Statistical Genomics: Linkage, Mapping, and QTL Analysis

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ISBN: 9780849331664 | 0849331668
Cover: Hardcover
Copyright: 12/29/1997

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This handbook on the statistical issues of genomics covers current methods and the tried-and-true classical approaches, providing a complete picture of genome statistics. It contains much basic information on the use of statistics in genomics, including how to determine a sample size and carry out a hypothesis test. This volume is different from other statistics books on genetics in that it contains a mixture of discrete and continuous variables and larger amounts of data, describes the need for bioinformatics, and is computationally intensive. It also features software available on the Internet.

FOREWORD

(2)

DR. RONALD R. SEDEROFF

PREFACE

vii

(6)

CHAPTER LIST

xiii

(2)

CONTENTS

CHAPTER 1 INTRODUCTION

(8)

1.1 INTRODUCING GENOMICS

(5)

1.1.1 Genomics and This Book

(2)

1.1.2 Genomics and Modern Biology

(1)

1.1.3 Genomics and Its Practical Applications

(2)

The Potential of Genome Research

(1)

Population and Quantitative Genetics

(1)

DNA Diagnosis of Human Genetic Disorders

(1)

Applications in Agriculture and Forestry

(1)

1.2 STATISTICAL GENOMICS

(1)

1.3 RELATED BOOKS

(2)

General Genetics

(1)

Molecular Biology

(1)

Population Genetics

(1)

Quantitative Genetics

(1)

Genetic Linkage Analysis

(1)

Statistical Methods

(1)

Statistical Theory

(1)

Mathematics and Algorithms

(1)

Computational Biology

(1)

History of Genome Research

(1)

CHAPTER 2 BIOLOGY IN GENOMICS

(36)

2.1 INTRODUCTION

(1)

2.2 MENDELIAN GENETICS AND CYTOGENETICS

(13)

2.2.1 Mendelian Genetics

(2)

Terminology

(1)

Mendelian Laws

(1)

Gene Linkage

(1)

2.2.2 Mechanisms of Mendelian Heredity -- Cytogenetics

(5)

Cell Division and Chromosomes

(1)

Meiosis

(1)

Linkage and Recombination

(2)

The Mechanism of Recombination

(1)

Linkage Phase

(1)

Factors Affecting Recombination

(1)

Importance of Manipulation of Genetic Recombination

(1)

2.2.3 Measurement of Genetic Recombination

(4)

Recombination Fraction

(1)

Interference

(1)

Haldane's Mapping Function

(1)

Chromosome Rearrangements

(1)

2.2.4 Approaches Used for Genetic Recombination Studies

(1)

Cytology

(1)

Genetics

(1)

2.2.5 Applications for Manipulating Recombination

(2)

Application to Fine Genetic Mapping

(1)

Application to Map-Based Cloning

(1)

Application to QTL Mapping

(1)

Application to Plant and Animal Breeding

(1)

Theory of Genetic Mapping

(1)

2.3 POPULATION GENETICS

(7)

2.3.1 Allelic Frequency

(1)

2.3.2 Hardy-Weinberg Equilibrium

(2)

2.3.3 Changes In Gene Frequency

(4)

2.4 QUANTITATIVE GENETICS

(6)

2.4.1 Single-Gene Model

(4)

Notation

(1)

Average Effect of Gene Substitution

(1)

Breeding Value

(1)

Dominance Deviation

(1)

Variance

(2)

2.4.2 Trait Models

(1)

2.4.3 Heritability

(1)

2.4.4 Genetic Correlation

(1)

2.5 MOLECULAR GENETICS

(4)

2.5.1 DNA

(1)

DNA Structure

(1)

DNA Sequence

(1)

2.5.2 DNA-RNA-Protein

(3)

Gene Expression

(2)

RNA Processing

(1)

Reading Frame

(1)

EXERCISES

(5)

CHAPTER 3 INTRODUCTION TO GENOMICS

(40)

3.1 GENOME

(3)

3.1.1 Genome Description

(1)

3.1.2 Genome Structure

(1)

3.1.3 Genome Variation and Colinearity

(1)

3.1.4 Sources of Genome Variation

(1)

Chromosomal Rearrangement

(1)

Point Mutation

(1)

3.2 BIOLOGICAL TECHNIQUES IN GENOMICS

(11)

3.2.1 Genetic Mapping

(2)

