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 xivAbout the companion websites xvi1 Thinking like a population geneticist 11.1   Expectations 1Parameters and parameter estimates 2Inductive and deductive reasoning 31.2 Theory and assumptions 41.3 Simulation 5Interact box 1.1 The textbook website 6Chapter 1 review 7Further reading 72 Genotype frequencies 82.1 Mendel’s model of particulate genetics 82.2 Hardy–Weinberg expected genotype frequencies 12Interact box 2.1 Genotype frequencies for one locus with two alleles 142.3 Why does Hardy–Weinberg work? 152.4 Applications of Hardy–Weinberg 18Forensic DNA profiling 18Problem box 2.1 The expected genotype frequency for a DNA profile 20Testing Hardy–Weinberg expected genotype frequencies 20Box 2.1 DNA profiling 21Assuming Hardy–Weinberg to test alternative models of inheritance 24Problem box 2.2 Proving allele frequencies are obtained from expected genotype frequencies 25Problem box 2.3 Inheritance for corn kernel phenotypes 262.5 The fixation index and heterozygosity 26Interact box 2.2 Assortative mating and genotype frequencies 27Box 2.2 Protein locus or allozyme genotyping 302.6 Mating among relatives 31Impacts of non-random mating on genotype and allele frequencies 31Coancestry coefficient and autozygosit, 33Box 2.3 Locating relatives using genetic genealogy methods 37Phenotypic consequences of mating among relatives 38The many meanings of inbreeding 412.7 Hardy–Weinberg for two loci 42Gametic disequilibrium 42Physical linkage 47Natural selection 47Interact box 2.3 Gametic disequilibrium under both recombination and natural selection 48Mutation 48Mixing of diverged populations 49Mating system 49Population size 50Interact box 2.4 Estimating genotypic disequilibrium 51Chapter 2 review 52Further reading 52End-of-chapter exercises 53Problem box answers 543 Genetic drift and effective population size 573.1 The effects of sampling lead to genetic drift 57Interact box 3.1 Genetic drift 623.2 Models of genetic drift 62The binomial probability distribution 62Problem box 3.1 Applying the binomial formula 64Math box 3.1 Variance of a binomial variable 66Markov chains 66Interact box 3.2 Genetic drift simulated with a markov chain model 69Problem box 3.2 Constructing a transition probability matrix 69The diffusion approximation of genetic drift 703.3 Effective population size 76Problem box 3.3 Estimating N e from information about N 813.4 Parallelism between Drift and mating among relatives 81Interact box 3.3 Heterozygosity over time in a finite population 843.5 Estimating effective population size 85Different types of effective population size 85Interact box 3.4 Estimating N e from allele frequencies and heterozygosity over time 89Breeding effective population size 90Effective population sizes of different genomes 923.6 Gene genealogies and the coalescent model 92Interact box 3.5 Sampling lineages in a Wright–Fisher population 94Math box 3.2 Approximating the probability of a coalescent event with the exponential distribution 99Interact box 3.6 Build your own coalescent genealogies 1003.7 Effective population size in the coalescent model 103Interact box 3.7 Simulating gene genealogies in populations with different effective sizes 103Coalescent genealogies and population bottlenecks 105Coalescent genealogies in growing and shrinking populations 106Interact box 3.8 Coalescent genealogies in populations with changing size 1073.8 Genetic drift and the coalescent with other models of life history 108Chapter 3 review 110Further reading 111End of chapter exercises 111Problem box answers 1134 Population structure and gene flow 1154.1 Genetic populations 115Box 4.1 Are allele frequencies random or clumped in two dimensions? 1214.2 Gene flow and its impact on allele frequencies in multiple subpopulations 122Continent-island model 123Two-island model 125Interact box 4.1 Continent-island model of gene flow 125Interact box 4.2 Two-island model of gene flow 1264.3 Direct measures of gene flow 127Problem box 4.1 Calculate the probability of a random haplotype match and the exclusion probability 133Interact box 4.3 Average exclusion probability for a locus 1344.4 Fixation indices to summarize the pattern of population subdivision 135Problem box 4.2 Compute FIS, FST, and FIT 138Estimating fixation indices 1404.5 Population subdivision and the Wahlund effect 142Interact box 4.4 Simulating the Wahlund effect 144Problem box 4.3 Impact of population structure on a DNA-profile match probability 1474.6 Evolutionary models that predict patterns of population structure 148Infinite island model 148Math box 4.1 The expected value of F ST in the infinite island model 150Problem box 4.4 Expected levels of F ST for Y-chromosome and organelle loci 153Interact box 4.5 Simulate FIS, FST, and FIT in the finite island model 154Stepping-stone and metapopulation models 155Isolation