For concreteness, we focus on 2 geographically separated groups of individuals (henceforth “populations”) who derive from a common ancestral group and ignore demographic effects such as those induced by changing population sizes or structure within populations. In practice, the classification of individuals into groups is at the discretion of the researcher and may depart from our assumptions (for example, because the groups subsequently came into contact and intermixed [41]). Even this simplified model suffices to highlight many interpretative challenges, however.

We consider a quantitative trait, whose individual values (Y) are given by the sum of the total genetic effect (G) across all causal sites in the genome, polymorphic or not, and the total environmental effect (E): Y=G+E. (1)

Here, the genetic differences among individuals are due to many independently evolving loci of small effect. We make the standard assumption that alleles are additive at a locus and across loci, thereby ignoring possible dominance or epistatic effects. We do so because an additive model provides a very good fit to existing GWAS data for humans [6,42–44]; because most theory for the evolution of complex traits has been developed for this model (e.g., [19,26,38,45,46]); and most importantly, because, while it is a simplification, the qualitative points that we make do not depend on it.

As is also standard, we assume that within each population, E is Normally distributed and independent of G⁷. For now, we also ignore possible interactions between genetics and environment. We note that the word “environment” has ambiguous uses in evolutionary genetics. Often, it refers to the ecological context that shapes the fitness function (i.e., the relationship between values of Y and fitness). Here, as is common in quantitative genetics, we mean the “environmental effect” on the trait, namely E in Eq 1.

In what follows, we focus on the true genetic effects on the trait and not what can currently be learned about them. We refer to the true, total genetic effect G on a trait as the “polygenic effect” (this quantity is akin to the breeding value in quantitative genetics [9] and to what in other contexts is called the genetic or genotypic value [2,19]). For a given individual, the polygenic effect is constructed by summing the alleles over every site in their genome, weighted by their effects on the trait value. Given this setup, a PGS can be viewed as an estimate of the polygenic effect (shifted by a constant). As noted above, PGS rely on results from GWAS and currently suffer from numerous limitations (e.g., [21,22,26,28]). Unless otherwise stated, however, when we discuss the genetics of trait variation, we do not mean the PGS, but the polygenic effect, assuming knowledge of the exhaustive set of causal loci and their exact effects on the trait.

Regardless of how population differences in polygenic effects arise, their mere existence implies nothing about their relationship to trait differences. Indeed, when both polygenic and environmental effects differ, all bets are off (see, e.g., [29,30,39,74,75,82]): The mean polygenic effect could differ substantially even when the mean trait value does not differ at all (Fig 2, case A). The mean polygenic effect could be higher in population 2 when the mean trait value is lower (Fig 2, case B). Or the differences in polygenic effects and trait values could align (Fig 2, case D). Only when environmental effects on the trait are similar in the 2 populations should we expect mean trait difference to mirror the difference in mean polygenic effect (Fig 2, case C).

Such considerations highlight an important—and at times implicit—assumption made in comparisons of PGS and observed mean trait values across groups with different genetic ancestries: that environmental effects are identical (e.g., [16,83,84]). As noted in these studies, mean differences in PGS among groups often do not track differences in mean trait values: For example, on the basis of the PGS, one would predict that, on average, individuals in 1 group should be shorter than individuals in the other, when in fact they are taller. Importantly, that observation alone is not evidence that PGS are unreliable outside of the ancestry in which they are estimated. There are many reasons to expect that PGS would not port reliably from a GWAS sample to individuals of other genetic ancestries and several lines of empirical evidence that they do not [16,21,22,25,26]. Even if all current limitations of PGS were surmounted, however, a discrepancy between a between-population difference in PGS and corresponding trait may well persist, owing to differences in environmental effects between populations.

Assumptions about environmental effects also matter critically when interpreting evidence for adaptive differences in polygenic effects. Under the standard quantitative genetic assumptions, a shift in the optimum of a trait given a fixed environmental effect has mathematically equivalent implications for selection on the polygenic effect as does shifting the mean environmental effect while keeping the optimum fixed. Thus, an increase in the polygenic effect for a trait such as height could reflect selection for increased height in a fixed nutritional environment or selection for the same optimal height in an environment where nutritional effects on height are suddenly much lower, or the combined effect of the two.