Genetic Map Construction

(1)

Comparative Mapping

(1)

Mapping Genes of Interest

(1)

3.2.2 Physical Mapping

(4)

DNA Fragmentation

(1)

DNA Vector

(1)

Physical Map Assembly

(2)

3.2.3 DNA Sequencing

(1)

3.2.4 Genomic Informatics

(1)

3.2.5 Relating Genetic Maps, Physical Maps and DNA Sequence

(3)

Traits, Maps and Sequence

(1)

3.3 MAPPING POPULATIONS

(3)

3.3.1 Populations from Controlled Crosses

(1)

3.3.2 Natural Populations

(2)

3.3.3 Mating Schemes and Genetic Marker Systems

(1)

3.4 GENETIC MARKERS

(20)

3.4.1 Polymorphism and Informativity

(1)

3.4.2 Morphological and Cytogenetic Markers

(2)

Morphological Markers

(1)

Cytogenetic Markers

(1)

In Situ Hybridization (ISH)

(1)

3.4.3 Protein Markers

(1)

3.4.4 DNA Markers (Rationale)

(1)

3.4.5 RFLP and Southern Blotting

(4)

3.4.6 PCR

(1)

3.4.7 Mini- and Micro-satellite Markers

(3)

3.4.8 STS and EST

(1)

3.4.9 Single-Strand Conformational Polymorphism (SSCP)

(1)

3.4.10 Random Amplified Polymorphic DNA (RAPD) Markers

(3)

3.4.11 Amplified Fragment Length Polymorphism (AFLP)

(2)

3.4.12 Comparison among Different Marker Systems

(2)

"Evolution" of Genetic Markers

(1)

Characteristics of Commonly Used Marker Systems

(1)

Marker Conversion

(1)

3.4.13 Automation

(1)

Robotic-Assisted Assay

(1)

Automated Scoring Systems

(1)

EXERCISES

(3)

CHAPTER 4 STATISTICS IN GENOMICS

(54)

4.1 INTRODUCTION

(1)

4.2 DISTRIBUTIONS

(7)

4.2.1 Distributions

(4)

Example: Data from Mendel

(1)

Distributions

(1)

Cumulative Distribution

(1)

Expectation and Variance

(1)

Joint, Marginal and Conditional Distributions

(2)

4.2.2 Standard Distributions Used in Genomic Analysis

(3)

Moments and Moment Generating Functions

(1)

The Binomial and Multinomial Distributions

(1)

The Poisson Distribution

(1)

The Normal Distribution

(1)

The Chi-Square Distribution

(1)

4.3 LIKELIHOOD

(2)

4.3.1 Definitions

(2)

4.3.2 Score

(1)

4.3.3 Information Content

(1)

4.4 HYPOTHESIS TESTS

(9)

4.4.1 Method of Hypothesis Testing

(5)

Critical Region

(1)

Significance Level

(1)

Chi-Square Tests

(2)

Likelihood Ratio Test

(1)

The Lod Score Approach

100

(1)

Nonparametric Hypothesis Test

101

(1)

4.4.2 The Power of the Test

101

(3)

Probability of False Positive and False Negative Errors

101

(2)

The Power of the Test

103

(1)

4.5 ESTIMATION

104

(15)

4.5.1 Maximum Likelihood Point Estimation

104

(1)

4.5.2 Analytical Approach Obtaining ML Estimator

105

(1)

4.5.3 Grid Search to Obtain ML Estimator

106

(4)

Example: Mapping a Gene for Resistance to Fusiform Rust Disease

107

(1)

Example: Grid Search

108

(2)

4.5.4 Newton-Raphson Iteration for Obtaining ML Estimator

110

(3)

Single Parameter

110

(1)

Multiple Parameters

110

(1)

Example: Newton-Raphson Iteration

111

(2)

4.5.5 Expectation-Maximization (EM) Algorithm

113

(3)

Example: EM Algorithm

114

(2)

4.5.6 Moment Estimation

116

(2)

Example: Moment Estimate

117

(1)

4.5.7 Least Squares Estimation

118

(1)

4.6 STATISTICAL PROPERTIES OF AN ESTIMATOR

119

(12)

4.6.1 Variance of an Estimator

119

(1)

Example: Variance

120

(1)

4.6.2 Variance of a Linear Function

120

(1)

4.6.3 Variance of a General Function

120

(1)

