The arc of selection on polygenic traits

A very important new preprint, Polygenic adaptation after a sudden change in environment:

Polygenic adaptation in response to selection on quantitative traits is thought to be ubiquitous in humans and other species, yet this mode of adaptation remains poorly understood. We investigate the dynamics of this process, assuming that a sudden change in environment shifts the optimal value of a highly polygenic quantitative trait. We find that when the shift is not too large relative to the genetic variance in the trait and this variance arises from segregating loci with small to moderate effect sizes (defined in terms of the selection acting on them before the shift), the mean phenotype’s approach to the new optimum is well approximated by a rapid exponential process first described by Lande (1976). In contrast, when the shift is larger or large effect loci contribute substantially to genetic variance, the initially rapid approach is succeeded by a much slower one. In either case, the underlying changes to allele frequencies exhibit different behaviors short and long-term. Over the short term, strong directional selection on the trait introduces small differences between the frequencies of minor alleles whose effects are aligned with the shift in optimum versus those with effects in the opposite direction. The phenotypic effects of these differences are dominated by contributions from alleles with moderate and large effects, and cumulatively, these effects push the mean phenotype close to the new optimum. Over the longer term, weak directional selection on the trait can amplify the expected frequency differences between opposite alleles; however, since the mean phenotype is close to the new optimum, alleles are mainly affected by stabilizing selection on the trait. Consequently, the frequency differences between opposite alleles translate into small differences in their probabilities of fixation, and the short-term phenotypic contributions of large effect alleles are largely supplanted by contributions of fixed, moderate ones. This process takes on the order of ~4Ne generations (where Ne is the effective population size), after which the steady state architecture of genetic variation around the new optimum is restored.

There is a lot to take in in this preprint. If you jump to the discussion it frames its importance pretty well. A lot of selection is probably quantitative and polygenic, but a lot of the empirical investigation has been of the sweep of single-locus alleles that rise up to fixation. It strikes me that some of the results here resemble R. A. Fisher’s geometric model of adaptation (The Genetical Theory is the first citation).

I read the whole preprint, but I didn’t double-check the formulae. I have neither the ability or the time. This is where I really which there was a lot of visible post-publication review. I am very interested in the topic under discussion, but it is outside of the purview of my competency, but I know enough that I would probably benefit from extensive comments by others.

This part of the discussion jumped out at me since it echoes my thoughts:

Another implication of our results pertains to the search for the genetic basis of human adaptation, as well as adaptation in other species. Efforts to uncover the identity of individual adaptive genetic changes on the human lineage were guided by the notion that their identity would offer insight into what “made us human”. Under the plausible assumption that many adaptive changes on the human lineage arose from selection on complex, quantitative traits, this approach may not be as informative as it appears (15, 19). Our results indicate that after a shift in the optimal trait value, the number of fixations of alleles whose effects are aligned to the shift are nearly equal to the number of alleles that are opposed (Fig. 6).