Theoretical population genetics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Unwin Hyman
1990
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 417 S. graph. Darst. |
| ISBN: | 0045750262 0045750270 |
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| 100 | 1 | |a Gale, Jeff S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Theoretical population genetics |c J. S. Gale |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a London u.a. |b Unwin Hyman |c 1990 | |
| 300 | |a XIV, 417 S. |b graph. Darst. | ||
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| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Genetics, Population | |
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| 650 | 4 | |a Population genetics | |
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Record in the Search Index
| _version_ | 1804122030477410304 |
|---|---|
| adam_text | THEORETICAL
POPULATION
GENETICS
J S GALE
Department of Genetics, University of Birmingham
London
UNWIN HYMAN
Boston Sydney Wellington
Contents
Preface page ix
1 Introduction 1
Notes and exercises 9
2 Wright-Fisher, Moran and other models 12
On simple models 12
Stochastic models: deterministic models 13
Random genetic drift: general approach 14
Distribution of allele frequency under drift 14
Change of allele frequency in one generation 16
The mean in any generation 17
Change of allele frequency in one generation: the variance 20
Is the binomial distribution of allele number relevant? 22
Effective population size 31
Variance of allele frequency in any generation 36
Inbreeding effective size 39
Populations under systematic pressure 42
A continuous approximation to the conditional distribution 43
Diffusion methods - 44
Moran s model 46
Notes and exercises 49
3 On the description of changes in allele frequency 56
A bewildering abundance of descriptions 56
Probability distribution of allele frequency 59
A numerical example 67
Probability of fixation , 69
Dominant latent root (maximum non-unit eigenvalue) 71
Modified process 75
Probability distribution of absorption time 78
Mean absorption time 82
Variance of absorption time 84
Mean sojourn times 86
Variance of sojourn time 89
Probability of ever reaching a given frequency 89
A matrix representation of mean sojourn time 90
Notes and exercises 91
xi
CONTENTS
4 Survival of new mutations: branching processes 106
On special methods 106
Probability of survival 107
The need for accuracy 107
Are diffusion methods appropriate? 108
A fundamental simplification 110
Probability generating functions 111
Independent propagation: branching processes - 113
Utility of the branching process approach 114
Fundamental equations for branching processes 115
Calculating the probability of survival 117
The case Nc N1 19
A problem in genetic conservation 123
Probability of survival when t is fairly large 124
Pattern of survival in natural populations 126
A caution 126
Genie selection 127
Probability of ultimate fixation 130
Calculating the probability of fixation 131
Population subdivision 137
Cyclical variation in population size 138
A note on epistasis and linkage 141
Spread of a fungal pathogen 143
Notes and exercises 144
Probability of fixation: the more general case 152
Fundamental equation 152
Uniqueness of the solution 153
Probability of fixation for Moran s model 155
Moran s method for the Wright-Fisher haploid model 159
Population subdivision 165
The case NC N 167
Effect of selection on fixation probability 170
Kimura s method for finding the probability of fixation 172
Population subdivision reconsidered 180
Fluctuating viabilities 182
Rate of evolution 183
Notes and exercises 189
6 Some notes on continuous approximations 194
The problem stated 194
Probability of reaching a given allele frequency 195
xii
CONTENTS
Events at the boundaries 200
The problem of representing the initial frequency 203
Ad hoc method 203
Objections to our ad hoc method 204
Dirac s delta function 205
Notes and exercises 208
7 Mean sojourn, absorption and fixation times 213
Retrospect 213
Fundamental equations 215
Uniqueness of solutions 217
Mean times for Moran s model 219
A tentative approach for the Wright-Fisher model , 222
A generating function for mean sojourn times 225
Calculating mean sojourn times for the Wright-Fisher model 227
Mean fixation times 235
Continuous approximations 237
Calculating mean sojourn and absorption times 243
Interpreting the results 249
Mean sojourn times in the modified process 251
Mean fixation time 252
Effect of selection 253
