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Evolution and Selection of Quantitative Traits$
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Bruce Walsh and Michael Lynch

Print publication date: 2018

Print ISBN-13: 9780198830870

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198830870.001.0001

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

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

(p.507) 14 Short-term Changes in the Mean: 2. Truncation and Threshold Selection
Evolution and Selection of Quantitative Traits

Bruce Walsh

Michael Lynch

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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