Use of mathematical models in the study of bodily growth in GIFT strain Nile tilapia

Abstract

-The objective of this study was to evaluate the accuracy of five mathematical models (Gompertz, Logistic, Linear Hyperbolic, Quadratic and Quadratic Logarithmic) to describe the growth curve of GIFT strain Nile tilapia, Oreochromis niloticus, and to characterize the growth trajectory of body parts. To do this, 1,000 fingerlings, with an initial weight of 2.4 g were placed into 20 brick tanks of 2 m 3 each, at a density of 25 fish m -3, for 180 days. The animals were fed daily, using the protein levels and number of meals appropriate to each stage. Every two weeks 20 fish were randomly sampled, submitted to a fasting period of 48 h and then slaughtered by thermal shock, in order to determine the weight of the whole fish, the skin without scales, skinless fillets, heart, liver, gills and gastrointestinal tract. The Gompertz and Logistic models presented the best fit to the growth curve for live weight, fillet and skin, however the Logistic model underestimated the asymptotic weights. Therefore, to describe the growth curve in GIFT strain Nile tilapia, the Gompertz model is suggested. According to the parameters estimated by the Gompertz model, Nile tilapia reach the age for maximum growth of the fillet and skin before that of body weight. Among the organs studied, growth of the gastrointestinal tract and gills takes place earlier than that of the heart and liver.Key words: Oreochromis niloticus. Growth curve. Gompertz. Growth rate.RESUMO -Objetivou-se com o presente estudo avaliar a acurácia de cinco modelos matemáticos (Gompertz, Logístico, Linear Hiperbólico, Quadrático e Quadrático Logarítmico) para descrever a curva de crescimento de tilápia nilótica Oreochromis niloticus da linhagem GIFT e, realizar a caracterização da trajetória do crescimento das partes corporais. Para tal, 1.000 alevinos com peso inicial de 2,4 g foram estocados em 20 tanques de alvenaria de 2 m 3 numa densidade de 25 peixes m -3 , por um período de 180 dias. Os animais foram alimentados diariamente, utilizando níveis de proteína e número de refeições diárias de acordo com cada fase. Quinzenalmente, foram amostrados aleatoriamente 20 peixes, submetidos a um jejum de 48 h e abatidos por choque térmico, para determinação dos pesos do peixe inteiro, peles sem escamas, filés sem pele, coração, fígado, brânquias e trato gastrointestinal. Os modelos Gompertz e Logístico foram os que mais se adequaram ao ajuste da curva de crescimento do peso vivo, do filé e da pele, todavia, o Logístico subestimou os pesos assintóticos. Desta forma, sugere-se o Gompertz para descrever a curva de crescimento de tilápia nilótica da linhagem GIFT. De acordo com os parâmetros estimados pelo modelo Gompertz, a tilápia nilótica atinge a idade de máximo crescimento do filé e pele antes da idade do peso vivo. Dentre os órgãos estudados, o crescimento do trato gastrointestinal e brânquias é mais precoce do que o do coração e fígado. Palavras-chave:Oreochromis niloticus. Curva de crescimento. Gompertz. Taxa de crescimento. *Autor para correspondência 1 Recebido ...

Nonlinear Models for Description of Cacao Fruit Growth With Assumption Violations

“…The estimation of parameters of nonlinear models was performed by minimizing the sum of squared errors from the nonlinear normal equations system, which has no explicit solution, requiring the use of iterative processes (SOUZA, 2007), for which the Gauss-Newton was adopted (MUNIZ; SAVIAN; SCALON, 2008;SOUZA et al, 2010;ZEVIANI et al, 2012;AMANCIO et al, 2014;CARNEIRO et al, 2014).…”

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Modelagem matem�tica do padr�o de crescimento do Tambaqui (Colossoma Macropomum) atrav�s do modelo de Gomertz

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Morphometric Growth Characteristics and Body Composition of Fish and Amphibians

“…As for the parameter A that refers to the asymptotic weight, Amancio et al [54] evaluated fitting of five mathematical models (Gompertz, Logistic, Linear Hyperbolic, Quadratic, and Logarithmic Quadratic) to describe the growth curve of genetically improved farmed tilapia (GIFT) Nile tilapia (Oreochromis niloticus). Nile tilapia fingerlings of the initial weight 2. fish for a period of 180 days.…”