Random Regression Models Are Suitable to Substitute the Traditional 305-Day Lactation Model in Genetic Evaluations of Holstein Cattle in Brazil

  • Padilha, Alessandro Haiduck (Department of Animal Science, Federal University of Rio Grande do Sul) ;
  • Cobuci, Jaime Araujo (Department of Animal Science, Federal University of Rio Grande do Sul) ;
  • Costa, Claudio Napolis (EMBRAPA) ;
  • Neto, Jose Braccini (Department of Animal Science, Federal University of Rio Grande do Sul)
  • Received : 2015.06.09
  • Accepted : 2015.09.06
  • Published : 2016.06.01


The aim of this study was to compare two random regression models (RRM) fitted by fourth ($RRM_4$) and fifth-order Legendre polynomials ($RRM_5$) with a lactation model (LM) for evaluating Holstein cattle in Brazil. Two datasets with the same animals were prepared for this study. To apply test-day RRM and LMs, 262,426 test day records and 30,228 lactation records covering 305 days were prepared, respectively. The lowest values of Akaike's information criterion, Bayesian information criterion, and estimates of the maximum of the likelihood function (-2LogL) were for $RRM_4$. Heritability for 305-day milk yield (305MY) was 0.23 ($RRM_4$), 0.24 ($RRM_5$), and 0.21 (LM). Heritability, additive genetic and permanent environmental variances of test days on days in milk was from 0.16 to 0.27, from 3.76 to 6.88 and from 11.12 to 20.21, respectively. Additive genetic correlations between test days ranged from 0.20 to 0.99. Permanent environmental correlations between test days were between 0.07 and 0.99. Standard deviations of average estimated breeding values (EBVs) for 305MY from $RRM_4$ and $RRM_5$ were from 11% to 30% higher for bulls and around 28% higher for cows than that in LM. Rank correlations between RRM EBVs and LM EBVs were between 0.86 to 0.96 for bulls and 0.80 to 0.87 for cows. Average percentage of gain in reliability of EBVs for 305-day yield increased from 4% to 17% for bulls and from 23% to 24% for cows when reliability of EBVs from RRM models was compared to those from LM model. Random regression model fitted by fourth order Legendre polynomials is recommended for genetic evaluations of Brazilian Holstein cattle because of the higher reliability in the estimation of breeding values.


Legendre Polynomials;305-Day Milk Yield;Breeding Values;Reliability;Brazilian Holstein


