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El. knyga: Linear Models for the Prediction of Animal Breeding Values [CABI E-books]

(Scotland's Rural College (SRUC), UK and the International Livestock Research Institute (ILRI), Kenya)
  • Formatas: 360 pages
  • Išleidimo metai: 28-Feb-2014
  • Leidėjas: CABI Publishing
  • ISBN-13: 9781780643915
Kitos knygos pagal šią temą:
  • CABI E-books
  • Kaina: 114,00 €*
  • * this price gives unlimited concurrent access for unlimited time
Linear Models for the Prediction of Animal Breeding ValuesDidesnis paveikslėlis
  • Formatas: 360 pages
  • Išleidimo metai: 28-Feb-2014
  • Leidėjas: CABI Publishing
  • ISBN-13: 9781780643915
Kitos knygos pagal šią temą:
Wiley OnlineMore info about CABI e-books
The prediction of producing desirable traits in offspring such as increased growth rate or superior meat, milk and wool production is a vital economic tool to the animal scientist. Summarizing the latest developments in genomics relating to animal breeding values and design of breeding programs, this new edition includes models of survival analysis, social interaction and sire and dam models, as well as advancements in the use of SNPs in the computation of genomic breeding values.
Preface xiii
Abbreviations xv
1 Genetic Evaluation with Different Sources of Records
1(21)
1.1 Introduction
1(1)
1.2 The Basic Model
1(1)
1.3 Breeding Value Prediction from the Animal's Own Performance
2(4)
1.3.1 Single record
2(1)
1.3.2 Repeated records
3(3)
1.4 Breeding Value Prediction from Progeny Records
6(3)
1.5 Breeding Value Prediction from Pedigree
9(1)
1.6 Breeding Value Prediction for One Trait from Another
10(1)
1.7 Selection Index
11(11)
1.7.1 Accuracy of index
12(2)
1.7.2 Examples of selection indices using different sources of information
14(2)
1.7.3 Prediction of aggregate genotype
16(2)
1.7.4 Overall economic indices using predicted genetic merit
18(1)
1.7.5 Restricted selection index
19(2)
1.7.6 Index combining breeding values from phenotype and genetic marker information
21(1)
2 Genetic Covariance Between Relatives
22(12)
2.1 Introduction
22(1)
2.2 The Numerator Relationship Matrix
22(1)
2.3 Decomposing the Relationship Matrix
23(2)
2.4 Computing the Inverse of the Relationship Matrix
25(5)
2.4.1 Inverse of the numerator relationship matrix ignoring inbreeding
26(2)
2.4.2 Inverse of the numerator relationship matrix accounting for inbreeding
28(2)
2.5 Inverse of the Relationship Matrix for Sires and Maternal Grandsires
30(2)
2.6 An Example of the Inverse of a Sire and Maternal Grandsire Relationship Matrix
32(2)
3 Best Linear Unbiased Prediction of Breeding Value: Univariate Models with One Random Effect
34(27)
3.1 Introduction
34(1)
3.2 Brief Theoretical Background
35(2)
3.3 A Model for an Animal Evaluation (Animal Model)
37(9)
3.3.1 Constructing the mixed model equations
38(4)
3.3.2 Progeny (daughter) yield deviation
42(2)
3.3.3 Accuracy of evaluations
44(2)
3.4 A Sire Model
46(3)
3.4.1 An illustration
46(3)
3.5 Reduced Animal Model
49(5)
3.5.1 Defining the model
49(2)
3.5.2 An illustration
51(3)
3.5.3 An alternative approach
54(1)
3.6 Animal Model with Groups
54(7)
3.6.1 An illustration
56(5)
4 Best Linear Unbiased Prediction of Breeding Value: Models with Random Environmental Effects
61(9)
4.1 Introduction
61(1)
4.2 Repeatability Model
