1 Basic Genetics
1.1 Introduction
1.2 Genes and Chromosomes
1.3 Meiosis
1.4 Mendel's Laws
1.4.1 Mendel's First Law
1.4.2 Mendel's Second Law
1.5 Linkage and Mapping
1.6 Interference
1.7 Quantitative Genetics
1.7.1 Population Properties of Genes
1.7.2 A General Quantitative Genetic Model
1.7.3 Genetic Models for the Backcross and F2 Design
1.7.4 Epistatic Model
1.7.5 Heritability and Its Estimation
1.7.6 Genetic Architecture
1.7.7 The Estimation of Gene Number
1.8 Molecular Genetics
1.9 SNP
1.10 Exercises
1.11 Note
1.11.1 Modeling Unequal Genetic EŽects by the Gamma Function
1.11.2 Modeling Unequal Genetic EŽects by a Geometric Series
2 Basic Statistics
2.1 Introduction
2.1.1 Populations and Models
2.1.2 Samples
2.2 Likelihood Estimation
2.3 Hypothesis Testing
2.3.1 The Pearson Chi-Squared Test
2.3.2 Likelihood Ratio Tests
2.3.3 Simulation-Based Approach
2.3.4 Bayesian Estimation
2.4 Exercises
3 Linkage Analysis and Map Construction
3.1 Introduction
3.2 Experimental Design
3.3 Mendelian Segregation
3.3.1 Testing Marker Segregation Patterns
3.4 Segregation Patterns in a Full-Sib Family
3.5 Two-Point Analysis
3.5.1 Double Backcross
3.5.2 Double Intercross - F2
3.6 Three-Point Analysis
3.7 Multilocus Likelihood and Locus Ordering
3.8 Estimation with Many Loci
3.9 Mixture Likelihoods and Order Probabilities
3.10 Map Functions
3.10.1 Mather's Formula
3.10.2 The Morgan Map Function
3.10.3 The Haldane Map Function
3.10.4 The Kosambi Map Function
3.11 Exercises
3.12 Notes: Algorithms and Software for Map Construction
4 A General Model for Linkage Analysis in Controlled Crosses
4.1 Introduction
4.2 Fully Informative Markers: A Diplotype Model
4.2.1 Two-Point Analysis
4.2.2 A More General Formulation
4.2.3 Three-Point Analysis
4.2.4 A More General Formulation
4.3 Fully Informative Markers: A Genotype Model
4.3.1 Parental Diplotypes
4.4 Joint modeling of the Linkage, Parental Diplotype, and Gene Order
4.5 Partially Informative Markers
4.5.1 Joint modeling of the Linkage and Parental Diplotype
4.5.2 Joint modeling of the Linkage, Parental Diplotype, and Gene
Order
4.6 Exercises
4.6.1 One dominant marker
4.6.2 One dominant marker and one F2 codominant marker
4.7 Notes
4.7.1 Linkage Analysis
4.7.2 The Diplotype Probability
4.7.3 Gene Order
4.7.4 M-Point Analysis
5 Linkage Analysis with Recombinant Inbred Lines
5.1 Introduction
5.2 RILs by SelŻng
5.2.1 Two-Point Analysis
5.2.2 Three-Point Analysis
5.3 RILs by Sibling Mating
5.3.1 Two-point Analysis
5.3.2 Three-Point Analysis
5.4 Bias Reduction
5.4.1 RILs by Selfing
5.4.2 RILs by Sibling Mating
5.5 Multiway RILs
5.6 Exercises
5.7 Note
6 Linkage Analysis for Distorted and Misclassified Markers
6.1 Introduction
6.2 Gametic Differential Viability
6.2.1 One-Gene Model
6.2.2 Two-Gene Model
6.2.3 Simulation
6.3 Zygotic Differential Viability
6.3.1 One-Gene Model
6.3.2 Two-Gene Model
6.3.3 Simulation
6.4 Misclassification
6.4.1 One-gene Model
6.4.2 Two-Gene Model
6.5 Simulation
6.6 Exercises
7 Special Considerations in Linkage Analysis
7.1 Introduction
7.2 Linkage Analysis with a Complicated Pedigree
7.2.1 A Nuclear Family
7.2.2
7.2.3 A Complex Pedigree
7.3 Information Analysis of Dominant Markers
7.3.1 Introduction
7.3.2 Segregation Analysis
7.3.3 Linkage Analysis
7.4 Exercises
8 Marker Analysis of Phenotypes
8.1 Introduction
8.2 QTL Regression Model
8.3 Analysis at the Marker
8.3.1 Two-Sample t Test
8.3.2 Analysis of Variance
