52a Reunião Anual da Sociedade Brasileira de
Zootecnia
Zootecnia: Otimizando Recursos e Potencialidades
Belo Horizonte – MG, 19 a 23 de Julho de 2015
Descrição de curvas de crescimento de animais da raça Nelore no contexto de modelos não lineares mistos¹
Flávio Luiz Menezes2, Cláudio Vieira de Araújo3, Simone Inoe Araújo3, Raysildo Barbosa Lôbo4, Luiz Antônio
Framartino Bezerra4, Monyka Marianna Massolini Laureano3, Luis Gustavo Girardi Figueiredo4
1
2
3
4
Financiando pelo CNPq.
Acadêmico do curso de Zootecnia da Universidade Federal de Mato Grosso-Campus de Sinop,Sinop-MT
Docentes da Federal de Mato Grosso-Campus de Sinop,Sinop-MT,[email protected]
Associação Nacional de Criadores e Pesquisadores –ANCP, Ribeirão Preto, SP.
Resumo: Foram utilizados 37.416 registros de peso corporal ao nascer, 120, 210, 365, 450 e 550 dias de idade na
raça Nelore. O peso corporal dos animais foi regredido pela idade (em dias), por sexo, utilizando a função não-linear
Brody, Gompertz, Logístico, Meloun 1, Von Bertalanffy. A função Brody apresentou o melhor ajustamento ao
descrever a curva de crescimento dos animais. Usando a função de Brody, mas considerando o peso assintótico e taxa
de maturação, A e K, respectivamente, como aleatória, houve uma redução na variância residual estima em
aproximadamente 79% e 83% para o sexo masculino e feminino, respectivamente, em comparação com as estimativas
obtidos nos mesmos modelos de contexto fixos. A abordagem de modelo misto não-linear em relação ao modelo nãolinear fixo melhora a precisão do modelo.
Palavras–chave: efeitos aleatórios, gado de corte, modelos estocásticos, parâmetros
Description of the growth curve of Nelore animals in the context of non-linear mixed models
Abstract: Were used 37,416 records of body weight at birth, 120, 210, 365, 450 and 550 days of age in Nellore cattle.
Body weight of the animals was regressed by age (in days), by sex, using the nonlinear function Brody, Gompertz,
Logistic, Meloun 1, Von Bertalanffy. The Brody function showed the best adjustment in describing the growth curve
of the animals. Using Brody function, but considering the asymptotic weight and maturation rate, A and K,
respectively, as random, there was a reduction in the residual variance estimates at approximately 79% and 83% for
males and females, respectively, as compared to the estimates obtained in the same context models fixed. The
approach of nonlinear mixed model compared to fixed non-linear model improves the accuracy of the model.
Keywords: beef cattle, parameters, random effect, stochastics models
Introduction
The body growth animals is an important event in beef cattle because their knowledge favors the information
management related to different formats of animal growth curves, allowing the identification of animals over early
growth.
Thus, the use of non-linear models mixed in the description of animal growth curve allows the incorporation
of the random effects in the model and may considerably better quality model adjustment by reducing the residual
variance. The objective was to compare the different nonlinear functions in fixed and mixed linear model to describe
the body growth of male and females animals of Nellore breed, raised in the Midwest of Brazil.
Material e Methods
Were used 37,416 records of body weight at birth, 120, 210, 365, 450 and 550 days of age in Nellore cattle,
being male animals 17 328 records and 20 088 female animals records, raised in the herds from Midwest Region of
Brazil, participating in the breeding program of the Associação Nacional de Criadores e Pesquisadores – ANCP.
Body weight of the animals was regressed by age (in days), by sex, using the nonlinear function Brody,
Gompertz, Logistic, Meloun 1, Von Bertalanffy. Initially, all models have been processed considering the function
parameters as fixed, after the selection of the function which best describes the growth curve of body weight of males
and females, it was used in the context of mixed models, considering the parameters with biological interpretation as
random.
