- 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

# Short-term Changes in the Variance: 1. Changes in the Additive Variance

# Short-term Changes in the Variance: 1. Changes in the Additive Variance

- Chapter:
- (p.549) 16 Short-term Changes in the Variance: 1. Changes in the Additive Variance
- Source:
- Evolution and Selection of Quantitative Traits
- Author(s):
### Bruce Walsh

### Michael Lynch

- Publisher:
- Oxford University Press

Selection changes the additive-genetic variance (and hence the response in the mean) by both changing allele frequencies and by generating correlations among alleles at different loci (linkage disequilibrium). Such selection-induced correlations can be generated even between unlinked loci, and (generally) are negative, such that alleles increasing trait values tend to become increasingly negative correlated under direction or stabilizing selection, and positively correlated under disruptive selection. Such changes in the additive-genetic variance from disequilibrium is called the Bulmer effects. For a large number of loci, the amount of change can be predicted from the Bulmer equation, the analog of the breeder's equation, but now for the change in the variance. Upon cessation of selection, any disequilibrium decays away, and the variances revert back to their additive-genic variances (the additive variance in the absence of disequilibrium). Assortative mating also generates such disequilibrium.

*Keywords:*
additive-genic variance, additive-genetic variance, assortative mating, Bulmer effect, Bulmer equation, disruptive selection, drift, inbreeding, infinitesimal model, linkage disequilibrium, Mendelian sampling variance, normalizing selection, segregation variance, stabilizing selection, truncation selection

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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