The Foundations of Population Genetics

by Weinreich

| ISBN: 9780262372565 | Copyright 2023

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An accessible but rigorous treatment of the theoretical foundations of population genetics.

Population genetics—the branch of evolutionary biology concerned with understanding how and why populations' genetic compositions change over time—rests on a well-developed theoretical foundation that draws on genetics, mathematics, and computer science. This textbook provides an approachable but rigorous treatment for advanced undergraduate and graduate students interested in building a quantitative understanding of the genetics of evolution. Existing texts either assume very mathematically advanced readers, or avoid much of the underlying theory, instead focusing on current methods of data analysis. In contrast, The Foundations of Population Genetics develops the theory from first principles. Requiring only confidence in algebra, this self-contained, student-friendly book illustrates the conceptual framework, terminology, and methods of mathematical modeling. It progressively introduces concepts from genetics as needed, while emphasizing biological implications throughout. As a result, readers come away with a deep understanding of the structure of population genetics without needing to master its mathematics.

•Connects theory with the most recent genetic data better than existing texts
•Features engaging real-world examples and extensive original figures
•Provides dozens of carefully scaffolded questions that deepen the reader's understanding of key concepts
•Ideal as a succinct reference for established scientists in biology, medicine, and computer science
•Instructor resources available

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Contents (pg. vii)
Preface (pg. xi)
Acknowledgments (pg. xii)
1. Deterministic Single-Locus Population Genetics (pg. 1)
1.1 Natural Selection (pg. 3)
1.1.1 An Exponentially Growing Population (pg. 3)
1.1.2 Darwin’s Model of Natural Selection (pg. 7)
1.1.3 The Time for a Selective Fixation (pg. 12)
1.1.4 Fisher’s Fundamental Theorem of Natural Selection (pg. 15)
1.1.5 Natural Selection in Populations with Nonoverlapping Generations (pg. 18)
1.2 Mutation (pg. 21)
1.2.1 The Evolution of Allele Frequencies under Mutation Alone (pg. 21)
1.2.2 Mutation/Selection Equilibrium (pg. 23)
1.2.3 The Error Catastrophe (pg. 25)
1.2.4 Beneficial Mutations (pg. 26)
1.2.5 Soft Selection and Hard Selection (pg. 26)
1.3 One-Locus Sexual Reproduction (pg. 28)
1.3.1 The Population Genetics of Diploid Reproduction (pg. 30)
1.3.2 Natural Selection in Diploids (pg. 35)
1.4 Population Structure, Migration, and Nonrandom Mating (pg. 39)
1.4.1 Models of Population Structure and Migration (pg. 40)
1.4.2 Migration/Selection Equilibrium (pg. 41)
1.4.3 Allele Frequency Clines (pg. 42)
1.4.4 Nonrandom Mating in Diploids (pg. 43)
1.5 Chapter Summary (pg. 50)
2. Stochastic Single-Locus Population Genetics (pg. 51)
2.1 Stochasticity While Rare, and Establishment (pg. 53)
2.1.1 The Establishment Problem (pg. 54)
2.1.2 Establishment of a New Beneficial Allele (pg. 59)
2.2 Stochasticity at All Frequencies and Random Genetic Drift (pg. 62)
2.2.1 The Chapman–Kolmogorov Equation (pg. 63)
2.2.2 The Diffusion Approximations of the Chapman–Kolmogorov Equation (pg. 67)
2.2.3 Representing Biology in the Chapman–Kolmogorov and Diffusion Equations (pg. 73)
2.2.4 Using the Backward Diffusion Approximation to Study Fixation Events (pg. 79)
2.2.5 Using the Forward Diffusion Approximation to Study Internal Equilibrium Allele Frequencies (pg. 88)
2.3 Random Genetic Drift and Heterozygosity (pg. 91)
2.3.1 The Rate of Decay in Heterozygosity under the Wright–Fisher Model (pg. 91)
2.3.2 The Infinite Alleles Model and Heterozygosity at Mutation/Drift Equilibrium under the Wright–Fisher Model (pg. 94)
2.3.3 Heterozygosity at Migration/Drift Equilibrium under the Wright–Fisher Model (pg. 97)
2.4 Coalescent Theory (pg. 97)
2.4.1 Modeling Genealogies under the Wright–Fisher Model (pg. 98)
2.4.2 The Infinite Sites Model and the Site Frequency Spectrum (pg. 102)
2.4.3 Population Subdivision and Incomplete Lineage Sorting (pg. 106)
2.5 The Effective Size of a Population (pg. 108)
2.6 Chapter Summary (pg. 112)
3. Multilocus Population Genetics (pg. 115)
3.1 Deterministic Multilocus Theory (pg. 117)
3.1.1 Pairwise Linkage Disequilibrium and Genetic Recombination (pg. 117)
3.1.2 The Two-Locus Wahlund Effect (pg. 121)
3.1.3 Pairwise Epistasis, Natural Selection and Recombination (pg. 123)
3.1.4 Multilocus Mutation/Selection Equilibrium (pg. 128)
3.1.5 The Multilocus Error Catastrophe (pg. 133)
3.1.6 Sequence Space and Fitness Landscapes (pg. 136)
3.1.7 Multilocus Adaptation on Fitness Landscapes under the Strong Selection/ Weak Mutation Assumption (pg. 140)
3.1.8 Stochastic Tunneling (pg. 144)
3.2 Stochastic Multilocus Theory (pg. 147)
3.2.1 Multilocus Coalescent Theory (pg. 148)
3.2.2 Selective Sweeps and Genetic Draft (pg. 151)
3.2.3 Background Selection (pg. 159)
3.2.4 The Hill–Robertson Effect (pg. 160)
3.3 Modifier Theory (pg. 168)
3.3.1 The Evolution of Sex (pg. 170)
3.3.2 The Evolution of Mutation Rate (pg. 173)
3.3.3 Other Modifiers (pg. 173)
3.4 Chapter Summary (pg. 174)
4. The Data (pg. 175)
4.1 Measuring Genetic Parameters (pg. 177)
4.1.1 Mutation Rate (pg. 178)
4.1.2 Recombination Rate (pg. 180)
4.2 Measuring Effective Population Size (pg. 181)
4.2.1 Direct Observation of Reproductive Variance (pg. 182)
4.2.2 Equilibrium Effective Population Size Estimates (pg. 182)
4.2.3 Nonequilibrium Mutation-Based Effective Population Size Estimates in Asexuals (pg. 185)
4.2.4 Nonequilibrium Mutation-Based Effective Population Size Estimates in Sexuals (pg. 190)
4.2.5 Nonequilibrium Recombination-Based Effective Population Size Estimates (pg. 195)
4.3 Describing Population Structure, Migration, and Admixture (pg. 198)
4.3.1 Detecting Population Structure (pg. 198)
4.3.2 Estimating Population Structure with FST (pg. 200)
4.3.3 Estimating Migration with the Joint Site Frequency Spectrum (pg. 201)
4.3.4 Estimating Admixture from Haplotype Structure (pg. 203)
4.4 Describing Natural Selection (pg. 205)
4.4.1 Quantifying Natural Selection with the Molecular Clock (pg. 205)
4.4.2 The McDonald/Kreitman Test (pg. 209)
4.4.3 Scanning Whole Genome Sequence Data for Natural Selection (pg. 211)
4.4.4 Hard and Soft Selective Sweeps (pg. 214)
4.5 Chapter Summary (pg. 217)
References (pg. 219)
Index (pg. 231)

Daniel M. Weinreich

Daniel M. Weinreich is Royce Professor of Teaching Excellence in Biology at Brown University.

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