On the other hand, ignoring overlapping data will inflate the type I error. Unlike the splitting method that requires individual-level genotype and phenotype data, our proposed method for testing gene-environment interaction handles the issue of overlapping data effectively and statistically efficiently at the meta-analysis level.Meta-analysis, which combines the results of multiple studies, is an important analytical method in genome-wide association studies. In genome-wide association studies practice, studies employing meta-analysis may have overlapping data, which could yield false positive results. Recent studies have proposed models to handle the issue of overlapping data when testing the genetic main effect of single nucleotide polymorphism. However, there is still no meta-analysis method for testing gene-environment interaction when overlapping data exist. Inspired by the methods of testing the main effect of gene with overlapping data, we proposed an overlapping meta-regulation method to address the issue in testing the gene-environment interaction. We generalized the covariance matrices of the regular meta-regression model by employing Lin’s and Han’s correlation structures to incorporate the correlations introduced by the overlapping data. Based on our proposed models, we further provided statistical significance tests of the gene-environment interaction as well as joint effects of the gene main effect and the interaction. Through simulations, we examined type I errors and statistical powers of our proposed methods at different levels of data overlap among studies. We demonstrated that our method well controls the type I error and simultaneously achieves statistical power comparable with the method that removes overlapping samples  Numerous associations between human traits or diseases and single nucleotide polymorphisms (SNPs) have been identified by genome-wide association studies (GWAS) . Meta-anMany meta-analysis methods are used in GWAS . The fixHowever, in GWAS practice, overlapping data between studies may occur. This may be caused inadvertently or intentionally by researchers. Spurious association may be achieved if overlapping data exist and are ignored in the meta-analysis . RecentlMeta-regression (MR)  is an efMany complex diseases or traits are owing to the combination of effects of genetic factors, environment factors, and gene-environment interactions and involve in complex regulatory networks . ConsideResults section, we simulate numerical examples and use them to examine the type I error and power of our method and the splitting method. We also show that the type I error is inflated with regular MR without considering overlapping samples. In the discussion and conclusion sections, we discuss the results and conclude the paper.In this paper, inspired by Lin’s method  and Han’Based on Lin’s and Han’s correlation structures , we geneBefore the MR analysis, individuals in each study are first stratified into several groups according to their environmental measurements. The main effects of SNP at the group level can be estimated via linear regression as follows:Y is a quantitative phenotype, G is the code of the SNP, and E is the environmental measurement.where i-th study and the j-th group where i= 1,2,…,n, j=1,2,…,in, The symbol n is the number of studies and in denotes the number of groups in the i-th study, and j-th group of the i-th study. The mean environmental measurement in the j-th group of the i-th study is ijE. α is the regression coefficient vector of interest. The symbol X is the interest matrix and iX is the interest matrix for the i-th study. ε is the standard error matrix and the iε is the standard error matrix for i-th study. In MR, the SNP effect is regressed on the environmental factor as follows:Assume that whereand α and Cov(α) are estimated by  can be specified as any nonlinear function of the environmental variable as necessary. For example, to test quadratic SNP-environment interaction, the model can be formulated aswhere2 distribution when testing the two interaction effects simultaneously. The Wald statistic follows a 3 df χ2 distribution for testing the SNP main and interactions jointly , the Wald statistic for the test of SNP-environment interaction and quadratic SNP-environment interaction follows a 2 df χC is an identity matrix, and the two covariance matrices becomeAs can be seen, our models are generalized versions of the regular MR. When the data of studies are independent, correlation matrix andIn this case, the covariance matrix is identical to that of the regular MR.We evaluated the type I error to ensure that the false positive rate is appropriately controlled by our proposed OMR method when overlapping data exist, that is, whether the empirical type I error rate is close to the specified level. We compared our method with the splitting method and regular MR method, which did not consider overlapping data. The power was then compared at different levels of sample overlap. We considered two scenarios where there were 100 and 400 overlapping subjects between every two studies.Y was simulated as being related to G and E, which were the genotypes of the SNP and environment variables, respectively. The simulation model representing this relationship is given as follows:The quantitative phenotype G was the code of SNP, which was the number of minor alleles. We generated random numbers by the runif function in R, then the values of G are determined by which intervals the random numbers fall into, and the intervals are determined by genotype frequency. Variable E was normally distributed, E~N. 10% of the variation in Y was explained by EEβ. The fixed effects Gβ and βG×E varied in our simulated datasets. The random error ε was normally distributed with zero mean and its variance was chosen such that phenotypic variance is unit. The environment variable and error term were generated by the rnorm function in R. In all our numerical experiments, we considered meta-analyses of data from 2, 3, 4, 5, and 6 studies, each of which had 1,000 unrelated individuals. In each study, we simulated three variables: the phenotype Y, environmental E, and genotype SNP. Across studies, there were 100 or 400 