Stochastic processes in genetics and evolution : computer experiments in the quantification of mutation and selection / Charles J. Mode, Candace K. Sleeman.

Author
Mode, Charles J., 1927- [Browse]
Format
Book
Language
English
Published/​Created
Singapore ; Hackensack, N.J. : World Scientific, ©2012.
Description
xxviii, 666 pages : illustrations ; 24 cm

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    Details

    Subject(s)
    Bibliographic references
    Includes bibliographical references and index.
    Contents
    • Machine generated contents note: 1. An Introduction to Mathematical Probability with Applications in Mendelian Genetics
    • 1.1. Introduction
    • 1.2. Mathematical Probability in Mendelian Genetics
    • 1.3. Examples of Finite Probability Spaces
    • 1.4. Elementary Combinatorial Analysis
    • 1.5. The Binomial Distribution
    • 1.6. The Multinomial Distribution
    • 1.7. Conditional Probabilities and a Bayesian Theorem
    • 1.8. Expectations and Generating Functions for Binomial and Multinomial Distributions
    • 1.9. Marginal and Conditional Distributions of the Multinomial Distribution
    • 1.10. A Law of Large Numbers and the Frequency Interpretation of Probability
    • 1.11. On Computing Monte Carlo Realizations of a Random Variable with a Binomial Distribution
    • 1.12. The Beta-Binomial Distribution
    • Bibliography
    • 2. Linkage and Recombination at Multiple Loci
    • 2.1. Introduction
    • 2.2. Some Thoughts on Constructing Databases of DNA Markers From Sequenced Genomes of Relatives
    • 2.3. Examples of Informative Matings for the Case of Two Loci
    • 2.4. General Case of Two Linked Loci
    • 2.5. General Case of Three Linked Loci
    • 2.6. General Case of Four or More Linked Loci
    • 2.7. Theoretical Calculations in Statistical and Population Genetics
    • 2.8. Appendix: Proof of Theorem 2.6.1
    • 3. Linkage and Recombination in Large Random Mating Diploid Populations Random Mating Diploid Populations
    • 3.1. Introduction
    • 3.2. The One Locus Case
    • 3.3. The Case of Many Autosomal Loci With Arbitrary Linkage
    • 3.4. Sex Linked Genes in Random Mating Populations
    • 3.5. Comments and Historical Notes
    • 4. Two Allele Wright-Fisher Process with Mutation and Selection
    • 4.1. Introduction
    • 4.2. Overview of Markov Chains with Stationary Transition Probabilities
    • 4.3. Overview of Wright-Fisher Perspective
    • 4.4. Absorbing Markov Chains with a Finite State Space
    • 4.5. Distributions of First Entrance Times Into an Absorbing State and Their Expectations and Variances
    • 4.6. Quasi-Stationary Distribution on the Set of Transient States
    • 4.7. Incorporating Mutation and Selection Into Two Allele Wright-Fisher Processes
    • 4.8. Genotypic Selection with no Mutation and Random Mating
    • 4.9. A Computer Experiment with the Wright-Fisher Neutral Model
    • 4.10. A Computer Experiment with Wright-Fisher Selection Model
    • 4.11. A Computer Experiment with Wright-Fisher Genotypic Selection Model
    • 4.12. A Computer Experiment with a Wright-Fisher Model Accommodating Selection and Mutation
    • 5. Multitype Gamete Sampling Processes, Generation of Random Numbers and Monte Carlo Simulation Methods
    • 5.1. Introduction
    • 5.2. A Wright-Fisher Model with Multiple Types of Gametes
    • Mutation and Selection
    • 5.3. Examples of Multiple Alleles and Types of Gametes Involving Two Chromosomes
    • 5.4. A Genetic Theory for Inherited Autism in Man
    • 5.5. An Evolutionary Genetic Model of Inherited Autism
    • 5.6. Multitype Gamete Sampling Processes as Conditioned Branching Processes
    • 5.7. On the Orderly Pursuit of Randomness Underlying Monte Carlo Simulation Methods
    • 5.8. Design of Software and Statistical Summarization Procedures
    • 5.9. Experiments in the Quantification of Ideas for the Evolution of Inherited Autism in Populations
