“Chapter 14. Short-Term Changes in the Mean: 2. Truncation and Threshold Selection [2013 Draft]”, 2013 (; backlinks; similar):
This brief chapter first considers the theory of truncation selection on the mean, which is of general interest, and then examines a number of more specialized topics that may be skipped by the casual reader. Truncation selection (Figure 14.1) occurs when all individuals on one side of a threshold are chosen, and is by far the commonest form of artificial selection in breeding and laboratory experiments. One key result is that for a normally-distributed trait, the selection intensity ī is fully determined by the fraction p saved (Equation 14.3a), provided that the chosen number of adults is large. This allows a breeder or experimentalist to predict the expected response given their choice of p.
The remaining topics are loosely organized around the theme of selection intensity and threshold selection. First, when a small number of adults are chosen to form the next generation, Equation 14.3a overestimates the expected ī, and we discuss how to correct for this small sample effect. This correction is important when only a few individuals form the next generation, but is otherwise relatively minor. The rest of the chapter considers the response in discrete traits. We start with a binary (present/absence) trait, and show how an underlying liability model can be used to predict response. We also examine binary trait response in a logistic regression framework (estimating the probability of showing the trait given some underlying liability scores) and the evolution of both the mean value on the liability scale and the threshold value. We conclude with a few brief comments on response when a trait is better modeled as Poisson, rather than normally, distributed…In addition to being the commonest form of artificial selection, truncation selection is also the most efficient, giving the largest selection intensity of any scheme culling the same fraction of individuals from a population (1978, Crow and 1979).
[Preprint chapter of Evolution and Selection of Quantitative Traits, 2018]