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Mathematical Population Genetics

01 Jan 1979-
TL;DR: In this paper, the authors present a model based on the Wright-Fisher In.nitely Many Alleles Model and the Cannings (Exchangeable) Model: Two-Alleles 3.4.
Abstract: Contents Preface Introduction 1 Historical Background 1.1 Biometricians, Saltationists and Mendelians 1.2 The Hardy-Weinberg Law 1.3 The Correlation Between Relatives 1.4 Evolution 1.4.1 The Deterministic Theory 1.4.2 Non-Random-Mating Populations 1.4.3 The Stochastic Theory 1.5 Evolved Genetic Phenomena 1.6 Modelling 1.7 Overall Evolutionary Theories 2 Technicalities and Generalizations 2.1 Introduction 2.2 Random Union of Gametes 2.3 Dioecious Populations 2.4 Multiple Alleles 2.5 Frequency-Dependent Selection 2.6 Fertility Selection 2.7 Continuous-Time Models 2.8 Non-Random-Mating Populations 2.9 The Fundamental Theorem of Natural Selection 2.10 Two Loci 2.11 Genetic Loads 2.12 Finite Markov Chains 3 Discrete Stochastic Models 3.1 Introduction 3.2 Wright-Fisher Model: Two Alleles 3.3 The Cannings (Exchangeable) Model: Two Alleles 3.4 Moran Models: Two Alleles 3.5 K-Allele Wright-Fisher Models 3.6 Infinitely Many Alleles Models 3.6.1 Introduction 3.6.2 The Wright-Fisher In.nitely Many Alleles Model 3.6.3 The Cannings In.nitely Many Alleles Model 3.6.4 The Moran In.nitely Many Alleles Model 3.7 The Effective Population Size 3.8 Frequency-Dependent Selection 3.9 Two Loci 4 Diffusion Theory 4.1 Introduction 4.2 The Forward and Backward Kolmogorov Equations 4.3 Fixation Probabilities 4.4 Absorption Time Properties 4.5 The Stationary Distribution 4.6 Conditional Processes 4.7 Diffusion Theory 4.8 Multi-dimensional Processes 4.9 Time Reversibility 4.10 Expectations of Functions of Di.usion Variables 5 Applications of Diffusion Theory 5.1 Introduction 5.2 No Selection or Mutation 5.3 Selection 5.4 Selection: Absorption Time Properties 5.5 One-Way Mutation 5.6 Two-Way Mutation 5.7 Diffusion Approximations andBoundary Conditions 5.8 Random Environments 5.9 Time-Reversal and Age Properties 5.10 Multi-Allele Diffusion Processes 6 Two Loci 6.1 Introduction 6.2 Evolutionary Properties of Mean Fitness 6.3 Equilibrium Points 6.4 Special Models 6.5 Modifier Theory 6.6 Two-Locus Diffusion Processes 6.7 Associative Overdominance and Hitchhiking 6.8 The Evolutionary Advantage of Recombination 6.9 Summary 7 Many Loci 7.1 Introduction 7.2 Notation 7.3 The Random Mating Case 7.3.1 Linkage Disequilibrium, Means and Variances 7.3.2 Recurrence Relations for Gametic Frequencies 7.3.3 Components of Variance 7.3.4 Particular Models 7.4 Non-Random Mating 7.4.1 Introduction 7.4.2 Notation and Theory 7.4.3 Marginal Fitnesses and Average Effects 7.4.4 Implications 7.4.5 The Fundamental Theorem of Natural Selection 7.4.6 Optimality Principles 7.5 The Correlation Between Relatives 7.6 Summary 8 Further Considerations 8.1 Introduction 8.2 What is Fitness? 8.3 Sex Ratio 8.4 Geographical Structure 8.5 Age Structure 8.6 Ecological Considerations 8.7 Sociobiology 9 Molecular Population Genetics: Introduction 9.1 Introduction 9.2 Technical Comments 9.3 In.nitely Many Alleles Models: Population Properties 9.3.1 The Wright-Fisher Model 9.3.2 The Moran Model 9.4 In.nitely Many Sites Models: Population Properties 9.4.1 Introduction 9.4.2 The Wright-Fisher Model 9.4.3 The Moran Model 9.5 Sample Properties of In.nitely Many Alleles Models 9.5.1 Introduction 9.5.2 The Wright-Fisher Model 9.5.3 The Moran Model 9.6 Sample Properties of In.nitely Many Sites Models 9.6.1 Introduction 9.6.2 The Wright-Fisher Model 9.6.3 The Moran Model 9.7 Relation Between In.nitely Many Alleles and Infinitely Many Sites Models 9.8 Genetic Variation Within and Between
Citations
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Journal ArticleDOI
01 Mar 1985-Nature
TL;DR: A probe based on a tandem-repeat of the core sequence can detect many highly variable loci simultaneously and can provide an individual-specific DNA ‘fingerprint’ of general use in human genetic analysis.
Abstract: The human genome contains many dispersed tandem-repetitive 'minisatellite' regions detected via a shared 10-15-base pair 'core' sequence similar to the generalized recombination signal (chi) of Escherichia coli. Many minisatellites are highly polymorphic due to allelic variation in repeat copy number in the minisatellite. A probe based on a tandem-repeat of the core sequence can detect many highly variable loci simultaneously and can provide an individual-specific DNA 'fingerprint' of general use in human genetic analysis.

3,552 citations

Journal ArticleDOI
TL;DR: A Monte Carlo computer program is available to generate samples drawn from a population evolving according to a Wright-Fisher neutral model, and the samples produced can be used to investigate the sampling properties of any sample statistic under these neutral models.
Abstract: A Monte Carlo computer program is available to generate samples drawn from a population evolving according to a Wright-Fisher neutral model. The program assumes an infinite-sites model of mutation, and allows recombination, gene conversion, symmetric migration among subpopulations, and a variety of demographic histories. The samples produced can be used to investigate the sampling properties of any sample statistic under these neutral models.

2,566 citations

Journal ArticleDOI
TL;DR: Why, then, all the recent (and not so recent) interest in such minor, nondirectional deviations from bilateral symmetry [fluctuating asymmetry (FA)?
Abstract: With these words Darwin opened a brief paragraph citing observations antithetical to his supposition: anecdotal reports of the inheritance of characters missing from one side of the body. His initial hunch, however, has stood the test of time: Genetic studies have confirmed that where only small, random deviations from bilateral symmetry exist, the deviations in a particular direction have little or no measurable heritability (17, 47, 51, 65a, 73a, 74, 91). The genetic basis of bilateral symmetry thus appears to differ fundamentally from that of virtually all other morphological features. Why, then, all the recent (and not so recent) interest in such minor, nondirectional deviations from bilateral symmetry [fluctuating asymmetry (FA); 60 cited in 99]? Four reasons. First, FA relates in a curious way to what is perhaps the major unsolved general problem in modem biology: the orderly expression of genotypes as complex, three-dimensional phenotypes. As was emphasized in a flurry of activity in the mid to late 1950s, and many times since, FA provides an appealing measure of 'developmental noise,' or minor environmentally induced departures from some ideal developmental program (101). Its appeal derives from an a priori knowledge of the ideal: perfect bilateral symmetry. For unilateral characters, the ideal is rarely known (but see 1, 2, and 59 for one possible approach). A second reason for interest in

2,025 citations

Journal ArticleDOI
01 Aug 1993-Genetics
TL;DR: Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.
Abstract: Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.

1,807 citations