by distance and by landscape connectivity 156Math box 4.2 Analysis of a circuit to predict gene flow across a landscape 1594.7 Population assignment and clustering 160Maximum likelihood assignment 161Bayesian assignment 161Interact box 4.6 Genotype assignment and clustering 162Math box 4.3 Bayes Theorem 166Empirical assignment methods 167Interact box 4.7 Visualizing principle components analysis 1674.8 The impact of population structure on genealogical branching 169Combining coalescent and migration events 169Interact box 4.8 Gene genealogies with migration between two demes 171The average length of a genealogy with migration 172Math box 4.4 Solving two equations with two unknowns for average coalescence times 175Chapter 4 review 176Further reading 177End of chapter exercises 178Problem box answers 1805 Mutation 1835.1 The source of all genetic variation 183Estimating mutation rates 187Evolution of mutation rates 1895.2 The fate of a new mutation 191Chance a mutation is lost due to mendelian segregation 191Fate of a new mutation in a finite population 193Interact box 5.1 Frequency of neutral mutations in a finite population 194Mutations in expanding populations 195Geometric model of mutations fixed by natural selection 196Muller’s ratchet and the fixation of deleterious mutations 199Interact box 5.2 Muller’s Ratchet 2015.3 Mutation models 201Mutation models for discrete alleles 201Interact box 5.3 Rst and Fst as examples of the consequences of different mutation models 204Mutation models for DNA sequences 205Box 5.1 Single nucleotide polymorphisms 2065.4 The influence of mutation on allele frequency and autozygosity 207Math box 5.1 Equilibrium allele frequency with two-way mutation 209Interact box 5.4 Simulating irreversible and two-way mutation 211Interact box 5.5 Heterozygosity and homozygosity with two-way mutation 2125.5 The coalescent model with mutation 213Interact box 5.6 Build your own coalescent genealogies with mutation 215Chapter 5 review 217Further reading 218End-of-chapter exercises 2196 Fundamentals of natural selection 2206.1 Natural selection 220Natural selection with clonal reproduction 220Problem box 6.1 Relative fitness of HIV genotypes 224Natural selection with sexual reproduction 225Math box 6.1 The change in allele frequency each generation under natural selection 2296.2 General results for natural selection on a diallelic locus 230Selection against a recessive phenotype 231Selection against a dominant phenotype 232General dominance 233Heterozygote disadvantage 234Heterozygote advantage 235Math box 6.2 Equilibrium allele frequency with overdominance 236The strength of natural selection 2376.3 How natural selection works to increase average fitness 238Average fitness and rate of change in allele frequency 238Problem box 6.2 Mean fitness and change in allele frequency 240Interact box 6.1 Natural selection on one locus with two alleles 240The fundamental theorem of natural selection 2416.4 Ramifications of the one locus, two allele model of natural selection 243The Classical and Balance Hypotheses 243How to explain levels of allozyme polymorphism, 245Chapter 6 review 246Further reading 247End-of-chapter exercises 247Problem box answers 2487 Further models of natural selection 2507.1 Viability selection with three alleles or two loci 250Natural selection on one locus with three alleles 250Problem box 7.1 Marginal fitness and Δp for the Hb C allele 253Interact box 7.1 Natural selection on one locus with three or more alleles 254Natural selection on two diallelic loci 2547.2 Alternative models of natural selection 259Natural selection via different levels of fecundity 260Natural selection with frequency-dependent fitness 262Math box 7.1 The change in allele frequency with frequency-dependent selection 263Interact box 7.2 Frequency-dependent natural selection 263Natural selection with density-dependent fitness 264Interact box 7.3 Density-dependent natural selection 2667.3 Combining natural selection with other processes 266Natural selection and genetic drift acting simultaneously 266Genetic differentiation among populations by natural selection 267Interact box 7.4 The balance of natural selection and genetic drift at a diallelic locus 268The balance between natural selection and mutation 271Genetic load 272Interact box 7.5 Natural selection and mutation 272Math box 7.2 Mean fitness in a population at equilibrium for balancing selection 2757.4 Natural selection in genealogical branching models 277Directional selection and the ancestral selection graph 278Problem box 7.2 Resolving possible selection events on an ancestral selection graph 281Interact box 7.6 Build an ancestral selection graph 282Genealogies and balancing selection 2837.5 Shifting balance theory 284Allele combinations and the fitness surface 284Wright’s view of allele frequency distribution 286Evolutionary