Covariance functions under B-spline polynomials to model Polled Nellore cattle growth
DOI:
https://doi.org/10.5433/1679-0359.2021v42n6SUPL2p3977Keywords:
Genetic parameters, Legendre, Random regression, Segmented polynomials.Abstract
B-spline functions have been used in random regression models (RRM) to model animal weight from birth to adulthood because they are less vulnerable to common difficulties of other methods. However, its application to model growth traits of Polled Nellore cattle has been little studied. Therefore, this study aimed to evaluate polynomial functions of different orders and segment numbers to model effects associated with the Polled Nellore cattle growth curve. For this purpose, we used 15,148 weight records of 3,115 animals aged between 1 and 660 days and reared in northern Brazil and born between 1995 and 2010. Random effects were modeled using B-spline polynomials. As random effects, we considered the direct and maternal genetic additives, as well as direct and maternal permanent environments. As fixed effects were included contemporary group, cow age at calving (linear and quadratic) and fourth-order Legendre polynomials to represent average growth curve. The residue was modeled by considering seven age classes. The best-fitted model was the one that considered cubic B-spline functions with four knots for direct additive genetic effects and three knots for maternal genetic, animal permanent environment, and maternal permanent environment effects (C6555). Therefore, covariance functions under B-spline polynomials are efficient and can be used to model the growth curve of Polled Nellore cattle from birth to 660 days of age.Downloads
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References
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Wolfinger, R. (1993). Covariance structure selection in general mixed models. Communications in Statistics. Simulation and Computation, 22(4), 1079-1106. doi: 10.1080/03610919308813143
Barros, I. C. D., Mota, R. R., Silva, L. P. D., Carneiro, P. L. S., Martins, R., & Malhado, C. H. M. (2018). Avaliação genética do crescimento de bovinos Nelore Mocho, por meio de modelos de multicaracterísticas1. Revista Ceres, 65(5), 402-406. doi: 10.1590/0034-737X201865050004
Boligon, A. A., Mercadante, M. E. Z., Forni, S., Lôbo, R. B., & Albuquerque, L. G. (2012). Random regression analyses using B-spline functions to model growth of Nellore cattle. Animal, 6(2), 212-220. doi: 10.1017/S1751731111001534
Cavalcante, D. H., Evangelista, A. F., Campêlo, J. E. G., Azevêdo, D. M. M. R., & Sousa, S. C., Jr. (2020b). Funções de covariâncias sobre polinômios B-splines para modelagem do crescimento de bovinos de corte: revisão. Medicina Veterinária (UFRPE), 14(1), 57-63. doi: 10.26605/medvet-v14n1-3714
Cavalcante, D. H., Sousa, S. C., Jr., Silva, L. P., Malhado, C. H. M., Martins, R., Fº., Azevêdo, D. M. M. R., & Campêlo, J. E. G. (2020a). Fitting of fixed regression curves with different residual variance structures for Nellore cattle growth modeling. Semina: Ciências Agrárias, 41(2), 545-558. doi: 10.5433/1679-0359.2020v41n2p545
Cavalcante, D. H., Sousa, S. C., Jr., Silva, L. P., Malhado, C. H. M., Martins, R., Fº., Campêlo, J. E. G., & Santos, K. R. (2019). Covariance function of Legendre polynomials for the modeling of Polled Nellore cattle growth in northern Brazil. Semina: Ciências Agrárias, 40(2), 781-792. doi: 10.5433/1679-0359.2019v40n2p781
Ferreira, J. L., Bresolin, T., Lopes, F. B., Garcia, J. A. S., Nepomuceno, L. L., Schmidt, A. B., & Lôbo, R. B. (2017). Modelos de regressão aleatória para característica de crescimento em bovinos da raça Guzerá. Ciência Animal Brasileira, 18(1), 1-12. doi: 10.1590/1089-6891v18e-39566
Ferreira, J. L., Lopes, F. B., Pereira, L. S., Nepomuceno, L. L., Garcia, J. A. S., Lôbo, R. B., & Sainz, R. D. (2015). Estimação de componentes de (co) variâncias para características de crescimento em bovinos Nelore criados no Trópico Úmido do Brasil por meio de regressão aleatória. Semina: Ciências Agrárias, 36(3), 1713-1724. doi: 10.5433/1679-0359.2015v36n3p1713
Lopes, F. B. Magnabosco, C. U., Paulini, F., Silva, M. C., Miyagi, E. S., & Lôbo, R. B. (2012). Analysis of longitudinal data of Nellore cattle from performance test at pasture using random regression model. Springer Plus, 1(49), 1-7. doi: 10.1186 / 2193-1801-1-49
Meyer, K. (2005). Estimates of covariance functions for growth of Angus cattle from random regression analyses fitting B-spline functions. Proceedings of the Association for Advancement of Animal Breeding Genetics, 16(1), 52-55.
