Genetic Structure and Selection in Subdivided Populations

Francois Rousset is a senior scientist in the Institute of Evolutionary Sciences (ISEM) in Montpellier, France, which operates under the aegis of the Centre National de la Recherche Scientifique and Montpellier University.

"For most of us reading his book, our task is to master the concepts behind the elegant equations presented in Rousset's monograph, if we are to have any hope of keeping up with future developments in the field of mathematical population genetics."--Wayne M .Getz, Bioscience "This book will be very useful to graduate students and researchers in population genetics and ecology, especially to those interested in the genetic structure of spatially extended populations. It will be a valuable source of reference and inspiration."--Reinhard Buerger, Biometrics

• List of Figures and Tables xi Acknowledgments xiii Preface xv What Is and Is Not There xv Assumed Background xv Of Gene and Fitness xvi 1. Introduction 1 Genetic Structure in Relation to Selection 1 Plan of the Book 5 2. Selection and Drift 9 Selection in Panmictic Populations 9 Evolution in Spatially Structured Populations 11 Selection and Local Drift 12 Effective Size in Subdivided Populations 13 Measuring Population Structure 14 Genetic Identity 14 Statistical Concepts of Equilibrium and Population 19 Summary 21 3. Spatially Homogeneous Dispersal: The Island Model and Isolation by Distance 23 Island Models 24 Isolation by Distance 28 Dispersal in Natural Populations 29 The Lattice Models 32 Differentiation under Isolation by Distance 35 Summary 44 Appendix 1: General Analysis of the Lattice Model 45 Appendix 2: Miscellaneous Results 49 Diversity in a Deme 49 Average Diversity in a Population 50 Differentiation under Low Dispersal 51 4. Interpretations of Inbreeding and Relatedness Coefficients in Subdivided Populations 53 Probabilities of Coalescence in Migration Matrix Models 54 Migration Matrix Models: Formulation 54 Probabilities of Coalescence 55 Interpretations of FST 56 Coalescence before Dispersal 56 Separation of Time Scales 57 An Ancestral Reference Population? 58 Differences between Distributions of Coalescence Times 58 Properties of Inbreeding Coefficients 62 Sensitivity to Mutation and to Past Demographic Events 62 No Mutation 63 Alternative Measures of Allelic Divergence 64 5. Evolutionary Dynamics 67 Fitness in a Panmictic Population 67 Example: Resource Competition 67 Convergence Stability 68 Evolutionary Stability 71 Applicability of This Framework 74 Fitness in a Subdivided Population 81 Frequency Dependence in Subdivided Populations 82 How to Measure Selection? 84 Conclusion 87 Appendix: The Prisoner's Dilemma Game 88 Noniterated Game 88 Iterated Game 89 6. Convergence Stability in a Spatially Homogeneous Population 91 Weak Selection Effects on Probability of Fixation 92 Fixation Probability as Allele Frequency Change 92 Fitness Functions 93 Fixation Probability: Direct Fitness Expansion 97 Expression in Terms of Parameters of Population Structure 97 Practical Computation of Convergence Stability 99 Island Model 99 Isolation by Distance 100 Conclusions 101 Direct Fitness Method 101 Fitness Maximization 103 7. Inclusive Fitness, Cooperation, and Altruism 105 What Inclusive Fitness Does Measure 106 Inclusive and Direct Fitness 106 Hamilton's Derivation of Inclusive Fitness 108 Isolation by Distance 109 Altruism in Spatially Subdivided Populations 111 Cost, Benefit, and Relatedness 111 Helping Neighbors 112 Other Examples 116 The Importance of Kin Competition 117 Kin Recognition 118 Implications for Modeling Approaches 119 Inclusive Fitness Theory 119 Other Frameworks 121 Appendix: Helping Neighbors under Isolation by Distance 124 8. Diploidy (and Sex) 127 Population Structure of Diploid Populations 128 Analysis of Pollen and Seed Dispersal 129 Joint Effects of Selfing and Selection on Population Structure 136 Selection in Sexual Diploid Populations 137 Parent and Offspring Control 138 Dominance 140 Highlights 141 9. Effective Size: Concepts and Applications to Stable Populations 143 Defining Effective Size 144 Application in Diffusion Approximations 147 Computation of Effective Size of a Total Population 152 Reproductive Value 153 Deme Structure: The Strong Migration Limit 155 Deme Structure: More Accurate Results 160 Additional Factors 162 Local Effective Size 167 Concluding Remarks 168 Appendix 171 Dispersal and Class Transitions 171 Strong Migration Limit 173 10. Fluctuating Demography: Neutral Models 175 Effective Size of an Isolated Deme 175 Defining Effective Size 176 An Example 177 Structured Populations 178 A Metapopulation Model 179 Propagule Models 184 Inferences 187 11. Selection in Class-Structured Populations 189 Fitness Measures 190 Stable Demography 190 Fluctuating Demography 192 Fitness as Eigenvalue 194 Diffusion Approximations 196 Inferences 196 12. Overview and Perspectives 199 Statistical Analyses of Genetic Structure 199 All Those Data 199 Estimation Methods 201 Robustness 203 Estimation of Effective Size 203 Some Easy Improvements 204 Prospects for the Analysis of Selection 206 Current State of Theory 206 Avenues for Simplifications 208 Conclusion 209 Appendix: Algorithms for Likelihood Estimation 211 Appendix A. Mathematical Appendix 215 Notation 215 Matrix Algebra 217 Eigenvalues and Eigenvectors 217 Diagonalizable Matrices 219 Generating Functions 220 Computation of Identity in State 221 Mutation Models 221 Identity in the Different Mutation Models 222 References 227 Index 261