overlapping samples between any two studies. Under each simulation setup, data were generated with 1,000 replicates.Here, the SNP was assumed to have an additive genetic effect; the minor allele frequency was 0.3, and E, before meta-analyses. In each group, we applied linear regression to estimate the main effects Gβ, its corresponding error ε, and the mean environment variable E. Meta-analysis were performed with 2, 3, 4, 5, and 6 studies.We divided 1,000 unrelated individuals in each study into five groups according to the distribution of To obtain the type I error of the interaction test, the effect of the SNP-environment interaction was set to be zero and the SNP main effect explained 0.5% variance of the trait variance. The empirical type I error of our method was calculated by transforming the covariance matrix with overlapping data into a diagonal matrix and then using regular MR. Under this simulation, the test of empirical type I error of our method followed a 1 df distribution. The empirical type I error of the splitting method with two studies was estimated by removing 100 or 400 overlapping subjects of study 1, and the data in study 2 were left unchanged. The empirical type I error of the splitting data method with 3, 4, 5, and 6 studies was estimated by discarding 100 or 400 overlapped subjects from each study. 2distribution. To calculate the type I error rates of the joint test of the SNP main effect and the interaction, we set both the SNP and the SNP-environment interaction effects to be zeros. The Wald test statistics followed a 2 df χIn real meta-analysis, sample sizes of studies vary and percentages of overlapping may be different for studies. Here, we set the sample sizes of the 6 studies as . Let the effect of the SNP-environment interaction to be zero and the SNP main effect explained 0.5% of trait variance. Type I errors of testing the SNP-environment interaction are shown in 2 distribution. To compare the statistical power of testing the SNP-environment interaction, both SNP-environment and SNP effects explained 0.5% variance of the trait variance. In this simulation, statistical significance was determined by the P values of the tests, which were smaller than 0.05. The empirical power was obtained by calculating the proportion of the significant results in 1,000 replicates. The P values were calculated using the Wald test (9), which followed a 1 df χ2 distribution. In the joint test of the SNP main effect and the SNP-environment interaction effect, both SNP-environment and SNP effects explained 0.5% variance of the trait variance. In this simulation, the P values were again calculated using the Wald test (10) following a 2 df χFor studies with unequal sample sizes , power of testing the SNP-environment interaction and power of the joint test for the SNP and the interaction are presented in In GWAS, it is a common phenomenon that effects of the SNP and SNP-environment interaction may have different directions. Here, we consider the scenario that both the SNP and the interaction explained 0.5% variance of the trait variance but the directions of their effects are opposite. As in the previous example, we tested the SNP-environment interaction as well as joint effects of the SNP and the interaction. Finally, we added simulation for nonlinear SNP-environment interaction when testing the effect of SNP-environment interaction and the joint effects of SNP and SNP-environment. Both the effect of SNP and the effect of SNP-environment interaction explained 0.5% variance of the trait variance, the effect of nonlinear SNP-environment interaction explained 0.05% variance of the trait variance. We compared the model considering nonlinear SNP-environment as in . with thE nonlinearly in real biological process. In this case, regressing the main effect of SNP on E linearly involved model mis-specification. On the other hand, such linear regression can hopefully capture a portion of the main effect. In this case, we can employ Hermite polynomials to the nonlinear interaction model to avoid this phenomenon (SNP may indeed interact with enomenon .The sample sizes of studies vary in real meta-analysis. As explained in the reference , there aWhen testing the SNP main effect, the splitting method for case-control studies was reported to yield a lower power than Lin’s method, which is because the studies share common controls . SplittiOur method is based on the MR in which one divides the studies into several groups according to the environmental variable. Thus, when calculating the correlation matrix, we must consider both the number of overlapping data among studies and the number of overlapping data among groups. When the overlaps among groups are unavailable and the data overlap is independent of the environment variable, the overlaps between two groups can be estimated by the overlaps between their studies and the sample proportions of the groups in the two studies. In either case, our method does not require individual-level data as the splitting method does.To the best of our knowledge, there is still no meta-analysis method for testing SNP-environment interaction with overlapping data among studies. Our OMR method was generalized from regular MR. When evaluating our proposed OMR method, we compared our method with the splitting method and regular MR. In this paper, we generalized the regular MR model to OMR by incorporating correlations among studies due to the overlapping data. We proposed a test for the SNP-environment interaction as well as a joint test for the SNP and the interaction under the OMR framework. The two test were compared with the splitting method in terms of their type I error rate and statistical power. Through simulation, we demonstrated that our method yielded comparative power with respect to the splitting method and the type I error rate of the regular MR is inflated when overlapping data are ignored. We also evaluated our OMR method with unequal sample sizes among studies, opposite directions of the SNP effect and the interaction effect, and assessed the robustness of our method when nonlinear interaction effect exists. Our method does not require individual-level genotype and phenotype data, which overcomes the major limitation of the splitting method. In GWAS practice, our OMR method can be used to control false positive results when the studies with overlapping individuals are included in the meta-analysis, thus improve the probability of finding genuine associations.