Chapter
1.3 Quantitative Genetics 1920–1980, or Who Needs Mendel?
1.4 QTL Detection 1930–1980, Theory and Experiments
1.5 From Biochemistry to Biotechnology, or More Markers Than We Will Ever Need
1.6 Genetic Mapping Functions
1.7 Physical and Genetic Mapping, Questions of Scale
2 Principles of Parameter Estimation
2.2 Desired Properties of QTL Parameter Estimates
2.3 Moments Method of Estimation
2.4 Least-squares Parameter Estimation
2.5 Least-squares Solutions for a Single Parameter
2.6 Least-squares Solutions for the General Linear Model
2.7 Maximum Likelihood Estimation for a Single Parameter
2.8 Maximum Likelihood Multi-parameter Estimation
2.9 Confidence Intervals and Hypothesis Testing for MLE
2.10 Methods to Maximize Likelihood Functions
2.11 Derivative-free Methods
2.12 Second Derivative-based Methods
2.13 First Derivative-based Methods (Expectation-maximization)
2.15 Minimum Difference Estimation
3 Random and Fixed Effects, the Mixed Model
3.2 The Mixed Linear Model
3.3 The Mixed Model Equations
3.4 Solving the Mixed Model Equations
3.5 Some Important Properties of Mixed Model Solutions
3.7 Multivariate Mixed Model Analysis
3.8 The Repeatability Model
3.9 The Individual Animal Model
3.10 Grouping Individuals with Unknown Ancestors
3.11 The Reduced Animal Model
3.12 Maximum Likelihood Estimation with Mixed Models
3.13 Estimation of Variance Components, Analysis of Variance-type Methods
3.14 Maximum Likelihood Estimation of Variance Components
3.15 Restricted Maximum Likelihood Estimation of Variance Components
3.16 The Problem of Variance Components Outside the Parameter Space
4 Experimental Designs to Detect QTL: Generation of Linkage Disequilibrium
4.2 Assumptions, Problems and Types of Effects Postulated
4.3 Experimental Designs for Detection of QTL in Crosses Between Inbred Lines
4.4 Linear Model Analysis of Crosses Between Inbred Lines
4.5 Experimental Designs for Detection of QTL in Segregating Populations: General Considerations
4.6 Experimental Designs for Detection of QTL in Segregating Populations: Large Families
4.7 Experimental Designs for Detection of QTL in Segregating Populations: Small Families
4.8 Experimental Designs Based on Additional Generations: Inbred Lines
4.9 Experimental Designs Based on Additional Generations: Segregating Populations
4.10 Comparison of the Expected Contrasts for Different Experimental Designs
4.11 Gametic Effect Models for Complete Population Analyses
5 QTL Parameter Estimation for Crosses between Inbred Lines
5.2 Moments Method of Estimation
5.3 Least-squares Estimation of QTL Parameters
5.4 Least-squares Estimation of QTL Location for Sib-pair Analysis with Flanking Markers
5.5 Linear Regression Mapping of QTL with Flanking Markers
5.6 Marker Information Content for Interval Mapping, Uninformative and Missing Marker Genotypes
5.7 Maximum Likelihood QTL Parameter Estimation for Crosses Between Inbred Lines and a Single Marker
5.8 Maximum Likelihood Tests of Significance for a Segregating QTL
5.9 Maximum Likelihood QTL Parameter Estimation for Crosses between Inbred Lines and Two Flanking Markers
5.10 Estimation of QTL Parameters by the Expectation-maximization Algorithm
5.11 Biases in Estimation of QTL Parameters with Interval Mapping
5.12 The Likelihood Ratio Test with Interval Mapping
6 Advanced Statistical Methods for QTL Detection and Parameter Estimation
6.2 Higher-order QTL Effects
6.3 QTL Interaction Effects
6.4 Simultaneous Analysis of Multiple Marker Brackets
6.5 Principles of Composite Interval Mapping
6.6 Properties of Composite Interval Mapping
6.7 Derivation of Maximum Likelihood Parameter Estimates by Composite Interval Mapping
