Holdings: Mathematical population genetics

Mathematical population genetics: 1 Theoretical introduction

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Bibliographic Details
Main Author:	Ewens, Warren John (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 2004
Edition:	2. ed.
Series:	Interdisciplinary applied mathematics
Online Access:	Inhaltsverzeichnis
Physical Description:	XIX, 417 S.
ISBN:	0387201912

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MARC


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adam_text	WARREN J. EWENS MATHEMATICAL POPULATION GENETICS I. THEORETICAL INTRODUCTION SECOND EDITION SPRINGER CONTENTS PREFACE VII INTRODUCTION XVII 1 HISTORICAL BACKGROUND 1 1.1 BIOMETRICIANS, SALTATIONISTS AND MENDELIANS 1 1.2 THE HARDY WEINBERG LAW 3 1.3 THE CORRELATION BETWEEN RELATIVES 6 1.4 EVOLUTION 11 1.4.1 THE DETERMINISTIC THEORY 11 1.4.2 NON-RANDOM-MATING POPULATIONS 18 1.4.3 THE STOCHASTIC THEORY 20 1.5 EVOLVED GENETIC PHENOMENA 31 1.6 MODELLING 35 1.7 OVERALL EVOLUTIONARY THEORIES 38 2 TECHNICALITIES AND GENERALIZATIONS 43 2.1 INTRODUCTION 43 2.2 RANDOM UNION OF GAMETES 44 2.3 DIOECIOUS POPULATIONS 44 2.4 MULTIPLE ALLELES 49 2.5 FREQUENCY-DEPENDENT SELECTION 54 2.6 FERTILITY SELECTION 54 2.7 CONTINUOUS-TIME MODELS 57 CONTENTS 2.8 NOII-RANDOM-MATING POPULATIONS 62 2.9 THE FUNDAMENTAL THEOREM OF NATURAL SELECTION 64 2.10 TWO LOCI 67 2.11 GENETIC LOADS 78 2.12 FINITE MARKOV CHAINS 86 3 DISCRETE STOCHASTIC MODELS 92 3.1 INTRODUCTION 92 3.2 WRIGHT-FISHER MODEL: TWO ALLELES 92 3.3 THE CANNINGS (EXCHANGEABLE) MODEL: TWO ALLELES .... 99 3.4 MORAN MODELS: TWO ALLELES 104 3.5 K-ALLELE WRIGHT-FISHER MODELS 109 3.6 INFINITELY MANY ALLELES MODELS ILL 3.6.1 INTRODUCTION ILL 3.6.2 THE WRIGHT-FISHER INFINITELY MANY ALLELES MODEL 111 3.6.3 THE CANNINGS INFINITELY MANY ALLELES MODEL ... 117 3.6.4 THE MORAN INFINITELY MANY ALLELES MODEL .... 117 3.7 THE EFFECTIVE POPULATION SIZE 119 3.8 FREQUENCY-DEPENDENT SELECTION 129 3.9 TWO LOCI 129 4 DIFFUSION THEORY 136 4.1 INTRODUCTION 136 4.2 THE FORWARD AND BACKWARD KOLMOGOROV EQUATIONS . . . 137 4.3 FIXATION PROBABILITIES 139 4.4 ABSORPTION TIME PROPERTIES 140 4.5 THE STATIONARY DISTRIBUTION 145 4.6 CONDITIONAL PROCESSES 146 4.7 DIFFUSION THEORY 148 4.8 MULTI-DIMENSIONAL PROCESSES 151 4.9 TIME REVERSIBILITY 153 4.10 EXPECTATIONS OF FUNCTIONS OF DIFFUSION VARIABLES 153 5 APPLICATIONS OF DIFFUSION THEORY 156 5.1 INTRODUCTION 156 5.2 NO SELECTION OR MUTATION 158 5.3 SELECTION 165 5.4 SELECTION: ABSORPTION TIME PROPERTIES 167 5.5 ONE-WAY MUTATION 171 5.6 TWO-WAY MUTATION 174 5.7 DIFFUSION APPROXIMATIONS AND BOUNDARY CONDITIONS ... 176 5.8 RANDOM ENVIRONMENTS 181 5.9 TIME-REVERSAL AND AGE PROPERTIES 188 5.10 MULTI-ALLELE DIFFUSION PROCESSES 192 CONTENTS XIII 6 TWO LOCI 201 6.1 INTRODUCTION 201 6.2 EVOLUTIONARY PROPERTIES OF MEAN FITNESS 202 6.3 EQUILIBRIUM POINTS 208 6.4 SPECIAL MODELS 209 6.5 MODIFIER THEORY 221 6.6 TWO-LOCUS DIFFUSION PROCESSES 227 6.7 ASSOCIATIVE OVERDOMINANCE AND HITCHHIKING 230 6.8 THE EVOLUTIONARY ADVANTAGE OF RECOMBINATION 235 6.9 SUMMARY 239 7 MANY LOCI 241 7.1 INTRODUCTION 241 7.2 NOTATION 242 7.3 THE RANDOM MATING CASE 243 7.3.1 LINKAGE DISEQUILIBRIUM, MEANS AND VARIANCES . . 243 7.3.2 RECURRENCE RELATIONS FOR GAMETIC FREQUENCIES . . 245 7.3.3 COMPONENTS OF VARIANCE 246 7.3.4 PARTICULAR MODELS 249 7.4 NON-RANDOM MATING 254 7.4.1 INTRODUCTION 254 7.4.2 NOTATION AND THEORY 255 7.4.3 MARGINAL FITNESSES AND AVERAGE EFFECTS 256 7.4.4 IMPLICATIONS 258 7.4.5 THE FUNDAMENTAL THEOREM OF NATURAL SELECTION . 259 7.4.6 OPTIMALLY PRINCIPLES 261 7.5 THE CORRELATION BETWEEN RELATIVES 266 7.6 SUMMARY 274 8 FURTHER CONSIDERATIONS 276 8.1 INTRODUCTION 276 8.2 WHAT IS FITNESS? 