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation, to any qualified researcher. QJ: conceived the concept, designed and conducted the simulation studies, and drafted the manuscript. GS: conceived the concept, supervised the work, and reviewed and revised the manuscript.This work was supported by the National Thousand Youth Talents Plan.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Quercus robur L.) trees from ten provenances with known family structure. We aimed at disentangling adaptive and plastic responses for growth (height and diameter at breast height) as well as for leaf and wood functional traits related to adaptation to dry environments. We used restricted maximum likelihood approaches to assess additive genetic variation expressed as narrow‐sense heritability (h2), quantitative trait differentiation among provenances (QST), and genotype‐by‐environment interactions (GxE). We found strong and significant patterns of local adaptation in growth in all three common gardens, suggesting that transfer of seed material should not exceed a climatic distance of approximately 1°C under current climatic conditions, while transfer along precipitation gradients seems to be less stringent. Moreover, heritability reached 0.64 for tree height and 0.67 for dbh at the dry margin of the testing spectrum, suggesting significant additive genetic variation of potential use for future selection and tree breeding. GxE interactions in growth were significant and explained less phenotypic variation than origin of seed source (4% versus 10%). Functional trait variation among provenances was partly related to drought regimes at provenances origins but had moderate explanatory power for growth. We conclude that directional selection, either naturally or through breeding, is the most likely and feasible outcome for pedunculate oak to adapt to warmer and drier climate conditions in the future.Understanding how tree species will respond to a future climate requires reliable and quantitative estimates of intra‐specific variation under current climate conditions. We studied three 10‐year‐old common garden experiments established across a rainfall and drought gradient planted with nearly 10,000 pedunculate oak ( The downscaled climate data were validated with observation data from the E‐obs dataset  and height after 10 years were measured in winter 2017/18 for all living trees by using a diameter measuring tape and a Vertex hypsometer , respectively. We additionally assessed leaf and wood functional traits that have been found to be involved in drought adaptation  to represent the much larger earlywood vessels of oak, vessel lumen fraction , and theoretical hydraulic conductivity (Kh), calculated based on the Hagen–Poiseuille law  × VD × Dh4, where ρw is the density of water (998.2 kg/m3 at 20°), η the viscosity of water (1.002 × 10−3 Pa s at 20°C), VD vessel density (vessels m−2), and Dh = (Σ D4/n)/4, where D is the average of minor and major axes of the diameter of each individual vessels and n the number of measured vessels.For wood samples, 30‐μm transverse sections were first cut with a rotary microtome , stained (safranin/ astrablue), and embedded in Euparal . Digital images with pixel size of 1.157 µm were taken with a DM5500B transmission light microscope . Vessels of the outer three growth rings (representing years 2015–2017) were marked manually in Adobe Photoshop CS6  and measured automatically with ImageJ  was calculated as leaf dry mass/leaf area and leaf dry matter content  as dry weight/ saturation weight. Subsamples of all ten leaves per branch (9 mm disk) were collected for stable carbon isotope analysis, a proxy for photosynthetic water‐use efficiency integrated over the growth and expansion of the leaf . Stomata were automatically identified using StomataCounter . For vein density, a leaf punch of 1.58 cm was taken from the same leaf and stored in a paraformaldehyde–glutaraldehyde fixative solution until analysis. Leaf punches were then prepared following Pérez‐Harguindeguy et al.  and mean annual precipitation (MAP), respectively . Both climatic variables (MAT and MAP) had been shown to explain a considerable amount of variation in tree growth in earlier studies  and distance between trial site climate and provenance climate following the quadratic regression model equation2.4.2ST, a measure of quantitative genetic differentiation that estimates the proportion of genetic variation in a trait among populations relative to the total amount of variation , but calculated only QST and its 95% confidence intervals without comparing QST to FST, since no neutral diploid markers were available in this study. QST was determined across all sites as well as separately for each site.We estimated whether provenances or climatic clusters are genetically differentiated in their growth (height and dbh) by applying Q Wright,  but takeWhitlock , which i2.4.32) across and within provenances from a mixed model of the form: 2site, n=3330) and 2prov, n = 330) with β being a vector of fixed effects (intercept), and p, b, and a random vectors of provenance (climatic cluster), block, and additive genetic effects, respectively. X and Z are incidence matrices assigning fixed and random effects to phenotypic observations in vector Y. Provenance (or climatic cluster) and block effects follow x ~ N with σp,b2 being the Provenance (Cluster), or block variance, respectively. Individual‐tree additive genetic effects follow a ~ N where σa2 is the additive variance and A the relationship matrix derived from a half‐sib family structure of open‐pollinated mother trees. In this model, we assumed that none of the progenies were full‐siblings, since previous studies have shown that the proportion of full‐siblings in wind‐pollinated trees sampled in forest stands is usually very small and has only little influence on the estimated additive genetic variance  which uses a restricted maximum likelihood (REML)‐based