4.6.4 Mean Square Error (MSE) and Bias

121

(1)

4.6.5 Confidence Interval

122

(1)

4.6.6 Normal Approximation for Obtaining a Confidence Interval

123

(1)

Example: Confidence Interval

123

(1)

4.6.7 A Nonparametric Approach to Obtain a Confidence Interval

124

(1)

Example: Confidence Intervals (Bootstrap Approach)

124

(1)

4.6.8 A Likelihood Approach for Obtaining a Confidence Interval

125

(2)

Example: Likelihood Approach

127

(1)

4.6.9 Lod Score Support for a Confidence Interval

127

(2)

Example: Lod Score Support

128

(1)

4.6.10 What Is a Good Estimator of a Confidence Interval?

129

(1)

4.6.11 What Is a Good Estimator?

129

(2)

4.7 SAMPLE SIZE DETERMINATION

131

(3)

4.7.1 Sample Size Needed for Specific Statistical Power

131

(1)

4.7.2 Sample Size Needed for a Specific Confidence Interval

132

(2)

Example: Sample Size Determination

132

(2)

SUMMARY

134

(1)

EXERCISES

134

(5)

CHAPTER 5 SINGLE-LOCUS MODELS

139

(24)

5.1 EXPECTED SEGREGATION RATIOS

139

(3)

5.1.1 Single Population

139

(1)

5.1.2 Multiple Populations

140

(2)

Example

141

(1)

5.2 MARKER SCREENING

142

(4)

5.2.1 Screening for Polymorphism

142

(2)

5.2.2 Screening 1:1 over 3:1

144

(1)

5.2.3 Distinguishing between Two-Class Segregations

145

(1)

5.3 NATURAL POPULATIONS

146

(15)

5.3.1 Number of Alleles and Their Frequencies

146

(9)

Notation

146

(1)

Estimating within Population Allelic Frequency

147

(2)

Single Allele Detection

149

(1)

Multiple Allele Detection

150

(5)

5.3.2 Hardy-Weinberg Equilibrium for a Single Locus

155

(2)

Di-Allelic System

155

(2)

Multiple-Allelic System

157

(1)

5.3.3 Heterozygosity

157

(4)

Definition

157

(2)

Screening Polymorphic Markers

159

(2)

EXERCISES

161

(2)

CHAPTER 6 TWO-LOCUS MODELS: THE CONTROLLED CROSSES

163

(52)

6.1 INTRODUCTION

163

(1)

6.2 LINKAGE DETECTION

163

(7)

6.2.1 Partition of Test Statistic

164

(4)

Partition of Goodness of Fit Statistic

164

(1)

Example: Partition of Goodness of Fit Statistic

165

(1)

Partitioning of Log Likelihood Ratio Test Statistic

166

(1)

Example: Partition of Log Likelihood Ratio Test Statistic

167

(1)

6.2.2 A Generalized Likelihood Approach

168

(2)

Log Likelihood Approach

168

(1)

Example: Log Likelihood Approach

169

(1)

The Lod Score

170

(1)

Example: Lod Score

170

(1)

6.3 RECOMBINATION FRACTION ESTIMATION

170

(9)

6.3.1 Backcross Model

171

(1)

6.3.2 F2 Model

171

(2)

Example: Data

173

(1)

6.3.3 Likelihood Profile Method

173

(2)

Example: Graphic Approach

174

(1)

6.3.4 Newton-Raphson Iteration for a Single Parameter

175

(1)

Example: Newton-Raphson Iteration

176

(1)

6.3.5 EM Algorithm

176

(3)

Example: EM Algorithm

177

(1)

Example: Heterogeneity Test

178

(1)

6.4 STATISTICAL PROPERTIES

179

(9)

6.4.1 Variance and Bias

181

(2)

Parametric Variance

181

(1)

Empirical Variance and Bias

182

(1)

6.4.2 Distribution and Confidence Intervals

183

(5)

Distribution

183

(1)

Confidence Intervals

183

(2)

Example: Confidence Interval (Normal Approximation)

185

(1)

Example: Confidence Interval (Bootstrap)

186

(1)

Example: Confidence Interval (Likelihood Approach)

186

(1)

Example: Confidence Interval (Lod Score Support)

186

(1)

Quality of a Confidence Interval

187

(1)

6.5 SAMPLE SIZE

188

(5)

6.5.1 Expected Likelihood Ratio Test Statistic and Power

189

(3)

