Population Genetics

MATTHEW B. HAMILTON, PHD, is Associate Professor of Biology at Georgetown University, where he teaches Population Genetics, Molecular Evolution, Evolutionary Processes, and similar undergraduate and graduate level courses. He is founding Director of Georgetown's Environmental Biology undergraduate major, past Director of the Georgetown Environment Initiative, and currently conducts research on the processes that influence the distribution of genetic variation within species.

Preface and acknowledgements xiv

About the companion websites xvi

1 Thinking like a population geneticist 1

1.1   Expectations 1

Parameters and parameter estimates 2

Inductive and deductive reasoning 3

1.2 Theory and assumptions 4

1.3 Simulation 5

Interact box 1.1 The textbook website 6

Chapter 1 review 7

Further reading 7

2 Genotype frequencies 8

2.1 Mendel’s model of particulate genetics 8

2.2 Hardy–Weinberg expected genotype frequencies 12

Interact box 2.1 Genotype frequencies for one locus with two alleles 14

2.3 Why does Hardy–Weinberg work? 15

2.4 Applications of Hardy–Weinberg 18

Forensic DNA profiling 18

Problem box 2.1 The expected genotype frequency for a DNA profile 20

Testing Hardy–Weinberg expected genotype frequencies 20

Box 2.1 DNA profiling 21

Assuming Hardy–Weinberg to test alternative models of inheritance 24

Problem box 2.2 Proving allele frequencies are obtained from expected genotype frequencies 25

Problem box 2.3 Inheritance for corn kernel phenotypes 26

2.5 The fixation index and heterozygosity 26

Interact box 2.2 Assortative mating and genotype frequencies 27

Box 2.2 Protein locus or allozyme genotyping 30

2.6 Mating among relatives 31

Impacts of non-random mating on genotype and allele frequencies 31

Coancestry coefficient and autozygosit, 33

Box 2.3 Locating relatives using genetic genealogy methods 37

Phenotypic consequences of mating among relatives 38

The many meanings of inbreeding 41

2.7 Hardy–Weinberg for two loci 42

Gametic disequilibrium 42

Physical linkage 47

Natural selection 47

Interact box 2.3 Gametic disequilibrium under both recombination and natural selection 48

Mutation 48

Mixing of diverged populations 49

Mating system 49

Population size 50

Interact box 2.4 Estimating genotypic disequilibrium 51

Chapter 2 review 52

Further reading 52

End-of-chapter exercises 53

Problem box answers 54

3 Genetic drift and effective population size 57

3.1 The effects of sampling lead to genetic drift 57

Interact box 3.1 Genetic drift 62

3.2 Models of genetic drift 62

The binomial probability distribution 62

Problem box 3.1 Applying the binomial formula 64

Math box 3.1 Variance of a binomial variable 66

Markov chains 66

Interact box 3.2 Genetic drift simulated with a markov chain model 69

Problem box 3.2 Constructing a transition probability matrix 69

The diffusion approximation of genetic drift 70

3.3 Effective population size 76

Problem box 3.3 Estimating N e from information about N 81

3.4 Parallelism between Drift and mating among relatives 81

Interact box 3.3 Heterozygosity over time in a finite population 84

3.5 Estimating effective population size 85

Different types of effective population size 85

Interact box 3.4 Estimating N e from allele frequencies and heterozygosity over time 89

Breeding effective population size 90

Effective population sizes of different genomes 92

3.6 Gene genealogies and the coalescent model 92

Interact box 3.5 Sampling lineages in a Wright–Fisher population 94

Math box 3.2 Approximating the probability of a coalescent event with the exponential distribution 99

Interact box 3.6 Build your own coalescent genealogies 100

3.7 Effective population size in the coalescent model 103

Interact box 3.7 Simulating gene genealogies in populations with different effective sizes 103

Coalescent genealogies and population bottlenecks 105

Coalescent genealogies in growing and shrinking populations 106

Interact box 3.8 Coalescent genealogies in populations with changing size 107

3.8 Genetic drift and the coalescent with other models of life history 108

Chapter 3 review 110

Further reading 111

End of chapter exercises 111

Problem box answers 113

4 Population structure and gene flow 115

4.1 Genetic populations 115

Box 4.1 Are allele frequencies random or clumped in two dimensions? 121

4.2 Gene flow and its impact on allele frequencies in multiple subpopulations 122

Continent-island model 123

Two-island model 125

Interact box 4.1 Continent-island model of gene flow 125

Interact box 4.2 Two-island model of gene flow 126

4.3 Direct measures of gene flow 127

Problem box 4.1 Calculate the probability of a random haplotype match and the exclusion probability 133

Interact box 4.3 Average exclusion probability for a locus 134

4.4 Fixation indices to summarize the pattern of population subdivision 135

Problem box 4.2 Compute FIS, FST, and FIT 138

Estimating fixation indices 140

4.5 Population subdivision and the Wahlund effect 142

Interact box 4.4 Simulating the Wahlund effect 144

Problem box 4.3 Impact of population structure on a DNA-profile match probability 147