variance estimator procedure allowing to infer random genetic effects at individual level. We used the average information matrix (function ai), which simulates standard errors from the asymptotic Gaussian joint sampling distribution, to estimate mean and standard errors of variance components. We considered the heritability estimate to be significant, when the lower bound of the 95% confidence interval for heritability was greater than 0.We estimated additive genetic effects in growth traits by calculating the narrow‐sense heritability ), belonging to the kth mother tree nested within provenance j (Mk(Pj), originating from provenance j (Pj) and growing in the ith trial site (Si). eijklm is a random error term, and SiPj and SiMk(Pj) are the crossed genotype × environment interaction terms separated for provenance‐by‐site and family‐by‐site interactions, respectively. Variance components were expressed as ratios relative to the total phenotypic variation as a percentage of variance explained by the single equation terms, and for this purpose only, all terms were treated as random effects in the model following x ~ N with × being the single predictors, respectively. In order to test whether variation in plasticity was uniform among families, we used BLUPs (best linear unbiased predictions) for the GxE family‐interaction term as predicted by the model in equation (6) and calculated the ecovalence  according to Wricke  divided by the total sum of squares across all families, where higher values indicate more plastic genotypes. We used an arbitrary threshold of 0.05 to define extraordinarily plastic genotypes and assigned extraordinary families to provenances in order to see whether they occur more frequently in some environments compared to others. Since our design does not explicitly allow for testing whether plasticity is heritable and therefore adaptive, we used this information just as a broad surrogate.To test for variation in phenotypic plasticity  and to estimate its contribution to overall phenotypic variation, we formulated a mixed model as follows for height and dbh:o Wricke  as follo2.4.5lme4 package in R. Given the limited number of trees that could be measured for functional traits, we decided to capture trait variation at the provenance level rather than at the family level by sampling a larger number of mother trees within provenances and test sites but not to replicate mother trees within site. We used Pearson‐moment correlation and correlated functional and growth traits at the individual‐tree level  as well as at the provenance level  to test whether functional traits can be used to select more vigorous or resilient trees. Finally, we calculated the summer heat:moisture index (SHM), an index used to describe the long‐term drought regime in seed zones , we used an ANOVA  approach and treated site, provenance, and provenance‐by‐site as main effects and family as random effect in a linear mixed‐effect model using the 33.1Using principal component analysis, provenances were assigned to five climatic clusters Figure , with thSurvival rate after 10 years was 94% , and mortality did not significantly differ between sites nor between provenances. As expected, mean height and dbh after 10 years were higher at the moist site  and lower at the intermediate  and dry sites .3.2ST was significantly different from zero for growth and higher for height growth  than for dbh . Congruently with the results from the temperature distance model above, mean QST was higher in the intermediate and dry sites  and significantly lower at the moist site  and remained also significant within most provenances within sites (h2prov) despite the much lower sample size  compared to the intermediate site , but did not significantly differ between the dry and moist sites nor between the intermediate and moist sites  were significant for height and dbh, but explained only a minor proportion of the overall variance when compared to the remaining terms Table . As suchThere were no differences depending on whether provenance or climatic cluster was used as covariate. In comparison, site alone explained approximately 22% of the phenotypic variation for height and 16% for dbh, while provenance explained 9% of the variation for height and 3% for dbh Table . Ecovale3.5p < .001 for SLA, LDMC, Leaf vein density, and δC13; p < .01 for vessel area fraction), but also significantly among provenances . Significant provenance‐by‐site interactions appeared only in δC13 (p < .05). Relative variance proportions explained by the three predictors are presented in Figure Functional traits varied significantly among sites . At the dry site, however, no significant relationship between seed source climate and functional trait variation was observed  and functional traits at provenance level varied strongly among sites: Provenances from drier regions had significantly lower leaf vein density (at the intermediate site), a higher mean vessel area (moist site), higher hydraulic conductivity (intermediate site), and a higher vessel area fraction (intermediate site). A trend in more negative δCd Figure .max (r = 0.358). For both trait combinations, correlation coefficients were highest at the intermediate site and lower at dry and moist sites when calculated site‐wise , but only moderate evidence for relations between functional traits and growth traits. Among those, tree height was strongest negatively related to leaf dry matter content with r = −0.35. Dbh was strongly correlated to VAe Figure .4ST, can be seen as indicators of local adaptation to home temperature regimes , which found analog patterns of maladaptation with increasing climatic distance from the provenances' source climate . Our data did not permit to compare QST to an estimate of historic gene flow among populations (such as FST) in order to control for effects of neutral genetic drift, as suggested by Gilbert & Whitlock  are similar to that for 6‐year height at a regional spatial scale for Q. petraea  is a measure that quantifies whether or not populations are able to adapt to environmental pressures via directional selection . Plasticity was largely uniform among families and provenances, and ecovalence was generally