Genomic Selection in Animals

Joel Ira Weller is a Research Scientist at the Institute of Animal Sciences, ARO, The Volcani Center in Bet Dagan, Israel.

Preface: Welcome to the “Promised Land” xiii

Chapter 1 Historical Overview 1

Introduction 1

The Mendelian Theory of Genetics 1

The Mendelian Basis of Quantitative Variation 2

Detection of QTL with Morphological and Biochemical Markers 2

DNA-Level Markers, 1974–1994 3

DNA-Level Markers Since 1995: SNPs and CNV 4

QTL Detection Prior to Genomic Selection 4

MAS Prior to Genomic Selection 5

Summary 6

Chapter 2 Types of Current Genetic Markers and Genotyping Methodologies 7

Introduction 7

From Biochemical Markers to DNA]Level Markers 7

DNA Microsatellites 8

Single Nucleotide Polymorphisms 8

Copy Number Variation 9

Complete Genome Sequencing 9

Summary 10

Chapter 3 Advanced Animal Breeding Programs Prior to Genomic Selection 11

Introduction 11

Within a Breed Selection: Basic Principles and Equations 11

Traditional Selection Schemes for Dairy Cattle 12

Crossbreeding Schemes: Advantages and Disadvantages 14

Summary 15

Chapter 4 Economic Evaluation of Genetic Breeding Programs 17

Introduction 17

National Economy versus Competition among Breeders 17

Criteria for Economic Evaluation: Profit Horizon, Interest Rate, and Return on Investment 18

Summary 20

Chapter 5 Least Squares, Maximum Likelihood, and Bayesian Parameter Estimation 21

Introduction 21

Least Squares Parameter Estimation 21

ML Estimation for a Single Parameter 22

ML Multiparameter Estimation 24

Methods to Maximize Likelihood Functions 26

Confidence Intervals and Hypothesis Testing for MLE 26

Bayesian Estimation 27

Parameter Estimation via the Gibbs Sampler 28

Summary 29

Chapter 6 Trait-Based Genetic Evaluation: The Mixed Model 31

Introduction 31

Principles of Selection Index 31

The Mixed Linear Model 34

The Mixed Model Equations 34

Solving the Mixed Model Equations 35

Important Properties of Mixed Model Solutions 36

Multivariate Mixed Model Analysis 37

The Individual Animal Model 38

Yield Deviations and Daughter Yield Deviations 39

Analysis of DYD as the Dependent Variable 40

Summary 41

Chapter 7 Maximum Likelihood and Bayesian Estimation of QTL Parameters with Random Effects Included in the Model 43

Introduction 43

Maximum Likelihood Estimation of QTL Effects with Random Effects Included in the Model, the Daughter Design 43

The Granddaughter Design 45

Determination of Prior Distributions of the QTL Parameters for the Granddaughter Design 46

Formula for Bayesian Estimation and Tests of Significance of a Segregating QTL in a Granddaughter Design 49

Summary 50

Chapter 8 Maximum Likelihood, Restricted Maximum Likelihood, and Bayesian Estimation for Mixed Models 51

Introduction 51

Derivation of Solutions to the Mixed Model Equations by Maximum Likelihood 51

Estimation of the Mixed Model Variance Components 52

Maximum Likelihood Estimation of Variance Components 52

Restricted Maximum Likelihood Estimation of Variance Components 54

Estimation of Variance Components via the Gibbs Sampler 55

Summary 58

Chapter 9 Distribution of Genetic Effects, Theory, and Results 59

Introduction 59

Modeling the Polygenic Variance 59

The Effective Number of QTL 61

The Case of the Missing Heritability 61

Methods for Determination of Causative Mutations for QTL in Animals and Humans 62

Determination of QTN in Dairy Cattle 63

Estimating the Number of Segregating QTL Based on Linkage Mapping Studies 64

Results of Genome Scans of Dairy Cattle by Granddaughter Designs 65

Results of Genome]Wide Association Studies in Dairy Cattle by SNP Chips 66

Summary 66

Chapter 10 The Multiple Comparison Problem 69

Introduction 69

Multiple Markers and Whole Genome Scans 69

QTL Detection by Permutation Tests 71

QTL Detection Based on the False Discovery Rate 71

A Priori Determination of the Proportion of False Positives 74

Biases with Estimation of Multiple QTL 75

Bayesian Estimation of QTL from Whole Genome Scans: Theory 76

Bayes A and Bayes B Models 77

Bayesian Estimation of QTL from Whole Genome Scans: Simulation Results 79

Summary 80

Chapter 11 Linkage Mapping of QTL 81

Introduction 81

Interval Mapping by Nonlinear Regression: The Backcross Design 81

Interval Mapping for Daughter and Granddaughter Designs 83

Computation of Confidence Intervals 84

Simulation Studies of CIs 85

Empirical Methods to Estimate CIs, Parametric and Nonparametric Bootstrap, and Jackknife Methods 86

Summary 87

Chapter 12 Linkage Disequilibrium Mapping of QTL 89

Introduction 89

Estimation of Linkage Disequilibrium in Animal Populations 89

Linkage Disequilibrium QTL Mapping: Basic Principles 90

Joint Linkage and Linkage Disequilibrium Mapping 92

Multitrait and Multiple QTL LD Mapping 93

Summary 93

Chapter 13 Marker-Assisted Selection: Basic Strategies 95

Introduction 95

Situations in Which Selection Index is Inefficient 95

Potential Contribution of MAS for Selection within a Breed: General Considerations 96

