Fundamentals of mathematical evolutionary genetics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1990
|
| Series: | Mathematics and its applications / Soviet ser.
22. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. - EST: Osnovy matematičeskoj genetiki <engl.> |
| Physical Description: | XVI, 395 S. Ill., graph. Darst. |
| ISBN: | 9027727724 |
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MARC
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Record in the Search Index
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| adam_text | Yuri M j yirezhev and Vladimir P Passekov
Department of Mathematical Modeling in Ecology and Medicine, USSJi Academy of Sciences,
Moscow, USS R
Fundamentals
of Mathematical
Evolutionary
Genetics
Kluwer Academic Publishers
Dordrecht / Boston / London
Table of Contents
Editor s Preface xiii
Preface xv
Part 1 Deterministic Models in Mathematical Genetics 1
Chapter 1 Brief Outline of Microevolution Theory with Some Facts from
Genetics 3
1 1 History and Personalia 3
1 2 Conceptual Model of Microevoluiion 6
1 3 Elementary Evolutionary Structure and Elementary Evolutionary
Phenomenon 6
1 4 Elementary Evolutionary Material 7
1 5 Elementary Evolutionary Factors 8
1 6 An Introduction to Principles of Inheritance 9
1 7 Notes and Bibliography 13
Chapter 2 Basic Equations of Population Genetics 16
2 1 Description of a Population 16
2 2 Sexless Population 17
2 3 Equations for Populations in Evolution 18
2 4 Evolution of Populations and Integral Renewal Equations 19
2 5 Panmixia and Other Systems of Mating 22
2 6 Principles of Inheritance 25
2 7 Multi-Allele Autosomal Gene: Equations of Evolution 26
2 8 Equations of Evolution with Specific Demographic Functions 29
281 Global Panmixia, Multiplicative Fecundity 29
282 Global Panmixia, Additive Fecundity 33
283 Local Panmixia 34
2 9 Equations of Evolution: Fecundity of a Couple is Determined by that
of the Female 35
2 10 Equal Fecundity, Different Mortality: Another Form for Evolutionary
Equations 37
2 11 Semelparity: Models with Discrete Time 39
2 12 More Realistic Assumptions About the Particular Form of Fecundity
and Mortality Functions 41
2 13 Some Generalizations of Classical Equations in Population Genetics
Another Way to Derive these Equations 45
2 14 Discrete-time Equations of Evolution 48
2 15 On the Relationship Between Continuous and Discrete Models 51
2 16 Notes and Bibliography 52
vijj Table of Contents
Chapter 3 Simplest Population Models 54
3 1 Introduction 54
3 2 Equations of Evolution 54
3 3 Existence Conditions for Polymorphism 55
3 4 Sufficient Conditions for Stability of Limiting States of a Population 58
3 5 Population Without Age Structure Continuous Model 63
3 6 Population Without Age Structure Discrete Model 65
3 7 Polymorphism Experiments and Theory What Are the Malthusian
Parameters or Genotype Fitnesses? 68
3 8 Genetico-Ecological Models 72
3 9 Special Cases of Genetico-Ecological Models 75
3 10 Passage from Genetico-Ecological Models to Models in Frequency
Form 79
3 11 Notes and Bibliography 81
Chapter 4 Multiple Alleles 84
4 1 Introduction 84
4 2 Stateof Genetic Equilibrium Polymorphism 84
4 3 Mean Population Fitness Fisher s Fundamental Theorem 86
4 4 Mean Fitness as a Lyapunov Function 88
4 5 Adaptive Topography of a Population 88
4 6 The Case of Three Alleles Search for Domains of Asymptotic
Stability 90
4 7 Necessary and Sufficient Existence Conditions for Polymorphism 97
4 8 Theorem About Limited Variations and Another Form of Existence
Conditions for Polymorphism 97
4 9 Elimination of Alleles and Theorem About Dominance 100
4 10 Simple Necessary Conditions of Existence for Polymorphic and Pure
Equilibria 104
4 11 Population Trajectory as a Trajectory of Steepest Ascent 105
4 11 1 Introduction of a New Metric Space 105
4 11 2 Equations of Evolution and Local Extremal Principle 106
4 12 Another Form for Equations of Evolution 109
4 13 Notes and Bibliography 111
Chapter 5 Sex-Limited and Sex-Linked Characters Models Taking Account of
Sex Distinctions 114
5 1 Introduction 114
5 2 Model Taking Account of Sex Distinctions 114
521 Autosomal Gene Continuous Model 114
5 3 New Types of Polymorphism and Their Stability 117
5 4 Model Taking Account of Sex Distinctions 122
541 Sex-Linked Gene Continuos Model 122
5 5 Sex-Linked Gene Discrete Model 126
Table of Contents IX
5 6 Sex-Linked Gene Multiple Alleles 129
5 7 Minimax Properties of the Mean Fitness Function in a Model of an
Age-Structured Population 130
