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Best 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.
Part 1 Genetic evaluation with different sources of records: the basic model; breeding value prediction from animal own performance; breeding value prediction from progeny records; breeding value prediction from pedigree; breeding value prediction for one trait from another; selection index. Part 2 Genetic relationship between relatives: the numerator relationship matrix; decomposing the relationship matrix; computing inverse of the relationship matrix; inverse of the relationship matrix for sizes and maternal grandsires. Part 3 Best linear unbiased prediction of breeding value - univariate models with one random effect: brief theoretical background; a model for an animal evaluation (animal model); a sire model; reduced animal model; animal model with groups. Part 4 Best linear unbiased prediction of breeding value - models with environmental effects: repeatability model; models with common environmental effects. Part 5 Best linear unbiased prediction of breeding value - multivariate models: equal design matrices and no missing records; canonical transformation; equal design matrices with missing records; Cholesky transformation; unequal design matrices; different traits measured on relatives. Part 6 Maternal trait models - animal and reduced animal models: animal model for a maternal trait; reduced animal model with maternal effects; multivariate maternal animal model. Part 7 Non-additive animal models: dominance relationship matrix; animal model with dominance effects; method for rapid inversion of the dominance matrix; epistatis. Part 8 Solving linear equations: direct inversion; iterating on the mixed model equations; iterating on the data.
R Mrode, Scottish Agricultural College, Edinburgh, UK