Comparing alternative random regression models to analyse first lactation daily milk yield data in Holstein–Friesian cattle

Abstract Test-day (TD) milk yields from Spanish Holstein cows were analysed in three independent data sets (35 615, 35 209 and 27 272 TD records, respectively) with a set of random regression models. Wilmink and Ali-Schaeffer lactation functions and, Legendre polynomials (RRL) of varying order (up to six coefficients) on additive genetic (AG) and permanent environmental (PE) effects were used. The analysis of the eigenvalues and eigenvectors of the AG and PE random regression (co)variance matrices revealed the possibility of reducing the dimension of the RRL submodels, particularly for the AG effects. Lactational submodels provided the largest daily AG variance estimates at the onset of lactation, as well as low or even negative genetic correlations between peripheral TD. Polynomials of higher order (four or above) showed oscillatory patterns with larger variances and lower genetic correlations predicted for the extremes of lactation. Model performance was assessed using a broad range of criteria. The results showed a strong consistency among data sets in terms of models ranking. Lactational models showed a worse performance than the RRL models with the same number of parameters. For RRL models, all criteria except the Bayesian information criterion, favoured the most complex model. This criterion selected a model with 2–3 coefficients for the AG effects and 5–6 coefficients for the PE effects.

[1]  Sue J. Welham,et al.  Likelihood Ratio Tests for Fixed Model Terms using Residual Maximum Likelihood , 1997 .

[2]  J. Pösö,et al.  Estimation of genetic parameters for daily milk yield of primiparous Ayrshire cows by random regression test-day models , 2000 .

[3]  S. Brotherstone,et al.  Genetic modelling of daily milk yield using orthogonal polynomials and parametric curves , 2000 .

[4]  G. Wiggans,et al.  Estimation of (Co)variance Function Coefficients for Test Day Yield with a Expectation-Maximization Restricted Maximum Likelihood Algorithm , 1999 .

[5]  G. Wiggans,et al.  Estimation of (Co)Variance Functions for Test-Day Yields During First and Second Lactations in the United States , 2001 .

[6]  T. Meuwissen,et al.  Prediction of daily milk yields from a limited number of test days using test day models. , 1999, Journal of dairy science.

[7]  M. Kirkpatrick,et al.  A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters , 1989, Journal of mathematical biology.

[8]  Alan E. Gelfand,et al.  Model choice: A minimum posterior predictive loss approach , 1998, AISTATS.

[9]  F. Reinhardt,et al.  Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. , 2000, Journal of dairy science.

[10]  M. Kirkpatrick,et al.  Analysis of the inheritance, selection and evolution of growth trajectories. , 1990, Genetics.

[11]  V. Ducrocq.  Calving ease evaluation of French dairy bulls with a heteroskedastic threshold model with direct and maternal effects , 2000 .

[12]  H H Swalve,et al.  Theoretical basis and computational methods for different test-day genetic evaluation methods. , 2000, Journal of dairy science.

[13]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[14]  J. Jamrozik,et al.  Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins. , 1997, Journal of dairy science.

[15]  N. L. Johnson,et al.  Breakthroughs in Statistics, Vol. III , 1998 .

[16]  T. Meuwissen,et al.  Genetic parameters of legendre polynomials for first parity lactation curves. , 2000, Journal of dairy science.

[17]  J. Dekkers,et al.  Comparison of possible covariates for use in a random regression model for analyses of test day yields. , 1997, Journal of dairy science.

[18]  William G. Hill,et al.  ESTIMATING VARIANCE COMPONENTS FOR TEST DAY MILK RECORDS BY RESTRICTED MAXIMUM LIKELIHOOD WITH A RANDOM REGRESSION ANIMAL MODEL , 1999 .

[19]  I. Misztal,et al.  Genetic parameters for first and second lactation milk yields of Polish black and white cattle with random regression test-day models. , 1999, Journal of dairy science.

[20]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[21]  C. Geyer,et al.  The genetic analysis of age-dependent traits: modeling the character process. , 1999, Genetics.

[22]  H. Swalve.  Test day models in the analysis of dairy production data: A review , 1995 .

[23]  M. Toro,et al.  Bayesian analysis of lactation curves of Holstein-Friesian cattle using a nonlinear model. , 2000, Journal of dairy science.

[24]  M. Bhaskara Rao,et al.  Model Selection and Inference , 2000, Technometrics.

[25]  L. R. Schaeffer,et al.  ACCOUNTING FOR COVARIANCES AMONG TEST DAY MILK YIELDS IN DAIRY COWS , 1987 .

[26]  T. Meuwissen,et al.  Strategies for estimating the parameters needed for different test-day models. , 2000, Journal of dairy science.

[27]  L R Schaeffer,et al.  Experience with a test-day model. , 2000, Journal of dairy science.

[28]  D. Gianola,et al.  A comparison between linear and poisson mixed models for litter size in iberian pigs , 1993 .

[29]  K. Burnham,et al.  Model selection: An integral part of inference , 1997 .

[30]  Ping Zhang.  On the Distributional Properties of Model Selection Criteria , 1992 .

[31]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[32]  W. G. Hill,et al.  Estimating the covariance structure of traits during growth and ageing, illustrated with lactation in dairy cattle. , 1994, Genetical research.

[33]  J.B.M. Wilmink,et al.  Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation , 1987 .

[34]  L. R. Schaeffer,et al.  Use of test day yields for genetic evaluation of dairy sires and cows , 1993 .

[35]  W. G. Hill,et al.  Estimation of genetic and phenotypic covariance functions for longitudinal or ‘repeated’ records by restricted maximum likelihood , 1997 .

[36]  L. Varona,et al.  Bayesian analysis of Wood's lactation curve for Spanish dairy cows. , 1998, Journal of dairy science.

[37]  Browne,et al.  Cross-Validation Methods. , 2000, Journal of mathematical psychology.

[38]  M. Goddard,et al.  The use of covariance functions and random regressions for genetic evaluation of milk production based on test day records. , 1998, Journal of dairy science.

[39]  M. Toro,et al.  Use of test day yields for the genetic evaluation of production traits in Holstein-Friesian cattle , 1999 .

[40]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[41]  S. Pletcher,et al.  Statistical models for estimating the genetic basis of repeated measures and other function-valued traits. , 2000, Genetics.