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Evolutionary Theory : Mathematical and Conceptual Foundations - Sean H. Rice

Evolutionary Theory

Mathematical and Conceptual Foundations

Paperback

Published: 1st July 2004
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Evolutionary Theory is for graduate students, researchers, and advanced undergraduates who want an understanding of the mathematical and biological reasoning that underlies evolutionary theory. The book covers all of the major theoretical approaches used to study the mechanics of evolution, including classical one- and two-locus models, diffusion theory, coalescent theory, quantitative genetics, and game theory. There are also chapters on theoretical approaches to the evolution of development and on multilevel selection theory. Each subject is illustrated by focusing on those results that have the greatest power to influence the way that we think about how evolution works. These major results are developed in detail, with many accompanying illustrations, showing exactly how they are derived and how the mathematics relates to the biological insights that they yield. In this way, the reader learns something of the actual machinery of different branches of theory while gaining a deeper understanding of the evolutionary process.

Roughly half of the book focuses on gene-based models, the other half being concerned with general phenotype-based theory. Throughout, emphasis is placed on the fundamental relationships between the different branches of theory, illustrating how all of these branches are united by a few basic, universal, principles.

The only mathematical background assumed is basic calculus. More advanced mathematical methods are explained, with the help of an extensive appendix, when they are needed.

All evolutionary biologists should be made to understand this material, and Rice's volume is the best place for them to begin. Anyone who wants to call themselves evolutionary theorists should work their way through this unique book. * Joe Felsenstein, The Quarterly Review of Biology *