4.6 Evolutionary models that predict patterns of population structure 148

Infinite island model 148

Math box 4.1 The expected value of F ST in the infinite island model 150

Problem box 4.4 Expected levels of F ST for Y-chromosome and organelle loci 153

Interact box 4.5 Simulate FIS, FST, and FIT in the finite island model 154

Stepping-stone and metapopulation models 155

Isolation by distance and by landscape connectivity 156

Math box 4.2 Analysis of a circuit to predict gene flow across a landscape 159

4.7 Population assignment and clustering 160

Maximum likelihood assignment 161

Bayesian assignment 161

Interact box 4.6 Genotype assignment and clustering 162

Math box 4.3 Bayes Theorem 166

Empirical assignment methods 167

Interact box 4.7 Visualizing principle components analysis 167

4.8 The impact of population structure on genealogical branching 169

Combining coalescent and migration events 169

Interact box 4.8 Gene genealogies with migration between two demes 171

The average length of a genealogy with migration 172

Math box 4.4 Solving two equations with two unknowns for average coalescence times 175

Chapter 4 review 176

Further reading 177

End of chapter exercises 178

Problem box answers 180

5 Mutation 183

5.1 The source of all genetic variation 183

Estimating mutation rates 187

Evolution of mutation rates 189

5.2 The fate of a new mutation 191

Chance a mutation is lost due to mendelian segregation 191

Fate of a new mutation in a finite population 193

Interact box 5.1 Frequency of neutral mutations in a finite population 194

Mutations in expanding populations 195

Geometric model of mutations fixed by natural selection 196

Muller’s ratchet and the fixation of deleterious mutations 199

Interact box 5.2 Muller’s Ratchet 201

5.3 Mutation models 201

Mutation models for discrete alleles 201

Interact box 5.3 Rst and Fst as examples of the consequences of different mutation models 204

Mutation models for DNA sequences 205

Box 5.1 Single nucleotide polymorphisms 206

5.4 The influence of mutation on allele frequency and autozygosity 207

Math box 5.1 Equilibrium allele frequency with two-way mutation 209

Interact box 5.4 Simulating irreversible and two-way mutation 211

Interact box 5.5 Heterozygosity and homozygosity with two-way mutation 212

5.5 The coalescent model with mutation 213

Interact box 5.6 Build your own coalescent genealogies with mutation 215

Chapter 5 review 217

Further reading 218

End-of-chapter exercises 219

6 Fundamentals of natural selection 220

6.1 Natural selection 220

Natural selection with clonal reproduction 220

Problem box 6.1 Relative fitness of HIV genotypes 224

Natural selection with sexual reproduction 225

Math box 6.1 The change in allele frequency each generation under natural selection 229

6.2 General results for natural selection on a diallelic locus 230

Selection against a recessive phenotype 231

Selection against a dominant phenotype 232

General dominance 233

Heterozygote disadvantage 234

Heterozygote advantage 235

Math box 6.2 Equilibrium allele frequency with overdominance 236

The strength of natural selection 237

6.3 How natural selection works to increase average fitness 238

Average fitness and rate of change in allele frequency 238

Problem box 6.2 Mean fitness and change in allele frequency 240

Interact box 6.1 Natural selection on one locus with two alleles 240

The fundamental theorem of natural selection 241

6.4 Ramifications of the one locus, two allele model of natural selection 243

The Classical and Balance Hypotheses 243

How to explain levels of allozyme polymorphism, 245

Chapter 6 review 246

Further reading 247

End-of-chapter exercises 247

Problem box answers 248

7 Further models of natural selection 250

7.1 Viability selection with three alleles or two loci 250

Natural selection on one locus with three alleles 250

Problem box 7.1 Marginal fitness and Δp for the Hb C allele 253

Interact box 7.1 Natural selection on one locus with three or more alleles 254

Natural selection on two diallelic loci 254

7.2 Alternative models of natural selection 259

Natural selection via different levels of fecundity 260

Natural selection with frequency-dependent fitness 262

Math box 7.1 The change in allele frequency with frequency-dependent selection 263

Interact box 7.2 Frequency-dependent natural selection 263

Natural selection with density-dependent fitness 264

Interact box 7.3 Density-dependent natural selection 266

7.3 Combining natural selection with other processes 266

Natural selection and genetic drift acting simultaneously 266

Genetic differentiation among populations by natural selection 267

Interact box 7.4 The balance of natural selection and genetic drift at a diallelic locus 268

The balance between natural selection and mutation 271

Genetic load 272

Interact box 7.5 Natural selection and mutation 272

Math box 7.2 Mean fitness in a population at equilibrium for balancing selection 275

7.4 Natural selection in genealogical branching models 277

Directional selection and the ancestral selection graph 278

Problem box 7.2 Resolving possible selection events on an ancestral selection graph 281