Expected Log Likelihood Ratio Test Statistic

189

(1)

Power and Sample Size

190

(2)

6.5.2 Minimum Confidence Interval

192

(1)

6.6 DOMINANT MARKERS IN F2 PROGENY

193

(6)

6.6.1 Disadvantage of Dominant Markers in F2 Progeny

193

(4)

Low Linkage Information Content

193

(1)

Bias Estimator for Recombination Fraction

194

(3)

6.6.2 Use of Trans Dominant Linked Markers (TDLM)

197

(2)

TDLM

197

(1)

Linkage Information Content for TDLM

198

(1)

Estimate of Recombination Fraction between a TDLM and a Marker

198

(1)

6.7 VIOLATION OF ASSUMPTIONS

199

(8)

6.7.1 Segregation Ratio Distortion

199

(5)

Additive Distortion

199

(3)

Penetrance Distortions

202

(1)

Impact of Segregation Ratio Distortion in Practical Linkage Analysis

203

(1)

6.7.2 Linkage Analysis Involving Lethal Genes

204

(3)

Single Gene Defect

204

(1)

Two-Locus Recessive Lethal

205

(2)

EXERCISES

207

(8)

CHAPTER 7 TWO-LOCUS MODELS: NATURAL POPULATIONS

215

(26)

7.1 THE LINKAGE PHASE PROBLEM

215

(7)

7.1.1 Linkage Phase Configurations for Two-Locus Models

215

(1)

7.1.2 Linkage Phase Determination

216

(3)

7.1.3 Phase-Unknown Linkage Analysis

219

(2)

7.1.4 Linkage Analysis with a Mixture of Linkage Phases

221

(1)

7.2 MIXTURES OF SELFS AND RANDOM MATING

222

(13)

7.2.1 Model

222

(2)

7.2.2 Allelic Frequency in Pollen Pool and Outcrossing Rate

224

(2)

Allelic Frequency in Pollen Pool

224

(1)

Outcrossing Rate

224

(2)

7.2.3 Estimation of Recombination Fraction

226

(3)

Method I

227

(1)

Method II Using EM Algorithm

227

(1)

Method II Using Newton-Raphson Iteration

228

(1)

7.2.4 Efficiency and Variances

229

(5)

Information Content for Codominant Markers

229

(3)

Information Content for Dominant Markers

232

(1)

Empirical Variance and Bias

232

(2)

7.2.5 Mapping Using Cross Between Two Heterozygotes

234

(1)

EXERCISES

235

(6)

CHAPTER 8 TWO-LOCUS MODELS: USING LINKAGE DISEQUILIBRIUM

241

(32)

8.1 LINKAGE DISEQUILIBRIUM

241

(10)

8.1.1 Two-Locus Disequilibrium Model

241

(1)

8.1.2 Detection and Estimation

242

(2)

Detection

242

(1)

Detection Power

243

(1)

8.1.3 Disequilibrium and Linkage

244

(4)

8.1.4 Disequilibrium-Based Analysis

248

(3)

8.2 THE TRANSMISSION DISEQUILIBRIUM TEST (TDT)

251

(10)

8.2.1 Genetic Model

251

(1)

8.2.2 Transmission/Disequilibrium Test

252

(1)

8.2.3 Genetic Interpretation of TDT

253

(1)

Example: Insulin-Dependent Diabetes Mellitus (IDDM)

254

(1)

8.2.4 Statistical Power of TDT

254

(1)

8.2.5 Why TDT?

255

(6)

8.3 OTHER DISEQUILIBRIUM BASED ANALYSES

261

(3)

8.3.1 Relative Risk

261

(1)

8.3.2 Genotype and Haplotype Relative Risk (GRR and HRR)

262

(2)

8.3.3 Linkage Analysis Using Population Admixture

264

(1)

8.4 ESTIMATION OF RECOMBINATION FRACTION

264

(5)

8.4.1 Fixed Large Population Size

265

(2)

8.4.2 Model

267

(1)

8.4.3 The Luria-Delbruck Algorithm

268

(1)

8.4.4 Maximum Likelihood Approach

268

(1)

EXERCISES

269

(4)

CHAPTER 9 LINKAGE GROUPING AND LOCUS ORDERING

273

(32)

9.1 LINKAGE GROUPING

273

(1)

9.1.1 Linkage Grouping Criteria

273

(1)

