Probability Models for DNA Sequence Evolution / Edition 2

Probability Models for DNA Sequence Evolution / Edition 2

by Richard Durrett
     
 

Second edition of a successful book covering genetics, one of the fastest growing areas of active research Author Durrett is a very well-known probabilist Assumes no previous knowledge of biology and only a basic knowledge of probability Includes data from numerous experimental studies from the biological literature How is genetic variability shaped by natural

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Overview

Second edition of a successful book covering genetics, one of the fastest growing areas of active research Author Durrett is a very well-known probabilist Assumes no previous knowledge of biology and only a basic knowledge of probability Includes data from numerous experimental studies from the biological literature How is genetic variability shaped by natural selection, demographic factors, and random genetic drift? To approach this question, we introduce and analyze a number of probability models beginning with the basics, and ending at the frontiers of current research. Throughout the book, the theory is developed in close connection with examples from the biology literature that illustrate the use of these results. Along the way, there are many numerical examples and graphs to illustrate the conclusions. This is the second edition and is twice the size of the first one. The material on recombination and the stepping stone model have been greatly expanded, there are many results form the last five years, and two new chapters on diffusion processes develop that viewpoint. This book is written for mathematicians and for biologists alike. No previous knowledge of concepts from biology is assumed, and only a basic knowledge of probability, including some familiarity with Markov chains and Poisson processes. The book has been restructured into a large number of subsections and written in a theorem-proof style, to more clearly highlight the main results and allow readers to find the results they need and to skip the proofs if they desire. Written for: Researchers, graduate students

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Product Details

ISBN-13:
9780387781686
Publisher:
Springer New York
Publication date:
06/28/2008
Series:
Probability and Its Applications Series
Edition description:
2nd ed. 2008
Pages:
431
Product dimensions:
6.30(w) x 9.30(h) x 1.00(d)

Meet the Author

Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of six books and 125 research papers, and is the academic father of more than 30 Ph.D. students. His current interests are the use of probability models in genetics and ecology, and decreasing the mean and variance of his golf.

Table of Contents

1 Basic Models 1

1.1 ATGCs of life 1

1.2 Wright-Fisher model 5

1.3 Infinite alleles model 14

1.4 Infinite sites model 29

1.5 Moran model 46

2 Estimation and Hypothesis Testing 53

2.1 Site frequency spectrum covariance 53

2.2 Estimates of [theta] 60

2.3 Hypothesis testing overview 63

2.4 Difference statistics 65

2.5 The HKA test 72

2.6 McDonald-Kreitman test 78

3 Recombination 83

3.1 Two loci 83

3.2 In loci 90

3.3 Linkage disequilibrium 97

3.4 Ancestral recombination graph 101

3.5 Counting recombinations 111

3.6 Estimating recombination rates 114

3.7 Haplotypes and hot spots 122

4 Population Complications 125

4.1 Large family sizes 125

4.2 Population growth 130

4.3 Founding effects and bottlenecks 138

4.4 Effective population size 143

4.5 Matrix migration models 146

4.6 Symmetric island model 150

4.7 Fixation indices 157

5 Stepping Stone Model 161

5.1 d = 1, Exact results 161

5.2 d = 1 and 2, Fourier methods 165

5.3 d = 2, Coalescence times 172

5.4 d = 2, Genealogies 179

5.5 d = 1, Continuous models 183

5.6 d = 2, Continuous models 188

6 Natural Selection 191

6.1 Directional selection 191

6.2 Balancing selection 201

6.3 Background selection 211

6.4 Muller's ratchet 219

6.5 Hitchhiking 225

6.6 Better approximations 234

6.7 Recurrent sweeps 241

7 Diffusion Processes 249

7.1 Infinitesimal mean and variance 250

7.2 Examples of diffusions 252

7.3 Transition probabilities 258

7.4 Flitting probabilities 262

7.5 Stationary measures 268

7.6 Occupation times 273

7.7 Green's functions 276

7.8 Examples 280

7.9 Conditioned processes 287

7.10 Boundary behavior 293

7.11 Site frequency spectrum298

7.12 Fluctuating selection 304

8 Multidimensional Diffusions 313

8.1 K allele model 313

8.2 Recombination 322

8.2 Recombination 322

8.4 Gene duplication 341

8.5 Watterson's double recessive null model 343

8.6 Subfunctionalization 347

9 Genome Rearrangement 355

9.1 Inversions 355

9.2 When is parsimony reliable? 362

9.3 Nadeau and Taylor's analysis 370

9.4 Genomic distance 375

9.5 Midpoint problem 382

9.6 Genome duplication 389

References 399

Index 427

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