scenarios imagined by wright 287Critique and controversy over shifting balance 290Chapter 7 review 292Further reading 293End-of-chapter exercises 293Problem box answers 2948 Molecular evolution 2968.1 Neutral theory 296Polymorphism 297Divergence 299Nearly neutral theory 301Interact box 8.1 Compare the neutral theory and nearly neutral theory 302The selectionist–neutralist debates 3028.2 Natural selection 305Hitch-hiking and rates of divergence 310Empirical studies 3108.3 Measures of divergence and polymorphism 313Box 8.1 DNA sequencing 313DNA divergence between specie, 314DNA sequence divergence and saturation 315Interact box 8.2 Compare nucleotide substitution models 316DNA polymorphism measured by segregating sites and nucleotide diversity 319Interact box 8.3 Estimating π and S from DNA sequence data 3238.4 DNA sequence divergence and the molecular clock 324Dating events with the molecular clock 325Problem box 8.1 Estimating divergence times with the molecular clock 327Interact box 8.4 Molecular clock estimates of evolutionary events 3288.5 Testing the molecular clock hypothesis and explanations for rate variation in molecular evolution 329The molecular clock and rate variation 329Ancestral polymorphism and poisson process molecular clock 331Math box 8.1 The dispersion index with ancestral polymorphism and divergence 333Relative rate tests of the molecular clock 334Patterns and causes of rate heterogeneity 3368.6 Testing the neutral theory null model of DNA sequence polymorphism 339HKA test of neutral theory expectations for DNA sequence evolution 340The McDonald–Kreitman (MK) test 342Mismatch distributions 343Tajima’s D 346Problem box 8.2 Computing Tajima’s D from DNA sequence data 3488.7 Recombination in the genealogical branching model 350Interact box 8.5 Build an ancestral recombination graph 353Consequences of recombination 353Chapter 8 review 354Further reading 355End-of-chapter exercises 356Problem box answers 3579 Quantitative trait variation and evolution 3599.1 Quantitative traits 359Problem box 9.1 Phenotypic distribution produced by Mendelian inheritance of three diallelic loci 361Components of phenotypic variation 362Components of genotypic variation (VG) 363Inheritance of additive (VA), dominance (VD), and epistasis (VI) genotypic variation 367Genotype-by-environment interaction (VG×E) 369Additional sources of phenotypic variance 372Math box 9.1 Summing two variances 3729.2 Evolutionary change in quantitative traits 374Heritability and the Breeder’s equation 374Changes in quantitative trait mean and variance due to natural selection 376Math box 9.2 Selection differential with truncation selection 376Estimating heritability by parent–offspring regression 379Interact box 9.1 Estimating heritability with parent-offspring regression 381Response to selection on correlated traits 381Interact box 9.2 Response to natural selection on two correlated traits 384Long-term response to selection 384Interact box 9.3 Response to selection and the number of loci that cause quantitative trait variation 387Neutral evolution of quantitative traits 391Interact box 9.4 Effective population size and genotypic variation in a neutral quantitative trait 3929.3 Quantitative trait loci (QTL) 393QTL mapping with single marker loci,394Problem box 9.2 Compute the effect and dominance coefficient of a QTL 399QTL mapping with multiple marker loci 400Problem box 9.3 Derive the expected marker-class means for a backcross mating design 402Limitations of QTL mapping studies 403Genome-wide association studies 404Biological significance of identifying QTL 405Interact box 9.5 Effect sizes and response to selection at QTLs 407Chapter 9 review 408Further reading 409End-of-chapter exercises 409Problem box answers 41010 The Mendelian basis of quantitative trait variation 41310.1 The connection between particulate inheritance and quantitative trait variation 413Scale of genotypic values 413Problem box 10.1 Compute values on the genotypic scale of measurement for IGF1 in dogs 41410.2 Mean genotypic value in a population 41510.3 Average effect of an allele 416Math box 10.1 The average effect of the A 1 allele 418Problem box 10.2 Compute average effects for IGF1 in dogs 42010.4 Breeding value and dominance deviation 420Interact box 10.1 Average effects, breeding values, and dominance deviations 424Dominance deviation 42510.5 Components of total genotypic variance 428Interact box 10.2 Components of total genotypic variance, V G  430Math box 10.2 Deriving the total genotypic variance, V G  43010.6 Genotypic resemblance between relatives 431Chapter 10 review 433Further reading 434End-of-chapter exercises 434Problem box answers 434Appendix 436Problem A.1 Estimating the variance 438Interact box A.1 The central limit theorem 439A.1 Covariance and Correlation 440Further reading 442Problem box answers 442Bibliography 443Index 468