Contents -- Preface: Theory Versus Results -- Preface to the Second Edition -- 1 Historical Overview -- 1.1 Introduction -- 1.2 From Mendel to Sax -- 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 -- 1.8 Summary -- 2 Principles of Parameter Estimation -- 2.1 Introduction -- 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) -- 2.14 Bayesian Estimation -- 2.15 Minimum Difference Estimation -- 2.16 Summary -- 3 Random and Fixed Effects, the Mixed Model -- 3.1 Introduction -- 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 -- 3.6 Equation Absorption -- 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 -- 3.17 Summary -- 4 Experimental Designs to Detect QTL: Generation of Linkage Disequilibrium -- 4.1 Introduction -- 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 -- 4.12 Summary -- 5 QTL Parameter Estimation for Crosses between Inbred Lines -- 5.1 Introduction -- 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 -- 5.13 Summary -- 6 Advanced Statistical Methods for QTL Detection and Parameter Estimation -- 6.1 Introduction -- 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 -- 6.20 Summary -- 7 Analysis of QTL as Random Effects -- 7.1 Introduction -- 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 -- 7.15 Summary -- 8 Statistical Power to Detect QTL, and Parameter Confidence Intervals -- 8.1 Introduction -- 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 -- 8.11 Summary -- 9 Optimization of Experimental Designs -- 9.1 Introduction -- 9.2 Economic Optimization of Marker Spacing When the Number of Individuals Genotyped Is Non-limiting -- 9.3 Economic Optimization with Replicate Progeny -- 9.4 Selective Genotyping -- 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 -- 9.8 Sequential Sampling -- 9.9 Summary -- 10 Fine Mapping of QTL -- 10.1 Introduction -- 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 -- 10.13 Summary -- 11 Complete Genome QTL Scans: The Problem of Multiple Comparisons -- 11.1 Introduction -- 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 -- 11.10 Summary -- 12 Multitrait QTL Analysis -- 12.1 Introduction -- 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.