Describing animal growth rate using non-linear models allows a detailed evaluation of growth behavior. Four non-linear models were used to fit weight gain and total length data of bullfrog (Lithobates catesbeianus) tadpoles, as follows: Gompertz, Y = A exp (-exp (-b (t-T))); Von Bertalanffy, Y = A (1 -K exp (-B t)) 3 ; Logistic, Y = A (1+ K exp (-B t)) -1 and Brody, Y=A (1 -K exp (-B t)). We used 3,240 tadpoles, with average initial weight 0.044 g and average total length 12.79 mm, stage 25 Gosner. The measurements were conducted every ten days on 10% of the animals in every tank. The criteria used to select the model that best described the growth curve were: Residual Mean Square (RMS); determination coefficient (R²); residual graphical analysis; residual mean absolute deviation (MAD). Brody mathematical model was not a good fit for weight gain and total length, while Von Bertalanffy model underestimated tadpole initial weight, thus showing the difficulty of mathematical models to describe biological data at this growth stage. However, the Gompertz and Logistic models were considered to be an adequate fitting to describe growth rate and total length of bullfrog tadpoles in captivity.Index terms: Frog farm, growth curve, Lithobates catesbeianus. RESUMODescrever o crescimento animal em modelos não lineares permite uma avaliação criteriosa desse comportamento, além de revelar informações importantes da resposta a um determinado tratamento. Neste estudo objetivou-se avaliar o ajuste do crescimento em peso e comprimento total de girinos de rã-touro (Lithobates catesbeianus) em quatro modelos não lineares: Gompertz, Y = A exp (-exp (-b (t-T))); Von Bertalanffy, Y = A (1 -K exp (-B t))3 ; Logístico, Y = A (1+ K exp (-B t)) -1 e Brody, Y=A (1 -K exp (-B t)). Foram utilizados 3.240 girinos, com peso médio inicial de 0,044g e comprimento total médio de 12,79 mm, no estágio 25 de Gosner. Os critérios utilizados para selecionar o modelo que melhor descreveu a curva de crescimento foram: o quadrado médio do resíduo (QMR); o coeficiente de determinação (R 2 ); análise gráfica dos resíduos; desvio médio absoluto dos resíduos (DMA). Os dados apresentados para peso e comprimento total não se ajustaram ao modelo de Brody, assim como o modelo de Von Bertalanffy subestimou os pesos iniciais, mostrando dificuldade de interpretação biológica, indicando que esses modelos não são apropriados para essa espécie na fase aquática. Os modelos de Gompertz e Logístico são adequados para descrever o crescimento e comprimento de girinos de rã-touro em cativeiro.Termos para indexação: Ranicultura, curva de crescimento, Lithobates catesbeianus.

Selenium (Se) is an essential nutrient for antioxidant defenses in fish because of its role in preventing immunosuppression caused by oxidative stress. In this study it was demonstrated the relation between the oxidative stress and immune status after a long Se supplementation period, as a result of the evaluation of immunological, hematological and antioxidant responses, as well as growth performance of pacu fed diets supplemented with different concentrations of organic selenium (0, 0.3, 0.6, 0.9, and 1.8 mg Se-yeast/kg, but the final analyzed selenium concentrations were 0.72, 0.94, 1.15, 1.57 and 2.51 mg/kg, respectively) for 65 days. Dietary Se supplementation at 1.15 mg Se-yeast/kg (analyzed value) restored the production of antioxidant enzymes (glutathione peroxidase (GPx) and glutathione S-transferase (GST)), and consequently allowed the increased of some immunological parameters (leukocyte respiratory burst activity and lysozyme activity), hematological parameters (red blood cell count (RBC), hematocrit (HTC), mean corpuscular volume (MCV), and white blood cell count (WBC)). Se supplementation in pacu diets at 1.15 mg Se-yeast/kg for 65 days improved immune response and antioxidant defenses, suggesting that oxidative stress impairs immune system response to prevent excessive reactive oxygen species in cells and indicating the occurrence of a physiological trade-off between immune and antioxidant systems. Higher Se levels, such as 1.57 mg Se-yeast/kg increased the leukocyte respiratory burst activity, the WBC and thrombocyte counts, the RBC and HTC, and the GST and GPx enzymes. However, 2.51 mg Se-yeast/kg decreased the lysozyme levels, the WBC and thrombocyte counts, the RBC, HTC and MCV, and the GST and GPx enzymes. Those findings are important to future studies because showed the negative effect of oxidative stress on immunity, and may help to prevent any inhibition of the expected immune response after immunomodulators administration and vaccination. Also it was possible to meet the dietary selenium requirement of pacu, that was estimated to be 1.56 mg/kg.

For the production and commercialization of ornamental fish species, it is indispensable to collect biometric data that facilitate the selection of animals for trade and genetic improvement of the stock. However, during the handling process, fish receive more stress if proper anesthetics are not used. Thus, application of appropriate anesthetics is an important tool for minimizing stress in animals. The objective of this study was to determine the effective concentrations of benzocaine, eugenol, and menthol for achieving anesthesia in Freshwater Angelfish Pterophyllum scalare and to develop induction and recovery response curves for different concentrations of these anesthetics. In total, 75 fish were exposed to five concentrations of the three anesthetics in a completely randomized design: benzocaine at 60, 85, 110, 135, and 160 mg/L; eugenol at 40, 80, 120, 160, and 200 mg/L; and menthol at 50, 75, 150, 200, and 250 mg/L. Each concentration (5 fish/concentration) consisted of five replicates, with each replicate represented by a single fish. The results indicated that the tested substances met the criteria of anesthetic efficiency. The effective concentrations of benzocaine, eugenol, and menthol for the anesthesia of Freshwater Angelfish were identified as 89.25, 90.6, and 92.1 mg/L, respectively.