6.8 Hypothesis Testing with Composite Interval Mapping
6.9 Multi-marker and QTL Analysis by Regression of Phenotype on Marker Genotypes
6.10 Estimation of QTL Parameters in Outbred Populations
6.11 Analysis of Field Data, Daughter and Granddaughter Designs
6.12 Maximum Likelihood Analysis of QTL Parameters for the Daughter Design with Linkage to a Single Marker
6.13 Non-linear and Linear Regression Estimation for Complex Pedigrees
6.14 Estimation of QTL Allelic Frequencies in Segregating Populations
6.15 Maximum Likelihood Estimation with Random Effects Included in the Model
6.16 Incorporation of Genotype Effects into Animal Model Evaluations When Only a Small Fraction of the Population Has Been Genotyped
6.17 Maximum Likelihood Estimation of QTL Effects on Categorical Traits
6.18 Estimation of QTL Effects with the Threshold Model
6.19 Estimation of QTL Effects on Disease Traits by the Allele-sharing Method
7 Analysis of QTL as Random Effects
7.2 ML Estimation of Variance Components for the Haseman–Elston Sib-pair Model
7.3 The Random Gametic Model of Fernando and Grossman, Computing G[sub(v)]
7.4 Computing the Inverse of G[sub(v)]
7.5 Analysis of the Random Gametic Model by a Reduced Animal Model
7.6 Analysis of the Random Gametic QTL Model with Multiple QTL and Marker Brackets
7.7 Computation of the Gametic Effects Variance Matrix
7.8 The Gametic Effect Model for Crosses Between Inbred Lines
7.9 REML Estimation of the QTL Variance and Recombination for the Model of Fernando and Grossman
7.10 REML Estimation of the QTL Variance and Location with Marker Brackets
7.11 Bayesian Estimation of QTL Effects, Determining the Prior Distribution
7.12 Formula for Bayesian Estimation and Tests of Significance of a Segregating QTL in a Simulated Granddaughter Design
7.13 Comparison of ML and Bayesian Analyses of a Simulated Granddaughter Design
7.14 Markov Chain Monte Carlo Algorithms, Gibbs Sampling
8 Statistical Power to Detect QTL, and Parameter Confidence Intervals
8.2 Estimation of Power in Crosses Between Inbred Lines
8.3 Replicate Progeny in Crosses Between Inbred Lines
8.4 Estimation of Power for Segregating Populations
8.5 Power Estimates for Likelihood Ratio Tests: General Considerations
8.6 The Effect of Statistical Methodology on the Power of QTL Detection
8.7 Estimation of Power with Random QTL Models
8.8 Confidence Intervals for QTL Parameters, Analytical Methods
8.9 Simulation Studies of Confidence Intervals
8.10 Empirical Methods to Estimate Confidence Intervals, Parametric and Nonparametric Bootstrap and Jackknife Methods
9 Optimization of Experimental Designs
9.2 Economic Optimization of Marker Spacing When the Number of Individuals Genotyped Is Non-limiting
9.3 Economic Optimization with Replicate Progeny
9.5 Sample Pooling: General Considerations
9.6 Estimation of Power with Sample Pooling
9.7 Comparison of Power and Sample Sizes with Random Genotyping, Selective Genotyping and Sample Pooling
10.2 Determination of the Genetic Map Critical Interval for a Marker Locus with a Saturated Genetic Marker Map
10.3 Confidence Interval for QTL Location with a Saturated Genetic Marker Map
10.4 Fine Mapping of QTL via Advanced Intercross Lines
10.5 Selective Phenotyping
10.6 Recombinant Progeny Testing
10.7 Interval-specific Congenic Strains
10.8 Recombinant Inbred Segregation Test
10.9 Fine Mapping of QTL in Outcrossing Populations by Identity by Descent
10.10 Estimation and Evaluation of Linkage Disequilibrium in Animal Populations
10.11 Linkage Disequilibrium QTL Mapping, Basic Principles
