Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T14:18:24.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Genetic modelling of daily milk yield using orthogonal polynomials and parametric curves

Published online by Cambridge University Press:  18 August 2016

S. Brotherstone ,
I. M. S. White  and
K. Meyer
S. Brotherstone
Affiliation:
Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT
I. M. S. White
Affiliation:
Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT
K. Meyer
Affiliation:
Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT
Get access

Abstract

Random regression models have been advocated for the analysis of test day records in dairy cattle. The effectiveness of a random regression analysis depends on the function used to model the data. To investigate functions suitable for the analysis of daily milk yield, test day milk yields of 7860 first lactation Holstein Friesian cows were analysed using random regression models involving three types of curves. Each analysis fitted the same curve to model overall trends through a fixed regression and random deviations due to animals. Curves included orthogonal polynomials, fitted to order 3 (quadratic), 4 (cubic) and 5 (quartic), respectively, a three-parameter parametric curve and a five-parameter parametric curve. Sets of random regression coefficients were fitted to model both animals’ genetic effects and permanent environmental effects. Temporary measurement errors were assumed independently but heterogeneously distributed, and assigned to one of 12 classes. Results showed that the measurement error variances were generally lowest around peak lactation, and higher at the beginning and end of lactation. Parametric curves yielded the highest likelihoods, but produced negative genetic associations between yield in early lactation and later lactation yields, while positive genetic correlations across the entire lactation were estimated with all models involving orthogonal polynomials. The fit of models using orthogonal polynomials to model test day yield was improved by including higher order fixed regressions.

Keywords

genetic modelsmilk yield
Type
Breeding and genetics
Information
Animal Science , Volume 70 , Issue 3 , June 2000 , pp. 407 - 415
Copyright
Copyright © British Society of Animal Science 2000

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

Abramowitz, M. and Stegun, I. A. 1965. Handbook of mathematical functions. Dover, New York.Google Scholar
Gengler, N., Tijani, A., Wiggans, G. R., Van Tassell, C. P. and Philpot, J. C. 1999. Estimation of (co)variances of test day yields for first lactation Holsteins in the United States. Journal Dairy Science 82: Accessed online.Google Scholar
Guo, Z. and Swalve, H. H. 1997. Comparison of different lactation curve sub-models in test day models. Proceedings of the 1997 Interbull meeting, Vienna, Austria.Google Scholar
Jamrozik, J. and Schaeffer, L. R. 1997. Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins. Journal of Dairy Science 80: 762–770.CrossRefGoogle ScholarPubMed
Jamrozik, J., Schaeffer, L. R. and Dekkers, J. C. M. 1997a. Genetic evaluation of dairy cattle using test day yields and random regression models. Journal of Dairy Science 80: 1217–1226.Google Scholar
Jamrozik, J., Schaeffer, L. R., Liu, Z. and Jansen, G. 1997b. Multiple trait random regression test day model for production traits. Proceedings of the 1997 Interbull meeting, Vienna, Austria.Google Scholar
Johnson, D. L. and Thompson, R. 1995. Restricted maximum-likelihood estimation of variance components for univariate animal models using sparse-matrix techniques and average information. Journal of Dairy Science 78: 449–456.Google Scholar
Kirkpatrick, M., Hill, W. G. and Thompson, R. 1994. Estimating the covariance structure of traits during growth and aging, illustrated with lactations in dairy cattle. Genetical Research 64: 57–69.CrossRefGoogle ScholarPubMed
Kirkpatrick, M., Lofsvold, D. and Bulmer, M. 1990. Analysis of inheritance, selection and evolution of growth trajectories. Genetics 124: 979–993.Google Scholar
Meyer, K. 1997. An ‘average information’ restricted maximum likelihood algorithm for estimating reduced rank genetic covariance matrices or covariance functions for animal models with equal design matrices. Genetics, Selection, Evolution 29: 97–116.Google Scholar
Meyer, K. 1998a. Estimating covariance functions for longitudinal data using a random regression model. Genetics, Selection, Evolution 30: 221–240.Google Scholar
Meyer, K. 1998b. ‘DxMRR’ — A program to estimate covariance functions for longitudinal data by restricted maximum likelihood. Proceedings of the sixth world congress on genetics applied to livestock production, Annidale, vol. 27, pp. 465–466.Google Scholar
Meyer, K. and Hill, W. G. 1997. Estimation of genetic and phenotypic covariance functions for longitudinal or ‘repeated’ records by restricted maximum likelihood. Livestock Production Science 47: 185–200.Google Scholar
Olori, V. E., Hill, W. G., McGuirk, B. J. and Brotherstone, S. 1999. Estimating variance components for test day milk yields by restricted maximum likelihood with a random regression animal model. Livestock Production Science 61: 53–63.Google Scholar
Pander, B. L., Hill, W. G. and Thompson, R. 1992. Genetic parameters of test day records of British Holstein-Friesian heifers. Animal Production 55: 11–21.Google Scholar
Pool, M. H. and Meuwissen, T. H. E. 2000. Reduction of the number of parameters needed for a polynomial random regression model. Livestock Production Science In press.Google Scholar
Ptak, E. and Schaeffer, L. R. 1993. Use of test day yields for genetic evaluation of dairy sires and cows. Livestock Production Science 34: 23–34.Google Scholar
Rekaya, R., Carabano, M. J. and Toro, M. A. 1999. Use of test day yields for the genetic evaluation of production traits in Holstein-Friesian cattle. Livestock Production Science 57: 203–217.Google Scholar
Schaeffer, L. R. and Dekkers, J. C. M. 1994. Random regressions in animal models for test-day production in dairy cattle. Proceedings of the fifth world congress on genetics applied to livestock production, Guelph, vol. 18, pp. 443–446.Google Scholar
Stram, D. O. and Lee, J. W. L. 1994. Variance component testing in the longitudinal mixed effects model. Biometrics 50: 1171–1177.Google Scholar
Tijani, A., Wiggans, G.R., Van Tassell, C. P., Philpot, J. C. M. and Gengler, N. 1999. Use of (co)variance functions to describe (co)variances for test day yield. Journal of Dairy Science 82: Accessed online.Google Scholar
Verbyla, A., Cullis, B. R., Kenwood, M. G. and Welham, S.J. 1999. The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Journal of the Royal Statistical Society, C. 48: 269–311.Google Scholar
Werf, J. van der, Goddard, M. and Meyer, K. 1998. The use of covariance functions and random regression for genetic evaluation of milk production based on test day records. Journal of Dairy Science 81: 3300–3308.Google Scholar
White, I. M. S., Thompson, R. and Brotherstone, S. 1999. Genetic and environmental smoothing of lactation curves with cubic splines. Journal of Dairy Science 82: 632–638.Google Scholar
Wilmink, J. B. M. 1987. Adjustment of test-day milk fat and protein yields for age season and stage of lactation. Livestock Production Science 16: 335–348.Google Scholar