9.1.2 Procedures

274

(1)

9.2 THREE-LOCUS ORDER

274

(7)

9.2.1 Introduction to Locus Ordering

274

(2)

9.2.2 Three-Locus Likelihood and The Concept of Interference

276

(2)

9.2.3 Double Crossover Approach

278

(1)

9.2.4 Two-Locus Recombination Fraction Approach

279

(1)

9.2.5 Log Likelihood Approach

279

(2)

9.3 MULTIPLE-LOCUS ORDERING

281

(8)

9.3.1 Multiple-Locus Ordering Statistic

281

(3)

Notation

281

(1)

Three-Locus Approach

282

(1)

Maximum Likelihood Approach

282

(1)

Minimum Sum or Product of Adjacent Recombination Fractions (SARF and PARF)

282

(1)

Maximum Sum of Adjacent Lod Score (SALOD)

283

(1)

Least Square Method

284

(1)

9.3.2 The Traveling Salesman Problem

284

(5)

Problem

284

(1)

Algorithms

284

(1)

Seriation

285

(1)

Simulated Annealing Algorithm

286

(1)

Branch-and-Bound (BB)

287

(2)

A Combination of SA and BB

289

(1)

9.4 PROBABILITY OF ESTIMATED LOCUS ORDERS

289

(11)

9.4.1 Likelihood Approach

290

(1)

9.4.2 Bootstrap Approach

291

(4)

Percentage of Correct Gene Order

291

(1)

An Example

292

(2)

Sample Size and PCO

294

(1)

9.4.3 Interval Support for Locus Order

295

(5)

Framework Map

295

(1)

Confidence Interval for Gene Order

296

(1)

An Example

297

(1)

Combination of Jackknife and Bootstrap

298

(2)

EXERCISES

300

(5)

CHAPTER 10 MULTI-LOCUS MODELS

305

(54)

10.1 INTERPRETATION OF MAP DISTANCE

305

(5)

10.1.1 Map and Physical Distances

305

(2)

10.1.2 Possible Genetic Control of Crossover

307

(1)

10.1.3 Genome Structure Variation Among Parents

308

(2)

10.2 THREE-LOCUS MODELS

310

(8)

10.2.1 Three-locus model

310

(1)

10.2.2 Crossover in a Three-Locus Model

311

(3)

Configurations

311

(2)

Double Crossover Issue

313

(1)

10.2.3 Likelihood Function

314

(4)

Triple-Backcross

315

(1)

F2 Progeny

316

(2)

10.3 MAPPING FUNCTIONS

318

(12)

10.3.1 Definitions

318

(1)

10.3.2 Commonly Used Map Functions

319

(9)

Morgan's Map Function

320

(1)

Haldane's Map Function

320

(2)

Kosambi's Map Function

322

(2)

Other Map Functions

324

(4)

10.3.3 Comparison of Commonly Used Mapping Functions

328

(2)

10.4 ESTIMATION OF MULTI-LOCUS MAP DISTANCE

330

(15)

10.4.1 Least Squares

331

(4)

Notation

331

(1)

Likelihood

332

(1)

Example

333

(1)

Variance of Estimated Map Distance

333

(1)

Least Square Approach Using Lod Score

334

(1)

10.4.2 EM Algorithm

335

(2)

10.4.3 Joint Estimation of Recombination and Interference

337

(1)

10.4.4 Simulation Approach

338

(7)

Crossover Distribution

338

(2)

Example

340

(1)

Simulation

341

(2)

Multilocus Feasible Map Function

343

(1)

Practical Implementation

344

(1)

10.5 MARKER COVERAGE AND MAP DENSITY

345

(10)

10.5.1 Definitions

345

(1)

10.5.2 Factors Influencing Marker Coverage and Map Density

346

(3)

Number of Markers

346

(1)

Marker and Crossover Distribution

346

(2)

Mapping Population

348

(1)

Data Analysis

348

(1)

10.5.3 Prediction of Marker Coverage and Map Density

349

(6)

Prediction of Map Density and Marker Coverage

349

(4)

Simulation Approach

353

(2)

EXERCISES

355

(4)

CHAPTER 11 LINKAGE MAP MERGING

359

(16)

11.1 INTRODUCTION

359

(3)

11.1.1 Linkage Mapping

359

(2)

11.1.2 Hypothesis Tests Are Needed

361

(1)

