ABSTRACT
Relationship between length and weight (LWR) is used to describe aspects concerning the life cycle of fish, but does not considers possible changes during the lifetime mainly due to the sexual maturation. Thus, this study aims to identify the size at first maturity of Auchenipterichthys longimanus (Siluriformes: Auchenipteridae) and infer if the reproductive engagement could change growth pattern, concerning the LWR. Estimates of the size at first maturity (L _{50} ) were made by visual identification of gonadal development and through the gonadosomatic index (G _{SI} ). L _{50} was estimated as 12.5 cm for males and 13.0 cm for females when applied visual identification of gonads development. L _{50} estimates increased to 13.05 cm for males and 13.7 cm for females when estimated from G _{SI} values. LWR was adjusted by using a regular power function and through the polyphasic growth model, with proportionality and allometric coefficients changing in a two phases. The results indicate differences in the growth pattern concerning males and females, as well as polyphasic growth. The change in the growth pattern of the polyphasic LWR was estimated at 11.42 cm for males and 12.53 cm for females, suggesting that changes in the growth pattern can signout the attainment maturity in this catfish.
Keywords:
Amazonia; Auchenipteridae; Fish reproduction; Growth pattern; Sexual maturity
RESUMO
O estudo da relação entre peso e comprimento é usado para investigar muitos aspectos do ciclo de vida dos peixes, mas não considera que o padrão de crescimento pode mudar durante o tempo vida, principalmente devido à maturação sexual. Desta forma, este estudo objetivou identificar o tamanho de primeira maturação do bagre Auchenipterichthys longimanus (Siluriformes: Auchenipteridae) e testar se início do engajamento reprodutivo pode ser responsável por mudanças no padrão de crescimento da espécie, concernindo à relação peso/comprimento. Estimativas de tamanho de primeira maturação sexual (L50) foram realizadas por meio da identificação visual dos estágios de maturação e pelos valores do Índice Gonadossomático (IGS). O L50 foi estimado em 12,5 cm para machos e 13,0 cm para fêmeas quando aplicados a identificação visual dos estágios de maturação. A estimativa do L50 aumentou para 13,05 cm para machos e 13,7 cm para fêmeas quando aplicados os valores de IGS. A relação peso/comprimento foi ajustada utilizando uma função potência e pelo modelo de crescimento polifásico, com coeficientes de proporcionalidade e alométrico diferentes para duas fases. Os resultados indicam diferenças no padrão de crescimento de machos e fêmeas, além de um crescimento polifásico para ambos os sexos. A mudança no padrão de crescimento foi estimada em 11,42 cm para machos e 12,53 cm para fêmeas, sugerindo que essas mudanças podem estar associadas ao início da vida reprodutiva desse bagre.
Introduction
The relationship between body length and weight is used since the late 19th century to depict many aspects concerning the life cycle of fish (see Le Cren, 1951Le Cren, E. D. 1951. The lengthweight relationship and seasonal cycle in gonad weight and condition in the perch (Perca fluviatilis ). Journal of Animal Ecology, 20: 201219.; Froese, 2006Froese, R. 2006. Cube law, condition factor and weightlength relationships: history, metaanalysis and recommendations. Journal of Applied Ichthyology, 22: 241253.), and is described following the equation proposed by Huxley (1924Huxley, J. S. 1924. Constant differential growthratios and their significance. Nature, 114: 895896.), ^{W=a*Lb} . This model considers that the body proportions increase according to a constant, b , defined as the coefficient of allometry. As usually applied, this parameter is kept constant during the animal's entire life cycle, without taking account any possible change in the growth pattern due to ontogeny (Swain & Foote, 1999Swain, D. P. & C. J. Foote. 1999. Stocks and chameleons: the use of phenotypic variation in stock identification. Fisheries Research, 43: 113128.).