    • 5.10. Comparative Experiments in the Quantification of Two Formulations of Gamete Sampling Models
    • 5.11. An Experiment with a Three Allele Neutral Model
    • 5.12. Rapid Selection and Convergence to a Stationary Distribution
    • 6. Nucleotide Substitution Models Formulated as Markov Processes in Continuous Time
    • 6.1. Introduction
    • 6.2. Overview of Markov Jump Processes in Continuous Time with Finite State Spaces and Stationary Laws of Evolution
    • 6.3. Stationary Distributions of Markov Chains in Continuous Time with Stationary Laws of Evolution
    • 6.4. Markov Jump Processes as Models for Base Substitutions in the Molecular Evolution of DNA
    • 6.5. Processes with Preassigned Stationary Distributions
    • 6.6. A Numerical Example for a Class of Twelve Parameters
    • 6.7. Falsifiable Predictions of Markov Models of Nucleotide Substitutions
    • 6.8. Position Dependent Nucleotide Substitution Models
    • 6.9. A Retrospective View of a Markov Process with Stationary Transition Probabilities
    • 7. Mixtures of Markov Processes as Models of Nucleotide Substitutions at Many Sites
    • 7.1. Introduction
    • 7.2. Mixtures of Markov Models and Variable Substitution Rates Across Sites
    • 7.3. Gaussian Mixing Processes
    • 7.4. Computing Realizations of a Gaussian Process with Specified Covariance Function
    • 7.5. Gaussian Processes That May be Computed Recursively
    • 7.6. Monte Carlo Implementation of Mixtures of Transition Rates for Markov Processes
    • 7.7. Transition Rates Based on Logistic Gaussian Processes
    • 7.8. Nucleotide Substitution in a Three Site Codon
    • 7.9. Computer Simulation Experiments
    • 8. Computer Implementations and Applications of Nucleotide Substitution Models at Many Sites
    • Other Non-SNP Types of Mutation
    • 8.1. Introduction
    • 8.2. Overview of Monte Carlo Implementations for Nucleotide Substitution Models with N Sites
    • 8.3. Overview of Genographic Research Project
    • Studies of Human Origins
    • 8.4. Simulating Nucleotide Substitutions in Evolutionary Time
    • 8.5. Counting Back and Parallel Mutations in Simulated Data
    • 8.6. Computer Simulation Experiments With a Logistic Gaussian Mixing Process
    • 8.7. Potential Applications of Many Site Models to the Evolution of Protein Coding Genes
    • 8.8. Preliminary Notes on Stochastic Models of Indels and Other Mutations
    • 9. Genealogies, Coalescence and Self-Regulating Branching Processes
    • 9.1. Introduction
    • 9.2. One Type Stochastic Genealogies
    • 9.3. Overview of the Galton-Watson Process
    • 9.4. Self-Regulating Galton-Watson Processes
    • 9.5. Fixed Points and Domains of Attraction
    • 9.6. Probabilities of Extinction
    • 9.7. Stochastic Genealogies in the Multitype Case
    • 9.8. Multitype Galton-Watson Processes
    • 9.9. Self-Regulating Multitype Processes
    • 9.10. Estimating the Most Recent Common Ancestor
    • 9.11. The Deterministic Model and Branching Process
    • 9.12. Realizations of a Poisson Random Variable
    • 10. Emergence, Survival and Extinction of Mutant Types in Populations of Self Replicating Individuals Evolving From Small Founder Populations
    • 10.1. Introduction
    • 10.2. Experiments with the Evolution of Small Founder Populations with Mutation but no Selection
    • 10.3. Components of Selection
    • Reproductive and Competitive Advantages of Some Types
    • 10.4. Survival of Deleterious and Beneficial Mutations From a Small Founder Populations
    • 10.5. Survival of Mutations with Competitive Advantages Over an Ancestral Type
    • 10.6. Chaotic Embedded Deterministic Model with Three Types
    • 10.7. Self Regulating Multitype Branching Processes in Random Environments
    • 10.8. Simulating Multitype Genealogies and Further Reading
    • 11. Two Sex Multitype Self Regulating Branching Processes in Evolutionary Genetics
    • 11.1. Introduction
    • 11.2. Gametes, Genotypes and Couple Types in a Two Sex Stochastic Population Process
