عنوان

Fundamentals of Mathematical Evolutionary Genetics

9400925891

9789400925892

b592909

Fundamentals of Mathematical Evolutionary Genetics

[Book]

by Yuri M. Svirezhev, Vladimir P. Passekov.

Dordrecht

Springer Netherlands

1989

(416 pages)

Mathematics and Its Applications, Soviet Series,, 22.

1. Deterministic Models in Mathematical Genetics.- 1. Brief Outline of Microevolution Theory with Some Facts from Genetics.- 1.1. History and Personalia.- 1.2. Conceptual Model of Microevolution.- 1.3. Elementary Evolutionary Structure and Elementary Evolutionary Phenomenon.- 1.4. Elementary Evolutionary Material.- 1.5. Elementary Evolutionary Factors.- 1.6. An Introduction to Principles of Inheritance.- 1.7. Notes and Bibliography.- 2. Basic Equations of Population Genetics.- 2.1. Description of a Population.- 2.2. Sexless Population.- 2.3. Equations for Populations in Evolution.- 2.4. Evolution of Populations and Integral Renewal Equations.- 2.5. Panmixia and Other Systems of Mating.- 2.6. Principles of Inheritance.- 2.7. Multi-Allele Autosomal Gene: Equations of Evolution.- 2.8. Equations of Evolution with Specific Demographic Functions.- 2.8.1. Global Panmixia, Multiplicative Fecundity.- 2.8.2. Global Panmixia, Additive Fecundity.- 2.8.3. Local Panmixia.- 2.9. Equations of Evolution: Fecundity of a Couple is Determined by that of the Female.- 2.10. Equal Fecundity, Different Mortality: Another Form for Evolutionary Equations.- 2.11. Semelparity: Models with Discrete Time.- 2.12. More Realistic Assumptions About the Particular Form of Fecundity and Mortality Functions.- 2.13. Some Generalizations of Classical Equations in Population Genetics. Another Way to Derive these Equations.- 2.14. Discrete-time Equations of Evolution.- 2.15. On the Relationship Between Continuous and Discrete Models.- 2.16. Notes and Bibliography.- 3. Simplest Population Models.- 3.1. Introduction.- 3.2. Equations of Evolution.- 3.3. Existence Conditions for Polymorphism.- 3.4. Sufficient Conditions for Stability of Limiting States of a Population.- 3.5. Population Without Age Structure. Continuous Model.- 3.6. Population Without Age Structure. Discrete Model.- 3.7. Polymorphism. Experiments and Theory. What Are the Malthusian Parameters or Genotype Fitnesses?.- 3.8. Genetico-Ecological Models.- 3.9. Special Cases of Genetico-Ecological Models.- 3.10. Passage from Genetico-Ecological Models to Models in Frequency Form.- 3.11. Notes and Bibliography.- 4. Multiple Alleles.- 4.1. Introduction.- 4.2. State of Genetic Equilibrium. Polymorphism.- 4.3. Mean Population Fitness. Fisher's Fundamental Theorem.- 4.4. Mean Fitness as a Lyapunov Function.- 4.5. Adaptive Topography of a Population.- 4.6. The Case of Three Alleles. Search for Domains of Asymptotic Stability.- 4.7. Necessary and Sufficient Existence Conditions for Polymorphism.- 4.8. Theorem About Limited Variations and Another Form of Existence Conditions for Polymorphism.- 4.9. Elimination of Alleles and Theorem About Dominance.- 4.10 Simple Necessary Conditions of Existence for Polymorphic and Pure Equilibria.- 4.11. Population Trajectory as a Trajectory of Steepest Ascent.- 4.11.1. Introduction of a New Metric Space.- 4.11.2. Equations of Evolution and Local Extremal Principle.- 4.12. Another Form for Equations of Evolution.- 4.13. Notes and Bibliography.- 5. Sex-Limited and Sex-Linked Characters. Models Taking Account of Sex Distinctions.- 5.1. Introduction.- 5.2. Model Taking Account of Sex Distinctions.- 5.2.1. Autosomal Gene. Continuous Model.- 5.3. New Types of Polymorphism and Their Stability.- 5.4. Model Taking Account of Sex Distinctions.- 5.4.1. Sex-Linked Gene. Continuos Model.- 5.5. Sex-Linked Gene. Discrete Model.- 5.6. Sex-Linked Gene. Multiple Alleles.- 5.7. Minimax Properties of the Mean Fitness Function in a Model of an Age-Structured Population.- 5.8. Notes and Bibliography.- 6. Populations With Deviations from Panmixia.- 6.1. Introduction.- 6.2. Preference in Crossing and Preference Matrix.- 6.3. Model of Population with Deviations from Panmixia Caused by Preference in Crossing.- 6.4. Evolution and Stability of Deviations from Hardian Equilibrium. Inbreeding.- 6.5. Preference in Crossing. Discrete Model.- 6.6. Evolution of Genetic Structure of Population Under Inbreeding. Discrete Model.- 6.7. Isolation by Distance and Deviations from Panmixia.- 6.8. Models with Particular Functions of Deviations from Panmixia.- 6.9. Notes and Bibliography.- 7. Systems of Linked Populations. Migration.- 7.1. Introduction.- 7.2. Migration Between Populations of Different Sizes.- 7.3. Migration Between Population Occupying Two Similar Ecological Niches.- 7.4. On 'Fast' and 'slow' Variables in Systems of Linked Populations.- 7.5. Genetic Interpretation. Why Stable Divergence is Important in Systems of Linked Populations.- 7.6. Systems of Weakly Linked Populations.- 7.7. Populations with Continuous Area (Spatially Distributed Populations).- 7.8. Genic Waves in Spatially Distributed Populations.- 7.9. Notes and Bibliography.- 8. Population Dynamics in Changing Environment.- 8.1. Introduction.- 8.2. Seasonal Oscillations in Coefficients of Relative Viability. Discrete Model.- 8.3. Polymorphism in Populations of Adalia Bipunctata.- 8.4. Environments Changing with Time. Continuous Model.- 8.5. How Variations in the Total Size of a Population Affect its Genetic Dynamics.- 8.6. How Periodic Variations in Coefficients of Relative Viability Affect the Total Population Size.- 8.7. Changing Environment. Adaption and Adaptability.- 8.8. Notes and Bibliography.- 9. Multi-Locus Models.- 9.1. Discrete Two-Locus Model of Segregation-Recombination and its Continuous Approximation.- 9.2. Continuous One- and Two-Locus Models with no Selection. Equations for Numbers and Frequencies, Fast and Slow Variables.- 9.3. Formalization of Recombination-Segregation in a Discrete-Time Multi-Locus System. Equations of Dynamics, Equilibria.- 9.4. Recombination-Segregation Model in a Multi-Locus Continuous-Time System.- 9.5. Additivity of Interaction Between Selection and Recombination-Segregation in Multi-Locus Models Presented by Differential Equations.- 9.6. Selection of Zygotes and Gametes in a Discrete-Time Model and its Continuous Approximation.- 9.7. Equations of Dynamics Under the Combined Action of Selection and Recombination-Segregation in Discrete- and Continuous-Time Models.- 9.8. Comparing the Dynamics in One-Locus and Multi-Locus Systems in the Presence of Selection.- 9.9. Model of Additive Selection in a Multi-Locus System.- 9.10. Models of Multiplicative and Additively Multiplicative Selection.- 9.11. Notes and Bibliography.- 2. Stochastic Models of Mathematical Genetics.- 10. Diffusion Models of Population Genetics.- 10.1. Types of Random Processes Relevant to Models of Population Genetics.- 10.2. Fundamental Problems in the Analysis of Stochastic Models.- 10.3. Forward and Backward Kolmogorov Equations.- 10.4. Diffusion Approximation of the Fisher-Wright and the Moran Models.- 10.5. Classification of Boundaries in Diffusion Models.- 10.6. Multidimensional Diffusion Models.- 10.7. Solutions to the Kolmogorov Equations by the Fourier Method. Transformations of Diffusion Processes. The Steady-State Density.- 10.8. Search for Moments of Some Functionals on Diffusion Processes.- 10.9. An Approach to Search for the Mean of a Function Defined on States of a Process.- 10.10. Notes and Bibliography.- 11. Random Genetic Drift in the Narrow Sense.- 11.1. The Kolmogorov Equations for a Single-Locus Model of Random Genetic Drift.- 11.2. Approximating the Random Genetic Drift Process within Small Intervals of Time.- 11.3. Asymptotics of the Fundamental Solution for the Random Genetic Drift Process When t ? ?.- 11.4. Boundary Attainment Probabilities.- 11.5. Characteristics of the Boundary Attainment Time.- 11.6. Probability Density Function for the Sojourn Time and the Age of an Allele.- 11.7. Moments of the Random Genetic Drift Process.- 11.8. Fundamental Solution to the Kolmogorov Equations.- 11.9. A Random Genetic Drift Model with Two Loci.- 11.10. Notes and Bibliography.- 12. Properties of Single-Locus Models under Several Microevolutionary Pressures.- 12.1. Kolmogorov Equations in Case of Several Microevolutionary Conditions.- 12.2.

