- Title Pages
- Dedication
- Preface
- I Introduction
- 1 Changes in Quantitative Traits Over Time
- II Evolution at One and Two Loci
- 2 Neutral Evolution in One- and Two-Locus Systems
- 3 The Genetic Effective Size of a Population
- 4 The Nonadaptive Forces of Evolution
- 5 The Population Genetics of Selection
- 6 Theorems of Natural Selection: Results of Price, Fisher, and Robertson
- 7 Interaction of Selection, Mutation, and Drift
- 8 Hitchhiking and Selective Sweeps
- 9 Using Molecular Data to Detect Selection: Signatures from Recent Single Events
- 10 Using Molecular Data to Detect Selection: Signatures from Multiple Historical Events
- III Drift and Quantitative Traits
- 11 Changes in Genetic Variation Induced by Drift
- 12 The Neutral Divergence of Quantitative Traits
- IV Short-Term Response on a Single Character
- 13 Short-term Changes in the Mean: 1. The Breeder’s Equation
- 14 Short-term Changes in the Mean: 2. Truncation and Threshold Selection
- 15 Short-term Changes in the Mean: 3. Permanent Versus Transient Response
- 16 Short-term Changes in the Variance: 1. Changes in the Additive Variance
- 17 Short-term Changes in the Variance: 2. Changes in the Environmental Variance
- 18 Analysis of Short-term Selection Experiments: 1. Least-squares Approaches
- 19 Analysis of Short-term Selection Experiments: 2. Mixed-model and Bayesian Approaches
- 20 Selection Response in Natural Populations
- V Selection in Structured Populations
- 21 Family-Based Selection
- 22 Associative Effects: Competition, Social Interactions, Group and Kin Selection
- 23 Selection Under Inbreeding
- VI Population-Genetic Models of Trait Response
- 24 The Infinitesimal Model and Its Extensions
- 25 Long-term Response: 1. Deterministic Aspects
- 26 Long-term Response: 2. Finite Population Size and Mutation
- 27 Long-term Response: 3. Adaptive Walks
- 28 Maintenance of Quantitative Genetic Variation
- VII Measuring Selection on Traits
- 29 Individual Fitness and the Measurement of Univariate Selection
- 30 Measuring Multivariate Selection
- Appendix 1 Diffusion Theory
- Appendix 2 Introduction to Bayesian Analysis
- Appendix 3 Markov Chain Monte Carlo and Gibbs Sampling
- Appendix 4 Multiple Comparisons: Bonferroni Corrections, False-discovery Rates, and Meta-analysis
- Appendix 5 The Geometry of Vectors and Matrices: Eigenvalues and Eigenvectors
- Appendix 6 Derivatives of Vectors and Vector-valued Functions
- Literature Cited
- Author Index
- Organism and Trait Index
- Subject Index

# Theorems of Natural Selection: Results of Price, Fisher, and Robertson

# Theorems of Natural Selection: Results of Price, Fisher, and Robertson

- Chapter:
- (p.145) 6 Theorems of Natural Selection: Results of Price, Fisher, and Robertson
- Source:
- Evolution and Selection of Quantitative Traits
- Author(s):
### Bruce Walsh

### Michael Lynch

- Publisher:
- Oxford University Press

This chapter reviews a number of “theorems” of natural selection. These include exact results (true mathematical theorems): the Robertson-Price identity, Price's general expression for any form of selection response, and the Fisher-Price-Ewens version of Fisher's fundamental theorem. Their generality comes as the cost of usually being very difficult to apply. An important exception is the Robertson-Price identity, which expresses the within-generation change in the mean of a trait as its covariance with relative fitness. This chapter also examines three classic approximations: Fisher's fundamental theorem for the behavior of mean population fitness, and Robertson's secondary theorem and the breeder's equation for the expected response in a trait under selection, showing both how these results are connected and the error given by the various approximations. Finally, the chapter examines the connection between the additive variance of a trait and its correlation with fitness.

*Keywords:*
asymptotic fundamental theorem, breeder's equation, evolvability, Fisher's fundamental theorem, Fisher-Price-Ewens theorem, Price's theorem, Robertson-Price identity, Robertson's secondary theorem

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- Title Pages
- Dedication
- Preface
- I Introduction
- 1 Changes in Quantitative Traits Over Time
- II Evolution at One and Two Loci
- 2 Neutral Evolution in One- and Two-Locus Systems
- 3 The Genetic Effective Size of a Population
- 4 The Nonadaptive Forces of Evolution
- 5 The Population Genetics of Selection
- 6 Theorems of Natural Selection: Results of Price, Fisher, and Robertson
- 7 Interaction of Selection, Mutation, and Drift
- 8 Hitchhiking and Selective Sweeps
- 9 Using Molecular Data to Detect Selection: Signatures from Recent Single Events
- 10 Using Molecular Data to Detect Selection: Signatures from Multiple Historical Events
- III Drift and Quantitative Traits
- 11 Changes in Genetic Variation Induced by Drift
- 12 The Neutral Divergence of Quantitative Traits
- IV Short-Term Response on a Single Character
- 13 Short-term Changes in the Mean: 1. The Breeder’s Equation
- 14 Short-term Changes in the Mean: 2. Truncation and Threshold Selection
- 15 Short-term Changes in the Mean: 3. Permanent Versus Transient Response
- 16 Short-term Changes in the Variance: 1. Changes in the Additive Variance
- 17 Short-term Changes in the Variance: 2. Changes in the Environmental Variance
- 18 Analysis of Short-term Selection Experiments: 1. Least-squares Approaches
- 19 Analysis of Short-term Selection Experiments: 2. Mixed-model and Bayesian Approaches
- 20 Selection Response in Natural Populations
- V Selection in Structured Populations
- 21 Family-Based Selection
- 22 Associative Effects: Competition, Social Interactions, Group and Kin Selection
- 23 Selection Under Inbreeding
- VI Population-Genetic Models of Trait Response
- 24 The Infinitesimal Model and Its Extensions
- 25 Long-term Response: 1. Deterministic Aspects
- 26 Long-term Response: 2. Finite Population Size and Mutation
- 27 Long-term Response: 3. Adaptive Walks
- 28 Maintenance of Quantitative Genetic Variation
- VII Measuring Selection on Traits
- 29 Individual Fitness and the Measurement of Univariate Selection
- 30 Measuring Multivariate Selection
- Appendix 1 Diffusion Theory
- Appendix 2 Introduction to Bayesian Analysis
- Appendix 3 Markov Chain Monte Carlo and Gibbs Sampling
- Appendix 4 Multiple Comparisons: Bonferroni Corrections, False-discovery Rates, and Meta-analysis
- Appendix 5 The Geometry of Vectors and Matrices: Eigenvalues and Eigenvectors
- Appendix 6 Derivatives of Vectors and Vector-valued Functions
- Literature Cited
- Author Index
- Organism and Trait Index
- Subject Index