11.1.3 Why Linkage Map Pooling and Bridging?

361

(1)

Cross Validation of Mapping Strategies

361

(1)

Applications of Genome Information to Applied Plant and Animal Breeding

361

(1)

Comparative Mapping

362

(1)

Structures of Genome Database

362

(1)

11.2 FACTORS RELATED TO LINKAGE MAP MERGING

362

(2)

11.2.1 Biology and Linkage Map Merging

362

(1)

Mating and Genetic Marker Systems

362

(1)

Cytogenetics

363

(1)

11.2.2 Statistics and Linkage Map Merging

363

(1)

Sampling Variation

363

(1)

Different Screening Strategies

364

(1)

Missing Data and Missing Linkage Information

364

(1)

Sample Size and Data Quality

364

(1)

11.3 HYPOTHESES ABOUT GENE ORDERS

364

(4)

11.3.1 Heterogeneity Test between Two-Point Recombination Fractions

365

(1)

11.3.2 Likelihood Ratio Tests Among Locus Orders and Multipoint Map Distances

366

(1)

11.3.3 Nonparametric Heterogeneity Tests for Locus Orders

367

(1)

11.4 LINKAGE MAP POOLING

368

(3)

11.4.1 Anchor Map Approach

368

(1)

11.4.2 Estimation of Missing Recombination Fractions Using EM Algorithm

369

(1)

11.4.3 Linkage Map Bridging

370

(1)

EXERCISES

371

(4)

CHAPTER 12 QTL MAPPING: INTRODUCTION

375

(12)

12.1 HISTORY

375

(2)

12.2 QUANTITATIVE GENETICS MODELS

377

(3)

12.2.1 Single-QTL Model

377

(2)

12.2.2 Multiple-Locus Model

379

(1)

12.3 DATA FOR QTL MAPPING

380

(5)

12.3.1 Data Structure

380

(1)

12.3.2 The Barley Data

381

(4)

Marker Data

381

(1)

Phenotype Data

381

(4)

EXERCISES

385

(2)

CHAPTER 13 QTL MAPPING: SINGLE-MARKER ANALYSIS

387

(30)

13.1 RATIONALE

387

(2)

13.2 SINGLE-MARKER ANALYSIS IN BACKCROSS PROGENY

389

(13)

13.2.1 Joint Segregation of QTL and Marker Genotypes

390

(1)

13.2.2 Simple t-Test Using Backcross Progeny

391

(3)

Example: Analysis of the Barley Malt Extract Data Using t-Test

393

(1)

13.2.3 Analysis of Variance Using Backcross Progeny

394

(1)

13.2.4 Linear Regression Using Backcross Progeny

394

(2)

Example: Analysis of the Barley Data Using Linear Regression

396

(1)

13.2.5 A Likelihood Approach Using Backcross Progeny

396

(6)

Example: Analysis of the Barley Data Using a Likelihood Approach

399

(3)

13.3 SINGLE-MARKER ANALYSIS USING F2 PROGENY

402

(11)

13.3.1 Joint Segregation of QTL and Marker Genotypes

402

(2)

13.3.2 Analysis of Variance Using F2 Progeny

404

(2)

Codominant Marker Model

404

(1)

Dominant Marker Model

405

(1)

13.3.3 Linear Regression Using F2 Progeny

406

(3)

Codominant Marker Model

406

(2)

Dominant Marker Model

408

(1)

13.3.4 Likelihood Approach

409

(2)

Codominant Marker Model

409

(2)

Dominant Marker Model

411

(1)

13.3.5 Use of Trans Dominant Linked Markers in F2 Progeny

411

(2)

SUMMARY

413

(1)

EXERCISES

414

(3)

CHAPTER 14 QTL MAPPING: INTERVAL MAPPING

417

(42)

14.1 INTRODUCTION

417

(1)

14.2 INTERVAL MAPPING OF QTL USING BACKCROSS PROGENY

418

(17)

14.2.1 Joint Segregation of QTL and Markers

418

(1)

14.2.2 A Likelihood Approach for QTL Mapping with Backcross Progeny

419

(4)

Example: A Likelihood Approach

421

(2)

14.2.3 A Nonlinear Regression Approach

423

(9)

Nonlinear Regression

423

(2)

Hypothesis Test

425

(1)

Confidence Interval for the Parameters

425

(1)

Example: Estimation, Hypothesis Tests and Confidence Interval

426

(1)

