed 23 March 2015).
  » http://www.fishbase.org
• FROESE, R. 2006. Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations. J. App. Ichthyol. 22(4):241-253. DOI:10.1111/j.1439-0426.2006.00805.x
  » https://doi.org/10.1111/j.1439-0426.2006.00805.x
• FROESE, R., STERN-PIRLOT, A., WINKER, H. & GASCUEL, D. 2008. Size matters: how single-species management can contribute to ecosystem-based fisheries management. Fish. Res. 92(2-3):231-241. DOI:10.1016/j.fishres.2008.01.005
  » https://doi.org/10.1016/j.fishres.2008.01.005
• GASALLA, M.A., VELASCO, G., ROSSI-WONGTSCHOWSKI, C.L.D.B., HAIMOVICI, M. & MADUREIRA, L.S.P. 2007. Modelo de equilíbrio de biomassas do ecossistema marinho da região Sudeste-Sul do Brasil entre 100-1000 m de profundidade. Instituto Oceanográfico - USP, São Paulo.
• HAIMOVICI, M. & VELASCO, G. 2000. Relações comprimento peso de peixes teleósteos marinhos do sul do Brasil com uma avaliação de diferentes métodos de ajuste. Atlântica 22(1):131-140.
• HUXLEY, J.S. 1993. Problems of relative growth. 2 ed. The John Hopkins University Press, Baltimore.
• JOYEUX, J.C., GIARRIZZO, T., MACIEIRA, R.M., SPACH, H.L. & VASKE, T. 2009. Length-weight relationships for Brazilian estuarine fishes along a latitudinal gradient. J. App. Ichthyol. 25(3):350-355. DOI:10.1111/j.1439-0426.2008.01062.x
  » https://doi.org/10.1111/j.1439-0426.2008.01062.x
• LANA, P.C., MARONE, E., LOPES, R.M. & MACHADO, E.C. 2001. The subtropical estuarine complex of Paranaguá Bay, Brazil. In Coastal Marine Ecosystems of Latin America (U. Seeliger, B. Kjerfve, eds). Springer, Berlin, p.131-145. DOI 10.1007/978-3-662-04482-7
  » https://doi.org/10.1007/978-3-662-04482-7
• MACIEIRA, R.M. & JOYEUX, J.C. 2009. Length-weight relationships for rockpool fishes in Brazil. J. App. Ichthyol. 25(3):358-359. DOI:10.1111/j.1439-0426.2008.01118.x
  » https://doi.org/10.1111/j.1439-0426.2008.01118.x
• MATSUURA, Y. 1998. Brazilian sardine (Sardinella brasiliensis) spawning in the southeast Brazilian bight over the period 1976-1993. Rev. Bras. Oceanogr. 46(1):33-43.
• MAURY, O., FAUGERAS, B., SHIN, Y.J., POGGIALE, J.C., ARI, T.B. & MARSAC, F. 2007. Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 1: the model. Prog. Oceanogr. 74(4):479-499. DOI:10.1016/j.pocean.2007.05.002
  » https://doi.org/10.1016/j.pocean.2007.05.002
• MENICONI, M.F.G., SILVA, T.A., FONSECA, M.L., LIMA, S.O.F., LIMA, E.F.A., LAVRADO, H.P. & FIGUEIREDO JUNIOR, A.G. 2012. Baía de Guanabara - Síntese do Conhecimento Ambiental: ambiente e influência antrópica volume 1. PETROBRAS, Rio de Janeiro.
• MOYLE, P.B. & CECH, J.J. 2004. Fishes: an introduction to ichthyology. 5 ed. Prentice Hall, Upper River Saddle.
• MPA, Ministério da Pesca e Aquicultura do Brasil. 2011. Boletim Estatístico da Pesca e Aquicultura. Ministério da Pesca e Aquicultura, Brasília.
• MUTO, E.Y., SOARES, L.S.H. & ROSSI-WONGTSCHOWSKI, C.L.D.B. 2000. Length-weight relationship of marine fish species off São Sebastião System, São Paulo, Southeastern Brazil. NAGA, The ICLARM Quartely. 23(4):27-29.
• NASCIMENTO, M.C., VELASCO, G., OKEY, T.A., CHRISTENSEN, V. & AMARAL, A.C.Z. 2012. Trophic model of the outer continental shelf and upper slope demersal community of the southeastern Brazilian Bight. Sci. Mar. 76(4):763-779. DOI:10.3989/scimar.03359.26a
  » https://doi.org/10.3989/scimar.03359.26a
• PAULY, D. 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators. ICLARM, Manila.
• POPE, J.G., RICE, J.C., DAAN, N., JENNINGS S. & GISLASON H. 2006. Modelling an exploited marine fish community with 15 parameters - results from a simple size-based model. ICES J. Mar. Sci. 63(6):1029-1044. DOI:10.1016/j.icesjms.2006.04.015.
  » https://doi.org/10.1016/j.icesjms.2006.04.015
• RAY, G.C. & MCCORMICK-RAY, J. 2014. Marine conservation: science, policy and management. Wiley-Blackwell, Oxford.
• SILVEIRA, E.L. & VAZ-DOS-SANTOS, A.M. 2015. Length-weight relationships for 22 Neotropical freshwater fishes from a subtropical river basin. J. App. Ichthyol. 31(3):552-554. DOI:10.1111/jai.12699
  » https://doi.org/10.1111/jai.12699
• VAZ-DOS-SANTOS, A.M. & ROSSI-WONGTSCHOWSKI, C.L.D.B. 2013. Length-weight relationships of the ichthyofauna associated with the Brazilian sardine, Sardinella brasiliensis, on the Southeastern Brazilian Bight (22ºS-29ºS) between 2008 and 2010. Biota Neotrop. 13(2):326-330. http://www.biotaneotropica.org.br/v13n2/en/abstract?short-communication+bn01613022013
  » http://www.biotaneotropica.org.br/v13n2/en/abstract?short-communication+bn01613022013
• VAZ-DOS-SANTOS, A.M., ROMAGOSA, E., GRIS, B., PEREIRA JUNIOR, M. R., JUSTINO, A.A. & GIOMBELLI-DA-SILVA, A. 2015. Ecologia populacional da ictiofauna: idade, crescimento e reprodução das principais espécies da baía do Araçá, São Sebastião (SP), Brasil. Relatório de Pesquisa. Universidade Federal do Paraná, Palotina.
• VIANNA, M., COSTA, F.E.S. & FERREIRA, C.N. 2004. Length-weight relationship of fish caught as by-catch by shrimp fishery in the Southeastern Coast of Brazil. Bol. Inst. Pesca 30(1):81-85.
• VIEIRA, S. 2006. Análise de variância. Atlas, São Paulo.
• ZAR, J.H. 2010. Bioestatistical analysis. 5 ed. Pearson, Upper River Saddle.

Data availability

Data citations

FROESE, R. & PAULY, D. 2015. FishBase. World Wide Web electronic publication, version (02/2015). Available at http://www.fishbase.org (last accessed 23 March 2015).

Publication Dates

• Publication in this collection
  2016

History

• Received
  08 Apr 2016
• Accepted
  20 July 2016