Population Genetics

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