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52a Reunião Anual da Sociedade Brasileira de
Zootecnia
Zootecnia: Otimizando Recursos e Potencialidades
Belo Horizonte – MG, 19 a 23 de Julho de 2015
For comparisons between the model we used the criteria of information Akaike (AIC) and Bayesian Schwarz
(BIC). All analyzes were performed by NLIN and Nlimixed procedures of SAS (SAS, 1999).
Results and Discussion
According to the estimates of AIC and BIC the Brody function showed the best adjustment in describing the
growth curve of the animals. Using Brody function, but considering the asymptotic weight and maturation rate, A
and K, respectively, as random, there was a reduction in the estimated asymptotic weight and increased rate
maturation in both sexes (Table 1). However, for age range studied, the description of the growth curves of the body
weight of males and females, and in similar fashion approach fixed and mixed models.
The mixed model methods led to partition of the total variance in more components, causing a reduction in
the residual variance estimates at approximately 79% and 83% for males and females, respectively, as compared to
the estimates obtained in the same context models fixed.
Thus, the non-linear regression model that used the Brody function, adopting the asymptotic weight and
maturing rate as random in describing growth in body weight curves for males and females Nellore, from the state of
Mato Grosso, It enables reduction of the residual variance and thus increase the accuracy of the model predictions
obtained.
Applying the methodology of nonlinear model mixed in adjusting the growth curve dairy goats by Brody, Van
Bertalanffy and Richards functions, Moreira et al. (2012) showed decreased residual variance making better estimates,
similarly to that obtained in this study.
Table 1. Estimates of Asymptotic weight (A), constant of integration (B), maturity rate (K),
estimates of variance components of residual (σ_e^2), of the asymptotic weight (σ_a^2), of
the maturation rate (σ_k^2) and covariance between asymptotic weight and maturation rate
(σ_(a,k)), logarithmic of the value of the likelihood function (-2 Log (L)), Akaike information
criterion (AIC) and Bayesian Schwarz (BIC) for models that used the Brody function under
mixed and fixed models.
Male
model mixed
Parameter
Female
model fixed
model mixed
model fixed
value
EP
value
EP
value
EP
value
EP
A
434.40
0.0033
479.45
0.0001
362.13
1,2951
377.08
2.1670
B
0.9242
0.0003
0.9216
0.0009
0.9123
0,0004
0.9067
0.0010
K
0.0023
0.0001
0.0019
0.0001
0.0028
0,0002
0.0025
0.0003
𝜎𝑒2
5.8662
𝜎𝑎2
27.8534
28.3107
𝜎𝑘2
0.0003
0.0003
𝜎𝑎,𝑘
0.0045
0.0043
-2 Log(L)
155530
165178
175488
186929
AIC
155544
165186
175502
186937
BIC
155598
165217
175558
186969
28.4300
4.2804
25.3763
Conclusions
The Brody function provides best fit the description of growth curves of male and female of the Nellore breed
raised in the Midwest region. The approach of nonlinear mixed model compared to fixed non-linear model improves
the accuracy of the model.
Acknowledgements
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52a Reunião Anual da Sociedade Brasileira de
Zootecnia
Zootecnia: Otimizando Recursos e Potencialidades
Belo Horizonte – MG, 19 a 23 de Julho de 2015
The authors thank the ANCP CNPq.
References
Moreira,K.F.;Regadas Filho, J. G. L.; Oliveira, T. S.; Brito, L.F. et al. Modelos não linear misto no ajuste de
curvas de crescimento de caprinos leiteiros In: REUNIÃO ANUAL DA SOCIEDADE BRASILEIRA DE
ZOOTECNIA, 49., 2012, Brasília. Anais... Brasília: Sociedade Brasileira de Zootecnia, 2012. (CD-ROM).
SAS Institute Inc. 2009. SAS/STAT User’s Guide, Version 9.2. SAS Institute Inc., Cary, NC.
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