## Stochastic Processes in Genetics and Evolution: Computer Experiments in the Quantification of Mutation and SelectionThe 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. |

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### Contents

1 An Introduction to Mathematical Probability with Applications in Mendelian Genetics | 1 |

2 Linkage and Recombination at Multiple Loci | 53 |

3 Linkage and Recombination in Large Random Mating Diploid PopulationsRandom Mating Diploid Populations | 83 |

4 Two Allele WrightFisher Process with Mutation and Selection | 110 |

5 Multitype Gamete Sampling Processes Generation of Random Numbers and Monte Carlo Simulation Methods | 150 |

6 Nucleotide Substitution Models Formulated as Markov Processes in Continuous Time | 196 |

7 Mixtures of Markov Processes as Models of Nucleotide Substitutions at Many Sites | 235 |

8 Computer Implementations and Applications of Nucleotide Substitution Models at Many Sites Other NonSNP Types of Mutation | 272 |

10 Emergence Survival and Extinction of Mutant Types in Populations of Self Replicating Individuals Evolving From Small Founder Populations | 357 |

11 Two Sex Multitype Self Regulating Branching Processes in Evolutionary Genetics | 401 |

12 Multitype SelfRegulatory Branching Process and the Evolutionary Genetics of Age Structured Two Sex Populations | 446 |

13 An Overview of the History of the Concept of a Gene and Selected Topics in Molecular Genetics | 505 |

14 Detecting Genomic Signals of Selection and the Development of Models for Simulating the Evolution of Genomes | 549 |

15 Suggestions for Further Research Reading and Viewing | 631 |

643 | |

9 Genealogies Coalescence and SelfRegulating Branching Processes | 306 |

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### Common terms and phrases

alleles array autism back mutation branching process chapter chromosome codon conditional probability consideration considered convergence couple types deﬁned deﬁnition denote the number embedded deterministic model equation estimate event evolution evolutionary example expectation females and males ﬁgure ﬁnd ﬁnding ﬁnite ﬁrst formula founder population frequency gametes gametic distribution gene conversion genetic recombination genomic region genotype genotype aa given graphs haplotypes human individuals of type initial integers interval large number let the random loci locus Markov chain mating matrix Q meiosis Monte Carlo simulation multinomial distribution multitype natural selection nucleotide substitution number of individuals number of offspring observed occur pairs parameter Poisson Poisson distribution population probability space protein random function random variable realizations replications risk function sample sequence simulation experiments stationary distribution statistical stochastic process strand symbols three genotypes tion total number trajectories transcription values vector Wright-Fisher