Mathematical Population Genetics 1: Theoretical IntroductionSpringer Science & Business Media, 2004/01/09 - 418 ページ 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. |
目次
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 |
387 | |
409 | |
413 | |