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Cited by 17Genetic Associations and EpidemiologyAnimal Behavior and ReproductionEvolution and Genetic Dynamics

Heritability within groups is uninformative about differences among groups: Cases from behavioral, evolutionary, and statistical genetics

Open access
Schraiber, Joshua G., Edge, Michael D.·2024·Proceedings of the National Academy of Sciences
DOI 10.1073/pnas.2319496121PMC PMC10962975
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Abstract

Without the ability to control or randomize environments (or genotypes), it is difficult to determine the degree to which observed phenotypic differences between two groups of individuals are due to genetic vs. environmental differences. However, some have suggested that these concerns may be limited to pathological cases, and methods have appeared that seem to give—directly or indirectly—some support to claims that aggregate heritable variation within groups can be related to heritable variation among groups. We consider three families of approaches: the “between-group heritability” sometimes invoked in behavior genetics, the statistic P ST used in empirical work in evolutionary quantitative genetics, and methods based on variation in ancestry in an admixed population, used in anthropological and statistical genetics. We take up these examples to show mathematically that information on within-group genetic and phenotypic information in the aggregate cannot separate among-group differences into genetic and environmental components, and we provide simulation results that support our claims. We discuss these results in terms of the long-running debate on this topic.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper generalizes Lewontin’s argument to show that within-group heritability provides no information about between-group heritability, and that even correctly estimated between-group heritability does not reveal the direction of genetic versus environmental contributions to group differences. It extends this critique to PST/QST analyses in evolutionary genetics and to ancestry-based heritability approaches in statistical genetics.

Key findings

  • For two groups, between-group heritability is \(h_B^2 = \delta_G^2 / ((\delta_G+\delta_E)^2)\), where \(\delta_G\) and \(\delta_E\) are mean genetic and environmental differences; this can exceed 1 when genetic and environmental effects point in opposite directions, and approaches infinity when \(\delta_E \approx -\delta_G\).
  • Given the phenotypic difference \(\delta\) and \(h_B^2\), two genetic-effect directions are consistent in the two-group case, \(\delta_G = \pm \delta \sqrt{h_B^2}\); with more than two groups, infinitely many configurations of genetic and environmental deviations are consistent with a given \(h_B^2\).
  • In PST analyses, the correct scaling parameter for \(PST=QST\) is \(c^* = h_B^2 / h_W^2\); because \(h_B^2\) is not bounded by 1, common sensitivity analyses exploring \(c\) between 0 and 1 can be conservative, and PST can be anti-conservative or conservative depending on timing and direction of environmental versus optimum shifts.
  • Local-ancestry heritability estimates depend on a variance component that does not estimate the mean genetic difference between source populations, \(\delta_G = 2\sum_j \beta_j(p_{2j}-p_{1j})\), so they do not resolve the genetic component of between-group differences.

Methods

  • The authors derive quantitative-genetic relationships among within-group heritability \(h_W^2\), between-group heritability \(h_B^2\), variance proportions \(r\) and \(t\), QST, and PST under additive genetic and environmental models.
  • They simulate stabilizing selection with SLiM: initial population of 500 diploid individuals, 1,000,000 positions, mutation rate \(10^{-7}\), recombination rate \(10^{-5}\), Gaussian stabilizing selection, split after 20,000 generations into two populations of 20,000 diploid individuals, then 500 generations post-split with 500 replicates per scenario.
  • They compare QST and PST to genome-wide FST using the Lewontin–Krakauer test, with concordant versus discordant environmental and optimum shifts; both scenarios use an optimum shift of +1, with environment shifts of +4 or −2 and \(h_B^2=9\) at equilibrium.

Limitations

  • The paper states its complications arise under simple additive models and that gene-by-environment interaction makes the situation more complicated; it defers a brief consideration of interaction to the Discussion.
  • It states that environmental control is often impossible, especially for humans and some wild organisms, and that without environmental control the sources of among-group differences remain ambiguous.
  • The text makes evident that the simulation results are specific to the modeled scenarios and parameters, and that local-ancestry heritability can be biased by selection in source populations, with a pathological worst case yielding estimates near 0 when true heritability is 1.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1073/pnas.2319496121

Cites

58 of 58 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

10 of 19 cited sources checked · 4 supported · 1 flagged · accuracy not yet measured

  • Findingreasoning

    The variation due to local ancestry that local-ancestry-based heritability estimation leverages has no clear relationship with between-group trait differences.