Probabilities of Allele Fixation.- 12.3. Characteristics of the Homozygosity Attainment Time.- 12.4. Steady-State Probability Density Function for the Case of a Single Diallelic Locus.- 12.5. Investigation of the Steady-State Probability Density Function for a Single Diallelic Locus.- 12.6. Steady-State Density Function and the Adaptive Landscape in the Two-Allele Case.- 12.7. Derivation of a Steady-State Density Function in the Case of Multiple Alleles.- 12.8. Contribution to the Steady-State Density Caused by Selection.- 12.9. Contribution Caused by Migrations and Mutations. The General Form of a Steady-State Density Function.- 12.10. Investigation of the Steady-State Probability Density Function for Concentrations of Multiple Alleles. A Multi-Locus Case.- 12.11. Steady-state Density and Objective Functions in Case of Multiple Alleles.- 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.- 12.13. Notes and Bibliography.- 13. Random Genetic Drift in Subdivided Populations.- 13.1. Generating Operator for the Random Genetic Drift Process in a Subdivided Finite-Sized Population with Migrations of the "Island" Type.- 13.2. Dynamics of Expected Allele Frequencies in a Subdivided Population.- 13.3. Behavior of Expected Heterozygosity Indices.- 13.4. Dynamics of Expected Indices of Linkage Disequilibrium in Case of Two Loci.- 13.5. Model of a Hierarchically Subdivided Population.- 13.6. Investigation of the Asymptotic Rate of Decrease in Heterozygosity in the Hierarchical Model.- 13.7. Model of Isolation by Distance.- 13.8. Properties of the Random Genetic Drift Process in a Subdivided Population with Migrations of the General Type.- 13.9. Notes and Bibliography.- Conclusion.- Short Glossary of Genetic Terms.

Human genetics.

Mathematics.

Statistics.

by Yuri M. Svirezhev, Vladimir P. Passekov.

Vladimir P Passekov

Yuri M Svirezhev

[Book]

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