Mathematical Population Genetics 1: Theoretical Introduction

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Springer Science & Business Media, Jan 9, 2004 - Science - 418 pages
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Population genetics occupies a central role in a number of important biological and social undertakings. It is fundamental to our understanding of evolutionary processes, of plant and animal breeding programs, and of various diseases of particular importance to mankind.

This is the first of a planned two-volume work discussing the mathematical aspects of population genetics, with an emphasis on the evolutionary theory. This first volume draws heavily from the author's classic 1979 edition, which appeared originally in Springer's Biomathematics series. It has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, e.g., the theory of molecular population genetics.

This book will appeal to graduate students and researchers in mathematical biology and other mathematically-trained scientists looking to enter the field of population genetics.

 

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You can get the main developmentof Theoretical Population genetics in this book. a simplified update of 1st edition.

Contents

Historical Background
1
12 The HardyWeinberg Law
3
13 The Correlation Between Relatives
6
14 Evolution
11
142 NonRandomMating Populations
18
143 The Stochastic Theory
20
15 Evolved Genetic Phenomena
31
16 Modelling
35
743 Marginal Fitnesses and Average Effects
256
744 Implications
258
745 The Fundamental Theorem of Natural Selection
259
746 Optimality Principles
261
75 The Correlation Between Relatives
266
76 Summary
274
Further Considerations
276
83 Sex Ratio
277

17 Overall Evolutionary Theories
38
Technicalities and Generalizations
43
22 Random Union of Gametes
44
24 Multiple Alleles
49
25 FrequencyDependent Selection
54
27 ContinuousTime Models
57
28 NonRandomMating Populations
62
29 The Fundamental Theorem of Natural Selection
64
210 Two Loci
67
211 Genetic Loads
78
212 Finite Markov Chains
86
Discrete Stochastic Models
92
Two Alleles
99
Two Alleles
104
35 KAllele WrightFisher Models
109
36 Infinitely Many Alleles Models
111
363 The Cannings Infinitely Many Alleles Model
117
37 The Effective Population Size
119
38 FrequencyDependent Selection
129
Diffusion Theory
136
42 The Forward and Backward Kolmogorov Equations
137
43 Fixation Probabilities
139
44 Absorption Time Properties
140
45 The Stationary Distribution
145
46 Conditional Processes
146
47 Diffusion Theory
148
48 Multidimensional Processes
151
49 Time Reversibility
153
Applications of Diffusion Theory
156
52 No Selection or Mutation
158
53 Selection
165
Absorption Time Properties
167
55 OneWay Mutation
171
56 Two Way Mutation
174
57 Diffusion Approximations and Boundary Conditions
176
58 Random Environments
181
59 TimeReversal and Age Properties
188
510 MultiAllele Diffusion Processes
192
Two Loci
201
62 Evolutionary Properties of Mean Fitness
202
63 Equilibrium Points
208
64 Special Models
209
65 Modifier Theory
221
66 TwoLocus Diffusion Processes
227
67 Associative Overdominance and Hitchhiking
230
68 The Evolutionary Advantage of Recombination
235
69 Summary
239
Many Loci
241
72 Notation
242
73 The Random Mating Case
243
732 Recurrence Relations for Gametic Frequencies
245
733 Components of Variance
246
734 Particular Models
249
74 NonRandom Mating
254
742 Notation and Theory
255
84 Geographical Structure
278
85 Age Structure
282
86 Ecological Considerations
283
87 Sociobiology
285
Molecular Population Genetics Introduction
288
92 Technical Comments
290
Population Properties
292
932 The Moran Model
294
Population Properties
297
942 The WrightFisher Model
298
943 The Moran Model
300
95 Sample Properties of Infinitely Many Alleles Models
301
953 The Moran Model
306
96 Sample Properties of Infinitely Many Sites Models
308
963 The Moran Model
314
97 Relation Between Infinitely Many Alleles and Infinitely Many Sites Models
316
98 Genetic Variation Within and Between Populations
319
Frequencies and Ages
320
Looking Backward in Time The Coalescent
328
102 Competing Poisson and Geometric Processes
329
103 The Coalescent Process
330
104 The Coalescent and Its Relation to Evolutionary Genetic Models
331
WrightFisher Models
333
Exact Moran Model Results
338
107 General Comments
341
108 The Coalescent and Human Genetics
342
Looking Backward Testing the Neutral Theory
346
112 Testing in the Infinitely Many Alleles Models
349
1123 Procedures Based on the Conditional Sample Frequency Spectrum
353
1124 AgeDependent Tests
354
113 Testing in the Infinitely Many Sites Models
355
1132 Estimators of 9
356
1133 The Tajima Test
358
1134 Other Tajimalike Testing Procedures
361
1135 Testing for the Signature of a Selective Sweep
362
1136 Combining Infinitely Many Alleles and Infinitely Many Sites Approaches
364
1137 Data from Several Unlinked Loci
365
1138 Data from Unlinked Sites
368
1139 Tests Based on Historical Features
369
Looking Backward in Time Population and Species Comparisons
370
1211 The Reversibility Criterion
372
122 Various Evolutionary Models
373
1222 The Kimura Model and Its Generalizations
374
1223 The Felsenstein Models
375
123 Some Implications
377
1233 The Kimura Model
380
124 Statistical Procedures
381
Eigenvalue Calculations
384
Significance Levels for F
385
Means and Variances of F
386
References
387
Author Index
409
Subject Index
413
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