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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-
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Format
Book
Language
English
Published/Created
Singapore ; Hackensack, N.J. : World Scientific, ©2012.
Description
xxviii, 666 pages : illustrations ; 24 cm
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
ReCAP - Remote Storage
QH390 .M64 2012
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Details
Subject(s)
Evolutionary genetics
—
Computer simulation
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Evolutionary genetics
—
Mathematics
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Molecular genetics
—
Computer simulation
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Molecular genetics
—
Mathematics
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Stochastic programming
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Related name
Sleeman, Candace K.
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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.
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ISBN
9789814350679
9814350672
OCLC
707966879
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