Multiple Environments Model

427

(2)

Implementation of the Nonlinear Regression

429

(1)

Example: The Multiple Environments Problem

430

(2)

14.2.4 The Linear Regression Approach

432

(3)

14.3 INTERVAL MAPPING USING F2 PROGENY

435

(9)

14.3.1 Joint Segregation of QTLs and Markers

435

(2)

14.3.2 A Likelihood Approach for QTL Analysis Using F2 Progeny

437

(3)

Codominant Markers

437

(2)

Dominant Markers

439

(1)

14.3.3 Regression Approach

440

(4)

Nonlinear Regression Approach (Codominant Markers)

440

(2)

Linear Regression (Codominant Markers)

442

(1)

Linear Regression (Dominant Markers)

442

(2)

14.3.4 Problems with the Simple Interval Mapping Approaches

444

(1)

14.4 COMPOSITE INTERVAL MAPPING

444

(11)

14.4.1 Model

444

(2)

14.4.2 Solutions

446

(1)

14.4.3 Hypothesis Test

447

(1)

14.4.4 CIM Using Regression

448

(4)

Example: CIM Using Regression

449

(3)

14.4.5 Implementing CIM

452

(1)

14.4.6 CIM Using F2 Progeny

453

(2)

14.4.7 Advantages of the CIM

455

(1)

SUMMARY

455

(1)

EXERCISES

456

(3)

CHAPTER 15 QTL MAPPING: NATURAL POPULATIONS

459

(22)

15.1 INTRODUCTION

459

(1)

15.2 OPEN-POLLINATED POPULATIONS

460

(9)

15.2.1 Joint Segregation of QTL and Markers

460

(1)

15.2.2 Model

461

(1)

15.2.3 Complete Outcrossing

462

(2)

15.2.4 Half Outcrossing

464

(2)

15.2.5 Expectation of the Additive Contrast

466

(3)

15.3 SIB-PAIR METHODS

469

(10)

15.3.1 Model for QTL Locating On Marker

469

(5)

Model

469

(1)

Identity by Descent

469

(1)

Sib-Pair Difference

470

(2)

Expected Square of the Sib-Pair Difference

472

(1)

Solutions for the Linear Model

472

(2)

15.3.2 Marker Model

474

(4)

15.3.3 Implementation of the Sib-Pair Method

478

(1)

EXERCISES

479

(2)

CHAPTER 16 QTL MAPPING: STATISTICAL POWER

481

(12)

16.1 INTRODUCTION

481

(1)

16.2 SINGLE QTL DETECTION POWER

482

(5)

16.2.1 Single Marker Analysis

482

(3)

16.2.2 Interval Mapping

485

(2)

16.3 MULTIPLE QTLS

487

(3)

16.3.1 Rationale

487

(1)

16.3.2 A Simulation Approach

488

(1)

16.3.3 The Percent of Genetic Variation Explained by QTL

488

(2)

EXERCISES

490

(3)

CHAPTER 17 QTL MAPPING: FUTURE CONSIDERATIONS

493

(26)

17.1 PROBLEMS WITH QTL MAPPING

493

(5)

17.1.1 Multiple-QTL Model

493

(2)

Practical Implementations

493

(2)

Problems

495

(1)

17.1.2 Multiple-Test Problem

495

(1)

17.1.3 Multiple Related Traits Problem

496

(1)

17.1.4 Are the QTLs Real?

497

(1)

17.2 QTL RESOLUTION

498

(4)

17.2.1 QTL Location

498

(2)

17.2.2 High Resolution QTL Mapping

500

(2)

Quantitative Analysis of the Trait

500

(2)

Conditional Marker Analysis

502

(1)

Mapping Population Extension

502

(1)

17.3 MAPPING STRATEGIES

502

(5)

17.3.1 Bulk Segregant Analysis

502

(4)

17.3.2 Selective Genotyping

506

(1)

17.3.3 Increase Marker Coverage

506

(1)

Comparative Mapping

506

(1)

Increase Useful Progeny Size

507

(1)

17.4 WHAT ARE QTLS?

507

(2)

17.4.1 What Are QTLs?

507

(1)

Limitations of QTL Mapping

508

(1)

17.4.2 Quantitative Genetics, Genomic Mapping and Molecular Biology

508

(1)

17.5 FUTURE QTL MAPPING

509

(5)