Prefacep. ix
Introductionp. 1
Selection on One Locusp. 5
Fitnessp. 6
Fitness and Population Growthp. 7
Two Alleles with Viability Selectionp. 9
Frequency-Independent Selectionp. 11
Frequency-Dependent Selectionp. 13
Continuous Timep. 14
Introducing Mutationp. 17
Mutational Loadp. 20
The Evolution of Outcrossingp. 20
Multiple Allelesp. 23
Fertility Selectionp. 27
Regression Interpretationp. 31
Additive Genetic Variancep. 33
Fitness Maximization, Optimization, and Potential Functionsp. 36
Selection on Two Locip. 39
No Selectionp. 41
Gametic Disequilibriump. 42
Introducing Selectionp. 44
Evolution of Gametic Disequilibriump. 47
Quasi-Gametic Equilibriump. 50
Epistasisp. 51
Nomenclature of Epistasisp. 54
Additive Genetic Variancep. 55
Applications of Two-Locus Theoryp. 59
Sexual Selectionp. 59
Cultural Transmissionp. 66
Meiotic Drivep. 69
Drift at Neutral Locip. 73
Reproduction as Samplingp. 73
Drift as a Markov Processp. 74
Evolution as a Random Walkp. 76
Drift as Random Covariancep. 78
The Coalescent Processp. 80
Time to Coalescencep. 82
Drift and Neutral Variationp. 84
Gene Trees and Species Treesp. 85
Coalescence of Multiple Allelesp. 86
Distribution of Pairwise Allelic Differencesp. 90
The Structured Coalescentp. 93
Finite Island Model with Symmetric Migrationp. 97
Asymmetric Migrationp. 99
Conservative Migrationp. 101
Proportional Migrationp. 102
Balancing Selection at a Linked Locusp. 102
The Coalescent versus Inbreeding Coefficientsp. 104
Effective Population Sizep. 109
Inbreeding Effective Population Size (N[superscript i subscript e])p. 111
Fluctuating Population Sizep. 111
Breeding Sex Ratiop. 113
Variation in Family Sizep. 114
Subdivided Populationp. 117
Variance Effective Population Size (N[superscript v subscript e])p. 119
Separate Sexesp. 125
Ecology of Effective Population Sizep. 127
Diffusion Theory: Combining Evolutionary Mechanismsp. 129
The Structure of Diffusion Theoryp. 130
Assumptions of the Diffusion Approximationp. 132
The Kolmogorov Forward Equationp. 133
Geometry of Diffusionp. 135
The Equilibrium Distributionp. 139
Mutation and Driftp. 141
Selection and Driftp. 143
Heterozygote Advantagep. 143
Heterozygote Intermediatep. 144
Mutation, Selection, and Driftp. 146
Migration between Populationsp. 147
Migration Maintaining Variationp. 148
Migration Opposing Selectionp. 150
Probability of Fixation with Selectionp. 151
The Kolmogorov Backward Equationp. 152
The Equilibrium Distributionp. 153
Probability of Fixationp. 154
Fixation of Deleterious Allelesp. 160
The Algebra of Evolution: Price's Theoremp. 165
Price's Theoremp. 166
Concepts Underlying Price's Theoremp. 169
A Note on Regressions and Covariancesp. 170
Generalized Marginal Fitnessp. 171
The Selection Differentialp. 173
Directional and Stabilizing Selectionp. 176
Relationship between Parents and Offspringp. 178
Breeder's Equationp. 180
Fisher's Fundamental Theoremp. 181
Generalized Driftp. 181
Putting It All Togetherp. 187
Quantitative Geneticsp. 189
A Preliminary Warning about Terminologyp. 190
Multivariate Normalityp. 191
Selection on One Trait: The Breeder's Equationp. 192
Multivariate Evolutionp. 194
Path Analysisp. 194
Sexual Selectionp. 199
Parent-Offspring Covariance versus Additive Genetic Variancep. 203
Measuring Selection: The Multivariate Selection Differentialp. 205
Maintenance of Genetic Variationp. 209
Diallelic Loci Modelp. 210
Continuum of Alleles Modelp. 214
Developmental Evolutionp. 219
Phenotype Landscapesp. 220
Tensor Analysisp. 224
Momentsp. 227
Selection on a Single Phenotypic Traitp. 228
The Meaning of Q Vectorsp. 230
The General Equationp. 232
Selection on Higher Momentsp. 237
Multiple Charactersp. 240
Adaptive Phenotypic Plasticityp. 241
Evolution of the Reaction Norm Slopep. 244
Evolution of the Reaction Norm Curvaturep. 248
Covariance between Traitsp. 251
Uncurved Landscapesp. 253
Curved Landscapesp. 254
Parent-Offspring Covariancep. 256
Entangled Traitsp. 260
Evolutionary Game Theory and Strategy Dynamicsp. 263
An Early Example: Sex Ratio Evolutionp. 263
Origins of Game Theoryp. 265
A Two-Strategy Gamep. 266
Mixed versus Pure Strategiesp. 269
General Rules for Discrete Gamesp. 270
Nash Equilibriump. 270
Evolutionarily Stable Strategy (ESS)p. 270
Game Geometryp. 273
Asymmetric Gamesp. 275
Cooperation and the Prisoner's Dilemmap. 277
Repeated Prisoner's Dilemma Gamep. 278
Continuous Games and Adaptive Dynamicsp. 282
Assumptions of Game Theoryp. 288
Drift in Strategy Evolutionp. 291
Multilevel Selectionp. 297
Kin Selectionp. 298
Two Levels with the Same Generation Timep. 302
A General Version of Hamilton's Inequalityp. 304
Inclusive Fitnessp. 307
Groups Persisting for a Few Individual Generationsp. 308
Sex Ratio Evolutionp. 308
Levels with Very Different Generation Timesp. 312
Nonoverlapping Group Generationsp. 314
Interactions between the Two Levels of Selectionp. 319
Groups with Overlapping Generationsp. 320
Properties Influencing the Efficacy of Multilevel Selectionp. 321
Identifying the Units of Selectionp. 323
Appendix Ap. 327
Variances, Covariances, and Regressionsp. 327
Path Analysisp. 330
Appendix Bp. 333
Distributions and Momentsp. 333
Binomial Distributionp. 333
Poisson Distributionp. 335
Normal Distributionp. 336
Momentsp. 337
Moment Generating Functionsp. 338
Appendix Cp. 341
Calculusp. 341
Taylor Seriesp. 342
Differential Equationsp. 343
Separable Equationsp. 344
First Order Linear Equationsp. 345
Appendix Dp. 347
Vectors, Matrices, and Tensorsp. 347
Tensorsp. 351
Coordinate Systemsp. 351
The Geometric Meaning of Inner Productsp. 354
Bibliographyp. 355
Indexp. 365
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9780878937028
ISBN-10: 0878937021
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 348
Published: 1st July 2004
Publisher: Oxford University Press Inc
Country of Publication: US
Dimensions (cm): 22.23 x 15.24  x 1.91
Weight (kg): 0.61
Edition Number: 1