Huxley (1924Huxley, J. S. 1924. Constant differential growthratios and their significance. Nature, 114: 895896.) himself identified this potential problem, which was subsequently referred to as polyphasic allometry by Strauss (1993Strauss, R. E. 1993. The study of allometry since Huxley. Pp. 4775. In: Huxley, J. S. (Ed.). Problems of relative growth. Baltimore, The Johns Hopkins University Press.). Based on this approach, Bervian et al. (2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.) proposed a mathematical model that considers possible variation in individual growth patterns over time. This model divides the growth process into stanzas, or growth phases, each one with unique values of a and b , depending on specific ontogenetic and environmental drivers.
Using this model, Bervian et al. (2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.) identified a change in the growth pattern related to the attainment of sexual maturity for Micropogonias furnieri (Desmarest, 1823) (Perciformes). This same approach was applied to determine if the length/weight relationship of Characid fish species were also signifying reproductive engagement through a change in the growth pattern (Fontoura et al., 2010Fontoura, N. F., A. S. Jesus, G. G. Larre & J. R. Porto. 2010. Can length/weight relationship predict size at first maturity? A case study with two species of Characidae. Neotropical Ichthyology, 8: 835840.). Although with no direct estimated size at first sexual maturity, the later authors identified that the middle point between two distinct growth phases (stanzas) were similar to published values of size at first maturity, or at least, to size at sexual maturity estimated by the general model proposed by Froese & Binohlan (2000Froese, R. & C. Binohlan. 2000. Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data. Journal of Fish Biology, 56: 758773. ).
Considering that fishes can change its growth pattern during the lifetime, and that many authors indicate this could signout the beginning of the reproduction engagement (Bervian et al. 2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.; Fontoura et al., 2010Fontoura, N. F., A. S. Jesus, G. G. Larre & J. R. Porto. 2010. Can length/weight relationship predict size at first maturity? A case study with two species of Characidae. Neotropical Ichthyology, 8: 835840.), the aim of the present work is to establish the length/weight relationship for a siluriform fish species in an attempt to verify possible changes in growth pattern and its relation to the size of the first gonadal maturation. The change in the coefficient of allometry was compared with two distinct models for the estimation of the size at first sexual maturity: (1) classification of developmental stages of the gonads and (2) values of the gonadosomatic index. The species used as model was Auchenipterichthys longimanus (Günther, 1864), a Neotropical endemic catfish belonging to the family Auchenipteridae, with wide distribution in the Amazon and Orinoco basins (Ferraris et al. , 2005Ferraris Jr., C. J., R. P. Vari & S.J. Raredon. 2005. Catfishes of the genus Auchenipterichthys (Osteichthyes: Siluriformes: Auchenipteridae). Neotropical Ichthyology, 3: 89106.).
Material and Methods
Data collection and processing. Samples of Auchenipterichthys longimanus were collected every two months between July 2008 and July 2009 in rivers of the Caxiuanã National Forest (1º45'27.5"S, 51º27'33.2"W), a protected area located in eastern Amazonia, Brazil (Fig. 1).
Sampling area in the National Forest of Caxiuanã, Pará State, showing the rivers where the fish were collected; Curuá River  Ferreira Penna Research Station (ECFPn), Caxiuanã River; Puraquequara River and Caquajó River. A single point on the map may represent more than one colleting site.
Specimens were collected using 100 m gillnets with a height of 1.5 m, and mesh sizes between 3 cm and 6 cm opposites knots. The nets were set for six hours per day at locations selected with the help of a local fisherman. Once captured, the specimens of A. longimanus were measured (total length, to nearest 0.1 cm), weighed (body weight, to nearest 0.1g) and eviscerated for gonadal removal, which were also weighed (to nearest 0.001g).
Sexual maturity was visually classified by gonad examination, following Vazzoler (1981Vazzoler, A. E. A. M. 1981. Manual de métodos para estudos biológicos de populações de peixes: reprodução e crescimento. Brasília, CNPq, Programa Nacional de Zoologia, 108p.): stage I (immature); gonads of reduced size, translucent, located adjacent to the vertebral column; stage II (maturing); gonads occupying a third of the abdominal cavity with welldeveloped capillary network; stage III (mature); gonads turgid, occupying the majority of the abdominal cavity (in the females, the oocytes are visible to the naked eye, while in the males, the testes are whitish); and stage IV (at rest or empty); gonad completely flaccid with a hemorrhagic aspect.
