## Linear Models for the Prediction of Animal Breeding ValuesBest Linear Unbiased Prediction (BLUP) has become the most widely accepted method for genetic evaluation of domestic livestock. Since its introduction, the method has evolved and despite this there is no simple text on the application of linear models to the prediction of breeding values. This book has been written with a good balance of theory and application to fill this gap. Equations for partitioning breeding values into contributions from various sources of information are derived under the various models. Recent developments in the analysis of longitudinal data with random regression models and the inclusion of genetic marker information in the evaluation of animals have been incorporated. Overall the book has been thoroughly updated since the first edition was published in 1996. |

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### Contents

1 | |

2 Genetic Covariance Between Relatives | 25 |

Univariate Models with One Random Effect | 39 |

Models with Random Environmental Effects | 71 |

Multivariate Models | 83 |

Animal and Reduced Animal Models | 121 |

7 Analysis of Longitudinal Data | 135 |

8 Use of Genetic Markers in Prediction of Breeding Values | 163 |

13 Solving Linear Equations | 259 |

Introductory Matrix Algebra | 289 |

Fast Algorithms for Calculating Inbreeding Based on the L Matrix | 297 |

Appendix C | 303 |

Methods for Obtaining Approximate Reliability for Genetic Evaluations | 307 |

Appendix E | 311 |

Procedure for Computing Deregressed Breeding Values | 317 |

Calculating 934 a Matrix of Legendre Polynomials Evaluated at Different Ages or Time Periods | 321 |

9 Nonadditive Animal Models | 193 |

10 Analysis of Ordered Categorical Traits | 211 |

11 Estimation of Genetic Parameters | 235 |

12 Application of Gibbs Sampling in Variance Component Estimation and Prediction of Breeding Value | 247 |

Computing the Covariance Matrix of Additive Genetic Effect of Marked QTL MQTL when Paternal or Maternal Origin of Marker Alleles cannot be ... | 325 |

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### Common terms and phrases

additive genetic effects ancestors animals with records assumed BLUP breeding value bull calculated calf calves coefficient matrix columns computed contributions convergence covariance matrix data set daughter defined design matrices DIAG diagonal element diagonal matrix distribution epistatic equal estimated breeding value Example 3.1 example data fixed effects fixed regression genetic covariance genetic evaluation genotype Gibbs sampling herd identity matrix illustrated inbreeding individual ith animal lactation Legendre polynomials linear model male marker information mate maternal effects matrix multiplication mixed model equations MQTL alleles multivariate analysis multivariate model non-parents obtained pedigree file permanent environmental effects phenotypic predicted breeding value prediction of breeding prog progeny R.A. Mrode relates records relationship matrix residual variance round of iteration sampling Section sex effect sire and dam Sire Dam sire model subclass effects test day tion traits transformed univariate unknown vector of observations weight yield deviation zero