8.3.3 Genetic Analysis
8.4 Moving Away from the Marker
8.4.1 Likelihood
8.5 Power Calculation
8.6 Marker Interaction Analysis
8.6.1 ANOVA
8.6.2 Genetic Analysis
8.7 Whole-Genome Marker Analysis
8.8 Exercises
9 The Structure of QTL Mapping
9.1 Introduction
9.2 The Mixture Model
9.2.1 Formulation
9.2.2 Structure, Setting, and Estimation
9.3 Population Genetic Structure of the Mixture Model
9.3.1 Backcross/F2
9.3.2 Outbred Crosses
9.3.3 Recombinant Inbred Lines
9.3.4 Natural Populations
9.4 Quantitative Genetic Structure of the Mixture Model
9.4.1 Additive-Dominance Model
9.4.2 Additive-Dominance-Epistasis Model
9.4.3 Multiplicative-Epistatic Model
9.4.4 Mechanistic Model
9.5 Experimental Setting of the Mixture Model
9.6 Estimation in the Mixture Model
9.7 Computational Algorithms for the Mixture Model
9.7.1 EM Algorithm
9.7.2
9.7.3 Stochastic EM
9.7.4 An EM Algorithm/Newton-Raphson Hybrid
9.7.5 Some Cautions
9.7.6 Bayesian Methods
9.7.7 Estimating the Number of Components in a Mixture Model
9.8 Exercises
10 Interval Mapping with Regression Analysis
10.1 Introduction
10.2 Linear Regression Model
10.3 Interval Mapping in the Backcross
10.3.1 Conditional Probabilities
10.3.2 Conditional Regression Model
10.3.3 Estimation and Test
10.4 Interval Mapping in an F2
10.5 Remarks
10.6 Exercises
11 Interval Mapping by Maximum Likelihood Approach
11.1 Introduction
11.2 QTL Interval Mapping in a Backcross
11.2.1 The Likelihood
11.2.2 Maximizing the Likelihood
11.3 Hypothesis Testing
11.3.1 Model for Incorporating Double Recombination
11.3.2 Model for Incorporating Interference
11.4 QTL Interval Mapping in an F2
11.4.1 No Double Recombination
11.4.2
11.4.3 Interference
11.4.4 Testing Hypotheses
11.5 Factors That Affect QTL Detection
11.6 Procedures for QTL Mapping
11.6.1 The Number of QTLs
11.6.2 Locations of Individual QTLs
11.7 Exercises
12 Threshold and Precision Analysis
12.1 Introduction
12.2 Threshold Determination
12.2.1 Background
12.2.2 Analytical Approximations
12.2.3 Simulation Studies
12.2.4 Permutation Tests
12.2.5 A Quick Approach
12.2.6 A Score Statistic
12.3 Precision of Parameter Estimation
12.3.1 Asymptotic Variance-Covariance Matrix
12.3.2 Simulation Studies
12.4 Confidence Intervals for the QTL Location
12.5 Exercises
13 Composite QTL Mapping
13.1 Introduction
13.2 Composite Interval Mapping for a Backcross
13.2.1 The Likelihood
13.2.2 Maximizing the Likelihood
13.2.3 Hypothesis Testing
13.3 Composite Interval Mapping for an F2
13.4 A Statistical Justification of Composite Interval Mapping
13.4.1 Conditional Marker (Co)variances
13.4.2 Conditional QTL Variance
13.4.3 Marker Selection
13.5 Comparisons Between Composite Interval Mapping and Interval
Mapping
13.6 Multiple Interval Mapping
13.7 Exercises
14 QTL Mapping in Outbred Pedigrees
14.1 Introduction
14.2 A Fixed-Effect Model for a Full-Sib Family
14.2.1 Introduction
14.2.2 A Mixture Model for a Parental Diplotype
14.2.3 Quantitative Genetic Model
14.2.4 Likelihood Analysis
14.2.5 Fitting Marker Phenotypes
14.2.6 Hypothesis Tests
14.2.7 The Influence of Linkage Phases
14.3 Random-Effect Mapping Model for a Complicated Pedigree
14.3.1 Introduction
14.3.2 Statistical Model
14.3.3 IBD at a QTL
14.3.4 The Likelihood
14.3.5 Hypothesis Testing
14.4 Exercises
A General Statistical Results and Algorithms
A.1 Likelihood Asymptotics
A.2 General Form of the EM Algorithm
B R Programs
B.1 Chapter 2
B.2 Chapter 8
C References