    “We show that the variation due to local ancestry that they leverage has no clear relationship with between-group trait differences.”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [15] N. Zaitlen, Leveraging population admixture to characterize the heritability of complex traits. Nat. Genet. 46, 1356– 1362 (2014). 25383972 PMC4244251 source

      The Results (Overview of method) and Online Methods describe how variation in local ancestry is used to estimate heritability. Our copy does not address whether that variation has a clear relationship with between-group trait differences; searches for population-level phenotype differences found no passage settling the claim. Page numbers were not available in the indexed copy. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [16] A. A. Zaidi, Investigating the case of human nose shape and climate adaptation. PLoS Genet. 13, 1– 31 (2017). PMC5354252 28301464 source

      The Results section (“Investigating heritability of nose shape within- and among-populations”; page unavailable) says local-ancestry variation represents genetic variation between populations. It explicitly treats the phenotypic variance explained by local ancestry as conceptually equivalent to the genetic contribution to between-population phenotypic variation, rather than having no clear relationship to it. (LLM, conf=0.87)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.
  • Premisecitation

    When traits evolve neutrally, QST is expected to be equal to FST at putatively neutral sites.

    “When traits evolve neutrally, QST is expected to be equal to FST at putatively neutral sites, which measures the genetic variation among populations (27).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [27] M. C. Whitlock, Neutral additive genetic variance in a metapopulation. Genet. Res. 74, 215– 221 (1999). 10689799 source

      Section 4 states that QST is expected to equal FST for neutral additive quantitative traits and neutral marker loci in the low-mutation limit. The citing sentence omits those conditions: the Conclusions (section 9) explain that dominance can make QST greater or less than FST even for neutral traits. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
  • Premisecitation

    QST is equal to r/(2−r) for diploids.

    “For diploids, in terms of the variance proportion r discussed in the previous section, it is equal to QST=r/(2−r) (26).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [26] M. D. Edge, N. A. Rosenberg, A general model of the relationship between the apportionment of human genetic diversity and the apportionment of human phenotypic diversity. Hum. Biol. 87, 313 (2015). 27737590 PMC8504698 source
  • Interpretationcitation

    The problem of bias in local-ancestry heritability estimates is most pronounced when the trait under consideration has experienced selection in the source populations.

    “This problem is most pronounced when the trait under consideration has experienced selection in the source populations, a scenario that Zaitlen et al. (15) recognized as potentially problematic for their estimator.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [15] N. Zaitlen, Leveraging population admixture to characterize the heritability of complex traits. Nat. Genet. 46, 1356– 1362 (2014). 25383972 PMC4244251 source

      The Discussion recognizes that selection acting on causal variants can bias the estimator, particularly when positive selection in one ancestral group raises their genetic differentiation. The Results sensitivity analysis qualifies this: significant bias from positive selection occurred only at extreme values of both locus differentiation and heritability. Selection in a source population alone is therefore not enough to establish the claim's broader 'most pronounced' characterization. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
  • Interpretationcitation

    It is difficult to interpret QST and PST in the presence of environmental differences between groups.

    “Moreover, we highlight the difficulty of interpreting QST and PST in the presence of environmental differences between groups, adding to recent arguments by Harpak and Przeworski (13).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Harpak and Przeworski [13] A. Harpak, M. Przeworski, The evolution of group differences in changing environments. PLoS Biol. 19, 1– 14 (2021). PMC7861633 33493148 source
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.
  • May combine two claims. 20
  • Classified as probably not a substantial claim. 10

  • May combine two claims.

    Interpretationcitation

    Directional or stabilizing selection in the history of the source populations can lead to upward or downward biases in heritability estimates, respectively.