Voucher specimens are deposited in the ichthyological collection of the Emílio Goeldi Museum (MPEG) in Belém, Pará, registered under the numbers MPEG 1525715259, MPEG 1526015264, MPEG 1543215442, MPEG 1549815507, MPEG 1554415555, MPEG 1584415860, and MPEG 1622116231.
Data analyses
The analyses consisted in three different approaches and were made for each sex: (1) the establishment of the length/weight relationship and (2) the size at first sexual maturity using two distinct models: (A) visual identification of gonads development (L_{50} Maturity Scale) and (B) values of the gonadosomatic index (G _{SI}  the weight of the gonads as a percentage of the total weight of the fish; L_{50} G_{SI}%).
The length/weight relationship for A. longimanus following the Huxley's original allometric equation (^{y=a.xb} ) was performed using the Solver routine of the Microsoft Office Excel^{(r)}2007 software (Newton search algorithm). Considering the heterocedasticity of the residual pattern, the least squares of proportional residues ([observedpredicted]/predicted) were applied as Loss function. In order to identify sex differences concerning growth pattern, the function was initially adjusted to merged sex, comparing males and females residuals with t test (5% of significance), following a methodological approach proposed by Fontoura & Conter (2008Fontoura, N. F. & M. R. Conter. 2008. Description of a new subspecies of the crayfish Parastacus brasiliensis (Von Martens, 1869) from São Francisco de Paula, RS, Brazil (Decapoda, Parastacidae). Zootaxa, 1849: 2834.) to compare morphometric measurements.
The existence of nonrandom patterns in the residuals of y (weight) in relation to x (length) was evaluated through linear/polynomial regressions and F tests for regression significance (Zar, 2009Zar, J. H. 2009. Biostatistical Analysis. New Jersey, PrenticeHall, 960p.). Once any anomaly in residual distribution was identified, the application of the polyphasic adjustment proposed by Bervian et al. (2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.) was performed.
The polyphasic model is a modified power equation, using a logistic function for the parameters a and b of Huxley (1924Huxley, J. S. 1924. Constant differential growthratios and their significance. Nature, 114: 895896.): ^{y=f(a).x f(b)} , where f(a)=a _{1}+(a_{2}a_{1} ^{)/(1+eRsc(a).(xLsc))} , and f(b) = b _{1}+(b_{2}b_{1} ^{)/(1+eRsc(b).(xLsc))} , and a _{1} and b _{1} are the coefficients of proportionality and allometry determined in the first stanza, and a _{2} and b _{2} are the same coefficients determined in the second stanza, R _{sc}(a/b) is the rate of change of the coefficients between stanzas 1 and 2, and L _{sc} is the length at the stanza changing point.
The polyphasic function was adjusted using the Solver routine available in the Microsoft Excel(r)2007 program (loss function using least squares of proportional residues, Newton search algorithm). Considering the lack of a clear point of change based on the residual distribution, the full data set was divided into two subsamples. The first subsample comprised all sizes from the smaller captured individual to the half of length range, and a second subsample comprising all the captured individuals from the half of length range to the larger individual. Then, a preliminary weight/length relationship was adjusted independently for each data subsample. The coefficients of allometry and proportionality of each of these preliminary stanzas were then used as seed values for the adjustment of the complete function. In this case, in the absence of known biological data, the rate of change R _{sc}(a/b) was assigned with an initial value of 1.0, while the stanza changing length (L _{sc} ) was defined as 12 cm, after a preliminary visual analysis of the residual pattern for females. The coefficient of determination was calculated as the ratio between the sum of the squares of the residuals and the total sum of squares (Zar, 2009Zar, J. H. 2009. Biostatistical Analysis. New Jersey, PrenticeHall, 960p.). The P values were obtained by testing the significance of the coefficient of determination, using the F statistic, with a significance level of 5% (Zar, 2009Zar, J. H. 2009. Biostatistical Analysis. New Jersey, PrenticeHall, 960p.).
