Coalescent Theory and Applications

Instructors: G. Coop and C.H. Langley
(CRN 44951)
The coalescent is an elegant and intuitive model to describe patterns of genetic polymorphism in samples from natural populations. It has been applied in many areas of evolutionary genetics from speciation to the mapping of phenotypic traits. The course will explore a number of aspects of coalescent theory and its applications, and will be based around the discussion of papers. We will also make use the new book by John Wakeley (Coalescent Theory) as a companion text. The first three chapters of the book are available as uncorrected poofs here. The course will be organized around 5 broad topics:
An introduction to coalescent theory
Demography and subdivision
The coalescent with recombination
Selection and the coalescent
Population history

The course is scheduled for the Winter Quarter and will meet in the Tropical Room (2346 Storer Hall) on Tuesdays and Thursdays at 11am.
Attendance of the course requires the permission of an instructor.


Introduction and basic coalescent processes: Week 1

   Reading in Wakeley: Sections 3.1.1, 3.1.2, 3.2.1, 3.2.2, 3.3.1, & 3.3.2

   Papers to discuss in class:

   This difficult little paper by one of the founders and most ardent proponents of the Neutral Theory is the beginning of the infinite sites model. It is filled with ideas, conclusions and questions that will reappear throughout the course. Don't let the diffusion theory differential analyses slow you down; get what you can and keep going.

   A simple early analysis of the coalescent process to address an important question about the observed pattern of genomic polymorphism. Don't worry about the SOD biology, focus on the population genetic hypothesis and test.

Introduction and basic coalescent processes: Week 2

   Reading in Wakeley: Chapter 4, pages 91 to 119.

   Papers to discuss in class:

   Genetics_Hudson_1987 This paper presents a Coalescent Process based test of the fit of the DNA sequence polymorphism and divergence data at 2 (or more loci) to the neutral theory.

Multiple Populations: Week 3

   Reading in Hudson 1991, Section 7, pages 19 to 24.

   Reading in Wakeley: Sections 5.2 and 5.2.1, pages 148 to 156.

   Papers to discuss in class:

   So far we have not been able to identify a single paper (other than the Section 7 in Hudson, 1991) that serves our goal of introducing the topic of population subdivision in a simple and heuristic manner. Below in the "Additional Interesting Reading" are a number of the early papers dealing with this issue from the coalescent process perspective. Each has its value but none focuses on the simplest case with most of the potential insight.


Variable Population Size: Week 3

   Slatkin and Hudson Genetics
This paper looks at the effects of exponential growth on the distribution of pairwise differences, an idea inspired by patterns seen in mtDNA.

   Voight, et al. PNAS
One of a number of papers that have estimated different models of population size changes for human populations using summary statistics from a set of unlinked loci.

Week 4: Introduction to coalescent processes with recombination
   Section 5 of Hudson_OxfordSurveysEvolBiol_1991 and 7.2-7.2.3 of Wakeley (pages 223-236) give an overview of the coalescent with recombination. This process is great for getting an intuition for the effect of recombination and a process to simulate from, however it does not lend itself to easily derived results (so don't be put off). The Nordborg and Tavare review (link given below) is also good if you are looking for additional insights and motivation.

   Two papers that cover the efforts in the early 2000's to understand what the scale of Linkage Disequilibrium is in humans, and what processes may have shaped this. Reich, et al., Nature Genetics 2002 provides one of the first genome-wide looks at the scale at which recombination is breaking down the correlation between genealogies, while Pritchard & Przeworski AmJHumGenet. 2001 is an accessible review on patterns on LD (pages 1-9 are the most relevant).

Week 5: More recombination

   We'll discuss Hudson's "Two-locus sampling distributions and their application" Hudson_Genetics _2001, which introduces an estimator of the population-scaled recombination rate based upon considering pairs of sites.

   We'll also discuss an application of this method to estimate the variation in recombination rates in humans from LD data by Mcvean_Sciencemag_2004. Have a look at the Nordborg and Tavare or Pritchard and Przeworski reviews (given below) if you need some helping thinking about LD.

Week 6: Coalescent Processes with Selection

   The topic for this week is the incorporation of linked selection into the coalescent processes.

The first reading for this week are section 5.4 of Wakeley plus
Kaplan, Darden & Hudson, Genetics 1988   This is a foundation paper. The basic model and most of the assumptions and limits are laid out. But it is substantial, not to say difficult.
Kaplan, Hudson & Langley, Genetics 1989   This paper addresses the classic hypothesis of Maynard Smith & Haigh about the impact of hitchhiking on expected heterozygosity.

   Further reading:
Braverman, et al. Genetics 1995   This paper addresses the specific question of the impact of hitchhiking on the frequency spectrum of segregating sites in a sample of alleles.
Kim & Nielsen Genetics 2004    This paper uses coalescent process simulations (with linked selection) to address the impact of hitchhiking on linkage disequilibrium.

   We already assigned Kim & Nielsen for last week. But we did not get to it, so it is the paper to discuss on the 24. We add to that one of the data papers that they reanalyze:
Schlenke & Begun 2004

   While this is not a coalescent process paper, it takes us to the frontier of the investigation of linked strong selection.

Additional Interesting Reading

Week 1 & 2: Introduction and basic coalescent processes





Week 3: More than one population






Week 3: Variable population size

Przeworski and Wall

Adams & Hudson

Week 4: Introduction to coalescent processes with recombination

Nordborg & Tavare Trends in Genetics 2002

Reich, et al., Nature Genetics 2002

Pritchard & Przeworski AmJHumGenet. 2001

Week 5: More coalescent processes with recombination

McVean, Awadalla & Fearnhead, early paper on the 2 locus likelihoods: McVean_Genetics_2002