- 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 Mean: 2. Truncation and Threshold Selection

# Short-term Changes in the Mean: 2. Truncation and Threshold Selection

- Chapter:
- (p.507) 14 Short-term Changes in the Mean: 2. Truncation and Threshold Selection
- Source:
- Evolution and Selection of Quantitative Traits
- Author(s):
### Bruce Walsh

### Michael Lynch

- Publisher:
- Oxford University Press

The selection intensity, the mean change in a trait within a generation expressed in phenotypic standard deviations, provides an important metric for comparing the strength of selection over designs. Further, under truncation selection (only individuals above some threshold leave offspring), the selection intensity is a function of the fraction saved, and hence the breeder's equation is often expressed in terms of the selection intensity. An important special case of truncation selection is a threshold trait, wherein an individual only expresses a particular phenotype when its underlying liability value exceeds some threshold. This chapter examines selection on such traits, and generalizes this binary-trait setting (with binomial residuals) to other classes of discrete traits, wherein some underling linear model (generating the threshold) is this transformed via a generalized linear mixed model into an observed trait value.

*Keywords:*
generalized linear mixed model, liability, log-linear model, logistic function, logistic regression, probit transformation, threshold trait, truncation selection, selection intensity, zero-inflated Poisson, zero-truncated Poisson

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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