For both estimation of size at first sexual maturity (L_{50} Maturity Scale or L_{50} GSI%) the individuals were binarized as nonreproductive or reproductive. In the L_{50} Maturity Scale specimens in gonadal development stages II, III, and IV were assigned as reproductive. The other method, the G _{SI} values were transformed into a percentage of the maximum value recorded for the species. As proposed by Fontoura et al. (2009Fontoura, N. F ., A. S. Braun & P. C. C. Milani. 2009. Estimating size at first maturity (L 50 ) from Gonadossomatic Index (G SI ) data. Neotropical Ichthyology, 7: 217222.), all individuals with G _{SI} values equal to or greater than 10% of the maximum recorded value for A. longimanus were considered as engaged in the reproductive process.
For both methods the following equation was applied: ^{P=A*(1+er.(LtL50))1} ; where P = the proportion of reproductive/adult individuals for each size class; A = the asymptote of the curve; r = rate of change between the nonreproductive and the reproductive phase; L _{t} = total length (cm), and L _{50} = size at fist sexual maturity, the estimated size (cm) at which 50% of the individuals have reached maturity. In the approach based on the scale of maturity, A = 1.0. For these methods, the equation parameters were estimated with the data set organized in 0.5 cm length classes by using nonlinear functions in the SPSS^{(r)} 17.0 software package (LevenbergMarquardt algorithm).
Results
A total of 564 specimens of A. longimanus (235 males and 329 females) were analyzed. Males were slightly smaller and lighter than females (p < 0.001 for both total length and body weight). Mean total length for males was 13.2±2.05 cm (min = 7.3 cm; max = 18.8 cm), while in females, it was 13.9± 2.02 cm (min = 8.5 cm; max = 19.1 cm). Mean weight for males (34.3±15.8 g; min = 5.0 g; max = 91.0 g) was also lower than that for females (42.7±18.5 g; min = 7.0 g; max = 110.0 g).
By comparing residuals of the combined length/weight relationship, a clear difference among males and females was identified (p < 0.001). The adjustment of the length/weight relationship for males using the single phase Huxley model (Fig. 2a) resulted in a nonrandom residual distribution (Fig. 2c). The nonrandomness of this arrangement was tested by using a linear regression of the residuals as a function of total length (x ), which resulted in significant angular coefficient (p < 0.001). For males the singlephase model of the length/weight relationship was inadequate (Fig. 2b; Table 1), and the Bervian et al. (2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.) polyphasic model was applied, which resulted in no residual trend (Fig. 2d; p = 0.999). The stanza changing length (L _{sc} ) was estimated as 11.4 cm. Individuals below this size presented a negatively allometric growth pattern (b = 2.88), while those above this size were characterized by positive allometry (b = 3.18).
Length/weight relationship of male Auchenipterichthys longimanus. A and C represent Huxley regular length/weight relationship and its distribution of proportional residuals. B and D represent polyphasic length/weight relationship its and distribution of proportional residuals.
Parameters obtained for the length/weight relationship for Auchenipterichthys longimanu s by the adjustments to the singlephase and polyphasic models.
For females, residuals derived from the singlephase length/weight relationship presented a more complex behavior, being described by a secondorder polynomial regression (Fig. 3c; p = 0.038). After a polyphasic adjustment (Fig. 3b; Table 1), a random distribution of the residuals was obtained (Fig. 3d), for which a linear regression of the residuals indicated no trend (p = 0.672). The stanza changing length (L _{sc} ) was estimated as 12.5 cm, below which individuals presented a positive allometric growth pattern (b = 3.22), whereas larger individuals are characterized by negative allometry (b = 2.95).
Length/weight relationship of female Auchenipterichthys longimanus. A and C represent Huxley regular length/weight relationship and its distribution of proportional residuals. B and D represent polyphasic length/weight relationship its and distribution of proportional residuals.