    “Specifically, directional or stabilizing selection in the history of the source populations can lead to upward or downward biases in heritability estimates, respectively (37).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [37] J. Huang, S. Basu, M. D. Shriver, A. A. Zaidi, Interpreting SNP heritability in admixed populations. bioRxiv (2023). https://www.biorxiv.org/content/10.1101/2023.08.04.551959v1 (Accessed 20 December 2023). PMC12273224 40404285 source

      The Results sections on genetic variance and HE estimation link divergent selection to positive LD and stabilizing selection to negative LD, then report upward and downward bias, respectively, for HE regression. But the Results section on GREML estimation reports the opposite directions in admixed populations with population structure. The claim omits this estimator-dependent qualification; page numbers are unavailable in our copy. (LLM, conf=0.88)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductcitation

    The variance in group means was computed without using Bessel's correction, as shown by Weaver (51) to be the correct formula for Nei's FST (52).

    “We note that we computed the variance in group means without using Bessel’s correction, as shown by Weaver (51) to be the correct formula for Nei’s FST (52).”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [51] T. D. Weaver, Estimators for QST and coalescence times. Ecol. Evol. 6, 7783– 7786 (2016). 30128128 PMC6093160 source
    • cites [52] M. Nei, Analysis of gene diversity in subdivided populations. Proc. Natl. Acad. Sci. U.S.A. 70, 3321– 3323 (1973). 4519626 PMC427228 source

  • May combine two claims.

    Findingreasoning

    Between-group heritability is not bounded between 0 and 1; if environmental and genetic effects point in different directions such that the magnitude of the phenotypic deviation δ=δG+δE is smaller than the magnitude of the genetic deviation δG, then hB2 will be larger than 1.

    “Second, it shows that the between-group heritability is not bounded between 0 and 1: In particular, if the environmental and genetic effects point in different directions, such that the magnitude of the phenotypic deviation, δ=δG+δE is smaller than the magnitude of the genetic deviation, δG, then the between-group heritability will be larger than 1.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: A standard quantitative-genetic model applies.

  • May combine two claims.

    Findingreasoning

    The trajectories of QST are identical regardless of the direction of the environmental shift, in line with the fact that knowledge of QST is not informative of the direction of environmental and genetic shifts.

    “Finally, the trajectories of QST are identical regardless of the direction of the environmental shift, in line with the fact that knowledge of QST is not informative of the direction of environmental and genetic shifts.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In the simulations, early in adaptation, QST rejects the null hypothesis approximately 5% of the time at the 5% significance threshold, showing that the test is well calibrated.

    “Early in adaptation, there should be very little genetic signal of adaptation, and QST rejects the null hypothesis approximately 5% of the time at the 5% significance threshold, showing that the test is well calibrated.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    As adaptation proceeds, QST detects adaptation with high power, although it loses power after approximately 300 generations because the neutral divergence between populations increases substantially.

    “Subsequently, as adaptation proceeds, QST detects adaptation with high power, although it loses power after approximately 300 generations, because the neutral divergence between populations increases substantially.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    For values of c<1, as typically explored in the literature, PST quickly becomes smaller than QST, and tests using PST fail to reject the null hypothesis significantly earlier into adaptation.

    “However, for values of c<1, as typically explored in the literature, PST quickly becomes smaller than QST, and tests using PST fail to reject the null hypothesis significantly earlier into adaptation.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Findingreasoning

    Under a linear gradient between environmental extremes, E(Yi∣θ)=μ1+E1+θ(δG+δE).

    “If we again define the difference between mean environmental effects to be, δE=E2−E1, then hE(θ)=E1+θδE, andE(Yi∣θ)=μ1+E1+θ(δG+δE).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: In the simple global-ancestry example, individuals with θ=0 experience environmental effects with expectation E1, individuals with θ=1 experience environmental effects with expectation E2, and there is a linear gradient between those extremes for individuals of intermediate admixture fraction.

  • May combine two claims.

