Mathematical Population Genetics 1

1 Historical Background.- 1.1 Biometricians, Saltationists and Mendelians.- 1.2 The Hardy-Weinberg Law.- 1.3 The Correlation Between Relatives.- 1.4 Evolution.- 1.5 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.- 3.7 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 Diffusion 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 and Boundary 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.- 7.4 Non-Random Mating.- 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 Infinitely Many Alleles Models: Population Properties..- 9.4 Infinitely Many Sites Models: Population Properties.- 9.5 Sample Properties of Infinitely Many Alleles Models..- 9.6 Sample Properties of Infinitely Many Sites Models.- 9.7 Relation Between Infinitely Many Alleles and Infinitely Many Sites Models.- 9.8 Genetic Variation Within and Between Populations.- 9.9 Age-Ordered Alleles: Frequencies and Ages.- 10 Looking Backward in Time: The Coalescent.- 10.1 Introduction.- 10.2 Competing Poisson and Geometric Processes.- 10.3 The Coalescent Process.- 10.4 The Coalescent and Its Relation to Evolutionary Genetic Models.- 10.5 Coalescent Calculations: Wright-Fisher Models.- 10.6 Coalescent Calculations: Exact Moran Model Results.- 10.7 General Comments.- 10.8 The Coalescent and Human Genetics.- 11 Looking Backward: Testing the Neutral Theory.- 11.1 Introduction.- 11.2 Testing in the Infinitely Many Alleles Models.- 11.3 Testing in the Infinitely Many Sites Models.- 12 Looking Backward in Time: Population and Species Comparisons.- 12.1 Introduction.- 12.2 Various Evolutionary Models.- 12.3 Some Implications.- 12.4 Statistical Procedures.- Appendix A: Eigenvalue Calculations.- References.- Author Index.