Page 5 - Linear Models for the Prediction of Animal Breeding Values

Contents

Preface xiii

Abbreviations xv
1. Genetic Evaluation with Different Sources of Records 1
1.1. Introduction 1
1.2. The Basic Model 1
1.3. Breeding Value Prediction from the Animal’s Own Performance 2
1.3.1. Single record 2
1.3.2. Repeated records 3
1.4. Breeding Value Prediction from Progeny Records 6
1.5. Breeding Value Prediction from Pedigree 9
1.6. Breeding Value Prediction for One Trait from Another 10
1.7. Selection Index 11
1.7.1. Accuracy of index 12
1.7.2. Examples of selection indices using different sources
of information 14
1.7.3. Prediction of aggregate genotype 16
1.7.4. Overall economic indices using predicted genetic merit 18
1.7.5. Restricted selection index 19
1.7.6. Index combining breeding values from phenotype
and genetic marker information 21

2. Genetic Covariance Between Relatives 22
2.1. Introduction 22
2.2. The Numerator Relationship Matrix 22
2.3. Decomposing the Relationship Matrix 23
2.4. Computing the Inverse of the Relationship Matrix 25
2.4.1. Inverse of the numerator relationship matrix ignoring
inbreeding 26
2.4.2. Inverse of the numerator relationship matrix
accounting for inbreeding 28
2.5. Inverse of the Relationship Matrix for Sires
and Maternal Grandsires 30
2.6. An Example of the Inverse of a Sire and Maternal
Grandsire Relationship Matrix 32
3. Best Linear Unbiased Prediction of Breeding Value: Univariate
Models with One Random Effect 34
3.1. Introduction 34
3.2. Brief Theoretical Background 35
3.3. A Model for an Animal Evaluation (Animal Model) 37

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