    Findingreasoning

    Because both QST and PST depend on the variance of between-population means, any evolutionary scenarios that produce identical hB2 will also produce identical QST and PST, indicating that knowledge of PST or QST is not sufficient for disentangling the directions of environmental and genetic effects.

    “Finally, because both QST and PST depend on the variance of between-population means, any evolutionary scenarios that produce identical hB² will also produce identical QST and PST, indicating that knowledge of PST or QST is not sufficient for disentangling the directions of environmental and genetic effects.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.

  • May combine two claims.

    Findingown data

    If the environmental shift is in the same direction as the optimum shift, then the adapting population will have a mean genetic value that is less than that of the population that did not experience an environmental shift; in the opposite scenario, the adapting population will have a mean genetic contribution to the trait that is greater than the population that did not experience a shift.

    “If the environmental shift is in the same direction as the optimum shift (panel C), then the adapting population will have a mean genetic value that is less than that of the population that did not experience an environmental shift; in the other scenario (panel D), the adapting population will have a mean genetic contribution to the trait that is greater than the population that did not experience”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Very different underlying evolutionary forces result in identical hB2 and QST, indicating that these statistics are insufficient for characterizing evolutionary history and may be misleading in some circumstances.

    “In particular, we developed a model in which very different underlying evolutionary forces result in identical hB² and QST, indicating that these statistics are insufficient for characterizing evolutionary history and may be misleading in some circumstances.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.

  • May combine two claims.

    Findingown data

    When the optimum and environment shift in opposite directions, hB2 becomes large when the phenotypic difference between the populations is near 0, and comes back down from infinity to settle at the equilibrium value; it is also much noisier across simulation replicates, with the middle 80% of the distribution spanning three orders of magnitude.

    “However, when the optimum and environment shift in opposite directions, hB² becomes large when the phenotypic difference between the populations is near 0, and comes back down from infinity to settle at the equilibrium value (panel F). It is also much noisier across simulation replicates, as evidenced by the middle 80% of the distribution spanning three orders of magnitude.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    The coefficients for PST are a=hB2, the between-group heritability, and b=hW2, the within-group heritability, so that the correct value of c to obtain PST=QST is c^(∗)=hB2/hW2.

    “In Materials and Methods, we show that the coefficients for PST are a=hB², the between-group heritability, and b=hW², the within-group heritability, so that the correct value of c to obtain PST=QST is[4] c^(∗)=hB²/hW².”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning

    In terms of the variance proportions t and r in DeFries' expression for between-group heritability, QST = r/(2−r).

    “In terms of the variance proportions t and r in DeFries’ expression for between-group heritability, it follows that QST=r/(2−r).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    With the definitions of hB2 and hW2 given, one can recover the relationship between hB2 and hW2 derived by DeFries (10).

    “In SI Appendix, section S1.2, we show that with these definitions, one can recover the relationship between hB² and hW² derived by DeFries (10).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [10] J. C. DeFries, “Quantitative aspects of genetics and environment in the determination of behavior” in Genetics, Environment and Behavior: Implications for Educational Policy (Academic Press, Oxford, England) (1972), p. 324. source
    • The authors state this as an assumption: The linear model of quantitative traits within and between groups assumes no gene-by-environment interactions.
    • The authors state this as an assumption: The phenomena discussed arise under the simplest possible models, in which phenotypes arise via additive influence of genotype and environment.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    In the simulations, hB2≈9 at equilibrium by construction.

    “Fig. 2 E and F show that hB²≈9 at equilibrium by construction.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    Perfect knowledge of within-group heritability provides no information about between-group heritability; between-group heritability is unconstrained by within-group heritability.

    “Perfect knowledge of within-group heritability provides no information about between-group heritability.”
    • Also stated in: § Between-Group Heritability Is Unconstrained by Within-Group Heritability and Underdetermines Genetic and Environmental Differences among Groups · plain
      “Within-group heritabilities, on their own, provide no information about the causes of between-group differences, in part because any configuration of group means for the genetic contributions to the trait is possible under some value of r.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.

  • May combine two claims.

