Mixed nonlinear models in ruminal in situ degradability trials
DOI:
https://doi.org/10.1590/1809-6891v21e-57596Abstract
Classical methods of analysis of nonlinear models are widely used in studies of ruminal degradation kinetics. As this type of study involves repeated measurements in the same experimental unit, the use of mixed nonlinear models (MNLM) is proposed, in order to solve problems of heterogeneity of variances of the responses, correlation among repeated measurements and consequent lack of sphericity in the covariance matrix. The aims of this work are to present an evaluation of the applicability of MNLM in the estimation of parameters to describe the in situ ruminal degradation kinetics of the dry matter of Tifton 85 hay and to compare the results with those obtained from the usual analysis in two-phases. The steers used in the trial were fed diets composed of three different combinations of roughage and concentrate and two hays with different nutritional qualities. The proposed approach was proven as effective as the traditional one for estimating model parameters. However, it adequately models the correlation among the longitudinal data, which can affect the estimates obtained, the standard error associated with them and potentially change the results of the inferences. It is quite attractive when the research seeks to understand the behavior of the process of food degradation throughout the incubation times.
Keywords: Ruminal degradation kinetics; Longitudinal data; Covariance matrix; Random effects; Dry matter.
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References
Moreira JFC, Rodriguez NM, Fernandes PCC, Veloso CM, Saliba EOS, Gonçalves LC, Borges I,
Borges ALCC. Concentrados protéicos para bovinos. 1. Digestibilidade in situ da matéria seca
e da proteína bruta [Protein concentrates for bovines.1. In situ digestibility of dry matter and
crude protein]. Arquivo Brasileiro de Medicina Veterinária e Zootecnia [periódico na Internet].
[citado 2016 Dez 10]; 55(3):315-323. Available in: http://dx.doi.org/10.1590/S0102-
Portuguese.
Cabral LS, Valadares Filho SC, Zervoudakis JT, Souza AL, Detmann E. Degradabilidade in situ
da matéria seca, da proteína bruta e da fibra de alguns alimentos [In situ degradability of dry
matter, crude protein and fiber of some feeds]. Pesquisa Agropecuária Brasileira [periódico
na Internet]. 2005 [citado 2016 Jul 15]; 40(8):777-81. Available in: http://dx.doi.org/10.1590/
S0100-204X2005000800007 . Portuguese.
Maggioni D, Marques JA, Rotta PP, Zawadzki F, Ito RH, Prado IN. Ingestão de Alimentos.
Semina: Ciências Agrárias. 2009; 30(4):963-974.
Santos S, Santos-Cruz CL, Rocha JB, Pires AJV, Santos IPA, Lima TR, Junqueira RS. [Ruminal degradation of silage of elephant grass with mesquite different components].
Revista Brasileira de Saúde e Produção animal [Internet]. 2012 [cited 2016 Jan 09]; 13(1):123-
Available in: http://www.scielo.br/pdf/rbspa/v13n1/a11v31n1.pdf . Portuguese.
Teixeira FA, Veloso CM, Pires AV, Silva FF, Nascimento PVN, Carvalho GGP. Degradação
ruminal da silagem de capim-elefante aditivado com cana-de-açúcar e farelo de cacau
[Ruminal degradation of elephant grass sillage added with sugarcane and cocoa meal].
Ciência e Agrotecnologia[Internet]. 2008 [cited 2016 Fev 13]; 32(3):948-954. Available in: http://
www.scielo.br/pdf/cagro/v32n3/a36v32n3.pdf . Portuguese.
Pereira ES, Carneiro MSS, Cavalcante MAB, Villarroel ABS, Pimentel PG. Degradação ruminal
da matéria seca e proteína bruta de silagens de híbridos de milho [Ruminal degradation
of dry matter and crude protein of differents silages of corn hybrids]. Revista Ciência
Agronômica[Internet]. 2008 [cited 2016 Fev 20]; 39(4):603-608. Available in: http://www.
ccarevista.ufc.br/seer/index.php/ccarevista/article/download/394/290. Portuguese.
