Page 8 - Linear Models for the Prediction of Animal Breeding Values

10.7. Directly Predicting the Additive Genetic
Merit at the MQTL 167
10.7.1. An illustration 168
10.8. Predicting Total Additive Genetic Merit 169
10.8.1. Numerical application 169
10.9. Analysis of Data with QTL Bracketed by Two Markers 171
10.9.1. Basic model 171
10.9.2. Calculating the covariance matrix, G 172
10.9.3. An illustration 174

11. Computation of Genomic Breeding Values and Genomic Selection 177
11.1. Introduction 177
11.2. General Linear Model 178
11.3. Coding and Scaling Genotypes 178
11.4. Fixed Effect Model for SNP Effects 179
11.5. Mixed Linear Model for Computing SNP Effects 182
11.5.1. SNP-BLUP model 183
11.5.2. Equivalent models: GBLUP 184
11.5.3. Equivalent models: selection index approach 187
11.6. Mixed Linear Models with Polygenic Effects 188
11.7. Single-step Approach 190
11.8. Bayesian Methods for Computing SNP Effects 193
11.8.1. BayesA 194
11.8.2. BayesB 197
11.8.3. BayesC 199
11.8.4. BayesCπ 201
11.9. Cross-validation and Genomic Reliabilities 202
11.10. Understanding SNP Solutions from
the Various Models 202

12. Non-additive Animal Models 204
12.1. Introduction 204
12.2. Dominance Relationship Matrix 204
12.3. Animal Model with Dominance Effect 205
12.3.1. Solving for animal and dominance genetic
effects separately 206
12.3.2. Solving for total genetic merit directly 208
12.4. Method for Rapid Inversion of the Dominance Matrix 209
12.4.1. Inverse of the relationship matrix of subclass effects 210
12.4.2. Prediction of dominance effects 211
12.4.3. Calculating the inverse of the relationship matrix
among dominance and subclass effects for example data 212
12.5. Epistasis 215
12.5.1. Rules for the inverse of the relationship matrix
for epistatic and subclass effects 216
12.5.2. Calculating the inverse relationship matrix for
epistasis and the subclass matrix for
an example pedigree 217

viii Contents