Page 13 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Preface

Best linear unbiased prediction (BLUP) has become the most widely accepted method
for genetic evaluation of domestic livestock. Since the method was first published by
Henderson (1949) it has evolved in terms of its application in models for genetic
evaluation, from sire, sire and maternal grandsire models in the early years, followed
by univariate and multivariate animal models, random regression models for the
analysis of longitudinal data and more recently, for the analysis of the genomic data
(SNP-BLUP or GBLUP). Advances in computational methods and computing power
have enhanced this development. Currently, most national genetic evaluation systems
for several domestic livestock species are based on animal or random regression mod-
els using BLUP.
In view of these developments and the proliferation of information in the litera-
ture, there is no simple and straightforward text on the application of linear models
to the prediction of breeding values. Moreover, in developing countries, where access
to journals is limited, there is a basic lack of practical information on the subject. This
book has been written with a good balance of theory and application to fill this gap.
It places at the hand of the reader the application of BLUP in modelling several
genetic situations in a single text. The book has been compiled from various publica-
tions and experience gained from several colleagues in the subject area and from
involvement in several national evaluation schemes over the last 14 years. Relevant
references are included to indicate sources of some of the materials.
Initially, in Chapter 1, the basic model and assumptions governing genetic evalu-
ation are presented, together with simple situations involving prediction of breeding
values from the records of an individual. This is followed by the introduction and use
of selection indices to predict genetic merit combining information on several traits
and individuals. Then the general framework on the application of BLUP in genetic
evaluation in a univariate and multivariate situations is presented in Chapters 3 to 5.
The simplification of multivariate evaluations by means of several transformations is
also examined, followed by maternal trait and social interaction models. Random
regression models for the analysis of longitudinal data are discussed in Chapter 9, fol-
lowed by a chapter on incorporating genetic marker information into genetic evalua-
tions in the context of marker-assisted selection and then genomic selection.
Non-additive genetic animal models are discussed with methods for rapidly computing
the inverse of the relationship matrices for dominance and epistasis effects. Next,
threshold and survival models are discussed. In Chapters 15 and 16, the basic concepts
for variance component estimation are introduced, followed by the application of the
Gibbs sampler in estimation of genetic parameter and evaluations for univariate and
multivariate models. Finally, computing strategies for solving mixed model equations
are examined, with a presentation of the several formulae governing iterative proce-
dures on the data. A knowledge of basic matrix algebra is needed to understand the
principles of genetic evaluation discussed in the text. For the benefit of those not

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