276 8.3 SEX RATIO 277 8.4 GEOGRAPHICAL STRUCTURE 278 8.5 AGE STRUCTURE 282 8.6 ECOLOGICAL CONSIDERATIONS 283 8.7 SOCIOBIOLOGY 285 9 MOLECULAR POPULATION GENETICS: INTRODUCTION 288 9.1 INTRODUCTION 288 9.2 TECHNICAL COMMENTS 290 9.3 INFINITELY MANY ALLELES MODELS: POPULATION PROPERTIES . . 292 9.3.1 THE WRIGHT-FISHER MODEL 292 9.3.2 THE MORAN MODEL 294 9.4 INFINITELY MANY SITES MODELS: POPULATION PROPERTIES . . . 297 XIV CONTENTS 9.4.1 INTRODUCTION 297 9.4.2 THE WRIGHT-FISHER MODEL 298 9.4.3 THE MORAN MODEL 300 9.5 SAMPLE PROPERTIES OF INFINITELY MANY ALLELES MODELS . . . 301 9.5.1 INTRODUCTION 301 9.5.2 THE WRIGHT FISHER MODEL 301 9.5.3 THE MORAN MODEL 306 9.6 SAMPLE PROPERTIES OF INFINITELY MANY SITES MODELS .... 308 9.6.1 INTRODUCTION 308 9.6.2 THE WRIGHT FISHER MODEL 308 9.6.3 THE MORAN MODEL 314 9.7 RELATION BETWEEN INFINITELY MANY ALLELES AND INFINITELY MANY SITES MODELS 316 9.8 GENETIC VARIATION WITHIN AND BETWEEN POPULATIONS . . . 319 9.9 AGE-ORDERED ALLELES: FREQUENCIES AND AGES 320 10 LOOKING BACKWARD IN TIME: THE COALESCENT 328 10.1 INTRODUCTION 328 10.2 COMPETING POISSON AND GEOMETRIC PROCESSES 329 10.3 THE COALESCENT PROCESS 330 10.4 THE COALESCENT AND ITS RELATION TO EVOLUTIONARY GENETIC MODELS 331 10.5 COALESCENT CALCULATIONS: WRIGHT-FISHER MODELS 333 10.6 COALESCENT CALCULATIONS: EXACT MORAN MODEL RESULTS . . 338 10.7 GENERAL COMMENTS 341 10.8 THE COALESCENT AND HUMAN GENETICS 342 11 LOOKING BACKWARD: TESTING THE NEUTRAL THEORY 346 11.1 INTRODUCTION 346 11.2 TESTING IN THE INFINITELY MANY ALLELES MODELS 349 11.2.1 INTRODUCTION 349 11.2.2 THE EWCNS AND THE WATTERSON TESTS 349 11.2.3 PROCEDURES BASED ON THE CONDITIONAL SAMPLE FRE- QUENCY SPECTRUM 353 11.2.4 AGE-DEPENDENT TESTS 354 11.3 TESTING IN THE INFINITELY MANY SITES MODELS 355 11.3.1 INTRODUCTION 355 11.3.2 ESTIMATORS OF 0 356 11.3.3 THE TAJIMA TEST 358 11.3.4 OTHER TAJIMA-LIKE TESTING PROCEDURES 361 11.3.5 TESTING FOR THE SIGNATURE OF A SELECTIVE SWEEP . . 362 11.3.6 COMBINING INFINITELY MANY ALLELES AND INFINITELY MANY SITES APPROACHES 364 11.3.7 DATA FROM SEVERAL UNLINKED LOCI 365 11.3.8 DATA FROM UNLINKED SITES 368 CONTENTS XV 11.3.9 TESTS BASED ON HISTORICAL FEATURES 369 12 LOOKING BACKWARD IN TIME: POPULATION AND SPECIES COMPARISONS 370 12.1 INTRODUCTION 370 12.1.1 THE REVERSIBILITY CRITERION 372 12.2 VARIOUS EVOLUTIONARY MODELS 373 12.2.1 THE JUKES CANTOR MODEL 373 12.2.2 THE KIMURA MODEL AND ITS GENERALIZATIONS .... 374 12.2.3 THE FELSENSTEIN MODELS 375 12.3 SOME IMPLICATIONS 377 12.3.1 INTRODUCTION 377 12.3.2 THE JUKES CANTOR MODEL 377 12.3.3 THE KIMURA MODEL 380 12.4 STATISTICAL PROCEDURES 381 APPENDIX A: EIGENVALUE CALCULATIONS 384 APPENDIX B: SIGNIFICANCE LEVELS FOR F 385 APPENDIX C: MEANS AND VARIANCES OF F 386 REFERENCES 387 AUTHOR INDEX 409 SUBJECT INDEX 413
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spelling	Ewens, Warren John Verfasser aut Mathematical population genetics 1 Theoretical introduction Warren J. Ewens 2. ed. New York [u.a.] Springer 2004 XIX, 417 S. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics (DE-604)BV025319301 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019283045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ewens, Warren John Mathematical population genetics
title	Mathematical population genetics
title_auth	Mathematical population genetics
title_exact_search	Mathematical population genetics
title_full	Mathematical population genetics 1 Theoretical introduction Warren J. Ewens
title_fullStr	Mathematical population genetics 1 Theoretical introduction Warren J. Ewens
title_full_unstemmed	Mathematical population genetics 1 Theoretical introduction Warren J. Ewens
title_short	Mathematical population genetics
title_sort	mathematical population genetics theoretical introduction
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019283045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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