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Stochastic Processes In Genetics And Evolution: Computer Experiments In The Quantification Of Mutation And Selection [Kõva köide]

(Drexel Univ, Usa), (Navteq Corp, Usa)
  • Formaat: Hardback, 696 pages
  • Ilmumisaeg: 15-Feb-2012
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814350672
  • ISBN-13: 9789814350679
Teised raamatud teemal:
  • Formaat: Hardback, 696 pages
  • Ilmumisaeg: 15-Feb-2012
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814350672
  • ISBN-13: 9789814350679
Teised raamatud teemal:
The scope of this book is the field of evolutionary genetics. The book contains new methods for simulating evolution at the genomic level. It sets out applications using up to date Monte Carlo simulation methods applied in classical population genetics, and sets out new fields of quantifying mutation and selection at the Mendelian level. A serious limitation of Wright-Fisher process, the assumption that population size is constant, motivated the introduction of self regulating branching processes in this book. While providing a short review of the principles of probability and its application and using computer intensive methods whilst applying these principles, this book explains how it is possible to derive new formulas expressed in terms of matrix algebra providing new insights into the classical Wright-Fisher processes of evolutionary genetics. Also covered are the development of new methods for studying genetics and evolution, simulating nucleotide substitutions of a DNA molecule and on self regulating branching processes. Components of natural selection are studied in terms of reproductive success of each genotype whilst also studying the differential ability of genotypes to compete for resources and sexual selection. The concept of the gene is also reviewed in this book, and it provides a current definition of a gene based on very recent experiments with micro-array technologies. A development of stochastic models for simulating the evolution of model genomes concludes the studies in this book. Deserving of a place on the book shelves of workers in biomathematics, applied probability, stochastic processes and statistics, as well as in bioinformatics and phylogenetics, it will also be relevant to those interested in computer simulation, and evolutionary biologists interested in quantitative methods.
Prologue vii
Acknowledgments xix
1 An Introduction to Mathematical Probability with Applications in Mendelian Genetics
1(52)
1.1 Introduction
1(1)
1.2 Mathematical Probability in Mendelian Genetics
2(5)
1.3 Examples of Finite Probability Spaces
7(4)
1.4 Elementary Combinatorial Analysis
11(4)
1.5 The Binomial Distribution
15(5)
1.6 The Multinomial Distribution
20(6)
1.7 Conditional Probabilities and a Bayesian Theorem
26(3)
1.8 Expectations and Generating Functions for Binomial and Multinomial Distributions
29(3)
1.9 Marginal and Conditional Distributions of the Multinomial Distribution
32(3)
1.10 A Law of Large Numbers and the Frequency Interpretation of Probability
35(4)
1.11 On Computing Monte Carlo Realizations of a Random Variable with a Binomial Distribution
39(4)
1.12 The Beta-Binomial Distribution
43(10)
Bibliography
51(2)
2 Linkage and Recombination at Multiple Loci
53(30)
2.1 Introduction
53(3)
2.2 Some Thoughts on Constructing Databases of DNA Markers From Sequenced Genomes of Relatives
56(4)
2.3 Examples of Informative Matings for the Case of Two Loci
60(5)
2.4 General Case of Two Linked Loci
65(3)
2.5 General Case of Three Linked Loci
68(4)
2.6 General Case of Four or More Linked Loci
72(4)
2.7 Theoretical Calculations in Statistical and Population Genetics
76(4)
2.8 Appendix: Proof of Theorem 2.6.1
80(3)
Bibliography
82(1)
3 Linkage and Recombination in Large Random Mating Diploid Populations Random Mating Diploid Populations
83(27)
3.1 Introduction
83(1)
3.2 The One Locus Case
84(7)
3.3 The Case of Many Autosomal Loci With Arbitrary Linkage
91(9)
3.4 Sex Linked Genes in Random Mating Populations
100(7)
3.5 Comments and Historical Notes
107(3)
Bibliography
108(2)
4 Two Allele Wright-Fisher Process with Mutation and Selection
110(40)
4.1 Introduction
110(1)
4.2 Overview of Markov Chains with Stationary Transition Probabilities
111(2)
4.3 Overview of Wright-Fisher Perspective
113(3)
4.4 Absorbing Markov Chains with a Finite State Space
116(6)
4.5 Distributions of First Entrance Times Into an Absorbing State and Their Expectations and Variances
122(6)
4.6 Quasi-Stationary Distribution on the Set of Transient States
128(4)
4.7 Incorporating Mutation and Selection Into Two Allele Wright-Fisher Processes