61(5)
4.2.1 Defining the model
62(1)
4.2.2 An illustration
62(4)
4.2.3 Calculating daughter yield deviations
66(1)
4.3 Model with Common Environmental Effects
66(4)
4.3.1 Defining the model
67(1)
4.3.2 An illustration
67(3)
5 Best Linear Unbiased Prediction of Breeding Value: Multivariate Animal Models
70(25)
5.1 Introduction
70(1)
5.2 Equal Design Matrices and No Missing Records
71(7)
5.2.1 Defining the model
71(1)
5.2.2 An illustration
72(2)
5.2.3 Partitioning animal evaluations from multivariate analysis
74(2)
5.2.4 Accuracy of multivariate evaluations
76(1)
5.2.5 Calculating daughter yield deviations in multivariate models
77(1)
5.3 Equal Design Matrices with Missing Records
78(2)
5.3.1 An illustration
78(2)
5.4 Unequal Design Matrices
80(4)
5.4.1 Numerical example
80(2)
5.4.2 Illustrating the computation of DYD from a multivariate model
82(2)
5.5 Multivariate Models with No Environmental Covariance
84(11)
5.5.1 Different traits recorded on relatives
84(2)
5.5.2 The multi-trait across-country evaluations (MACE)
86(9)
6 Methods to Reduce the Dimension of Multivariate Models
95(14)
6.1 Introduction
95(1)
6.2 Canonical Transformation
95(3)
6.2.1 The model
96(1)
6.2.2 An illustration
97(1)
6.3 Cholesky Transformation
98(3)
6.3.1 Calculating the transformation matrix and defining the model
98(1)
6.3.2 An illustration
99(2)
6.4 Factor and Principal Component Analysis
101(8)
6.4.1 Factor analysis
102(3)
6.4.2 Principal component analysis
105(1)
6.4.3 Analysis with reduced rank PC model
106(3)
7 Maternal Trait Models: Animal and Reduced Animal Models
109(12)
7.1 Introduction
109(1)
7.2 Animal Model for a Maternal Trait
110(5)
7.2.1 An illustration
110(5)
7.3 Reduced Animal Model with Maternal Effects
115(4)
7.3.1 An illustration
116(3)
7.4 Sire and Maternal Grandsire Model
119(2)
8 Social Interaction Models
121(9)
8.1 Introduction
121(2)
8.2 Animal Model with Social Interaction Effects
123(4)
8.2.1 Illustration of a model with social interaction
125(2)
8.3 Partitioning Evaluations from Associative Models
127(1)
8.4 Analysis Using Correlated Error Structure
128(2)
9 Analysis of Longitudinal Data
130(26)
9.1 Introduction
130(1)
9.2 Fixed Regression Model
131(5)
9.2.1 An illustration
132(4)
9.3 Random Regression Model
136(13)
9.3.1 Numerical application
138(4)
9.3.2 Partitioning animal solutions from random regression model
142(3)
9.3.3 Calculating daughter yield deviations
145(1)
9.3.4 Reliability of breeding values
146(1)
9.3.5 Random regression models with spline function
147(1)
9.3.6 Random regression model for maternal traits
148(1)
9.4 Covariance Functions
149(6)
9.4.1 Fitting a reduced order covariance function
151(4)
9.5 Equivalence of the Random Regression Model to the Covariance Function
155(1)
10 Use of Genetic Markers in Breeding Value Prediction
156(21)
10.1 Introduction
156(1)
10.2 Defining a Model with Marker Information
156(1)
10.3 Calculating the Covariance Matrix (Gv) for MQTL Effects
157(3)
10.3.1 Numerical application
158(2)
10.4 An Alternative Approach for Calculating Gv
160(1)
10.5 Calculating the Inverse of Gv
161(4)
10.6 Prediction of Breeding Values with Marker Information
165(2)
10.6.1 An illustration
165(2)
10.7 Directly Predicting the Additive Genetic Merit at the MQTL
167(2)
10.7.1 An illustration
168(1)
10.8 Predicting Total Additive Genetic Merit