low Figure . Ahrens 4.3Quercus oleoides. Leaf stable carbon isotope ratio (δ13C), as a proxy for water‐use efficiency, was by trend more negative in provenances that originated from drier regions, suggesting that these provenances experienced less drought stress in the intermediate and moist sites. Overall, our results are in concordance with findings of other studies on closely related oak species which found moderate to strong differentiation among provenances for leaf and wood functional traits  in growth is stronger than plastic responses (GxE). Although plastic responses have been intensively discussed as a potential evolutionary strategy for trees to avoid mismatches between biological requirements and environmental change (e.g., Corcuera, Cochard, Gil‐Pelegrin, & Notivol, Quercus robur distribution. Consequently, the evidence suggests that directional selection within populations will likely determine the future trajectory of Quercus robur under climate change. This has several implications for future adaptive forest management, since the high heritability in growth observed in the dry testing site (see Figure Our analysis of intra‐specific variation in this important tree species suggests that adaptive variation (hNone declared.Fig S1Click here for additional data file.Figs S2–S9Click here for additional data file.Table S1Click here for additional data file.


Genome-wide association studies (GWAS) is one of the most popular methods of studying the genetic control of traits. This methodology has been intensely performed on inbred genotypes to identify causal variants. Nonetheless, the lack of covariance between the phenotype of inbred lines and their offspring in cross-pollinated species (such as maize) raises questions on the applicability of these findings in a hybrid breeding context. To address this topic, we incorporated previously reported parental lines GWAS information into the prediction of a low heritability trait in hybrids. This was done by marker-assisted selection based on significant markers identified in the lines and by genomic prediction having these markers as fixed effects. Additive-dominance GWAS of hybrids, a non-conventional procedure, was also performed for comparison purposes. Our results suggest that incorporating information from parental inbred lines GWAS led to decreases in the predictive ability of hybrids. Correspondingly, inbred lines and hybrids-based GWAS yielded different results. These findings do not invalidate GWAS on inbred lines for selection purposes, but mean that it may not be directly useful for hybrid breeding. Marker Assisted Selection  is a coOver the last decades, a realm of GP methods have been suggested for predicting agronomically relevant traits . Bayesiaa priori assumptions regarding the variance and effect of genomic markers. Then, it is inferable that studying the genetic control of traits, in addition to be a crucial breeding practice, may lead to insights regarding the idealization and employment of GP methods.Simulations and empirical studies have shown that the ability of GP to associate phenotypic patterns to genomic variations is intrinsically related to the genetic architecture of traits ,11,12. HOne of the most popular methods of studying the genetic control is by genome-wide association studies (GWAS). GWAS has been extensively applied to maize populations for important agronomical traits such as foliar architecture , seed oiThe concept of GWAS is centered at the possibility of using a wide range of populations, with few restrictions regarding the genetic structure of genotypes being utilized. In maize, some GWAS are reported in non-inbred populations , but moHence, markers identified by GWAS can be utilized for MAS or in a MAS + GP combination. Thus, efforts have been employed in the use of GWAS-found markers for whole genomic prediction of the same  and diffTo verify the usefulness of inbred line GWAS in hybrid maize breeding, we selected the case study of Low Nitrogen Tolerance Index (LNTI), a critical, lowly heritable trait. Inbred line GWAS on this trait has been reported by Morosini et al. . The gen-1) and low N ], at two sites [Piracicaba-São Paulo  and Anhembi-São Paulo ], during two years (second growing seasons of 2016 and 2017). The single-crosses (738 in 2016 and 789 in 2017) were phenotyped for grain yield  which was estimated based on the plot production (7 m row) corrected for 13% moisture. Treatments were arranged in augmented block schemes . Each incomplete block was composed of 16 regular treatments and two checks.Field trials were carried out in two nitrogen (N) regimes , , [Ms as in . Models Ms as in  of R. MCMs as in .Pearson’s product-moment correlations of GEBV across all iterations represented the predictive ability of the method.The GEBVs of the test population of hybrids (25%) were predicted by LN, or GYLN values of hybrids; X is the incidence matrix for S is the additive , dominance  or addivive + dominance (SASD) genomic incidence matrix associated to fixed marker effect m; T is the incidence matrix of hybrids related to the vector of polygenic genetic effects with p and q are the allelic frequencies for the jth marker (j = 1…m) as in [ε refers to the vector of residuals having p-values of the markers were tested against a threshold estimated by permutation with 400 repetitions to determine significance. The association analyses were performed using the adapted functions of the Sommer package in R [p and q are the allelic frequencies and α is the allelic substitution effect (ASE), a is the additive effect and d is the dominance deviation of the significant SNP. The regression coefficient obtained by the GWAS regression depends on the type of the modeled effects, and conclusions should be drawn accordingly.For further comparisons, GWAS was performed on the hybrids, including a dominance effect, considering the single-marker regression following the model:m) as in ; ε referage in R . Additio−1, with mean 6.50 Mg ha−1. Under IN the means were higher, varying from 4.24 Mg ha−1 to 9.62 Mg ha−1, averaging 7.37 Mg ha−1. The LNTI, estimated from the mentioned GY means, ranged from -14.54 to 30.78% with mean 11.65% . Additionally, the heritability