132(4)
4.8 Genotypic Selection with no Mutation and Random Mating
136(3)
4.9 A Computer Experiment with the Wright-Fisher Neutral Model
139(3)
4.10 A Computer Experiment with Wright-Fisher Selection Model
142(3)
4.11 A Computer Experiment with Wright-Fisher Genotypic Selection Model
145(2)
4.12 A Computer Experiment with a Wright-Fisher Model Accommodating Selection and Mutation
147(3)
Bibliography
149(1)
5 Multitype Gamete Sampling Processes, Generation of Random Numbers and Monte Carlo Simulation Methods
150(46)
5.1 Introduction
150(1)
5.2 A Wright-Fisher Model with Multiple Types of Gametes - Mutation and Selection
151(4)
5.3 Examples of Multiple Alleles and Types of Gametes Involving Two Chromosomes
155(2)
5.4 A Genetic Theory for Inherited Autism in Man
157(1)
5.5 An Evolutionary Genetic Model of Inherited Autism
158(8)
5.6 Multitype Gamete Sampling Processes as Conditioned Branching Processes
166(8)
5.7 On the Orderly Pursuit of Randomness Underlying Monte Carlo Simulation Methods
174(4)
5.8 Design of Software and Statistical Summarization Procedures
178(4)
5.9 Experiments in the Quantification of Ideas for the Evolution of Inherited Autism in Populations
182(6)
5.10 Comparative Experiments in the Quantification of Two Formulations of Gamete Sampling Models
188(3)
5.11 An Experiment with a Three Allele Neutral Model
191(1)
5.12 Rapid Selection and Convergence to a Stationary Distribution
192(4)
Bibliography
195(1)
6 Nucleotide Substitution Models Formulated as Markov Processes in Continuous Time
196(39)
6.1 Introduction
196(1)
6.2 Overview of Markov Jump Processes in Continuous Time with Finite State Spaces and Stationary Laws of Evolution
197(6)
6.3 Stationary Distributions of Markov Chains in Continuous Time with Stationary Laws of Evolution
203(6)
6.4 Markov Jump Processes as Models for Base Substitutions in the Molecular Evolution of DNA
209(8)
6.5 Processes with Preassigned Stationary Distributions
217(3)
6.6 A Numerical Example for a Class of Twelve Parameters
220(3)
6.7 Falsifiable Predictions of Markov Models of Nucleotide Substitutions
223(2)
6.8 Position Dependent Nucleotide Substitution Models
225(3)
6.9 A Retrospective View of a Markov Process with Stationary Transition Probabilities
228(7)
Bibliography
233(2)
7 Mixtures of Markov Processes as Models of Nucleotide Substitutions at Many Sites
235(37)
7.1 Introduction
235(1)
7.2 Mixtures of Markov Models and Variable Substitution Rates Across Sites
236(4)
7.3 Gaussian Mixing Processes
240(5)
7.4 Computing Realizations of a Gaussian Process with Specified Covariance Function
245(3)
7.5 Gaussian Processes That May be Computed Recursively
248(7)
7.6 Monte Carlo Implementation of Mixtures of Transition Rates for Markov Processes
255(6)
7.7 Transition Rates Based on Logistic Gaussian Processes
261(4)
7.8 Nucleotide Substitution in a Three Site Codon
265(3)
7.9 Computer Simulation Experiments
268(4)
Bibliography
271(1)
8 Computer Implementations and Applications of Nucleotide Substitution Models at Many Sites - Other Non-SNP Types of Mutation
272(34)
8.1 Introduction
272(1)
8.2 Overview of Monte Carlo Implementations for Nucleotide Substitution Models with N Sites
273(7)
8.3 Overview of Genographic Research Project - Studies of Human Origins
280(2)
8.4 Simulating Nucleotide Substitutions in Evolutionary Time
282(7)
8.5 Counting Back and Parallel Mutations in Simulated Data
289(6)
8.6 Computer Simulation Experiments With a Logistic Gaussian Mixing Process
295(3)
8.7 Potential Applications of Many Site Models to the Evolution of Protein Coding Genes
298(2)
8.8 Preliminary Notes on Stochastic Models of Indels and Other Mutations
300(6)
Bibliography
304(2)
9 Genealogies, Coalescence and Self-Regulating Branching Processes
306(51)
9.1 Introduction
306(3)
9.2 One Type Stochastic Genealogies
309(6)
9.3 Overview of the Galton-Watson Process
315(6)
9.4 Self-Regulating Galton-Watson Processes
321(3)
9.5 Fixed Points and Domains of Attraction
324(3)
9.6 Probabilities of Extinction
327(3)
9.7 Stochastic Genealogies in the Multitype Case
330(3)
9.8 Multitype Galton-Watson Processes
333(5)
9.9 Self-Regulating Multitype Processes
338(4)
9.10 Estimating the Most Recent Common Ancestor
342(4)
9.11 The Deterministic Model and Branching Process
346(5)
9.12 Realizations of a Poisson Random Variable
351(6)
Bibliography
355(2)
10 Emergence, Survival and Extinction of Mutant Types in Populations of Self Replicating Individuals Evolving From Small Founder Populations
357(44)
10.1 Introduction
357(4)
10.2 Experiments with the Evolution of Small Founder Populations with Mutation but no Selection