Mean times under genie selection in the modified process 257
Effect of selection: some results
e 258
Calculation of mean times under~selection: a numerical example 261
Mean fixation time under selection 263
Variance of sojourn, absorption and fixation times 265
Concerted evolution of multigene families 267
Notes and exercises 269
8 Introduction to probability distributions: probability flux 277
On the need to calculate probability distributions 277
Continuous approximation of the allele frequency 279
Approximation of zero and unit frequencies 281
Continuous time approximation 284
Probability flux 286
Components of flux 290
Calculating the probability flux 292
Probability flux for discontinuous frequency 296
Expressions for M and V • 297
Values of P(x, t) when x takes limiting values 300
Notes and exercises 301
Xlll
CONTENTS
9 Stationary distributions: frequency spectra 303
Long-term distributions 303
Wright s formula for the stationary distribution 306
Stationary distributions (case of no selection): mean and variance 307
Variation at nucleotide sites: effective number of bases 310
Finding the stationary distribution in the case of no selection 313
Stationary distribution (continued): allele frequencies zero and unity 316
Accuracy of the results 320
Nucleotide sites (resumed): probability of monomorphism 322
Multiple alleles: infinite alleles model 324
Mean number of alleles present 325
Mean number of alleles in a given frequency range 329
The frequency spectrum 331
Infinite sites models 334
Frequency spectrum for transposable elements 336
Stationary distributions under selection 336
Harmful recessives 340
Notes and exercises 344
10 Diffusion methods 347
Aims: notation 347
Forward equation 347
Backward equation 348
Generality of the backward equation 350
Kimura-Ohta equation 353
Initial, terminal and boundary conditions 355
An alternative approach 357
Finding 4 (p, x, t) in the neutral, no-mutation case 359
Finding v(p, t) and u(p, t) in the neutral, no-mutation case 370
Voronka-Keller formulae 374
Moments of the distribution • 375
Fisher s view on the reliability of diffusion methods 379
Two-way mutation: no selection 383
Selection 387
Notes and exercises • 387
11 General comments and conclusions 397
A note on methods 397
General summary and conclusions 399
References 403
Index 411
xiv
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:07:24Z |
| institution | BVB |
| isbn | 0045750262 0045750270 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005033977 |
| oclc_num | 19815343 |
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| owner | DE-355 DE-BY-UBR DE-N2 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-N2 DE-11 DE-188 |
| physical | XIV, 417 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| publisher | Unwin Hyman |
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| spelling | Gale, Jeff S. Verfasser aut Theoretical population genetics J. S. Gale 1. publ. London u.a. Unwin Hyman 1990 XIV, 417 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Distribution (Probability theory) Genetics, Population Models, Genetic Population genetics Probability Theorie (DE-588)4059787-8 gnd rswk-swf Populationsgenetik (DE-588)4046804-5 gnd rswk-swf Populationsgenetik (DE-588)4046804-5 s Theorie (DE-588)4059787-8 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005033977&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gale, Jeff S. Theoretical population genetics Distribution (Probability theory) Genetics, Population Models, Genetic Population genetics Probability Theorie (DE-588)4059787-8 gnd Populationsgenetik (DE-588)4046804-5 gnd |
| subject_GND | (DE-588)4059787-8 (DE-588)4046804-5 |
| title | Theoretical population genetics |
| title_auth | Theoretical population genetics |
| title_exact_search | Theoretical population genetics |
| title_full | Theoretical population genetics J. S. Gale |
| title_fullStr | Theoretical population genetics J. S. Gale |
| title_full_unstemmed | Theoretical population genetics J. S. Gale |
| title_short | Theoretical population genetics |
| title_sort | theoretical population genetics |
| topic | Distribution (Probability theory) Genetics, Population Models, Genetic Population genetics Probability Theorie (DE-588)4059787-8 gnd Populationsgenetik (DE-588)4046804-5 gnd |
| topic_facet | Distribution (Probability theory) Genetics, Population Models, Genetic Population genetics Probability Theorie Populationsgenetik |
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