  1. Abdullahpour, R., M. Shahrbabak, A. Nejati-Javaremi, and R. V. Torshizi. 2010. Genetic analysis of daily milk, fat percentage and protein percentage of Iranian first lactation Holstein cattle. World Appl. Sci. J. 10:1042-1046.
  2. Aliloo, H., S. R. Miraie-Ashtiani, M. M. Shahrbabak, J. I. Urioste, and M. Sadeghi. 2014. Accounting for heterogeneity of phenotypic variance in Iranian Holstein test-day milk yield records. Livest. Sci. 167:25-32.
  3. Araujo, C. V., R. A. Torres, C. V. Costa, R. A. T. Filho, S. I. Araújo, P. S. Lopes, A. J. Regazzi, C. S. Pereira, and J. L. R. Sarmento. 2006. Random regressions models to describe the genetic variation of milk yield in Holstein breed. Rev. Bras. Zootec. 35:975-981.
  4. Biassus, I. O., J. A. Cobuci, C. N. Costa, P. R. N. Rorato, J. B. Neto, and L. L. Cardoso. 2010. Persistence in milk, fat and protein production of primiparous Holstein cows by random regression models. Rev. Bras. Zootec. 39:2617-2624.
  5. Bignardi, A. B., L. El Faro, L. G. Albuquerque, V. L. Cardoso, and P. F. Machado. 2009. Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil. Livest. Sci. 123:1-7.
  6. Bignardi, A. B., L. Faro, T. R. A. A. Júnior, V. L. Cardoso, P. F. Machado, and L. G. Albuquerque. 2011. Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows. Genet. Mol. Res. 10:3565-3575.
  7. Bilal, G. and M. S. Khan 2009. Use of test-day milk yield for genetic evaluation in dairy cattle: A review. Pakistan Vet. J. 29:35-41.
  8. C ankaya, S., C . Takma, S. H. Abaci, and M. A. U lker. 2014. Comparison of some random regression models for first lactation test day milk yields in Jersey cows and estimating of genetic parameters. Kafkas Univ. Vet. Fak. Derg. 20:5-10.
  9. Cobuci, J. A., C. N. Costa, J. B. Neto, and A. F. Freitas. 2011. Genetic parameters for milk production by using random regression models with different alternatives of fixed regression modeling. Rev. Bras. Zootec. 40:557-567.
  10. Costa, C. N., C. M. R. Melo, I. U. Packer, A. F. Freitas, N. M. Teixeira, and J. A. Cobuci. 2008. Genetic parameters for test day milk yield of first lactation Holstein cows estimated by random regression using Legendre polynomials. Rev. Bras. Zootec. 37:602-608.
  11. Dorneles, C. K. P., J. A. Cobuci, P. R. N. Rorato, T. Weber, J. S. Lopes, and H. N. Oliveira. 2009. Estimation of genetic parameters for Holstein cows milk production by random regression. Arq. Bras. Med. Vet. Zootec. 61:407-412.
  12. Dzomba, E. F., K. A. Nephawe, A. N. Maiwashe, S. W. P. Cloete, M. Chimonyo, C. B. Banga, C. J. C. Muller, and K. Dzama. 2010. Random regression test-day model for the analysis of dairy cattle production data in South Africa: creating the framework. S. Afr. J. Anim. Sci. 40:273-284.
  13. Jamrozik, J. and L. R. Schaeffer. 1997. Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins. J. Dairy Sci. 80:762-770.
  14. Kim, B.W., D. Lee, J. Jeon, and J. Lee. 2009. Estimation of genetic parameters for milk production traits using a random regression test-day model in Holstein cows in Korea. Asian Australas. J. Anim. Sci. 22:923-930.
  15. Kirkpatrick, M., R. Thompson, and W. G. Hill. 1994. Estimating of covariance structure of traits during growth and ageing, illustrated with lactation in dairy cattle. Genet. Res. 64:57-69.
  16. Lidauer, M., E. A. Mantysaari, and I. Stranden. 2003. Comparison of test-day models for genetic evaluation of production traits in dairy cattle. Livest. Prod. Sci. 79:73-86.
  17. Melo, C. M. R., I. U. Packer, C. N. Costa, P. F. Machado, and M. Patrício. 2007. Breeding values prediction for test day and lactation milk yields in Holstein cattle using different statistical models. Rev. Bras. Zootec. 36:1295-1303.
  18. Miglior F., W. Gong, Y. Wang, G. J. Kistemaker, A. Sewalem, and J. Jamrozik. 2009. Short communication: Genetic parameters of production traits in Chinese Holsteins using a random regression test-day model. J. Dairy Sci. 92:4697-4706.
  19. Misztal, I. and G. R. Wiggans. 1988. Approximation of prediction error variance in large-scale animal models. J. Dairy Sci. 71:27-32.
  20. Misztal, I., S. Tsuruta, I. Aguilar, A. Legarra, Z. Vitezica. 2014. Manual for BLUPF90 family of programs. ll1.pdf. Accessed October 30, 2014.
  21. Muir, B. L., G. Kistemaker, J. Jamrozik, and F. Canavesi. 2007. Genetic parameters for a multiple-trait multiple-lactation random regression test-day model in Italian Holsteins. J. Dairy Sci. 90:1564-1574.
  22. Naranchuluum, G., H. Ohmiya, Y. Masuda, K. Hagiya, and M. Suzuki. 2011. Selecting the desirable method for predicting 305-day lactation yields in Mongolia. Anim. Sci. J. 82:383-389.
  23. Pereira, R. J., A. B. Bignardi, L. El Faro, R. S. Verneque, A. E. Vercesi Filho, and L. G. Albuquerque. 2013. Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle. J. Dairy Sci. 96:565-574.
  24. Sawalha, R. M., J. F. Keown, S. D. Kachman, and L. D. Van Vleck. 2005. Genetic evaluation of dairy cattle with test-day models with autoregressive covariance structures and with a 305-d model. J. Dairy Sci. 88:3346-3353.
  25. Takma, C. and Y. Akbas. 2009. Comparison of fitting performance of random regression models to test day milk yields in Holstein Friesians. Kafkas Univ. Vet. Fak. Derg. 15:261-266.