10.12 Linkage Disequilibrium Mapping, Advanced Topics
11 Complete Genome QTL Scans: The Problem of Multiple Comparisons
11.2 Multiple Markers and Whole-genome Scans
11.3 QTL Detection by Permutation Tests
11.4 QTL Detection Based on the False Discovery Rate
11.5 A Priori Determination of the Proportion of False Positives
11.6 Analysis of Multiple Pedigrees
11.7 Biases with Estimation of Multiple QTL
11.8 Bayesian Estimation of QTL from Whole-genome Scans, Theory
11.9 Bayesian Estimation of QTL from Whole-genome Scans, Simulation Results
12 Multitrait QTL Analysis
12.2 Problems and Solutions for Multitrait QTL Analyses
12.3 Multivariate Estimation of QTL Parameters for Correlated Traits
12.4 Comparison of Power for Single and Multitrait QTL Analyses
12.5 Pleiotropy Versus Linkage
12.6 Estimation of QTL Parameters for Correlated Traits by Canonical Transformation
12.7 Determination of Statistical Significance for Multitrait Analyses
12.8 Selective Genotyping with Multiple Traits
12.9 Multitrait LD Mapping
13 From the QTL to the Gene
13.2 The Molecular Basis of QTL Discovered So Far
13.3 Determination of QTL Candidate Genes
13.4 Determination of Concordance
13.5 QTN Validation by Other Statistical Methods
13.6 QTN Validation by Functional Studies
14 Principles of Selection Index and Traditional Breeding Programmes
14.2 Selection Index for a Single Trait
14.3 Changes in QTL Allelic Frequencies Due to Selection
14.4 Multitrait Selection Index
14.5 The Value of Genetic Gain
14.6 Dairy Cattle Breeding Programmes, Half-sib and Progeny Tests
14.7 Nucleus Breeding Schemes
15 Marker-assisted Selection: Theory
15.2 Situations in which Selection Index Is Inefficient
15.3 Potential Contribution of MAS for Selection Within a Breed: General Considerations
15.4 Phenotypic Selection Versus MAS for Individual Selection
15.5 MAS for Sex-limited Traits
15.6 Two-stage Selection: MAS on Juveniles, and Phenotypic Selection of Adults
15.7 MAS Including Marker and Phenotypic Information on Relatives
15.8 Maximum Selection Efficiency of MAS with All QTL Known, Relative to Trait-based Selection, and the Reduction in RSE Due to Sampling Variance
15.9 Marker Information in Segregating Populations
15.10 Inclusion of Marker Information in ‘Animal Model’ Genetic Evaluations
15.11 Genetic Evaluation Based on Dense Whole-genome Scans
15.12 Velogenetics: the Synergistic Use of MAS and Germ-line Manipulation
16 Marker-assisted Selection: Current Status and Results of Simulation Studies
16.2 Modelling the Polygenic Variance
16.3 The Effective Number of QTL
16.4 Proposed Dairy Cattle Breeding Schemes with MAS: Overview
16.5 Inclusion of Marker Information into Standard Progeny Test and MOET Nucleus Breeding Schemes
16.6 Progeny Test Schemes, in Which Information on Genetic Markers is Used to Preselect Young Sires
16.7 The Current Status of MAS in Dairy Cattle
16.8 Selection of Sires Based on Marker Information Without a Progeny Test
16.9 Computation of Reliabilities of Genetic Evaluations Based on Complete Genome Scans
16.10 Long-term Considerations, MAS Versus Selection Index
16.11 MAS for a Multitrait Breeding Objective with a Single Identified QTL
16.12 MAS for a Multitrait Breeding Objective with Multiple Identified QTL
17 Marker-assisted Introgression
17.2 Marker-assisted Introgression: General Considerations
17.3 Marker-assisted Introgression of a Major Gene into an Inbred Line
17.4 Marker-assisted Introgression of a QTL into a Donor Population Under Selection
17.5 Marker-assisted Introgression for Multiple Genes
Quantitative Trait Loci Analysis in Animals
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