    • 11.3. The Parameterization of Couple Formation Processes
    • 11.4. An Example of Couple Formation Process with Respect to an Autosomal Locus with Two Alleles
    • 11.5. Genetics and Offspring Distributions
    • 11.6. Overview of a Self-Regulating Population Process
    • 11.7. Embedding Non-Linear Difference Equations in the Stochastic Population Process
    • 11.8. On the Emergence of a Beneficial Mutation From a Small Founder Population
    • 11.9. An Alternative Evolutionary Genetic Model of Inherited Autism
    • 11.10. Autism in a Population Evolving From a Small Founder Population
    • 11.11. Sexual Selection in Populations Evolving From a Small Founder Population
    • 11.12. Two Sex Processes with Linkage at Two Autosomal Loci
    • 12. Multitype Self-Regulatory Branching Process and the Evolutionary Genetics of Age Structured Two Sex Populations
    • 12.1. Introduction
    • 12.2. An Overview of Competing Risks and Semi-Markov Processes
    • 12.3. Age Dependence and Types of Singles and Couples
    • 12.4. Altruism and Semi-Markovian Processes for Evolution of Single Individuals
    • 12.5. On an Age Dependent Couple Formation Process
    • 12.6. A Semi-Markovian Model for Deaths, Dissolutions and Transitions Among Couple Types
    • 12.7. Gamete, Genotypic and Offspring Distributions for Each Couple Type
    • 12.8. Overview of Stochastic Population Process with Two Sexes and Age Dependence
    • 12.9. Overview of Non-Linear Difference Equations Embedded in the Stochastic Population Process
    • 12.10. A Two Sex Age Dependent Population Process Without Couple Formation
    • 12.11. Parametric Latent Risk Functions for Death by Age
    • 12.12. Sexual Selection in an Age Dependent Process Without Couple Formation
    • 12.13. Population Momentum and Emergence of a Beneficial Mutation
    • 12.14. Experiments with a Version of the Age Dependent Model with Couple Formation
    • 13. An Overview of the History of the Concept of a Gene and Selected Topics in Molecular Genetics
    • 13.1. Introduction
    • 13.2. A Brief History of the Definition of a Gene
    • 13.3. Transcription and Translation Processes
    • 13.4. Pre-processing Messenger RNA
    • 13.5. Difficulties with Current Gene Concepts
    • 13.6. Acronyms in Tiling Array Technology
    • 13.7. Genome Activity in the ENCODE Project
    • Note continued: 13.8. Interpreting Tiling Array Experiments
    • 13.9. A Tentative Updated Definition of a Gene
    • 13.10. ABO Blood Group Genetics in Humans
    • 13.11. Duffy Blood Group System in Man
    • 13.12. Regulation of the Shh Locus in Mice
    • 14. Detecting Genomic Signals of Selection and the Development of Models for Simulating the Evolution of Genomes
    • 14.1. Introduction
    • 14.2. Types of Selection and Genomic Signals
    • 14.3. DNA Sequence Evolution in Large Genomic Regions
    • 14.4. Statistics Used in Genome Wide Scans
    • 14.5. Detecting Signals of Natural Selection
    • 14.6. Simulated Genomic Data in Statistical Tests
    • 14.7. Species and Gene Trees From Mammalian Genomic Data
    • 14.8. Overview of Markovian Codon Substitution Models
    • 14.9. Simulating Genetic Recombination
    • 14.10. Modelling Gene Conversion
    • 14.11. Nucleotide Substitutions During Meiosis
    • 14.12. Simulating Insertions and Deletions
    • 14.13. Simulating Copy Number Variation
    • 14.14. Simulating Mutational Events and Genetic Recombination
    • 15. Suggestions for Further Research, Reading and Viewing
    • 15.1. Introduction
    • 15.2. Suggestions for Further Research on Self-Regulating Branching Processes
    • 15.3. Suggestions for Continuing Development of Stochastic Models of Genomic Evolution
    • 15.4. A Brief List of References on Genetics and Evolution for Further Study
    • Bibliography.
    ISBN
    • 9789814350679
    • 9814350672
    OCLC
    707966879
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