361(6)
10.3 Components of Selection - Reproductive and Competitive Advantages of Some Types
367(5)
10.4 Survival of Deleterious and Beneficial Mutations From a Small Founder Populations
372(4)
10.5 Survival of Mutations with Competitive Advantages Over an Ancestral Type
376(6)
10.6 Chaotic Embedded Deterministic Model with Three Types
382(8)
10.7 Self Regulating Multitype Branching Processes in Random Environments
390(7)
10.8 Simulating Multitype Genealogies and Further Reading
397(4)
Bibliography
399(2)
11 Two Sex Multitype Self Regulating Branching Processes in Evolutionary Genetics
401(45)
11.1 Introduction
401(2)
11.2 Gametes, Genotypes and Couple Types in a Two Sex Stochastic Population Process
403(2)
11.3 The Parameterization of Couple Formation Processes
405(4)
11.4 An Example of Couple Formation Process with Respect to an Autosomal Locus with Two Alleles
409(2)
11.5 Genetics and Offspring Distributions
411(4)
11.6 Overview of a Self-Regulating Population Process
415(2)
11.7 Embedding Non-Linear Difference Equations in the Stochastic Population Process
417(3)
11.8 On the Emergence of a Beneficial Mutation From a Small Founder Population
420(3)
11.9 An Alternative Evolutionary Genetic Model of Inherited Autism
423(5)
11.10 Autism in a Population Evolving From a Small Founder Population
428(5)
11.11 Sexual Selection in Populations Evolving From a Small Founder Population
433(6)
11.12 Two Sex Processes with Linkage at Two Autosomal Loci
439(7)
Bibliography
445(1)
12 Multitype Self-Regulatory Branching Process and the Evolutionary Genetics of Age Structured Two Sex Populations
446(59)
12.1 Introduction
446(2)
12.2 An Overview of Competing Risks and Semi-Markov Processes
448(6)
12.3 Age Dependence and Types of Singles and Couples
454(3)
12.4 Altruism and Semi-Markovian Processes for Evolution of Single Individuals
457(4)
12.5 On an Age Dependent Couple Formation Process
461(4)
12.6 A Semi-Markovian Model for Deaths, Dissolutions and Transitions Among Couple Types
465(3)
12.7 Gamete, Genotypic and Offspring Distributions for Each Couple Type
468(6)
12.8 Overview of Stochastic Population Process with Two Sexes and Age Dependence
474(2)
12.9 Overview of Non-Linear Difference Equations Embedded in the Stochastic Population Process
476(3)
12.10 A Two Sex Age Dependent Population Process Without Couple Formation
479(4)
12.11 Parametric Latent Risk Functions for Death by Age
483(5)
12.12 Sexual Selection in an Age Dependent Process Without Couple Formation
488(5)
12.13 Population Momentum and Emergence of a Beneficial Mutation
493(4)
12.14 Experiments with a Version of the Age Dependent Model with Couple Formation
497(8)
Bibliography
504(1)
13 An Overview of the History of the Concept of a Gene and Selected Topics in Molecular Genetics
505(44)
13.1 Introduction
505(1)
13.2 A Brief History of the Definition of a Gene
506(4)
13.3 Transcription and Translation Processes
510(4)
13.4 Pre-processing Messenger RNA
514(4)
13.5 Difficulties with Current Gene Concepts
518(2)
13.6 Acronyms in Tiling Array Technology
520(3)
13.7 Genome Activity in the ENCODE Project
523(6)
13.8 Interpreting Tiling Array Experiments
529(3)
13.9 A Tentative Updated Definition of a Gene
532(5)
13.10 ABO Blood Group Genetics in Humans
537(3)
13.11 Duffy Blood Group System in Man
540(1)
13.12 Regulation of the Shh Locus in Mice
541(8)
Bibliography
545(4)
14 Detecting Genomic Signals of Selection and the Development of Models for Simulating the Evolution of Genomes
549(82)
14.1 Introduction
549(2)
14.2 Types of Selection and Genomic Signals
551(5)
14.3 DNA Sequence Evolution in Large Genomic Regions
556(6)
14.4 Statistics Used in Genome Wide Scans
562(7)
14.5 Detecting Signals of Natural Selection
569(5)
14.6 Simulated Genomic Data in Statistical Tests
574(7)
14.7 Species and Gene Trees From Mammalian Genomic Data
581(5)
14.8 Overview of Markovian Codon Substitution Models
586(8)
14.9 Simulating Genetic Recombination
594(7)
14.10 Modelling Gene Conversion
601(5)
14.11 Nucleotide Substitutions During Meiosis
606(6)
14.12 Simulating Insertions and Deletions
612(9)
14.13 Simulating Copy Number Variation
621(3)
14.14 Simulating Mutational Events and Genetic Recombination
624(7)
Bibliography
627(4)
15 Suggestions for Further Research, Reading and Viewing
631(14)
15.1 Introduction
631(1)
15.2 Suggestions for Further Research on Self-Regulating Branching Processes
632(2)
15.3 Suggestions for Continuing Development of Stochastic Models of Genomic Evolution
634(3)
15.4 A Brief List of References on Genetics and Evolution for Further Study
637(8)
Bibliography
641(4)
Index 645