17.5.1 Genetic and Physical Maps

510

(1)

17.5.2 Trait -- Maps -- Sequence

511

(1)

17.5.3 Metabolic Genetic Model (MGM)

512

(2)

EXERCISES

514

(5)

CHAPTER 18 COMPUTER TOOLS

519

(26)

18.1 COMPUTER TOOLS FOR GENOMIC DATA ANALYSIS

520

(6)

18.1.1 Linkage Analysis and Map Construction

520

(3)

18.1.2 Specific Packages for QTL Mapping

523

(1)

18.1.3 QTL Analysis Using SAS

523

(3)

Interval Mapping Using Nonlinear Regression

524

(1)

Composite Interval Mapping Using Regression

525

(1)

18.2 FUTURE CONSIDERATIONS

526

(3)

18.2.1 Commercial Quality Software Is Needed

526

(2)

18.2.2 Structure of Bioinformation Analysis and Management System (BIAMS)

528

(1)

18.2.3 Data Quality Problem

528

(1)

18.3 PLANT GENOME RESEARCH INITIATIVE (PGRI)

529

(16)

18.3.1 Data Type

530

(1)

18.3.2 Data Format

531

(2)

18.3.3 Linkage Analysis and Map Construction

533

(5)

18.3.4 Linkage Map Merging

538

(1)

18.3.5 QTL Analysis and Breeding Plan

538

(3)

18.3.6 Output Samples

541

(4)

Linkage Map Merging

541

(2)

QTL Analysis

543

(2)

CHAPTER 19 RESAMPLING AND SIMULATION IN GENOMICS

545

(26)

19.1 INTRODUCTION

545

(1)

19.2 RESAMPLING

546

(6)

19.2.1 Bootstrap

546

(3)

Bootstrap Sample

546

(1)

Bootstrap Replication

546

(1)

Bootstrap Mean, Variance and Bias

547

(1)

Bootstrap Confidence Interval

547

(1)

Example: Bootstrap Approach

547

(2)

19.2.2 Jackknife

549

(1)

Jackknife Sample

549

(1)

Jackknife Mean, Variance and Bias

549

(1)

19.2.3 Combination of Jackknife and Bootstrap

549

(1)

19.2.4 Shuffling or Permutation Test

550

(2)

Shuffling a Sample and Permutation

550

(1)

Empirical Distribution of the Test Statistic

551

(1)

Example: Permutation Test

551

(1)

19.3 COMPUTER SIMULATIONS

552

(3)

19.3.1 Overview

552

(1)

19.3.2 Random Sampling from Continuous Distributions

553

(1)

19.3.3 Random Sampling from Discrete Distributions

554

(1)

19.4 SIMULATION OF DISCRETE MARKERS

555

(2)

19.4.1 A Joint Distribution Approach for Two Loci

555

(1)

19.4.2 A Conditional Frequency Approach for Multiple Loci

556

(1)

19.4.3 Conversion of Map Distance to Recombination Fraction

557

(1)

19.5 QUANTITATIVE TRAITS: A TWO-GENE MODEL

557

(3)

19.5.1 Two-Gene Model

557

(1)

19.5.2 Model Specification

558

(1)

19.5.3 Simulation of the Trait Values

559

(1)

19.6 QUANTITATIVE TRAIT: MULTIPLE-GENE MODEL

560

(2)

19.6.1 Multiple-Gene Model

560

(1)

19.6.2 Distribution of Genetic Effects

560

(2)

19.6.3 Simulation of Trait Values

562

(1)

19.7 MULTIPLE QUANTITATIVE TRAITS

562

(4)

19.7.1 The Model

562

(1)

19.7.2 Model Specification

563

(1)

19.7.3 Linkage and Genetic Correlation

564

(1)

19.7.4 Multinormal Distribution

565

(1)

19.8 SIMULATION OF DATA WITH MULTIPLE GENERATIONS

566

(4)

19.8.1 Introduction

566

(1)

19.8.2 Single Gene

567

(1)

19.8.3 Two Loci

568

(2)

19.8.4 Multiple Loci

570

(1)

EXERCISES

570

(1)

GLOSSARY

571

(8)

BIBLIOGRAPHY

579

(18)

AUTHOR INDEX

597

(4)

SUBJECT INDEX

601

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Statistical Genomics: Linkage, Mapping, and QTL Analysis

Summary

Table of Contents

Supplemental Materials