Alves AA, Sales RO, Neiva JNM, Medeiros AN, Braga AP, Azevedo AR. Degradabilidade
ruminal in situ de vagens de faveira (Parkia platycephala Benth.) em diferentes tamanhos
de partículas [In situ ruminal degradability of faveira (Parkia platycephala Benth.) pods in
different particle sizes]. Arquivo Brasileiro de Medicina Veterinária e Zootecnia [periódico na
Internet].2007 [citado 2017 Jul 04]; 59(4):1045-1051. Available in: http://dx.doi.org/10.1590/
S0102-09352007000400034. Portuguese.
Santoro KR, Barbosa SBP, Brasil LHA, Santos ES. Estimativas de parâmetros de curvas de
crescimento de bovinos Zebu, criados no estado de Pernambuco [Growth curve parameters
for Zebu breeds raised at Pernambuco State, Northeastern Brazil]. Revista Brasileira de
Zootecnia [periódico na Internet]. 2005 [citado 2017 Jul 21]; 34(6): 2262-2279. Available in:
http://dx.doi.org/10.1590/S1516-35982005000700013. Portuguese.
Jobim CC, Ferreira GA, Bumbieris Junior VH, Calixto Junior M, Santos GT. Cinética de
degradação ruminal dos fenos de alfafa e Tifton-85 e da silagem de milho. Ciências Agrárias.
; 32(2):747-758.
Rego AC, Paiva PCA, Muniz JA, Cleef EHCB, Machado-Neto OR. Degradação ruminal de
silagem de capim-elefante com adição de vagem de algaroba triturada [Ruminal degradation
of elephant grass silage with mesquite pods]. Revista Ciência Agronômica [periódico na
Internet]. 2011 [citado 2017 Set 05]; 42(1):199-207. Available in: http://dx.doi.org/10.1590/
S1806-66902011000100025. Portuguese.
Muniz EB, Mizubuti IY, Pereira ES, Pimentel PG, Ribeiro ELA, Pinto AP. Cinética ruminal
da fração fibrosa de volumosos para ruminantes [Ruminal kinetics of the fibrous fraction
of ruminant roughages]. Revista Ciência Agronômica [Internet]. 2012 [citado 2016 Dez 12];
(3):604-610. Available in: http://www.scielo.br/pdf/rca/v43n3/a25v43n3.pdf. Portuguese.
Santos EJ, Pereira MLA, Presídio PJA, Moreira JV, Souza ACS, Pereira CAR.Mesquite pod
meal in sheep diet: intake, apparent digestibility of nutrients and nitrogen balance. Acta
Scientiarum, Animal Sciences [Internet]. 2015 [cited 2017 Jul 29]; 37(1):55-59. Available in:
http://dx.doi.org/10.4025/actascianimsci.v37i1.24466. English.
Pasternak H, Shalev BA. The effect of a feature of regression disturbance on the efficiency
of fitting growth curves. Growth, Development & Aging, Bar Harbor. 1994; 58(1):33-39.
Sartorio SD. Modelos não lineares mistos em estudos de degradabilidade ruminal in situ.
188f. Tese (Doutorado em Ciências) - Escola Superior de Agricultura “Luiz de Queiroz”,
Universidade de São Paulo, Piracicaba, 2013. Available in: http://www.teses.usp.br/teses/
disponiveis/11/11134/tde-08012013-151513/pt-br.php. Portuguese.
Carvalho LR, Pereira GMS, Silva HOF, Mischan MM, Furtado EL. Ajuste de modelos não
lineares de efeitos fixos, com ponderação e misto - aplicações. Revista Brasileira de Biometria
[Internet]. 2014 [cited 2016 Nov 30]; 32(2):296-307. Available in: http://jaguar.fcav.unesp.br/
RME/fasciculos/v32/v32_n2/A9_LidiaRaquel.pdf. Portuguese
Orskov ER, McDonald IM. The estimation of protein degradability in the rumen from
incubation measurements weighted according to rate of passage. Journal of Agricultural
Science [periódico na Internet]. 1979Abr [cited 2017 Out 28]; 92(2):499-503. Available in:
https://doi.org/10.1017/S0021859600063048. English.
