Theories of Population Variation in Genes and Genomes

About this book

Theories of Population Variation in Genes and Genomes provides an authoritative introduction to both classical and coalescent approaches to population genetics. Written for graduate students and advanced undergraduates by one of the world's leading authorities in the field, Theories of Population Variation in Genes and Genomes focuses on the theoretical background of population genetics, while emphasizing the close interplay between theory and empiricism.

Traditional topics such as genetic and phenotypic variation, mutation, migration, and linkage are covered and advanced by contemporary coalescent theory, which describes the genealogy of genes in a population, ultimately connecting them to a single common ancestor. Effects of selection, particularly genomic effects, are discussed with reference to molecular genetic variation.

Theories of Population Variation in Genes and Genomes is designed for students of population genetics, bioinformatics, evolutionary biology, molecular evolution, and theoretical biology – as well as biologists, molecular biologists, breeders, biomathematicians, and biostatisticians.

Contents

Preface and Acknowledgments ix
Introduction 1

Part I: Genetic Variation 5

Chapter 1: Genetics 7
1.1 Genetic Variation 9
1.1.1 Gene structure and function 13
1.1.2 Molecular genetic variation 17

Chapter 2: Conservation of Variation 21
2.1 Stochastic Fluctuations 23
2.2 Wright-Fisher Process 26
2.2.1 Multiple alleles 30
2.3 Gene Identity in a Finite Population 31
2.4 Coalescence of Genes 33
2.5 Characteristic Time Unit 41
2.6 Diffusion Approximation 42
2.6.1 The Wright-Fisher model 43
2.6.2 The coalescent 46
2.6.3 The 1-coalescent 49
2.7 Moran's Model 50

Chapter 3: Diploid Populations 53
3.1 Random Mating 54
3.1.1 Mating of individuals 58
3.1.2 Random mating and selfing 59
3.2 Effective Population Size 62
3.2.1 Lose variation or gain identity 64
3.2.2 An exponentially growing population 64
3.2.3 Overlapping generations 68
3.3 Genotypic Frequencies 69

Chapter 4: Mutation and Variation 71
4.1 Mutation 72
4.1.1 Induced mutation 74
4.1.2 Somatic mutation 75
4.1.3 Effects of mutations 76
4.2 The Two-Allele Model 77
4.2.1 Distribution of the gene frequency 80
4.3 Genealogy and Variation 84
4.3.1 Alcohol dehydrogenase in Drosophila 86
4.4 Mutation and Coalescence 87
4.4.1 The appearance of a sample 91
4.4.2 Gene identity and mutation 93
4.5 The Infinite Alleles Model 95
4.5.1 Heterozygosity in the infinite alleles model 99
4.6 The Infinite Sites Model 100
4.7 Age of an Allele 104
4.8 Numerical Simulations 105

Chapter 5: Migration 108
5.1 Population Genetics of Migration 109
5.1.1 Genealogy in a structured population 112
5.1.2 The final waiting time 115
5.2 Population Structure 118
5.2.1 The simple two-island model 121
5.2.2 Coalescence in a widespread population 124
5.2.3 Strong migration 128
5.2.4 The stepping-stone model 129
5.3 Genotypic Proportions 133
5.3.1 Description of population structure 135

Chapter 6: Linkage 139
6.1 The Karyotype 141
6.1.1 Sex linkage 143
6.1.2 Linkage map 144
6.2 Population Genetics of Linkage 148
6.3 Linkage Equilibrium 150
6.3.1 The forward equations 155
6.3.2 Population mixing 156
6.3.3 Recurrent mixing and migration 157
6.3.4 Stochastic effects 159
6.3.5 Backcrosses 160
6.4 The Ancestral Recombination Graph 161
6.4.1 Genealogy and recombination 167
6.4.2 The mechanism of recombination 171
6.4.3 Gene conversion 173
6.4.4 The APOE risk factor in Alzheimer's disease 174
6.5 Recombination and Physical Distance 177

Chapter 7: Phenotypic Variation 181
7.1 Quantitative Inheritance 185
7.1.1 Conservation of variation 186
7.1.2 Random genetic drift 187
7.2 Kin Resemblance 188
7.2.1 The additive model 190
7.2.2 Parent-offspring covariance 191
7.2.3 Covariance between sibs 194
7.3 Inference on the Genotypic Variance 195
7.3.1 Comparison of populations 199
7.3.2 Random genetic drift 201
7.3.3 Applications of quantitative genetics 202
7.4 Mapping of Quantitative Trait Loci 202
7.4.1 Diallel crosses 204
7.4.2 Inference 207

Part II: Variation and Selection 213

Chapter 8: Effects of Selection 216
8.1 Selection Components 219
8.2 Viability Selection 222
8.2.1 Viability selection in Zoarces 233
8.3 Selection on a Quantitative Character 234
8.3.1 Genetic effects of selection 236
8.3.2 Fitness maximization 241
8.3.3 An experiment on growth rate in Mus 243
8.4 Mutation and Selection 245
8.4.1 Mutation, selection, and variation 248
8.5 Stability of an Equilibrium 248
8.6 The Coalescent and Selection 255
8.6.1 Microcephalin alleles in humans 259
8.6.2 Adh alleles in Drosophila 260

Chapter 9: Genomic Effects of Selection 264
9.1 Multilocus Selection 268
9.1.1 Selection on one of the loci 271
9.1.2 Tight linkage 272
9.1.3 Loose linkage and weak selection 275
9.1.4 Intermediate linkage 277
9.2 Selection Experiments in Drosophila 279
9.2.1 An experiment using the ebony allele 281
9.2.2 An experiment using white alleles 283
9.3 Hitchhiking 285
9.3.1 An experiment on a bristle character in Drosophila 289
9.4 Inbreeding Depression 291
9.4.1 Inbreeding in inbred populations 295
9.4.2 Hitchhiking and inbreeding depression 296
9.4.3 Inbreeding effects on a bristle character 298
9.5 Sweeps by Selection 301
9.5.1 Selection on a bristle character 306

Chapter 10: Population Structure 309
10.1 Polymorphism 310
10.1.1 Local and global effects of selection 312
10.1.2 Transient polymorphism 313
10.1.3 Migration-selection balance 314
10.1.4 Environmental homogeneity 316
10.1.5 A butterfly metapopulation 318
10.1.6 Geographical variation in another butterfly 319
10.2 Introgression 320
10.2.1 Karyotypic variation 322
10.2.2 Genetic barrier 330
10.2.3 Introgression of a microcephalin allele 334
10.2.4 Vertical transmission of infection 335
10.2.5 Emerging barrier 336
10.3 Divergence of Populations 338

Appendix: Probability Theory and Statistics 345
A.1 Discrete Stochastic Variables 345
A.1.1 Moments 347
A.1.2 Conditional probabilities 348
A.1.3 The binomial distribution 351
A.1.4 The geometric distribution 352
A.1.5 The Poisson distribution 355
A.2 Markov Chains 355
A.3 Continuous Random Variables 359
A.3.1 The exponential distribution 360
A.3.2 The Gaussian distribution 361
B Solutions to Exercises 363

Bibliography 383
Index 413

Customer Reviews

Biography

Freddy Bugge Christiansen is professor of population biology at the University of Aarhus in Denmark. He is the author of Population Genetics of Multiple Loci and coauthor of Theories of Populations in Biological Communities and Population Genetics.