Linear Models for the Prediction of Animal Breeding Values

New edition due to be published April 2005Best Linear Unbiased Prediction (BLUP) has become the most widely accepted method for the genetic evaluation of domestic livestock. Since its introduction, the method has evolved in terms of its application to sire models, and to sire and maternal grandsire models in the early years, to animal models and multivariate analysis more recently. Despite these developments, there has been no straightforward text available on the application of linear models to the prediction of animal breeding values. This book fills this gap, providing a blend of theory and practical applications. It covers basic principles of breeding value predictions and the application of BLUP to genetic evaluations under various models. Some knowledge of basic matrix algebra and of quantitative genetics is assumed on the part of the reader, although some introductory matrix algebra is included in an appendix.

Table of Contents:
a: Preface 1: GENETIC EVALUATION WITH DIFFERENT SOURCES OF RECORDS 1.1: The basic model 1.2: Breeding value prediction from animal own performance 1.3: Breeding value prediction from progeny records 1.4: Breeding value prediction from pedigree 1.5: Breeding value prediction for one trait from another 1.6: Selection index 2: GENETIC RELATIONSHIP BETWEEN RELATIVES 2.1: The numerator relationship matrix 2.2: Decomposing the relationship matrix 2.3: Computing inverse of the relationship matrix 2.4: Inverse of the relationship matrix for sires and maternal grandsires. 3: BEST LINEAR UNBIASED PREDICTION OF BREEDING VALUE - Univariate models with one random effect 3.1: Brief theoretical background 3.2: A model for an animal evaluation (animal model) 3.3: A sire model 3.4: Reduced animal model 3.5: Animal model with groups 4: BEST LINEAR UNBIASED PREDICTION OF BREEDING VALUE - Models with environmental effects 4.1: Repeatability model 4.2: Models with common environmental effects 5: BEST LINEAR UNBIASED PREDICTION OF BREEDING VALUE - Multivariate models 5.1: Equal design matrices and no missing records 5.2: Canonical transformation 5.3: Equal design matrices with missing records 5.4: Cholesky transformation 5.5: Unequal design matrices 5.6: Different traits measured on relatives 6: MATERNAL TRAIT MODELS - Animal and Reduced animal models 6.1: Animal model for a maternal trait 6.2: Reduced animal model with maternal effects 6.3: Multivariate maternal animal model 7: NON ADDITIVE ANIMAL MODELS 7.1: Dominance relationship matrix 7.2: Animal model with dominance effects 7.3: Method for rapid inversion of the dominance matrix 7.4: Epistatis 8: SOLVING LINEAR EQUATIONS 8.1: Direct inversion 8.2: Iterating on the mixed model equations 8.3: Iterating on the data

About the Author :
Raphael Mrode is Professor of Quantitative Genetics and Genomics at Scotland's Rural College and Principal Scientist in Quantitative Genetics in Dairy Cattle at the International Livestock Research Institute, Nairobi, Kenya. He has been lecturing on Edinburgh University's Masters course on quantitative genetics and genome analysis since 2005, and has given lectures on mixed linear models and the use of various BLUP models for genetic prediction. His research interests include data modelling and analysis, the incorporation of molecular information in genetic evaluation procedures, the application of innovative approaches for data capture, analysis and feedback and investigating methods for generating alternative and novel phenotypes in small dairy systems in developing countries.