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Probability Models for DNA Sequence Evolution

by: Durrett, Richard

Probability Models for DNA Sequence Evolution

by: Durrett, Richard

ISBN 13:
9780387781686
ISBN 10:
0387781684
Edition: 2nd
Format: Hardcover
Copyright: 08/01/2008
Publisher: Springer Verlag

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Summary

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.

Preface	p. V
Basic Models	p. 1
ATGCs of life	p. 1
Wright-Fisher model	p. 5
The coalescent	p. 8
Shape of the genealogical tree	p. 11
Infinite alleles model	p. 14
Hoppe's urn, Ewens' sampling formula	p. 15
Chinese restaurants and sufficient statistics	p. 20
Branching process viewpoint	p. 26
Infinite sites model	p. 29
Segregating sites	p. 31
Nucleotide diversity	p. 39
Pairwise differences	p. 40
Folded site frequency spectrum	p. 43
Moran model	p. 46
Fixation probability and time	p. 47
Site frequency spectrum mean	p. 50
Estimation and Hypothesis Testing	p. 53
Site frequency spectrum covariance	p. 53
Estimates of [theta]	p. 59
Hypothesis testing overview	p. 63
Difference statistics	p. 65
Tajima's D	p. 65
Fu and Li's D	p. 67
Fay and Wu's H	p. 69
Conditioning on S[subscript n]	p. 71
The HKA test	p. 72
McDonald-Kreitman test	p. 78
Recombination	p. 83
Two loci	p. 83
Sample of size 2	p. 83
Sample of size n	p. 87
m loci	p. 90
Samples of size 2	p. 91
Samples of size n	p. 91
Pairwise differences	p. 93
Linkage disequilibrium	p. 97
Ancestral recombination graph	p. 101
Simulation	p. 105
Two approximate algorithms	p. 107
Counting recombinations	p. 111
Estimating recombination rates	p. 114
Equations for the two-locus sampling distribution	p. 115
Simulation methods	p. 118
Composite likelihood estimation of [rho]	p. 120
Haplotypes and hot spots	p. 122
Population Complications	p. 125
Large family sizes	p. 125
Population growth	p. 130
Exponential growth	p. 131
Sudden population expansion	p. 134
Founding effects and bottlenecks	p. 138
Effective population size	p. 143
Matrix migration models	p. 146
Strobeck's theorem	p. 148
Fast migration limit	p. 149
Symmetric island model	p. 150
Identity by descent	p. 150
Mean and variance of coalescence times	p. 152
Effective population sizes	p. 153
Large n limit	p. 154
Fixation indices	p. 157
Stepping Stone Model	p. 161
d = 1, Exact results	p. 161
d = 1 and 2, Fourier methods	p. 165
d = 2, Coalescence times	p. 172
Random walk results	p. 172
Samples of size 2	p. 175
Fixation indices F[subscript ST]	p. 177
d = 2, Genealogies	p. 179
Simulation results	p. 181
d = 1, Continuous models	p. 183
d = 2, Continuous models	p. 188
Natural Selection	p. 191
Directional selection	p. 191
Fixation probability	p. 192
Time to fixation	p. 194
Three phases of the fixation process	p. 197
Ancestral selection graph	p. 199
Balancing selection	p. 201
Background selection	p. 211
Muller's ratchet	p. 219
Evolutionary advantages of recombination	p. 220
Sex, epistasis, and Kondrashov	p. 222
Hitchhiking	p. 225
Better approximations	p. 234
Recurrent sweeps	p. 241
Nucleotide diversity	p. 241
Genealogies	p. 243
Segregating sites	p. 245
Diffusion Processes	p. 249
Infinitesimal mean and variance	p. 250
Examples of diffusions	p. 252
Transition probabilities	p. 258
Hitting probabilities	p. 262
Stationary measures	p. 268
Occupation times	p. 273
Green's functions	p. 276
Examples	p. 280
Conditioned processes	p. 287
Boundary behavior	p. 293
Site frequency spectrum	p. 298
Poisson random field model	p. 300
Fluctuating selection	p. 304
Multidimensional Diffusions	p. 313
K allele model	p. 313
Fixation probabilities and time	p. 315
Stationary distributions	p. 318
Recombination	p. 322
A clever change of variables	p. 323
Time-dependent behavior	p. 326
Equilibrium when there is mutation	p. 329
Hill-Robertson interference	p. 334
Gene duplication	p. 341
Watterson's double recessive null model	p. 343
Subfunctionalization	p. 347
Genome Rearrangement	p. 355
Inversions	p. 355
Breakpoint graph	p. 355
Hurdles	p. 358
When is parsimony reliable?	p. 362
Phase transition	p. 365
Bayesian approach	p. 367
Nadeau and Taylor's analysis	p. 370
Genomic distance	p. 375
Graph distance	p. 375
Bayesian estimation	p. 377
Midpoint problem	p. 382
Genome duplication	p. 389
Yeast	p. 389
Maize	p. 393
Arabidopsis thaliana	p. 396
References	p. 399
Index	p. 427
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Probability Models for DNA Sequence Evolution

Probability Models for DNA Sequence Evolution

9780387781686

0387781684

Summary

Author Biography

Table of Contents

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