In the present study, juvenile (live body weight, 54.3 ± 8.2 g), preadult (live body weight, 822.5 ± 33.9 g), and adult (live body weight, 1,562.8 ± 41.8 g) pacu, Piaractus mesopotamicus, were used to estimate their dietary essential amino acid (EAA) requirements using the whole‐body amino acid (AA) pattern. The results showed that whole‐body moisture, crude protein, total lipid, and ash contents expressed on a wet weight basis (%) were significantly different among the studied growth phases. No significant differences were observed in the dietary EAA requirements estimated for the three growth phases of pacu. These dietary EAA requirements were found to be different than those previously estimated for the same fish through its muscle AA pattern. Based on whole‐body EAA to total EAA ratios {A/E ratios; [(each EAA/total EAA) × 1,000]}, EAA requirements were estimated to be histidine (0.42%), arginine (1.36%), threonine (0.82%), valine (0.90%), methionine (0.45%), isoleucine (0.83%), leucine (1.29%), phenylalanine (0.74%), lysine (1.64%), and tryptophan (0.14%) for pacu. These estimated requirements may serve as a reference line in the formulation of practical and experimental diets until dose–response‐based optimum EAA requirements are available for pacu.

Knowledge of the growth of animals is important so that zootechnical activity can be more accurate and sustainable. The objective of this study was to describe the live weight, development of liver tissue and fat body, leg growth, and cumulative food intake of bullfrogs during the fattening phase using nonlinear models. A total of 2,375 bullfrog froglets with an initial weight of 7.03 ± 0.16 g were housed in five fattening pens (12 m 2 ). Ten samplings were performed at intervals of 14 days to obtain the variables studied. These data were used to estimate the parameters of Gompertz and logistic models as a function of time. The estimated values of weight (W m ) and food intake (FI m ) at maturity and time when the growth rate is maximum (t*) were closer to expected values when the logistic model was used. The W m values for live weight and liver, adipose and leg weights and the FI m value for food intake were 343.7, 15.7, 19.6, 96.03 and 369.3 g, respectively, with t* at 109, 98, 105, 109 and 107 days. Therefore, the logistic model was the best model to estimate the growth and food intake of bullfrogs during the fattening phase.Index terms: Frog farming, growth curves, growth rate, logistic model. RESUMOO conhecimento do crescimento dos animais é importante para a atividade zootécnica ser mais precisa e sustentável. O objetivo do estudo foi descrever o crescimento em peso vivo, dos tecidos hepático e adiposo, da coxa e o consumo alimentar acumulado da rã-touro na engorda, através de ajuste de modelos não lineares. Foram utilizados 2.375 imagos de rã-touro com peso inicial de 7,03±0,16g, os quais foram alojados em cinco baias de engorda com 12 m 2 . Foram realizadas 10 amostragens, a cada 14 dias, para obtenção das variáveis estudadas. Os dados amostrados foram utilizados para estimar os parâmetros dos modelos de Gompertz e Logístico em função do tempo. Os valores estimados de peso (Pm) e consumo à maturidade (Cm) e tempo em que a taxa de crescimento é máxima (t*) dos parâmetros avaliados foram mais próximos do esperado no modelo Logístico. Os valores de Pm para peso vivo, tecido hepático e adiposo, coxas e Cm para consumo alimentar foram 343,7 g; 15,7g; 19.6g; 96,03 e 369,3g, respectivamente, com t* aos 109, 98, 105, 109 e 107 dias, respectivamente. Portanto, o modelo Logístico foi a melhor ferramenta para estimar o crescimento e o consumo alimentar da rã-touro na fase de engorda.Termos para indexação: Ranicultura, curvas de crescimento, taxa de crescimento, logístico.

Feed management needs to be improved in frog farming to reduce the indirect effects of inadequate feeding and, consequently, to increase growth rates and nutrient deposition, obtaining better quality animals. The objective of this study was to establish morphometric growth curves for bullfrog tadpoles (Lithobates catesbeianus) and to determine nutrient deposition in the carcass. A total of 6,480 bullfrogs (Gosner stage 25) received an experimental diet (26.23% digestible protein and 32.68% crude protein) and a commercial diet (37.92% crude protein) ad libitum. A Gompertz model was used to describe the growth curve. Tadpoles fed the experimental diet presented higher final protein deposition. In addition, the sigmoidal curve was much more homogenous, indicating a more constant daily protein deposition rate. The Gompertz model provided an excellent fit of the data to describe the morphometric growth curve and carcass nutrient deposition of bullfrog tadpoles, showing that animals fed the experimental diet presented a better growth rate and nutrient deposition.

Describing animal growth through the nonlinear models allows a detailed evaluation of their behavior, besides revealing important information of the response to a particular treatment. In this chapter, the parameters of mathematical models (Gompertz, Von Bertalanffy, Logistic and Brody) for live weight, feed and protein intakes, total and standard lengths and nutrient deposition are described systematically and comprehensively. Also the relative growth and allometric coefficients of body components in relation to body weight of fish and amphibians are described, explaining better the use of the allometric equation and classifying the growth of the body components.

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