This equivalence between an environmental shift for a fixed optimum and a shift in the trait optimum shines a different light on the interpretation of tests for polygenic selection. Given mounting evidence that many adaptations in human evolution were likely polygenic [6,35,54,55,85–87], there has been a recent push to identify the signature of polygenic adaptation in sets of loci associated with a trait in a GWAS [18–20,32,88–93]. Interpreting the results is extremely tricky, as a number of authors have underscored [19,28–30,40], both because of technical challenges (e.g., residual stratification in GWAS and the poor portability of PGS [21–23,28,84,94,95]) and deeper conceptual issues, such as the problem of selection on correlated traits [6,30,53,62,92,96,97]. Nonetheless, where these methods have identified possible signatures of polygenic selection, they have often been interpreted as pointing to a trait (or a correlated trait) whose optimum value has shifted in response to natural selection in the course of human evolution. An alternative interpretation is that the optimal trait value has remained the same, but environmental effects have shifted [6,19,40,75,90]. Thus, evidence of polygenic adaptation could be reflective of a change of trait optimum, but need not be. Of course, it is also possible that drastic changes in environmental effects are often accompanied by shifts in the optimum trait value.

This interpretative ambiguity is heightened by the fact that traits are inevitably somewhat arbitrary constructs [6,40,48]. Consider body size as 1 example. Bergmann’s rule [98] proposes that in homeotherms, body shape varies across the globe in part in order to optimize heat retention. Under Bergmann’s rule, smaller body size leads to lower ratios of surface area to volume and higher heat retention and is therefore favored in colder climates (e.g., [99–101] and references therein). This selection pressure could be interpreted either as favoring different body sizes in different ecological settings or as maintaining the same heat retention optimum in the face of a changing environmental effect. Another example may be provided by skin pigmentation levels, which mediate UVR penetration into the skin and vary with UVR exposures across the globe. The extent of UVR penetration is thought to be subject to a trade-off that arises from dual effects of UVR on folate degradation and vitamin D synthesis—2 critically important vitamins [58]. Numerous studies have reported evidence for polygenic adaptation at the loci that contribute to variation in skin pigmentation levels, both across the globe and over time (e.g., [102,103]). These signatures of polygenic adaptation are usually viewed as resulting from repeated episodes of directional selection on skin pigmentation in environments with different UVR levels, but could also be seen as arising from selection for a similar degree of UVR penetration in the face of varying UVR levels. In other cases, much less is known about the relationship between the traits and fitness, and the interpretation will be all the more challenging.

That polygenic adaptation can arise both from a shift in the fitness optimum and from stabilizing selection for a fixed optimum in the face of shifting environmental effects further suggests that transient polygenic adaptation may be widespread [6,74,104]. Just how common we should expect such adaptive bouts to be depends, among other factors, on the timescale over which environmental effects change (relative to the timescale of causal allele dynamics) and their degree of autocorrelation across time [53,105], and remains to be investigated. In any case, these considerations raise interesting questions about the proper framing of tests for polygenic adaptation, if indeed polygenic adaptation has been the norm rather than the exception in human evolution.

In discussing how traits are expected to evolve, we have ignored the possibility of gene by environment (GxE) interactions, in which the genetic effects manifest themselves differently in distinct environments. In model organisms, in which environments can be controlled and manipulated, such interactions are ubiquitous (e.g., [2,106,107]). In humans, the same types of experiments obviously cannot be conducted, and statistical approaches to detect GxE have identified few clear-cut cases [25]. If GxE interactions turn out to be prevalent in humans too, they would only amplify the points highlighted in this Essay: (1) that we should expect polygenic effects to differ across groups; and (2) that relating differences in polygenic effects to trait differences requires strong assumptions about the stability of environmental effects.

GxE interactions are more than a complication for the models whose results we have summarized, however. Their existence challenges the validity of the generative models on which we rely to make inferences about complex traits (e.g., heritability estimation [108]). These models envision variation in a trait as arising from strictly genetic effects, independent environmental effects, and in some cases, a specific way in which genetics and environment could interact. For traits such as behaviors, for which genetic effects plausibly arise entirely and inextricably by interaction with environmental effects, it is not obvious to us that this conception is apt—even when a statistical model based on it appears to capture substantial trait variance [29,40,109,110]. If instead it is more sensible to think of such traits as emerging from GxE interactions, polygenic effects will be incommensurable across environments. These considerations are beyond the scope of this Essay, but seem to us worth keeping in mind, especially when these models are relied on, at times implicitly, to interpret differences among people over time and across the globe.