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Index

Accuracy Back-solving for non-parents 61
animal model evaluations 50–52, with genetic marker
307–309 information 178
multivariate evaluations 90 for maternal traits 131
pedigree information 9
prediction from correlated trait Base animal 46, 62
12 Best linear prediction see Selection
progeny records 8
random regression model 152–154, index
309–310 Best linear unbiased prediction
repeated records 5
selection index 14–15 definition and properties 39
single record 2 derivation 303–305
for maternal traits 121–127
Analysis of quantitative and binary multivariate model 83–92
traits, jointly 224–233 non-additive effects 193–209
theoretical background 40–42
Analysis of variance 235, 237, 238 univariate animal model 42–52
Animal model Borderless evaluations 119
BREEDPLAN 40
approximate reliabilities Burn-in period 248, 251
for 307–309
Canonical transformation 92–95,
best linear unbiased 311–312
prediction 42–52
with missing records 312–314
with dominance effects Categorical traits 211
193–206 Cholesky decomposition 98–101, 258,

with groups 62–69 316
multivariate 83–92 Coancestry 25
with random environmental Coefficient of relationship see

effects 71–77 Coancestry
sire model 52–55
Average information 242

341

342 Index

Common environmental effects 77–81 Epistasis 2, 121, 206
Conditional posterior inverse of relationship
matrix 206–209
distribution 247, 249–251,
255–257 Fixed regression model 136–141
Contingency table 214, 224 partitioning evaluations 141
Convergence criterion 260–261, 288
Correlated response 12 Functions of the normal
Covariance function 136, 154–157 distribution 212–213
equivalence to random
regression 161–162 Gauss–Seidel iteration 263–264
Covariance matrix for MQTL effects Genetic marker information 163
definition and calculation 164–166,
167–169 in prediction of breeding
incomplete marker value 173–191
information 325, 331–332 animal model 173–174
inverse of 169–173 direct prediction of additive
origin of paternal and maternal genetic merit 19–81
marker alleles predicting total additive
unknown 325–328 genetic merit 179–181
with QTL bracketed by two
Daughter yield deviation markers 184–191
definition 48–50 in selection index 23
multivariate model 91–92, 104–105
random regression model 152 Genotype-by-environment
univariate model 50, 77 interaction 109, 118

Degrees of freedom 236, 237, 238, 239 Gibbs sampling 247
Deregression of breeding values 109 inferences from Gibbs
sampler 251–252
computation 317–319 multivariate animal model 254
Design matrices univariate animal model
248–251
equal, with missing records 95
equal, with no missing records 84 Groups, animal model 62–69
Direct genetic effect 121
Dominance 2, 121 Henderson’s method 3 238
animal model with dominance
Identical by descent (IBD) 164, 325
effects 194–198 Inbreeding
rapid inverse of relationship
conditional inbreeding
matrix 198–203 coefficient 327
relationship matrix 191–194
fast algorithm
Effective daughter contribution 111 inbreeding coefficient 25, 28
EM algorithm 241 and inverse of relationship matrix
Environmental effects Indirect genetic effect 121
Infinitesimal model 2
common environmental Intra-class correlation 7
effects 77–81
Jacobi iteration 260–261
permanent environmental effects 4, second-order Jacobi 261
7, 76, 121

random environmental
effects 71–77

temporary environmental effects 4

Index 343

Joint analysis of quantitative and Cholesky transformation 98–101
binary traits 224–233 different traits on relatives 106
equal design matrices
Joint distribution 249
missing records 95
Kronecker product 293 multi-trait across country

Lactation curve 140–141, 148 evaluations 109–111
Least-square equations (LSE) 44 no environmental
Legendre polynomials 137
covariance 105
computation matrix of 321–323 no missing records 84
Liability 211 Multi-trait across-country evaluations
Linear model, solving 259–288 (MACE) 109–114
Log-likelihood 240 limitations of MACE 118–119
LOKI 332 partitioning MACE
Longitudinal data 136 evaluations 114–118

Marker-assisted selection 163 Non-additive animal models
Markov Chain Monte Carlo 193–209

(MCMC) 247, 332 Non-linear model 211
Maternal traits 121 Numerator relationship matrix 25–26

animal model with 122–127 accounting for inbreeding 32–33
multivariate model with 133–134 decomposing 27
reduced animal model 127–133 with groups 64
Matrix ignoring inbreeding 29–30
addition and subtraction 292 inverse 28
definition 289–290 for sires and maternal
diagonal 290
direct product 293 grandsires 34, 110
eigenvalues 295–296
eigenvectors 295–296 Overall economic indices 20
generalized inverse 295
inverse 293 Permanent environmental effect 4, 72,
multiplication 292 76, 121
rank 294
square 290 PEST 40
symmetric 291 PEV see Prediction error variance
transpose of 291 Phantom parents 62, 64, 67
triangular 290 Preconditioned conjugate gradient
Mendelian sampling 2, 27, 47, 56
Meuwissen and Luo algorithm (PCG) 283–285
Prediction error variance 51, 240
algorithm 297–300 Prior distributions 247, 248–249,
modified 300–301
Mixed model equations (MME) 254–255
Probability of descent of a marker
41, 43
Mothering ability see Maternal traits allele (PDM) 326–327
Multivariate best linear unbiased Probability of descent of a QTL allele

prediction 83–92 (PDQ) 326
canonical transformation 92–95 Probable producing ability 76
Progeny contribution 46

derivation 305–306
Progeny yield deviation see Daughter

yield deviation

344 Index

Quantitative trait loci (QTL) 163, 184 aggregate genotype 18–20
for correlated traits 15–16
Random regression model 136, means of records 17–18
143–148 overall economic indices 20–21
phenotype and genetic marker
equivalence to covariance
function 161–162 information 23
properties 13
for maternal traits 154 single records 16–17
partitioning evaluations 148 Sire model 52–55
reliabilities, approximate 309–310 Standard error of prediction 51
RAM see Reduced animal model
Recombination rate 165 Threshold model 211, 212–215
Reduced animal model 55–58, Transmitting ability

127–133 estimated 3
with genetic marker predicted 2, 3

information 174–179, 191 Underlying continuous trait 211
Relatives
Variance component estimation
genetic covariance between 25–37 animal model 240–242
Relaxation factor 261 extended model 237–240
Reliability see Accuracy univariate sire model 235
REML see Restricted maximum
Variance of estimated breeding
likelihood value 4
Repeatability model 71–73, 135
Response to selection Yield deviation 46, 76
fixed regression model 141
pedigree information 10 multivariate model 88
progeny records 8 random regression model 149
repeated records 6
single record 3
Restricted maximum likelihood 42,

240

Segregation indicators 332
Selection index 12–14, 39, 41