دانلود کتاب Linear Models for the Prediction of Animal Breeding Values (Cabi Publishing)

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Contents......Page 5
Preface......Page 11
1.1 The Basic Model......Page 15
1.2.1 Single record......Page 17
1.2.2 Repeated records......Page 18
1.3 Breeding Value Prediction from Progeny Records......Page 21
1.4 Breeding Value Prediction from Pedigree......Page 24
1.5 Breeding Value Prediction for One Trait from Another......Page 25
1.6 Selection Index......Page 26
1.6.1 Accuracy of index......Page 28
1.6.2 Examples of selection indices using different sources of information......Page 29
1.6.3 Prediction of aggregate genotype......Page 32
1.6.4 Overall economic indices using predicted genetic merit......Page 34
1.6.5 Restricted selection index......Page 35
1.6.6 Index combining breeding values from phenotype and genetic marker information......Page 37
2.1 The Numerator Relationship Matrix......Page 39
2.2 Decomposing the Relationship Matrix......Page 41
2.3 Computing the Inverse of the Relationship Matrix......Page 42
2.3.1 Inverse of the numerator relationship matrix, ignoring inbreeding......Page 43
2.3.2 Inverse of the numerator relationship matrix accounting for inbreeding......Page 46
2.4 Inverse of the Relationship Matrix for Sires and Maternal Grandsires......Page 48
2.4.1 An example of the inverse of the relationship matrix for sires and maternal grandsires......Page 50
3 Best Linear Unbiased Prediction of Breeding Value: Univariate Models with One Random Effect......Page 53
3.1 Brief Theoretical Background......Page 54
3.2 A Model for an Animal Evaluation (Animal Model)......Page 56
3.2.1 Constructing the mixed model equations......Page 57
3.2.2 Progeny (daughter) yield deviation......Page 62
3.2.3 Accuracy of evaluations......Page 64
3.3 A Sire Model......Page 66
3.3.1 An illustration......Page 67
3.4 Reduced Animal Model......Page 69
3.4.1 Defining the model......Page 70
3.4.2 An illustration......Page 72
3.4.3 An alternative approach......Page 75
3.5 Animal Model with Groups......Page 76
3.5.1 An illustration......Page 78
4.1 Repeatability Model......Page 85
4.1.1 Defining the model......Page 86
4.1.2 An illustration......Page 87
4.2 Model with Common Environmental Effects......Page 91
4.2.1 Defining the model......Page 92
4.2.2 An illustration......Page 93
5 Best Linear Unbiased Prediction of Breeding Value: Multivariate Models......Page 97
5.1.1 Defining the model......Page 98
5.1.2 An illustration......Page 99
5.1.3 Partitioning animal evaluations from multivariate analysis......Page 102
5.1.4 Accuracy of multivariate evaluations......Page 104
5.1.5 Calculating daughter yield deviations in multivariate models......Page 105
5.2 Canonical Transformation......Page 106
5.2.2 An illustration......Page 107
5.3 Equal Design Matrices with Missing Records......Page 109
5.3.1 An illustration......Page 110
5.4.1 Calculating the transformation matrix and defining the model......Page 112
5.4.2 An illustration......Page 113
5.5 Unequal Design Matrices......Page 115
5.5.1 Numerical example......Page 116
5.5.2 Illustrating the computation of DYD from a multivariate model......Page 118
5.6 Multivariate Models with No Environmental Covariance......Page 119
5.6.1 Different traits recorded on relatives......Page 120
5.6.2 The multi-trait across-country evaluations (MACE)......Page 123
6 Maternal Trait Models: Animal and Reduced Animal Models......Page 135
6.1 Animal Model for a Maternal Trait......Page 136
6.1.1 An illustration......Page 137
6.2 Reduced Animal Model with Maternal Effects......Page 141
6.2.1 An illustration......Page 143
6.3 Multivariate Maternal Animal Model......Page 147
7 Analysis of Longitudinal Data......Page 149
7.1 Fixed Regression Model......Page 150
7.1.1 Illustration......Page 151
7.2 Random Regression Model......Page 157
7.2.1 Numerical application......Page 158
7.2.2 Partitioning animal solutions from the random regression model......Page 162
7.2.4 Reliability of breeding values......Page 166
7.3 Covariance Functions......Page 168
7.3.1 Fitting a reduced-order covariance function......Page 171
7.4 Equivalence of the Random Regression Model to the Covariance Function......Page 175
8.1 Defining a Model with Marker Information......Page 177
8.2 Calculating the Covariance Matrix (G[sub(v)]) for MQTL Effects......Page 178
8.2.1 Numerical application......Page 180
8.3 An Alternative Approach for Calculating (G[sub(v)])......Page 181