5 8 Notes and Bibliography 132
Chapter 6 Populations With Deviations from Panmixia 134
6 1 Introduction 134
6 2 Preference in Crossing and Preference Matrix 134
6 3 Model of Population with Deviations from Panmixia Caused by
Preference in Crossing 135
6 4 Evolution and Stability of Deviations from Hardian Equilibrium
Inbreeding 138
6 5 Preference in Crossing Discrete Model 141
6 6 Evolution of Genetic Structure of Population Under Inbreeding
Discrete Model 143
6 7 Isolation by Distance and Deviations from Panmixia 144
6 8 Models with Particular Functions of Deviations from Panmixia 147
6 9 Notes and Bibliography 149
Chapter 7 Systems of Linked Populations Migration 152
7 1 Introduction 152
7 2 Migration Between Populations of Different Sizes 152
7 3 Migration Between Population Occupying Two Similar Ecological
Niches 155
7 4 On Tast and Slow Variables in Systems of Linked Populations 160
7 5 Genetic Interpretation Why Stable Divergence is Important in
Systems of Linked Populations 162
7 6 Systems of Weakly Linked Populations 163
7 7 Populations with Continuous Area (Spatially Distributed Populations) 166
7 8 Genie Waves in Spatially Distributed Populations 171
7 9 Notes and Bibliography 174
Chapter 8 Population Dynamics in Changing Environment 177
8 1 Introduction 177
8 2 Seasonal Oscillations in Coefficients of Relative Viability Discrete
Model 177
8 3 Polymorphism in Populations oiAdalia Bipunctata 180
8 4 Environments Changing with Time Continuous Model 182
8 5 How Variations in the Total Size of a Population Affect its Genetic
Dynamics 184
8 6 How Periodic Variations in Coefficients of Relative Viability Affect
the Total Population Size 186
8 7 Changing Environment Adaption and Adaptability 187
8 8 Notes and Bibliography 189
x Table of Contents
Chapter 9 Multi-Locus Models 191
9 1 Discrete Two-Locus Model of Segregation-Recombination and its
Continuous Approximation 191
9 2 Continuous One- and Two-Locus Models with no Selection Equa-
tions for Numbers and Frequencies, Fast and Slow Variables 196
9 3 Formalization of Recombination-Segregation in a Discrete-Time
Multi-Locus System Equations of Dynamics, Equilibria 200
9 4 Recombination-Segregation Model in a Multi-Locus Continuous-
Time System 205
9 5 Additivity of Interaction Between Selection and Recombination-
Segregation in Multi-Locus Models Presented by Differential
Equations 208
9 6 Selection of Zygotes and Gametes in a Discrete-Time Model and its
Continuous Approximation 210
9 7 Equations of Dynamics Under the Combined Action of Selection and
Recombination-Segregation in Discrete- and Continuous-Time
Models 216
9 8 Comparing the Dynamics in One-Locus and Multi-Locus Systems in
the Presence of Selection 220
9 9 Model of Additive Selection in a Multi-Locus System 223
9 10 Models of Multiplicative and Additively Multiplicative Selection 226
9 11 Notes and Bibliography 232
Part 2 Stochastic Models of Mathematical Genetics 237
Chapter 10 Diffusion Models of Population Genetics 239
10 1 Types of Random Processes Relevant to Models of Population
Genetics 239
10 2 Fundamental Problems in the Analysis of Stochastic Models 241
10 3 Forward and Backward Kolmogorov Equations 242
10 4 Diffusion Approximation of the Fisher-Wright and the Moran Models 247
10 5 Classification of Boundaries in Diffusion Models 249
10 6 Multidimensional Diffusion Models 251
10 7 Solutions to the Kolmogorov Equations by the Fourier Method
Transformations of Diffusion Processes The Steady-State Density 253
10 8 Search for Moments of Some Functionals on Diffusion Processes 259
10 9 An Approach to Search for the Mean of a Function Defined on States
of a Process 262
10 10 Notes and Bibliography 266
Chapter 11 Random Genetic Drift in the Narrow Sense 269
11 1 The Kolmogorov Equations for a Single-Locus Model of Random
Genetic Drift 269
Table of Contents xi
11 2 Approximating the Random Genetic Drift Process within Small
Intervals of Time 270
11 3 Asymptotics of the Fundamental Solution for the Random Genetic
Drift Process When / -» °° 276
11 4 Boundary Attainment Probabilities 278
11 5 Characteristics of the Boundary Attainment Time 281
11 6 Probability Density Function for the Sojourn Time and the Age of an
Allele 288
11 7 Moments of the Random Genetic Drift Process 291
11 8 Fundamental Solution to the Kolmogorov Equations 294
11 9 A Random Genetic Drift Model with Two Loci 297
11 10 Notes and Bibliography 300
Chapter 12 Properties of Single-Locus Models under Several Microevolutionary
