Probability Models for DNA Sequence Evolution

Rick Durrett

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Chapter 1. Basic Models

1.1. The ATGCs of Life
1.2. Wright-Fisher Model
1.3. Infinite alleles model
1.4. Infinite sites model
1.5. Moran model

Chapter 2. Estimation and Hypothesis Testing

2.1. Site frequency spectrum covariance
2.2. Estimates of theta
2.3. Hypothesis testing overview 2.4. Difference statistics
2.5. HKA test
2.6. McDonald-Kreitman test

Chapter 3. Recombination

3.1. Two loci
3.2. m loci
3.3. Linkage disequilibrium
3.4. Ancestral recombination graph
3.5. Counting recombinations
3.6. Estimating recombination rates
3.7. Haplotypes and hot spots

Chapter 4. Population Complications

4.1. Large family sizes
4.2. Population growth
4.3. Founding effects and bottlenecks
4.4. Effective population size
4.5. Matrix migration models
4.6. Symmetric island model
4.7. Fixation indices

Chapter 5. Stepping stone model

5.1. d=1, Exact results
5.2. d=1 and 2, Fourier methods
5.3. d=2, Coalescence times
5.4. d=2, Genealogies
5.5. d=1, Continuous models
5.6. d=2, Continuous models

Chapter 6. Natural Selection

6.1. Directional selection
6.2. Balancing selection
6.3. Background selection
6.4. Hitchhiking
6.5. Better approximations
6.6. Recurrent sweeps

Chapter 7. Diffusion Processes

7.1. Infinitesimal mean and variance
7.2. Examples
7.3. Transition probabilities
7.4. Hitting probabilities
7.5. Stationary distribution
7.6. Occupation times
7.7. Green's functions
7.8. Examples
7.9. Conditioned Processes
7.10. Boundary behavior
7.11. Site freqeuncy spectrum
7.12. Fluctuating selection

Chapter 8. Multidimensional Diffusions

8.1. K allele model
8.2. Recombination
8.3. Hill-Robertson interference
8.4. Gene duplication
8.5. Wattersons's double recessive null model
8.6. Subfunctionalization

Chapter 9. Genome Rearrangement

9.1. Inversions
9.2. When is parsimony reliable?
9.3. Nadeau and Taylor's analysis
9.4. Genomic distance
9.5. Midpoint problem
9.6. Genome duplication


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