Feitosa JV, Malheiros EB, Ezequiel JMB, Araújo AA. Uso de modelos de regressão para
o estudo da curva de degradação do feno de capim-Tifton 85 com 10% de proteína bruta
e diferentes níveis de concentrados [The use of regression models for the study of the
degradation curve of the hay grass-tifton 85 with 10% crude protein and different levels of
concentrate]. Ciência Animal [Internet]. 2004 [cited 2016 Dez 20]; 14(2):77-88. Available in:
http://www.uece.br/cienciaanimal/dmdocuments/Artigo2.2004.2.pdf. Portuguese.
Lindstrom MJ, Bates DM. Nonlinear Mixed Effects Models for Repeated Measures Data.
Biometrics [Internet] 1990 Sep [cited 2017 Nov 11]; 46(3):673-687. Available in: https://www.
ncbi.nlm.nih.gov/pubmed/2242409. English.
Gómez DAA, Muñoz MFC, Betancur LFR. Modelación de las funciones de crecimiento
aplicadas a la producción animal [Modeling of growth functions applied to animal production].
Revista Colombiana de Ciências Pecuárias [Internet]. 2008 [cited Jun 12]; 21(1):39-58. Available
in: http://www.scielo.org.co/pdf/rccp/v21n1/v21n1a05.pdf. Spanish.
Pinheiro JC, Bates DM. Mixed-Effects Models in S and S-PLUS. 1 st ed. New York: Springer-
Verlag; 2000. 528 p. English.
Hirst K, Zerbe GO, Boyle DW, Wilkening RB. On nonlinear random effects models for
repeated measurements. Communications in Statistics B, Simulation and Computation. 1991;
(2):463-478.
Vonesh EF, Carter RL. Mixed effect nonlinear regression for unbalanced repeated
measures. Biometrics [Internet]. 1992 [cited Aug 27]; 48:1-18. Available in: https://www.ncbi.
nlm.nih.gov/pubmed/1581479 . English.
R Core Team. R: A language and environment for statistical computing, versão 3.4.3. R
Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/. 2018.
Vaz MAB, Pacheco PS, Seidel EJ, Ansuj AP. Classification of the coefficient of variation to
variables in beef cattle experiments. Cienc. Rural [Internet]. 2017 [cited 2019-04-27]; 47(11), e20160946. Available in: http://dx.doi.org/10.1590/0103-8478cr20160946. English.
Balieiro Neto G, Melotti L. Efeitos de níveis de sebo sobre a degradabilidade in situ do
farelo de soja e do feno de Tifton Cynodon dactylon (L.) pers. em vacas secas. Brazilian Journal
of Veterinary Research and Animal Science [periódico na Internet]. 2007 [citado Oct 04];
(4): 243-253. Available in: http://dx.doi.org/10.11606/issn.1678-4456.bjvras.2007.26624.
Portuguese.
Assis MA, Santos GT, Cecato U, Damasceno JC, Petit HV, Bett V, Gomes LH, Daniel M.
Degradabilidade in situ de gramíneas do gênero Cynodon submetidas ou não a adubação
nitrogenada. Acta Scientiarum. 1999; 21(3):657-663.
Zanton GI, Heinrichs AJ. Evaluation of modeling procedure for fitting in situ
feed degradation profiles. American Society of Animal Science [Internet]. 2014 Dec
[cited Ago 10]; 87:2080-2088. Available in: https://pdfs.semanticscholar.org/6ca8/
c2697d4d48a53cf37d8c9254dfe38d9c6489.pdf. English.
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