was 0.25 at plot and 0.57 at entry-mean levels. Under the statistical evidence of nitrogen application effect on yield, the phenotypic analysis was performed in each regime. The heritabilities at the plot level were 0.25 and 0.19 for trials under low and normal nitrogen conditions, respectively. At the entry mean level, it was 0.55 for LN and 0.49 for IN. The adjusted GY values under LN ranged from 3.23 to 8.54 Mg han 11.65% . Two genLow magnitude differences between methods regarding genetic and residual variances were found . Nonethet-test. Furthermore, the results indicate that integrating GP and MAS (MAS|GBLUP and MAS|RKHS) under the studied scenario did not lead to any prediction improvements.Low prediction ability (PA) values for LNTI were found . Values GA, GD or GAD) and the number of principal components for controlling population structure . Using a single principal component led to the best adjustments, and only analyses with the best QQ plots were reported , 2 , 3 , 7 , and 9 .LN and GYIN were also reported  varied from 0.0017 to 0.0645 for LNTI and from 0.0018 to 0.0099 for GY. It is essential to notice that some regression coefficients could be overestimated.Absolute values of regression coefficient ranged from 1.6 to 11.38 for LNTI. For GY, values were from 0.69 to 1.69. The heritability of the markers (HBernardo  introducα) of a given gene depends on the allele frequencies (p and q) and genotypic values (a and d), since α = a+d(q−p) [α of any marker in inbred lines would be represented by α = a, since d = 0. On the other hand, the phenotype of hybrids is believed to be consistently driven by dominance effects (high d) due to the expression of high-level heterosis in the species.Our results suggest that there is no advantage in modeling markers identified in parental lines as fixed effects for the prediction of hybrids in both MAS and MAS + GP scenarios. It might be due to the lack of connection between the genotype-phenotype relationship of parental inbred lines and hybrids given the changes in the allele substitution effect. Allele substitution effect (a+d(q−p) . Despiteper se information has been reported not to be effective for polygenic traits due to the masking of non-additive effects and genotype by environment interactions [After all, predicting traits based on information extracted from the parental inbred lines ractions –38. By aractions , our resractions ). That mAlthough there is strong evidence that carrying out GWAS on hybrids seems a better fit in a breeding context, some factors may hamper the direct use of GWAS in the conventional pipeline. First, it conceptually requires diverse germplasm for maximizing the quality of results. It might not be achieved in breeding populations, which commonly fixed for the majority of favorable alleles (elite germplasm). In Simulations have shown which scenarios are favorable for utilizing GWAS-significant markers/major genes in GP ,11. Our Modeling dominance effect in GP of maize hybrids is a recurrent practice that generally yields favorable results ,39. Howeβ; allele substitution effects/additive effect/dominance deviations). These markers had in common a low MAF (<0.10), which might be leading to these results as well as other factors such as the Beavis effect [GWAS suggested eleven significant marker-trait associations, eight for LNTI and three for GY under two N fertilization regimes. The annotations revealed that seven out of nine markers were flanked by putative genes. However, some associations presented unrealistic (overestimated) regression coefficients , presented the lowest regression coefficients for LNTI, which are consistent with the expected genetic architecture of the trait. Additionally, HThe putative genes found in the inbred lines were associated with transcription regulation, DNA repair, lipid biosynthesis, and GMP Synthetase. There was no direct correspondence among the putative genes found in hybrids compared to the ones identified in the lines panel . NeverthRegarding the GWAS in maize hybrids, the putative genes are mostly related to the expression of chloroplast genes; cell elongation and plant development; catalytic function of protein kinases, which operates as an on/off switch for many cellular processes, including physiological ones; cellular response to heat, and cytokinin biosynthesis. Therefore, due to the traits evaluated, all these processes are very likely related to the amount of nitrogen available to the plant.2), LNTI can be improved by increasing the frequency of favorable alleles of additive genes in all groups or; increasing the frequency of each allele in the respective groups for genes expressing dominance effects. Morosini et al. [The GWAS results suggest the presence of both additive and dominance effects controlling LNTI in maize hybrids . The brei et al.  reportedi et al. ,31 make After all, the purpose of this work is not convincing that GWAS should only be performed in hybrids. Regardless, our results show that, under situations similar to the one here exposed, GWAS performed in hybrids and lines lead to contrasting results, meaning that inbred-line GWAS might not be directly used for breeding. Nevertheless, it is still relevant as a tool for understanding the physiological base of traits and should not be neglected.S1 FigThe distribution of minor allele frequency (left) and heterozygosity (right) on the utilized population of maize hybrids.(DOCX)Click here for additional data file.S2 FigDensity plot of grain yield under two nitrogen application regimes (top) and low nitrogen tolerance index (LNTI) of 904 maize hybrids (bottom).(DOCX)Click here for additional data file.S3 Fig(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.