169(2)
10.8.1 Numerical application
169(2)
10.9 Analysis of Data with QTL Bracketed by Two Markers
171(6)
10.9.1 Basic model
171(1)
10.9.2 Calculating the covariance matrix, G
172(2)
10.9.3 An illustration
174(3)
11 Computation of Genomic Breeding Values and Genomic Selection
177(27)
11.1 Introduction
177(1)
11.2 General Linear Model
178(1)
11.3 Coding and Scaling Genotypes
178(1)
11.4 Fixed Effect Model for SNP Effects
179(3)
11.5 Mixed Linear Model for Computing SNP Effects
182(6)
11.5.1 SNP-BLUP model
183(1)
11.5.2 Equivalent models: GBLUP
184(3)
11.5.3 Equivalent models: selection index approach
187(1)
11.6 Mixed Linear Models with Polygenic Effects
188(2)
11.7 Single-step Approach
190(3)
11.8 Bayesian Methods for Computing SNP Effects
193(9)
11.8.1 BayesA
194(3)
11.8.2 BayesB
197(2)
11.8.3 BayesC
199(2)
11.8.4 BayesCπ
201(1)
11.9 Cross-validation and Genomic Reliabilities
202(1)
11.10 Understanding SNP Solutions from the Various Models
202(2)
12 Non-additive Animal Models
204(15)
12.1 Introduction
204(1)
12.2 Dominance Relationship Matrix
204(1)
12.3 Animal Model with Dominance Effect
205(4)
12.3.1 Solving for animal and dominance genetic effects separately
206(2)
12.3.2 Solving for total genetic merit directly
208(1)
12.4 Method for Rapid Inversion of the Dominance Matrix
209(6)
12.4.1 Inverse of the relationship matrix of subclass effects
210(1)
12.4.2 Prediction of dominance effects
211(1)
12.4.3 Calculating the inverse of the relationship matrix among dominance and subclass effects for example data
212(3)
12.5 Epistasis
215(4)
12.5.1 Rules for the inverse of the relationship matrix for epistatic and subclass effects
216(1)
12.5.2 Calculating the inverse relationship matrix for epistasis and the subclass matrix for an example pedigree
217(2)
13 Analysis of Ordered Categorical Traits
219(21)
13.1 Introduction
219(1)
13.2 The Threshold Model
220(10)
13.2.1 Defining some functions of the normal distribution
220(1)
13.2.2 Data organization and the threshold model
221(2)
13.2.3 Numerical example
223(7)
13.3 Joint Analysis of Quantitative and Binary Traits
230(10)
13.3.1 Data and model definition
230(4)
13.3.2 Numerical application
234(6)
14 Survival Analysis
240(11)
14.1 Introduction
240(1)
14.2 Functional Survival
240(1)
14.3 Censoring
240(1)
14.4 Models for Analysis of Survival
241(10)
14.4.1 Linear models
241(1)
14.4.2 Random regression models for survival
241(2)
14.4.3 Proportional hazard models
243(2)
14.4.4 Non-parametric estimation of the survival function
245(1)
14.4.5 Regression survival models
246(1)
14.4.6 Mixed survival models
247(3)
14.4.7 Group data survival model
250(1)
15 Estimation of Genetic Parameters
251(9)
Robin Thompson
15.1 Introduction
251(1)
15.2 Univariate Sire Model
251(1)
15.3 Numerical Example of Sire Model
252(1)
15.4 Extended Model
253(1)
15.5 Numerical Example
254(1)
15.6 Animal Model
255(2)
15.7 Numerical Example
257(3)
16 Use of Gibbs Sampling in Variance Component Estimation and Breeding Value Prediction
260(11)
16.1 Introduction
260(1)
16.2 Univariate Animal Model
261(5)
16.2.1 Prior distributions
261(1)
16.2.2 Joint and full conditional distributions
262(2)
16.2.3 Inferences from the Gibbs sampling output
264(1)
16.2.4 Numerical application
265(1)
16.3 Multivariate Animal Model
266(5)
16.3.1 Prior distributions
267(1)