Interact box 7.6 Build an ancestral selection graph 282

Genealogies and balancing selection 283

7.5 Shifting balance theory 284

Allele combinations and the fitness surface 284

Wright’s view of allele frequency distribution 286

Evolutionary scenarios imagined by wright 287

Critique and controversy over shifting balance 290

Chapter 7 review 292

Further reading 293

End-of-chapter exercises 293

Problem box answers 294

8 Molecular evolution 296

8.1 Neutral theory 296

Polymorphism 297

Divergence 299

Nearly neutral theory 301

Interact box 8.1 Compare the neutral theory and nearly neutral theory 302

The selectionist–neutralist debates 302

8.2 Natural selection 305

Hitch-hiking and rates of divergence 310

Empirical studies 310

8.3 Measures of divergence and polymorphism 313

Box 8.1 DNA sequencing 313

DNA divergence between specie, 314

DNA sequence divergence and saturation 315

Interact box 8.2 Compare nucleotide substitution models 316

DNA polymorphism measured by segregating sites and nucleotide diversity 319

Interact box 8.3 Estimating π and S from DNA sequence data 323

8.4 DNA sequence divergence and the molecular clock 324

Dating events with the molecular clock 325

Problem box 8.1 Estimating divergence times with the molecular clock 327

Interact box 8.4 Molecular clock estimates of evolutionary events 328

8.5 Testing the molecular clock hypothesis and explanations for rate variation in molecular evolution 329

The molecular clock and rate variation 329

Ancestral polymorphism and poisson process molecular clock 331

Math box 8.1 The dispersion index with ancestral polymorphism and divergence 333

Relative rate tests of the molecular clock 334

Patterns and causes of rate heterogeneity 336

8.6 Testing the neutral theory null model of DNA sequence polymorphism 339

HKA test of neutral theory expectations for DNA sequence evolution 340

The McDonald–Kreitman (MK) test 342

Mismatch distributions 343

Tajima’s D 346

Problem box 8.2 Computing Tajima’s D from DNA sequence data 348

8.7 Recombination in the genealogical branching model 350

Interact box 8.5 Build an ancestral recombination graph 353

Consequences of recombination 353

Chapter 8 review 354

Further reading 355

End-of-chapter exercises 356

Problem box answers 357

9 Quantitative trait variation and evolution 359

9.1 Quantitative traits 359

Problem box 9.1 Phenotypic distribution produced by Mendelian inheritance of three diallelic loci 361

Components of phenotypic variation 362

Components of genotypic variation (VG) 363

Inheritance of additive (VA), dominance (VD), and epistasis (VI) genotypic variation 367

Genotype-by-environment interaction (VG×E) 369

Additional sources of phenotypic variance 372

Math box 9.1 Summing two variances 372

9.2 Evolutionary change in quantitative traits 374

Heritability and the Breeder’s equation 374

Changes in quantitative trait mean and variance due to natural selection 376

Math box 9.2 Selection differential with truncation selection 376

Estimating heritability by parent–offspring regression 379

Interact box 9.1 Estimating heritability with parent-offspring regression 381

Response to selection on correlated traits 381

Interact box 9.2 Response to natural selection on two correlated traits 384

Long-term response to selection 384

Interact box 9.3 Response to selection and the number of loci that cause quantitative trait variation 387

Neutral evolution of quantitative traits 391

Interact box 9.4 Effective population size and genotypic variation in a neutral quantitative trait 392

9.3 Quantitative trait loci (QTL) 393

QTL mapping with single marker loci,394

Problem box 9.2 Compute the effect and dominance coefficient of a QTL 399

QTL mapping with multiple marker loci 400

Problem box 9.3 Derive the expected marker-class means for a backcross mating design 402

Limitations of QTL mapping studies 403

Genome-wide association studies 404

Biological significance of identifying QTL 405

Interact box 9.5 Effect sizes and response to selection at QTLs 407

Chapter 9 review 408

Further reading 409

End-of-chapter exercises 409

Problem box answers 410

10 The Mendelian basis of quantitative trait variation 413

10.1 The connection between particulate inheritance and quantitative trait variation 413

Scale of genotypic values 413

Problem box 10.1 Compute values on the genotypic scale of measurement for IGF1 in dogs 414

10.2 Mean genotypic value in a population 415

10.3 Average effect of an allele 416

Math box 10.1 The average effect of the A 1 allele 418

Problem box 10.2 Compute average effects for IGF1 in dogs 420

10.4 Breeding value and dominance deviation 420

Interact box 10.1 Average effects, breeding values, and dominance deviations 424

Dominance deviation 425

10.5 Components of total genotypic variance 428

Interact box 10.2 Components of total genotypic variance, V G  430

Math box 10.2 Deriving the total genotypic variance, V G  430

10.6 Genotypic resemblance between relatives 431

Chapter 10 review 433

Further reading 434

End-of-chapter exercises 434

Problem box answers 434

Appendix 436

Problem A.1 Estimating the variance 438

Interact box A.1 The central limit theorem 439

A.1 Covariance and Correlation 440

Further reading 442

Problem box answers 442

Bibliography 443

Index 468