The increasing predictive power of polygenic scores for education has led to their promotion by some as a potential tool for genetically informed policy. How accurately polygenic scores predict an individual pupil's educational performance conditional on other phenotypic data is however not well understood. Using data from a UK cohort study with data linkage to national schooling records, we investigated how accurately polygenic scores for education predicted pupils’ test score achievement. We also assessed the performance of polygenic scores over and above phenotypic data that are available to schools. Across our sample, there was high overlap between the polygenic score and achievement distributions, leading to poor predictive accuracy at the individual level. Prediction of educational outcomes from polygenic scores were inferior to those from parental socioeconomic factors. Conditional on prior achievement, polygenic scores failed to accurately predict later achievement. Our results suggest that while polygenic scores can be informative for identifying group level differences, they currently have limited use for accurately predicting individual educational performance or for personalised education. The way that people learn in school and other educational settings differs from person to person for a wide range of reasons. Over the past 15 years there has been a shift in the way that children are taught in the UK and some other countries. Education has become more focused on the students as individuals, recognising that different people learn in different ways and at different speeds. This has led to the idea of ‘personalised education’, a way of tailoring students’ learning to suit their individual needs and differences.One way that individuals differ is in the genetic material they inherit from their parents. Except for identical twins, no two people have completely identical genomes. It is now easier and cheaper to study the genetic material of individuals than ever before. This has led to a lot of research investigating how our DNA relates to our health, education and other aspects of life.Some researchers and politicians are now suggesting that individuals’ genetic data should be routinely collected by organisations so that their education or health care can be personalised. However, it remains unclear whether this genetic personalisation would be more useful than demographic or socioeconomic data – such as sex, age and family background – that is already available.To investigate whether an individual’s DNA could be used to predict how well they will perform in school, Morris et al. combined genetic data and school test results from a group of 3,500 UK children born in the early 1990s. This revealed that the genetic data did not predict how the children would perform throughout their time at school as accurately as more general information about their family background and other socioeconomic factors.The findings of Morris et al. suggest that knowledge of students’ DNA is unlikely to help educators who want to identify individuals who need extra help or will be at the top of the class. More research is needed on larger groups of children from a broader range of backgrounds, but it is unclear whether a student's DNA will ever be useful for tailoring their education. Currently, it appears that DNA would be less useful for personalising education than easily measured information like test results taken in primary school, education of the child's parents and other social data. The increase in genetic discoveries from large-scale genomewide association studies (GWAS) has greatly advanced scientific understanding of the way in which complex social and health outcomes may arise. GWAS with sample sizes of over one million participants have identified hundreds of genetic variants  that associate with educational attainment and other social phenotypes . While idownstream of genotype; for example, pupil’s selecting certain subjects based on their genotype. Passive gene-environment correlation can be thought of as environment upstream of genotype; for example, children of highly educated parents being more likely to inherit education associated environments as well as education associated genes , to investigate the potential value of genotypic data for predicting pupil achievement and personalising education. We answer three related questions: 1) How predictive of realised educational achievement are polygenic scores? 2) Does polygenic prediction outperform phenotypic prediction from family background measures available to schools? 3) What incremental increase in predictive performance do polygenic scores offer over and above phenotypic information?−8) and the second used all education associated SNPs. Our measure of educational achievement was fine graded point scores from educational exams taken at ages 7 and 16, obtained through data linkage to national school records. The all SNP polygenic score was more strongly correlated with educational achievement  . Childre2) in achievement than age and sex alone. Pupil characteristics outperformed polygenic scores in terms of explanatory power, but together they explained up to 21.5% (95% CI: 18.9 to 24.1) of the variation in age 7 achievement. Including information on the social background of pupils’ parents that is potentially obtainable by schools further increased the explanatory power of the models up to a maximum R2 of 26.3% (23.4 to 29.2). The incremental R2 of the polygenic scores over pupil characteristics were 1.8% (-0.7 to 4.3) and 4.8 (2.1 to 7.3), suggesting that they provide some additional predictive information over currently available or easily collectable data.Next, we assessed the explanatory power of polygenic scores for educational achievement at age 7. We assessed this using the incremental gain in variance of educational achievement explained by the polygenic scores over and above pupil characteristics available to schools , parents' years of education, and parent socioeconomic position . Both thThe genomewide significant and all SNP polygenic scores explained more variation of achievement in exams sat at the end of compulsory education at age 16, explaining an additional 3.4% (1.7 to 5.0) and 12.9% (10.6 to 15.3) of educational achievement over age and sex alone . By compWe next investigated how well the polygenic scores could identify high achieving pupils, defined as those with the highest 10% of educational test scores. To investigate the potential performance of polygenic scores for correctly identifying individual high achieving students from all other pupils, we used Receiver Operating Characteristic (ROC) curves to calculate Area Under the Curve (AUC). ROC curves