Males reached sexual maturity at a smaller size than females (Fig. 4; Table 2). When L _{50} was estimated by using relative frequency of reproductive animals identified through testes or ovarian morphology, the values was 12.5 cm for males (R² = 0.89; p = 0.02) and 13.0 cm for females (R² = 0.97; p = 0.004). By using the G _{SI} method proposed by Fontoura et al. (2009Fontoura, N. F ., A. S. Braun & P. C. C. Milani. 2009. Estimating size at first maturity (L 50 ) from Gonadossomatic Index (G SI ) data. Neotropical Ichthyology, 7: 217222.), L _{50} was estimated as 13.1 cm for males (R² = 0.95; p = 0.003) and 13.7 cm for females (R² = 0.95; p = 0.002). For males, values of L _{50} and the stanza changing length (L _{sc} ) were not different taking into account the 95% confidence interval (Table 2), although this was not the case for females, with estimates of L _{sc} 0.5 to 1.0 cm below the estimates of L _{50} .
Frequency of mature individuals as a function of the total length. Female sexual maturity identified by visual inspection of ovarian (A) and G _{SI} values (B). Male sexual maturity identified by visual inspection of testes (C) and G _{SI} values (D).
Parameters obtained for the estimate of size at first sexual maturity in Auchenipterichthys longimanu s using the maturity scale and gonadosomatic index (G_{SI}) approaches.
Discussion
Huxley's allometric equation (^{y=a.xb} ) is widely used in studies of animal growth (Froese, 2006Froese, R. 2006. Cube law, condition factor and weightlength relationships: history, metaanalysis and recommendations. Journal of Applied Ichthyology, 22: 241253.; Freitas et al., 2015Freitas, T. M. S., B. S. Prudente, V. A. Oliveira, M. N. C. Oliveira, E. G. Prata, H. Leão, & L. F. A. Montag. 2015. Influence of the flood pulse on the reproduction of Tocantinsia piresi (Miranda Ribeiro) and Auchenipterus nuchalis (Spix & Agassiz) (Auchenipteridae) of the middle Xingu River, Brazil. Brazilian Journal of Biology, 75: 158167.), but presents clear constrains to describe the length/weight relationship as it assumes constant descriptive parameters during the entire ontogenetic development (Swain & Foote, 1999Swain, D. P. & C. J. Foote. 1999. Stocks and chameleons: the use of phenotypic variation in stock identification. Fisheries Research, 43: 113128.). Once identified this problem, Bervian et al. (2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.) developed a statistical model that considered possible changes in the growth pattern over time.
In the catfish A. longimanus, the change in the growth pattern identified as the stanza changing length (L _{sc} ) was close to the estimated onset of reproductive activity (L _{50} ), which occurs in males at a body length of around 11.512.0 cm and in females at approximately 13.013.8 cm. This transition may be due to a shift in the pattern of individual energy investment reflected in the length/weight relationship.
For males A. longimanus, a shift from a negative allometry (b = 2.88) to a positively allometric coefficient (b = 3.18) suggests that energy acquired as immature juveniles is invested mainly in length body growth. This may reflect the need to growup faster in order to increase a competitive advantage in relation to other males in terms of female access. Once males have reached a minimum size for reproduction, the second stanza begins, in which energy is carriedout to weight growth and accumulation of fatty reserves.
The opposite pattern was observed in the females. In the first stanza, prior to the onset of reproduction, the females invest energy to weight increase (positive allometry: b = 3.22), wears once the reproductive engagement is achieved, this pattern is modified by the loss of body mass through spawning (negative allometry: b = 2.95). A similar pattern was recorded in Parauchenipterus striatus by Araújo et al. (2000Araújo, F. G., S. Duarte, R. S. Goldberg & I. Fichberg. 2000. Ciclo reprodutivo de Parauchenipterus striatulus (Pisces  Auchenipteridae) na represa de Ribeirão das Lajes  RJ. Arquivo Brasileiro de Medicina Veterinária e Zootecnia, 52: 276284.), in which females were heavier than males up to the 15 cm, but with an inverted trend above this body length. For Parauchenipterus galeatus , in contrast, Andrian & Barbieri (1992Andrian, I. F. & G. Barbieri. 1992. Relação peso total/comprimento total e fator de condição do cangati, Parauchenipterus galeatus Linnaeus, 1766 (Siluriformes, Auchenipteridae) da região do reservatório de Itaipú, PR. Revista Unimar, 14: 177191.) recorded just the opposite, suggesting no standard pattern for Auchenipteridae and the need of additional investigation.
