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