8.4 Calculating the Inverse of (G[sub(v)])......Page 183
8.5.1 An illustration......Page 187
8.6 Reduced Animal Model with Marker Information......Page 188
8.6.1 Numerical example......Page 190
8.6.2 Back-solving for solutions of non-parents......Page 192
8.7 Directly Predicting the Additive Genetic Merit at the MQTL......Page 193
8.7.1 An illustration......Page 195
8.8 Predicting Total Additive Genetic Merit......Page 196
8.8.1 Numerical application......Page 197
8.9.1 Basic model......Page 198
8.9.2 Calculating the covariance matrix, G......Page 199
8.9.3 An illustration......Page 202
8.10 Reduced Animal Model......Page 205
9.1 Dominance Relationship Matrix......Page 207
9.2 Animal Model with Dominance Effect......Page 208
9.2.1 Solving for animal and dominance genetic effects separately......Page 209
9.3 Method for Rapid Inversion of the Dominance Matrix......Page 212
9.3.1 Inverse of the relationship matrix of subclass effects......Page 214
9.3.3 Calculating the inverse of the relationship matrix among dominance and subclass effects for example data......Page 216
9.4.1 Rules for the inverse of the relationship matrix for epistatic and subclass effects......Page 220
9.4.2 Calculating the inverse relationship matrix for epistasis and the subclass matrix for an example pedigree......Page 221
10 Analysis of Ordered Categorical Traits......Page 225
10.1.1 Defining some functions of the normal distribution......Page 226
10.1.2 Data organization and the threshold model......Page 227
10.1.3 Numerical example......Page 229
10.2.1 Data and model definition......Page 238
10.2.2 Numerical application......Page 242
11.1 Univariate Sire Model......Page 249
11.2 Numerical Example of Sire Model......Page 250
11.3 Extended Model......Page 251
11.4 Numerical Example......Page 253
11.5 Animal Model......Page 254
11.6 Numerical Example......Page 256
12.1 Introduction......Page 261
12.2.1 Prior distributions......Page 262
12.2.2 Joint and full conditional distributions......Page 263
12.2.3 Inferences from the Gibbs sampling output......Page 265
12.2.4 Numerical application......Page 267
12.3.1 Prior distributions......Page 268
12.3.2 Conditional distributions......Page 269
12.3.3 Numerical illustration......Page 271
13.1 Direct Inversion......Page 273
13.2.1 Jacobi iteration......Page 274
13.2.2 Gauss–Seidel iteration......Page 277
13.3 Iterating on the Data......Page 278
13.3.1 Animal model without groups......Page 281
13.3.2 Animal model with groups......Page 285
13.3.3 Reduced animal model with maternal effects......Page 288
13.4 Preconditioned Conjugate Gradient Algorithm......Page 297
13.4.1 Computation strategy......Page 298
13.4.2 Numerical application......Page 299
A.1 Matrix: a Definition......Page 303
A.2.3 Triangular matrix......Page 304
A.3.1 Transpose of a matrix......Page 305
A.3.3 Matrix multiplication......Page 306
A.3.5 Matrix inversion......Page 307
A.3.6 Rank of a matrix......Page 308
A.3.8 Eigenvalues and eigenvectors......Page 309
B.1 Meuwissen and Luo Algorithm......Page 311
B.1.1 Illustration of the algorithm......Page 312
B.2 Modified Meuwissen and Luo Algorithm......Page 314
B.2.1 Illustration of the algorithm......Page 315
C.1 Outline of the Derivation of the Best Linear Unbiased Prediction (BLUP)......Page 317
C.2 Proof that b and â from the Mixed Model Equations are the Generalized Least-square Solution of b and the Best Linear Unbiased Prediction of a, Respectively......Page 318
C.3 Deriving the Equation for Progeny Contribution (PC)......Page 319
D.1 Computing Approximate Reliabilities for an Animal Model......Page 321
D.2 Computing Approximate Reliabilities for Random Regression Models......Page 323
E.1 Canonical Transformation: Procedure to Calculate the Transformation Matrix and its Inverse......Page 325
E.2 Canonical Transformation with Missing Records and Same Incidence Matrices......Page 326
E.2.1 Illustration......Page 328
E.3 Cholesky Decomposition......Page 330
Appendix F: Procedure for Computing De-regressed Breeding Values......Page 331
Appendix G: Calculating Φ, a Matrix of Legendre Polynomials Evaluated at Different Ages or Time Periods......Page 335
H.1 Covariance Between Individuals......Page 339
H.2 Covariance Within Individuals......Page 341
H.3.1 An illustration......Page 342
H.4 Computing Inverse of G[sub(v)]......Page 344
H.5 Incomplete Marker Data......Page 345
References......Page 347
C......Page 355
J......Page 356
P......Page 357
Y......Page 358