Coalescent Theory

An Introduction

By: John Wakely

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Paperback | 1 June 2008

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Coalescent theory provides the foundation for molecular population genetics and genomics. It is the conceptual framework for studies of DNA sequence variation within species, and is the source of essential tools for making inferences about mutation, recombination, population structure and natural selection from DNA sequence data. This monograph is intended mainly for biologists but it will also be of interest to mathematicians who wish to see how this branch of applied probability theory plays out in a biological setting.

Industry Reviews

"The case studies are a terrific feature... I think many biologists will be greatly buoyed by these, and motivated to think deeper about the models and how they can be analyzed." -- Richard Hudson, University of Chicago "I am thrilled John Wakeley is writing this book... For those (like myself ) excited to learn about the coalescent, I expect this book will be a godsend." -- Ben Kerr, University of Washington

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Preface	p. xi
Gene Genealogies	p. 1
Genealogies and Genealogical Thinking	p. 5
Mutation and Mutation Models	p. 10
Measures of DNA Sequence Polymorphism	p. 13
Variation at the PDHA1 Locus in Humans	p. 18
Probability Theory	p. 25
Fundamentals of Probability Theory	p. 25
Events, Probabilities, and Random Variables	p. 25
Four Famous Probability Distributions	p. 37
Poisson Processes	p. 45
Poisson Process Results for the Coalescent	p. 48
Convolutions of Exponential Distributions	p. 51
The Coalescent	p. 53
Population Genetic Models	p. 54
The Wright-Fisher Model	p. 54
The Moran Model	p. 57
The Standard Coalescent Model	p. 59
Wright-Fisher Model Derivation	p. 62
Moran Model Derivation	p. 66
Breeding Structure and Exchangeability	p. 68
Some Properties of Coalescent Genealogies	p. 74
Two Measures of the Size of a Genealogy	p. 75
The Branching Structure of Genealogies	p. 80
Human-Neanderthal Couples?	p. 83
Neutral Genetic Variation	p. 91
The Infinite-Sites Model and Measures of DNA Sequence Polymorphism	p. 93
The Number Segregating Sites	p. 94
Pairwise Differences	p. 97
Site Frequencies	p. 102
The Infinite-Alleles Model and the Ewens Sampling Formula	p. 106
Deviations from the Coalescent: Testing "Neutrality"	p. 113
Test Statistics Based on Site Frequencies	p. 114
Demographic History and Patterns of Polymorphism	p. 119
Footprints of Positive Selection in Drosophila simulans	p. 125
The Structured Coalescent	p. 131
Markov Processes	p. 134
Classification of States and Limiting Behavior	p. 138
Continuous-Time Approximations and Jump Chains	p. 141
First-Step Analysis	p. 143
The Structured Coalescent	p. 148
Predictions for Samples of Size 2	p. 151
Geographic Structure	p. 156
Subdivision with Migration	p. 158
Gene Trees versus Species Trees in Australian Grass Finches	p. 163
Strong Natural Selection	p. 167
Selective Sweeps	p. 175
Balancing Selection at the Adh Locus in Drosophila melanogaster	p. 178
Separation of Time Scales	p. 181
Diploidy and Two Sexes	p. 183
Markov Processes with Two Time Scales	p. 188
Strong Migration	p. 191
Partial Selfing	p. 195
Many Demes	p. 198
Samples Larger than Two and Other Extensions	p. 202
Ancestral Graphs	p. 207
The Ancestral Selection Graph	p. 208
The Ancestry of a Highly Deleterious Allele	p. 217
The Ancestral Recombination Graph	p. 223
The Two-Locus Model: Covariance in Ancestry	p. 225
The Number of Segregating Sites	p. 229
The Number of Recombination Events	p. 234
Linkage Disequilibrium and Coalescence Times	p. 236
Linkage Disequilibrium in the Human Genome	p. 243
Simulations and Inference	p. 247
The Age of the ZFY Intron in Humans	p. 248
Monte Carlo Integration and the Coalescent	p. 252
Mutation Models	p. 257
Concepts of Statistical Inference and the Coalescent	p. 259
Frequentist versus Bayesian Approaches	p. 263
Computing Likelihoods of Full Data Patterns	p. 266
Importance Sampling Methods	p. 270
Markov Chain Monte Carlo Methods	p. 283
Future Directions	p. 289
References	p. 293
Author Index	p. 317
Subject Index	p. 321
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Coalescent Theory

An Introduction

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