Phenotypic Selection versus MAS for Individual Selection 97

MAS for Sex-Limited Traits 98

MAS Including Marker and Phenotypic Information on Relatives 99

Maximum Selection Efficiency of MAS with All QTL Known, Relative to

Trait-Based Selection, and the Reduction in RSE Due to Sampling Variance 99

Marker Information in Segregating Populations 100

Inclusion of Marker Information in “Animal Model” Genetic Evaluations 100

Predicted Genetic Gains with Genomic Estimated Breeding Values: Results of Simulation Studies 101

Summary 102

Chapter 14 Genetic Evaluation Based on Dense Marker Maps: Basic Strategies 103

Introduction 103

The Basic Steps in Genomic Evaluation 103

Evaluation of Genomic Estimated Breeding Values 104

Sources of Bias in Genomic Evaluation 104

Marker Effects Fixed or Random? 105

Individual Markers versus Haplotypes 106

Total Markers versus Usable Markers 106

Deviation of Genotype Frequencies from Their Expectations 107

Inclusion of All Markers versus Selection of Markers with Significant Effects 107

The Genomic Relationship Matrix 108

Summary 109

Chapter 15 Genetic Evaluation Based on Analysis of Genetic Evaluations or Daughter-Yield Evaluations 111

Introduction 111

Comparison of Single]Step and Multistep Models 111

Derivation and Properties of Daughter Yields and DYD 112

Computation of “Deregressed” Genetic Evaluations 113

Analysis of DYD as the Dependent Variable with All Markers Included as Random Effects 114

Computation of Reliabilities for Genomic Estimated Breeding Values 116

Bayesian Weighting of Marker Effects 116

Additional Bayesian Methods for Genomic Evaluation 117

Summary 117

Chapter 16 Genomic Evaluation Based on Analysis of Production Records 119

Introduction 119

Single-Step Methodologies: The Basic Strategy 119

Computation of the Modified Relationship Matrix when only a Fraction of the Animals are Genotyped: The Problem 120

Criteria for Valid Genetic Relationship Matrices 120

Computation of the Modified Relationship Matrix when only a Fraction of the Animals are Genotyped, the Solution 121

Solving the Mixed Model Equations without Inverting H 121

Inverting the Genomic Relationship Matrix 122

Estimation of Reliabilities for Genomic Breeding Values Derived by Single]Step Methodologies 122

Single-Step Computation of Genomic Evaluations with Unequally Weighted Marker Effects 123

Summary 124

Chapter 17 Validation of Methods for Genomic Estimated Breeding Values 125

Introduction 125

Criteria for Evaluation of Estimated Genetic Values 125

Methods Used to Validate Genomic Genetic Evaluations 126

Evaluation of Two-Step Methodology Based on Simulated Dairy Cattle Data 127

Evaluation of Multistep Methodology Based on Actual Dairy Cattle Data 127

Evaluation of Single-Step Methodologies Based on Actual Dairy Cattle Data 128

Evaluation of Single- and Multistep Methodologies Based on Actual Poultry Data 129

Evaluation of Single- and Multistep Methodologies Based on Actual Swine Data 130

Evaluation of GEBV for Plants Based on Actual Data 130

Summary 131

Chapter 18 By-Products of Genomic Analysis: Pedigree Validation and Determination 133

Introduction 133

The Effects of Incorrect Parentage Identification on Breeding Programs 133

Principles of Parentage Verification and Identification with Genetic Markers 134

Paternity Validation Prior to High]Density SNP Chips 135

Paternity Validation and Determination with SNP Chips 135

Validation of More Distant Relationships 136

Pedigree Reconstruction with High]Density Genetic Markers 137

Summary 137

Chapter 19 Imputation of Missing Genotypes: Methodologies, Accuracies, and Effects on Genomic Evaluations 139

Introduction 139

Determination of Haplotypes for Imputation 139

Imputation in Humans versus Imputation in Farm Animals 140

Algorithms Proposed for Imputation in Human and Animal Populations 141

Comparisons of Accuracy and Speed of Imputation Methods 142

Effect of Imputation on Genomic Genetic Evaluations 143

Summary 144

Chapter 20 Detection and Validation of Quantitative Trait Nucleotides 145

Introduction 145

GWAS for Economic Traits in Commercial Animals 146

Detection of QTN: Is It Worth the Effort? 146

QTN Determination in Farm Animals: What Constitutes Proof? 147

Concordance between DNA-Level Genotypes and QTL Status 148

Determination of Concordance by the “APGD” 148

Determination of Phase for Grandsires Heterozygous for the QTL 149

Determination of Recessive Lethal Genes by GWAS and Effects Associated with Heterozygotes 150

Verification of QTN by Statistical and Biological Methods 150

Summary 151

Chapter 21 Future Directions and Conclusions 153

Introduction 153

More Markers versus More Individuals with Genotypes 153

Computation of Genomic Evaluations for Cow and Female Calves 154

Improvement of Genomic Evaluation Methods 154

Long-Term Considerations 155

Weighting Evaluations of Old versus Young Bulls 156

Direct Genetic Manipulation in Farm Animals 156

Velogenetics: The Synergistic Use of MAS and Germ-Line Manipulation 157

Summary 157

References 159

Index 171