Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T11:03:09.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Random regression analyses using B-spline functions to model growth of Nellore cattle

Published online by Cambridge University Press:  12 September 2011

A. A. Boligon ,
M. E. Z. Mercadante ,
R. B. Lôbo ,
F. Baldi  and
L. G. Albuquerque
A. A. Boligon*
Affiliation:
Departamento de Zootecnia, Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista, Jaboticabal, CEP 14884-900, São Paulo, Brazil
M. E. Z. Mercadante
Affiliation:
Instituto de Zootecnia, Estação Experimental de Zootecnia de Sertãozinho, 14160-000 Sertãozinho, São Paulo, Brazil
R. B. Lôbo
Affiliation:
Departamento de Genética, Faculdade de Medicina de Ribeirão Preto, Universidade de São Paulo, 14049-900 Ribeirão Preto, São Paulo, Brazil
F. Baldi
Affiliation:
Departamento de Zootecnia, Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista, Jaboticabal, CEP 14884-900, São Paulo, Brazil
L. G. Albuquerque
Affiliation:
Departamento de Zootecnia, Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista, Jaboticabal, CEP 14884-900, São Paulo, Brazil
*
†E-mail: [email protected]
Get access

Abstract

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Keywords

growth curvecovariance functionssegmented polynomialsNellore cattle
Type
Full Paper
Information
animal , Volume 6 , Issue 2 , 03 January 2012 , pp. 212 - 220
Copyright
Copyright © The Animal Consortium 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albuquerque, LG, Meyer, K 2001. Estimates of covariance functions for growth from birth to 630 days of age in Nellore cattle. Journal of Animal Science 79, 2776–2789.CrossRefGoogle Scholar
Arango, JA, Cundiff, LV, Van Vleck, LD 2004. Covariance functions and random regression models for cow weight in beef cattle. Journal of Animal Science 82, 54–67.CrossRefGoogle ScholarPubMed
Baldi, FS, Alencar, MM, Albuquerque, LG 2010. Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle. Journal of Animal Breeding and Genetics 127, 433–441.Google Scholar
Boligon, AA, Albuquerque, LG, Mercadante, MEZ, Lobo, RB 2009. Herdabilidades e correlações entre pesos do nascimento a idade adulta em rebanhos da raça Nelore. Revista Brasileira de Zootecnia 38, 2320–2326.Google Scholar
Boligon, AA, Mercadante, MEZ, Forni, S, Lobo, RB, Albuquerque, LG 2010. Covariance functions for weights from birth to maturity in Nellore cows. Journal of Animal Science 88, 849–859.CrossRefGoogle ScholarPubMed
De Boor, C 2001. A practical guide to splines, vol. 27 of Springer Series in Applied Mathematics, 2nd edition. Springer Verlag, New York.Google Scholar
Iwaisaki, H, Tsuruta, S, Misztal, I, Bertrand, JK 2005. Genetic parameters estimated with multi-trait and linear splines-random regression models using Gelbvieh early growth data. Journal of Animal Science 83, 499–506.CrossRefGoogle Scholar
Jenkins, TG, Ferrell, CL 1994. Productivity through weaning of nine breeds of cattle under varying feed availabilities: I. Initial evaluation. Journal of Animal Science 72, 2787–2797.CrossRefGoogle ScholarPubMed
Marx, BD, Eilers, PHC 1998. Direct generalized additive modelling with penalized likelihood. Computational Statistic and Data Analysis 28, 193–209.CrossRefGoogle Scholar
Meyer, K 1999. Estimates of genetic and phenotypic covariance functions for post weaning growth and mature weight of beef cows. Journal of Animal Science 116, 181–205.Google Scholar
Meyer, K 2000. Random regressions to model phenotypic variation in monthly weights of Australian beef cows. Livestock Production Science 65, 19–38.CrossRefGoogle Scholar
Meyer, K 2001. Estimates of direct and maternal covariance functions for growth of Australian beef calves from birth to weaning. Genetic Selection Evolution 33, 487–514.CrossRefGoogle ScholarPubMed
Meyer, K 2004. Scope for a random regression model in genetic evaluation of beef cattle for growth. Livestock Production Science 86, 69–83.CrossRefGoogle Scholar
Meyer, K 2005a. Estimates of genetic covariance functions for growth of Angus cattle. Journal of Animal Breeding and Genetics 122, 73–85.CrossRefGoogle ScholarPubMed
Meyer, K 2005b. Random regression analyses using B-splines to model growth of Australian Angus cattle. Genetic Select Evolution 37, 473–500.Google Scholar
Meyer, K 2005c. Advances in methodology for random regression analyses. Australian Journal of Experimental Agriculture 45, 847–859.Google Scholar
Meyer, K 2006. ‘WOMBAT’ – digging deep for quantitative genetic analyses by restricted maximum likelihood. Proceedings of the 8th World Congress on Genetics Applied to Livestock Production, Belo Horizonte, Brazil, CD-ROM.Google Scholar
Misztal, I 2006. Properties of random regression models using linear splines. Journal of Animal Breeding and Genetics 123, 74–80.Google Scholar
Mrode, RA 2005. Linear models for the prediction of animal breeding values, 2nd edition, CABI Publishing, Cambridge, MA, USA, 344pp.Google Scholar
Nephawe, KA 2004. Application of random regression models to the genetic evaluation of cow weight in Bonsmara cattle of South Africa. South African Journal of Animal Science 34, 166–173.Google Scholar
Nobre, PRC, Misztal, I, Tsuruta, S, Bertrand, JK, Silva, LOC, Lopes, PS 2003. Analyses of growth curves of Nellore cattle by multiple-trait and random regression models. Journal of Animal Science 81, 918–926.CrossRefGoogle ScholarPubMed
Rice, JA, Wu, CO 2001. Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57, 253–259.CrossRefGoogle ScholarPubMed
Ruppert, D, Wand, MP, Carroll, RJ 2003. Semiparametric regression. Cambridge University Press, New York.Google Scholar
Sakaguti, ES, Silva, MA, Quaas, RL, Martins, EN, Lopes, PS, Silva, LOC 2003. Avaliação do crescimento de bovinos jovens da raça Tabapuã, por meio de análises de funções de covariância. Revista Brasileira de Zootecnia 32, 864–874.CrossRefGoogle Scholar
Sánchez, JP, Misztal, I, Aguilar, I, Bertrand, JK 2008. Genetic evaluation of growth in a multibreed beef cattle population using random regression-linear splines models. Journal of Animal Science 86, 267–277.Google Scholar
Schwarz, G 1978. Estimating the dimension of a model. Annals of Statistics 6, 461–464.Google Scholar
Tier, B, Meyer, K 2004. Approximating prediction error covariances in multiple-trait and random regression models. Journal of Animal Breeding and Genetics 121, 77–89.Google Scholar