    Findingown data

    When the environment and optimum shift in opposite directions, the behavior of QST remains monotonic, but the behavior of PST for a given c becomes nonmonotonic, reaching a minimum when the phenotypic difference between populations is small and then increasing again.

    “Fig. 3 C and D show that when the environment and optimum shift in opposite directions, the behavior of QST remains monotonic, but the behavior of PST for a given c becomes nonmonotonic, reaching a minimum when the phenotypic difference between populations is small and then increasing again.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    hB2 rapidly approaches infinity when δE≈−δG, and larger genetic deviations result in a larger range of environmental deviations over which hB2>1.

    “One striking feature of the behavior of hB² is that it rapidly approaches infinity when δE≈−δG and that larger genetic deviations result in a larger range of environmental deviations over which hB²>1.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: A standard quantitative-genetic model applies.

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    The linear model of quantitative traits within and between groups is applicable to a trait regardless of genetic architecture, as long as there are no gene-by-environment interactions.

    “This model is applicable to a trait regardless of genetic architecture, as long as there are no gene-by-environment interactions.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The linear model of quantitative traits within and between groups assumes no gene-by-environment interactions.

  • Classified as probably not a substantial claim.

    Premisecitation

    Between-group heritability hB2 is mathematically related to within-group heritability hW2 as hB2≈hW2((1−t)r)/((1−r)t), if groups are large.

    “With some algebra, he showed that the between-group heritability is mathematically related to the within-group heritability, hW². Specifically, defining r and t as in the previous paragraph, he showed that[2] hB²≈hW²((1−t)r)/((1−r)t),”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites DeFries [10] J. C. DeFries, “Quantitative aspects of genetics and environment in the determination of behavior” in Genetics, Environment and Behavior: Implications for Educational Policy (Academic Press, Oxford, England) (1972), p. 324. source
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.
    • The authors state this as an assumption: Groups are large.

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given

    The fact that c can be much larger than 1 is not widely understood, nor is the fact that it can achieve very large values in realistic evolutionary scenarios.

    “However, to our knowledge, the fact that c can be much larger than 1 is not widely understood, nor is the fact that it can achieve very large values in realistic evolutionary scenarios.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Limiting to within-sibship comparisons would remove some confounds of global ancestry proportion, but it would not exclude environmentally mediated phenotypic differences caused by variation in global ancestry.

    “Limiting to within-sibship comparisons would remove some confounds of global ancestry proportion, but it would not exclude environmentally mediated phenotypic differences caused by variation in global ancestry.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The complications pointed out arise under simple additive models, and the situation is only more complicated in models with interactions among genetic or environmental influences.

    “The complications we point out arise under simple additive models, and the situation is only more complicated in models with interactions among genetic or environmental influences.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.

  • May combine two claims.

    Interpretationreasoning

    Even if the between-group heritability were estimable, it is consistent with potentially infinitely many configurations of genetic differences among populations and cannot be used to infer the direction(s) of group differences in genetic contributions to a trait.

    “Moreover, even if the between-group heritability were estimable, it is consistent with potentially infinitely many configurations of genetic differences among populations and cannot be used to infer the direction(s) of group differences in genetic contributions to a trait.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The linear model of quantitative traits within and between groups assumes no gene-by-environment interactions.
    • The authors state this as an assumption: The phenomena discussed arise under the simplest possible models, in which phenotypes arise via additive influence of genotype and environment.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    Heritability estimates based on local ancestry offer the potential to address one of the main issues facing SNP heritability estimates, since segments of local ancestry tag both common and rare variants.

    “Heritability estimates based on local ancestry offer the potential to address one of the main issues facing SNP heritability estimates, since segments of local ancestry tag both common and rare variants.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Because hB2 is unconstrained by any measure of genetic and environmental variability within groups, and because hB2 is not constrained to be between 0 and 1, a sensitivity analysis that explores values of c between 0 and 1 may lead to extremely conservative tests for divergent selection.

