Table of Contents
Preface vii
Acknowledgments ix
Chapter 1 An Example of an Application of Variance and Covariance Models in Quantitative Genetics in the 1950s 1
Background 1
A Retrospective and Prospective View of the Paper by Mode and Robinson (1959) 4
1 Introduction and Theory 5
2 Properties of Covariance Matrices 9
3 A One-Way Classification for Estimating Variance Components of a Quantitative Trait 13
4 A Multivariate Version of the One-Way Classification for Estimating Variance and Covariance Components of Multiple Traits 16
5 An Experimental Design and Data 20
6 A Prospective View of Mode and Robinson (1959) 29
Appendix 32
References 34
Chapter 2 On Fitting a Genetic Model to Data 35
Background 35
A Distribution-Free Test for Major Gene Differences in Quantitative Inheritance 36
1 Introduction 36
2 A Brief Review of Theory 38
3 An Application of the Smirnov Test 40
4 A Look into the Future on Fitting Models to Data in an Era of Sequenced Genomes 44
References 44
Chapter 3 Estimating Effects and Variance Components in Models of Quantitative Genetics in an Era of Sequenced Genomes 47
Abstract 47
1 Introduction 48
2 The Case of One Locus with Multiple Alleles 51
3 A Partition of the Genetic Variance into the Additive and Intra-allelelic Components for the Case of One Autosomal Locus 56
4 Estimation of Parameters and Effects from Data 62
5 The Case of Two Autosomal Loci 67
6 An Overview of the Case of 11 Autosomal Loci 76
Acknowledgments 82
References 83
Chapter 4 Estimating Statistical Measures of Pleiotropic and Epistatic Effects in the Genomic Era 85
Abstract 85
1 Introduction 86
2 Pleiotropism and the Phenotypic, Genetic and Environmental Covariance Matrices for the Case of One Autosomal Locus 88
3 Partitioning the Genetic Covariance Matrix into Component Covariance Matrices for the Case of One Autosomal Locus 95
4 Estimation of Mean Genetic Vector and Covariance Matrices from Data for the Case of One Locus 98
5 Measures of Pleiotropism and Epistasis for the Case of Two Autosomal Loci 104
6 Searching for Unusual Effects and Interactions Among the Alleles at Two Autosomal Loci 111
7 An Overview of Cases for l > 2 Autosomal Loci 114
Acknowledgments 118
References 119
Chapter 5 Direct Estimation of Effects and Tests of Their Statistical Significance for the Case of One Autosomal Locus with Two Alleles 121
Abstract 121
1 Introduction 122
2 Nonidentifiability of Heterozygotes in the Case of One Autosomal Locus 123
3 Estimating Effects Directly for the Case of One Autosomal Locus 128
4 Permutation Tests for Statistical Significance of Estimated Effects 134
5 Testing the Statistical Significance of Estimated Effects Based on Monte Carlo Simulation Methods 138
6 Monte Carlo Simulation Experiments on Simulating Data and Testing the Null Hypotheses 143
7 Two Monte Carlo Simulation Experiments to Simulate Data and Test Null Hypotheses 148
8 Further Developments and Potential Applications 151
Appendix 154
References 161
Subject Index 163