16.3.2 Conditional probabilities
267(2)
16.3.3 Numerical illustration
269(2)
17 Solving Linear Equations
271(28)
17.1 Introduction
271(1)
17.2 Direct Inversion
271(1)
17.3 Iteration on the Mixed Model Equations
271(5)
17.3.1 Jacobi iteration
272(3)
17.3.2 Gauss--Seidel iteration
275(1)
17.4 Iterating on the Data
276(16)
17.4.1 Animal model without groups
278(4)
17.4.2 Animal model with groups
282(2)
17.4.3 Reduced animal model with maternal effects
284(8)
17.5 Preconditioned Conjugate Gradient Algorithm
292(7)
17.5.1 Computation strategy
293(1)
17.5.2 Numerical application
294(5)
Appendix A Introduction to Matrix Algebra
299(7)
A.1 Matrix: A Definition
299(1)
A.2 Special Matrices
300(1)
A.2.1 Square matrix
300(1)
A.2.2 Diagonal matrix
300(1)
A.2.3 Triangular matrix
300(1)
A.2.4 Symmetric matrix
301(1)
A.3 Basic Matrix Operations
301(5)
A.3.1 Transpose of a matrix
301(1)
A.3.2 Matrix addition and subtraction
301(1)
A.3.3 Matrix multiplication
302(1)
A.3.4 Direct product of matrices
302(1)
A.3.5 Matrix inversion
303(1)
A.3.6 Rank of a matrix
304(1)
A.3.7 Generalized inverses
305(1)
A.3.8 Eigenvalues and eigenvectors
305(1)
Appendix B Fast Algorithms for Calculating Inbreeding Based on the L Matrix
306(5)
B.1 Meuwissen and Luo Algorithm
306(2)
B.1.1 Illustration of the algorithm
307(1)
B.2 Modified Meuwissen and Luo Algorithm
308(3)
B.2.1 Illustration of the algorithm
309(2)
Appendix C
311(3)
C.1 Outline of the Derivation of the Best Linear Unbiased Prediction (BLUP)
311(1)
C.2 Proof that b and a from MME are the GLS of b and BLUP of a, Respectively
312(1)
C.3 Deriving the Equation for Progeny Contribution (PC)
313(1)
Appendix D Methods for Obtaining Approximate Reliability for Genetic Evaluations
314(4)
D.1 Computing Approximate Reliabilities for an Animal Model
314(2)
D.2 Computing Approximate Reliabilities for Random Regression Models
316(2)
D.2.1 Determine value of observation for an animal
316(1)
D.2.2 Value of records on descendants
316(1)
D.2.3 Value of records on ancestors
317(1)
Appendix E
318(5)
E.1 Canonical Transformation: Procedure to Calculate the Transformation Matrix and its Inverse
318(1)
E.2 Canonical Transformation with Missing Records and Same Incidence Matrices
319(3)
E.2.1 Illustration
320(2)
E.3 Cholesky Decomposition
322(1)
Appendix F Procedure for Computing Deregressed Breeding Values
323(2)
Appendix G Calculating Φ, a Matrix of Legendre Polynomials Evaluated at Different Ages or Time Periods
325(2)
References 327(10)
Index 337
Raphael Mrode is Professor of Quantitative Genetics and Genomics at Scotland's Rural College and Principal Scientist in Quantitative Genetics in Dairy Cattle at the International Livestock Research Institute, Nairobi, Kenya. He has been lecturing on Edinburgh University's Masters course on quantitative genetics and genome analysis since 2005, and has given lectures on mixed linear models and the use of various BLUP models for genetic prediction. His research interests include data modelling and analysis, the incorporation of molecular information in genetic evaluation procedures, the application of innovative approaches for data capture, analysis and feedback and investigating methods for generating alternative and novel phenotypes in small dairy systems in developing countries.
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