ESTIMATION OF GROWTH PARAMETERS OF FIVE FISH SPECIES (ACTINOPTERYGII) CAUGHT IN THE CENTRAL AMAZON

For some tropical fishes, the information on growth parameters is still scarce, and few or no records are available in FishBase. Therefore, the objective of this study was to estimate the growth curves for Brycon amazonicus (Spix et Agassiz, 1829), Piaractus brachypomus (Cuvier, 1818), Prochilodus nigricans Spix et Agassiz, 1829, Semaprochilodus insignis (Jardine, 1841), and Semaprochilodus taeniurus (Valenciennes, 1821), and to build the auximetric plots for each of the families to which these species belong: Characidae, Prochilodontidae, and Serrasalmidae. Samples were obtained from commercial catches landed in the Port of Manaus. Growth parameters were estimated using the Electronic Length Frequency Analysis (ELEFAN) routine of the Length Frequency Distribution Analysis (LFDA) program. Twenty-six sets of growth parameters were thus estimated, and 66 further sets were located in the literature and FishBase. Prochilodontidae and Serrasalmidae showed a strong inverse relation between the variables composing the auximetric plots.


INTRODUCTION
Growth is one of the most critical measurable characteristics of individuals, stocks, and species, and it is fundamental to our understanding of the life histories, demographics, ecosystem dynamics, and sustainability of fisheries (Pardo et al. 2013). Fishes are the primary food source of the Amazon's local inhabitants, with some areas showing the highest consumption rates in the world (with fish consumed six out of every seven days, at a mean rate of 169 kg per person per year) (Isaac et al. 2015). The dynamics of fish stocks may alter due to environmental changes ( Barletta et al. 2010), overfishing, climate change, pollution, deforestation, etc. (Li et al. 2011, Freitas et al. 2013. However, growth parameters of fishes from the central Amazon-key indicators that will enable the assessment of the impact of such processes on fish populations-are still scarce for Brycon amazonicus (Spix et Agassiz, 1829), Piaractus brachypomus (Cuvier, 1818), Prochilodus nigricans Spix et Agassiz, 1829, Semaprochilodus insignis (Jardine, 1841), and Semaprochilodus taeniurus (Valenciennes, 1821). This study aimed to estimate the von Bertalanffy growth parameters for five fish species of significant commercial interest within six rivers in the Amazon region. In addition, the study built auximetric plots of each of the three families to which these species belong (Characidae, Prochilodontidae, and Serrasalmidae).

MATERIAL AND METHODS
The samples were obtained from the catches of commercial fisheries along the Amazon, Japurá, Juruá, Madeira, Negro, and Purus rivers that landed at the Port of Manaus, Brazil (03º08′47′′S, 60º06′35′′W). The sampling protocol was designed to measure the fish length of a total of 300 individuals per month. Thus, 30 individuals per species per night had their fork length (FL, cm) measured (as the caudal fin was often damaged) on 10 randomly selected days within a month-long period. To ensure a 'knife-edge' selection, only those fish captured with 20 mm mesh seine net were used in this analysis (see Batista and Freitas (2003) for technological fishing details). Five out of the 10 species with the highest catches in the database were examined, namely Prochilodus nigricans, Semaprochilodus insignis, Semaprochilodus taeniurus, Brycon amazonicus, and Piaractus brachypomus.
Growth parameters were estimated using the seasonal growth curve proposed by Hoenig and Hanumara (1990). The equation is: where K is the growth coefficient, L ∞ the asymptotic size, t 0 the theoretical age at zero length, C the relative amplitude of seasonal oscillations, and the t s describes the phase of seasonal oscillations. Finally, the Winter Point (WP) (García-Berthou et al. 2012) was determined using the following equation: The ELEFAN routine of the LFDA program (Kirkwood et al. 2001) was used with sets of between two and six years, depending on data availability. A growth curve was fitted using any arbitrary 'seed' input values of L ∞ and K (Pauly and David 1981).

RESULTS
In some years, only juveniles were caught. Thus, the length at first maturity available in the literature, as well as the maximum length found here, were used to ensure that the data used-and, consequently, the estimates foundwere reliable. Thus, we only used years in which data were available for both juveniles and adults. Moreover, we used the age at first maturity available in the literature to evaluate the reliability of the growth curve estimates for each species (Table 1).
The growth parameter estimates are shown in Table 3, and the LFDA growth curves in Figs. 1-7. Additional information used in the estimation of these parameters is available in Table 1.

DISCUSSION
Fish exhibit differences in growth as a result of being subjected to environmental fluctuations (King 2007). Amazonian fish are also subject to the annual flood regime, as well as periodical natural climatic phenomena (Junk 1983, Tomasella et al. 2012, Camacho Guerreiro et al. 2016, Guerreiro 2017. The variations observed in the growth parameters of some of the species sampled appear to accord with the high degree of environmental variation observed in this type of ecosystem. No trend was observed in the auximetric plot of Characidae (Spearman rs test, r s = -0.14, P = 0.60) (Fig.  8A). However, for the Prochilodontidae (Spearman rs test, r s = -0.67, P < 0.001) (Fig. 8B) and Serrasalmidae (Spearman rs test, r s = -0.65, P < 0.001) ( Fig. 8C) families, a significant and inverse relation was found between the growth parameters. Growth parameters were found in the literature for only 10 species out of the 1113 species belonging to the Characidae (Froese and Pauly 2018). Thus, great effort is required to fill this research gap before it will be possible to build an auximetric plot for this family.
Finally, the pattern observed here between the growth parameters of Prochilodontidae and Serrasalmidae was similar to that recorded by Pauly (1998), supporting the reliability of the estimates obtained. In fact, the clusters of points on the auximetric plot seem to reflect similarities between the various species within these families.