Pressures 302
12 1 Kolmogorov Equations in Case of Several Microevolutionary
Conditions 302
12 2 Probabilities of Allele Fixation 304
12 3 Characteristics of the Homozygosity Attainment Time 311
12 4 Steady-State Probability Density Function for the Case of a Single
Diallelic Locus 313
12 5 Investigation of the Steady-State Probability Density Function for a
Single Diallelic Locus 316
12 6 Steady-State Density Function and the Adaptive Landscape in the
Two-Allele Case 319
12 7 Derivation of a Steady-State Density Function in the Case of Multiple
Alleles 321
12 8 Contribution to the Steady-State Density Caused by Selection 323
12 9 Contribution Caused by Migrations and Mutations The General Form
of a Steady-State Density Function 326
12 10 Investigation of the Steady-State Probability Density Function for
Concentrations of Multiple Alleles A Multi-Locus Case 329
12 11 Steady-state Density and Objective Functions in Case of Multiple
Alleles 332
12 12 Relation of Objective Functions to the Sphere Motion Potential
Mechanical Interpretation of Single-Locus Genetic Processes in
Terms of Motion in a Force Field 335
12 13 Notes and Bibliography 341
Chapter 13 Random Genetic Drift in Subdivided Populations 343
13 1 Generating Operator for the Random Genetic Drift Process in a
Subdivided Finite-Sized Population with Migrations of the Island
Type 343
13 2 Dynamics of Expected Allele Frequencies in a Subdivided Population 347
13 3 Behavior of Expected Heterozygosity Indices 349
xii Table of Contents
13 4 Dynamics of Expected Indices of Linkage Disequilibrium in Case of
Two Loci 355
13 5 Model of a Hierarchically Subdivided Population 360
13 6 Investigation of the Asymptotic Rate of Decrease in Heterozygosity in
the Hierarchical Model 363
13 7 Model of Isolation by Distance 366
13 8 Properties of the Random Genetic Drift Process in a Subdivided
Population with Migrations of the General Type 372
13 9 Notes and Bibliography 380
Conclusion 382
Short Glossary of Genetic Terms 387
Subject Index 391
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:48:40Z |
| institution | BVB |
| isbn | 9027727724 |
| language | English |
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| publisher | Kluwer |
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| series2 | Mathematics and its applications / Soviet ser. |
| spelling | Svirešev, Jurij M. 1938-2007 Verfasser (DE-588)137337779 aut Osnovy matematicheskoĭ genetiki Fundamentals of mathematical evolutionary genetics Yuri M. Svirezhev and Vladimir P. Passekov Dordrecht u.a. Kluwer 1990 XVI, 395 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet ser. 22. Aus d. Russ. übers. - EST: Osnovy matematičeskoj genetiki <engl.> Genetik (DE-588)4071711-2 gnd rswk-swf Populationsgenetik (DE-588)4046804-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Populationsgenetik (DE-588)4046804-5 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Genetik (DE-588)4071711-2 s Pasekov, Vladimir P. Verfasser aut Soviet ser. Mathematics and its applications 22. (DE-604)BV004708148 22 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004200256&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Svirešev, Jurij M. 1938-2007 Pasekov, Vladimir P. Fundamentals of mathematical evolutionary genetics Genetik (DE-588)4071711-2 gnd Populationsgenetik (DE-588)4046804-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4071711-2 (DE-588)4046804-5 (DE-588)4114528-8 |
| title | Fundamentals of mathematical evolutionary genetics |
| title_alt | Osnovy matematicheskoĭ genetiki |
| title_auth | Fundamentals of mathematical evolutionary genetics |
| title_exact_search | Fundamentals of mathematical evolutionary genetics |
| title_full | Fundamentals of mathematical evolutionary genetics Yuri M. Svirezhev and Vladimir P. Passekov |
| title_fullStr | Fundamentals of mathematical evolutionary genetics Yuri M. Svirezhev and Vladimir P. Passekov |
| title_full_unstemmed | Fundamentals of mathematical evolutionary genetics Yuri M. Svirezhev and Vladimir P. Passekov |
| title_short | Fundamentals of mathematical evolutionary genetics |
| title_sort | fundamentals of mathematical evolutionary genetics |
| topic | Genetik (DE-588)4071711-2 gnd Populationsgenetik (DE-588)4046804-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Genetik Populationsgenetik Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004200256&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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