The different approaches to the assessment of the minimum size at first maturity (L _{50} ) in males of A. longimanus , including the stanza changing length (L _{sc} ) of the polyphasic growth model, presented equal statistical results. However, for females these methods produced divergent results. Though, in general, in all three methods females matured at larger sizes than males, a pattern found for most teleosts (Helfman et al., 1997Helfman, G. S., B. B. Collette & D. E. Facey. 1997. The diversity of fishes. Oxford, Blackwell Science, 544p.). This study also corroborate the methodological approach that estimate the size at first sexual maturity from G _{SI} values, as proposed by Fontoura et al. (2009Fontoura, N. F ., A. S. Braun & P. C. C. Milani. 2009. Estimating size at first maturity (L 50 ) from Gonadossomatic Index (G SI ) data. Neotropical Ichthyology, 7: 217222.). However, the approach appears to be conservative, given that it provided slightly higher estimates of L _{50} in comparison with the usual methods.
Concluding, the shift in the growth pattern of the siluriform A. longimanus , as revealed by the stanza changing length (L _{sc} ), appears to be an useful marker of reproductive phase, as already described for a perciform species (Bervian et al., 2006Bervian, G., N. F. Fontoura & M. Haimovici. 2006. Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri (Actinopterygii, Sciaenidae). Journal of Fish Biology, 68: 196208.) and characids (Fontoura et al., 2010Fontoura, N. F., A. S. Jesus, G. G. Larre & J. R. Porto. 2010. Can length/weight relationship predict size at first maturity? A case study with two species of Characidae. Neotropical Ichthyology, 8: 835840.). However, as the L _{sc} values were lower than those estimated for L _{50} , the shift in the growth rate may represent a process of adjustment of physiological parameters for the incoming sexual maturation. Also, considering the large set of available information concerning length/weight relationship of fish (OlivaPaterna et al., 2009OlivaPaterna, F. J., M. Torralva & E. D. Carvalho. 2009. Lengthweight relationships for 20 species collected in the Jurumirim reservoir (Paranapanema Basin, Brazil). Journal of Applied Ichthyology, 25: 360361. ; Joyeux et al., 2009Joyeux, J. C., T. Giarrizzo, R. M. Macieira, H. L. Spach & T. Vaske Jr. 2009. Lengthweight relationships for brazilian estuarine fishes along a latitudinal gradient. Journal of Applied Ichthyology, 25: 350355. ; Freire et al., 2009Freire, K. M. F., G. R. A. Rocha & I. L. Souza. 2009. Lengthweight relationships for fishes caught by shrimp trawl in southern Bahia, Brazil. Journal of Applied Ichthyology, 25: 356357. ), estimates of the stanza changing length of the polyphasic growth model may be used as an additional method for signalizing size at first maturity when no other information is available.
Acknowledgements
We are grateful to Benedito Brazão and Renato Calisto for the field assistance. We also thanks the Fundação O Boticário de Proteção à Natureza (process nº 0799/20082), the Programa de Pesquisa em Biodiversidade (PPBio/Caxiuanã) and CNPq for financial support. We also thank CAPES, for its financial support through the Programa Nacional de Cooperação Acadêmica (PROCAD/UFPA; process nº 23038.042984/200830) and the Estação Científica Ferreira Penna (ECFPn/MPEG) for logistical support.
References
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Publication Dates

Publication in this collection
2016
History

Received
21 Sept 2015 
Accepted
24 Aug 2016