    “As shown above, hB² is unconstrained by any measure of genetic and environmental variability within groups. Moreover, because hB² is not constrained to be between 0 and 1, a sensitivity analysis that explores values of c between 0 and 1 may lead to extremely conservative tests for divergent selection.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.
    • The authors state this as an assumption: There is no epistasis or dominance.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given

    To estimate QST requires arduous common-garden experiments that eliminate environmental confounds.

    “However, to estimate QST requires arduous common-garden experiments that eliminate environmental confounds.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    If the environment is not controlled, then the sources of among-group differences become ambiguous, and this ambiguity cannot be resolved by study of within-group variation in aggregate.

    “At the same time, if the environment is not controlled, then the sources of among-group differences become ambiguous, and this ambiguity cannot be resolved by study of within-group variation in aggregate.”
    Quote in the paperSubstantial claim
29 of 29

  • The authors state this as an assumption.

    Phenotype value Y is formed from additive genetic and environmental components, Yi=Gi+Ei for individual i.

    “Consider a phenotype value Y formed from additive genetic and environmental components, i.e., Yi=Gi+Ei for individual i.”

  • The authors state this as an assumption.

    There is no epistasis or dominance.

    “It is standard to define the (narrow-sense) heritability as h²=VA/VP, where the additive genetic variance VA is the variance of the genetic component (Gi), assuming no epistasis or dominance, and VP is the variance of the phenotype.”

  • The authors state this as an assumption.

    Groups are large.

    “Then, when groups are large, the “between-group” heritability is[1] hB²=rVA/tVP.”

  • The authors state this as an assumption.

    A standard quantitative-genetic model applies.

    “Then, under a standard quantitative-genetic model,[3] hB²=δG²/((δG+δE)²).”

  • The authors state this as an assumption.

    In the simple global-ancestry example, individuals with θ=0 experience environmental effects with expectation E1, individuals with θ=1 experience environmental effects with expectation E2, and there is a linear gradient between those extremes for individuals of intermediate admixture fraction.

    “As a simple example, consider a case in which individuals with θ=0 experience environmental effects with expectation E1, individuals with θ=1 experience environmental effects with expectation E2, and there is a linear gradient between those extremes for individuals of intermediate admixture fraction.”

  • The authors state this as an assumption.

    The linear model of quantitative traits within and between groups assumes no gene-by-environment interactions.

    “This model is applicable to a trait regardless of genetic architecture, as long as there are no gene-by-environment interactions.”

  • The authors state this as an assumption.

    The phenomena discussed arise under the simplest possible models, in which phenotypes arise via additive influence of genotype and environment.

    “All of the phenomena we have discussed so far arise under the simplest possible models, in which phenotypes arise via additive influence of genotype and environment.”
7 of 7

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Reference accessed before its dated preprint existed

    Minor

    Reference 42 says it was accessed on 8 August 2023, but its bioRxiv identifier dates the cited version to 18 December 2023.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. D. Falconer T. Mackay Quantitative Genetics (Pearson Prentice-Hall 4th edition 1996).

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Authors
Schraiber, J. G., & Edge, M. D.
Affiliations
University of Southern California (US)
Corresponding author
Edge, Michael D.
ORCID
Venue
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences
Published
2024-03-12
Volume
121
Issue
12
Pages
e2319496121-e2319496121
ISSN
  • 0027-8424 (ISSN-L)
  • 1091-6490
DOI
10.1073/pnas.2319496121
PMC
PMC10962975
OpenAlex
W4392696419
Cited by
17
References
56
Citations by year
2026: 4 · 2025: 6 · 2024: 6 · 2023: 1
FWCI
4.25
Type
journal article
Language
en
Open access
Licence
Locations
  • Proceedings of the National Academy of Sciences (publishedVersion, cc-by-nc-nd)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
  • PubMed Central (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • PubMed Central (submittedVersion, cc-by-nc-nd)
Funders
HHS | NIH | National Institute of General Medical Sciences (R35GM137758)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
  • Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Animal Behavior and Reproduction
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
Keywords
heritability, behavioral genetics, admixture, statistical genetics

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-29.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-29.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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