Meyer, K. (2007). WOMBAT - A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML). Journal of Zhejiang University Science B, 8(11), 815-821. doi: 10.1631/jzus.2007.B0815
Mota, R. R., Lopes, P. S., Marques, L. F. A., Silva, L. P. D., Resende, M. D. V. D., & Torres, R. D. A. (2013). The influence of animals from embryo transfer on the genetic evaluation of growth in Simmental beef cattle by using multi-trait models. Genetics and Molecular Biology, 36(1), 43-49. doi: 10.1590/S1415-47572013005000008
Oliveira, M. R., Azevêdo, D. M., Malhado, C., Pires, L., Martins, R., & Sousa, S. (2017). Weight evaluation of Tabapuã cattle raised in northeastern Brazil using random-regression models. Arquivo Brasileiro de Medicina Veterinária e Zootecnia, 69(2), 457-464. doi: 10.1590/1678-4162-9070
Passafaro, T. L., Fragomeni, B. O., Gonçalves, D. R., Morais, M. M., & Toral, F. L. B. (2016). Genetic analysis of body weight in a Nellore cattle herd. Pesquisa Agropecuária Brasileira, 51(2), 149-158. doi: 10.1590/S0100-204X2016000200007
Portes, J. V., Cyrillo, J. N. D. S. G., El Faro, L., Mercadante, M. E. Z., Almeida Teixeira, R. de, & Dias, L. T. (2020). Evaluation of body weight and hip height in Nellore cows in a tropical environment. Livestock Science, 233, 103953. doi: 10.1016/j.livsci.2020.103953
Sas. Institute Inc., SAS/STAT®. (2004). User’s Guide, Version 9.1, Cary, NC: SAS Institute Inc.
Scalez, D. C. B., Fragomeni, B. O., Passafaro, T. L., Pereira, I. G., & Toral, F. L. B. (2014). Polynomials to model the growth of young bulls in performance tests. Animal, 8(3), 370-378. doi: 10.1017/S1751731113002334
Scalez, D. C. B., Fragomeni, B. de O., Santos, D. C. C. D., Passafaro, T. L., Alencar, M. M. D., & Toral, F. L. B. (2018). Random regression models with B-splines to estimate genetic parameters for body weight of young bulls in performance tests. Revista Brasileira de Zootecnia, 47(20150300), 2-9. doi: 10.1590/rbz4720150300
Teixeira, B. B., Mota, R. R., Lôbo, R. B., Silva, L. P., Carneiro, A. P. S., Silva, F. G.,... Silva, F. F. (2018). Genetic evaluation of growth traits in nellore cattle through multi-trait and random regression models. Czech Journal of Animal Science, 63(6), 212-221. doi: 10.17221/21/2017-CJAS
Wolfinger, R. (1993). Covariance structure selection in general mixed models. Communications in Statistics. Simulation and Computation, 22(4), 1079-1106. doi: 10.1080/03610919308813143
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Published
2021-10-08
How to Cite
Cavalcante, D. H., Luz, C. S. M., Oliveira, M. R. A. de, Fonseca, W. J. L., Evangelista, A. F., Martins Filho, R., … Sousa Júnior, S. C. de. (2021). Covariance functions under B-spline polynomials to model Polled Nellore cattle growth. Semina: Ciências Agrárias, 42(6SUPL2), 3977–3990. https://doi.org/10.5433/1679-0359.2021v42n6SUPL2p3977
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