assess the sensitivity  and the specificity  of a classifier as its discrimination threshold is varied. Compared to measures of parental socioeconomic position , the polygenic scores have a lower AUC and therefore poorer sensitivity and specificity to discriminate high achievers at age 7  . The traAt age 16, prior achievement data were available. If a school headteacher or principal wanted to use polygenic scores as a selection criterion to select the highest performing students, would they identify a group that has higher educational attainment at age 16 than when that selection had been made on other criteria? If they selected the students with the top 10% of polygenic scores, they would on average only sample 24% of the top 10% highest achievers at age 16, and 76% of those not in the top 10%. In contrast, if the principal or policy maker used phenotypic measures from age 11, they would sample 51% of the top 10% highest achievers at age 16, and 49% of those not in the top 10%. This suggests that polygenic scores cannot be used to identify high achieving students more accurately than available phenotypic measures. The group of pupils with the highest polygenic scores do - on average - have higher achievement, but the predictive information provided from the polygenic scores is inferior to that provided by phenotypic predictors. We investigated how predictive polygenic scores for education were of realised educational achievement and the incremental increase in explanatory and predictive power that they offered over and above readily available phenotypic measures. Our results demonstrated that the polygenic scores were predictive of educational achievement, accounting for 3.4% and 12.9% of the variance (above age and sex) across our sample at age 7 and 16 respectively. This was higher than the 9.2% reported for high school GPA in the original GWAS . For infThe lack of genotypic predictive power that we observed over and above phenotypic data may be because prior achievement mediates genotypic effects on educational outcomes; genetic variants that affect educational achievement at earlier ages are likely to also affect achievement at later ages. It has been suggested that for complex phenotypes, accurate prediction at the individual level may require a polygenic score that explains up to 75% of the total genetic variance of the phenotype . It is tAt the individual level, polygenic scores and parental social background provided similar, but relatively imprecise predictions of achievement within our sample. This reflects a wider issue of the different challenges in analysing group and individual level differences : while sIn fields such as medicine, where genetic risk can be of clinical significance for some diseases , personaThis study has several limitations. First, the ALSPAC cohort is not fully representative of the UK population and as such our results may not be generalisable to all UK pupils. Other studies, such as the Millennium Cohort Study are more representative and therefore could provide further evidence about personalised education for the broader UK population. Second, the educational achievement polygenic score that we use was based on a GWAS of years of education rather than exam scores. Years of education can be considered a more social measure of education than exam performance, and previous work has demonstrated that the educational attainment polygenic score strongly reflects parental social position (and through this access to further or higher education) . Future In conclusion, our results suggest that currently available genetic scores are unlikely to provide more accurate predictions of how well a pupil will perform in school exams than easily measured phenotypes. Genetic data provide little additional information on an individual's school performance over and above more readily available and easily collected phenotypic data, except where prior achievement measures are unavailable. The greatest value of genetic data may lie instead for researchers investigating the etiology of educational differences between groups of pupils, teachers and schools and for novel sociogenomic analyses into socioeconomic inequalities in education achievement and attainment.SCR_007260). Pregnant women resident in Avon, UK with expected dates of delivery 1 st April 1991 to 31st December 1992 were invited to take part in the study. The initial number of pregnancies enrolled was 14,541. When the oldest children were approximately 7 years of age, an attempt was made to bolster the initial sample with eligible cases who had failed to join the study originally. This additional recruitment resulted in a total sample of 15,454 pregnancies, resulting in 14,901 children who were alive at one year of age. From this sample genetic data was available for 7988 after quality control and removal of related individuals. For full details of the cohort profile and study design see http://www.bristol.ac.uk/alspac/researchers/our-data/. The ALSPAC cohort is largely representative of the UK population when compared with 1991 Census data; there is under representation of some ethnic minorities, single parent families, and those living in rented accommodation   were removed. Cryptic relatedness was measured as proportion of identity by descent (IBD) >0.1. Related subjects that passed all other quality control thresholds were retained during subsequent phasing and imputation. 9115 participants and 500,527 SNPs passed these quality control filters. ALSPAC mothers were genotyped using the Illumina human660W-quad array at Centre National de Génotypage (CNG) and genotypes were called with Illumina GenomeStudio. PLINK (v1.07) was used to carry out quality control measures on an initial set of 10,015 participants and 557,124 directly genotyped SNPs. SNPs were removed if they displayed more than 5% missingness or a Hardy-Weinberg equilibrium P value of less than 1.0e-06. Additionally SNPs with a minor allele frequency of less than 1% were removed. Samples were excluded if they displayed more than 5% missingness, had indeterminate X chromosome heterozygosity or extreme autosomal heterozygosity. Samples showing evidence of population stratification were identified by multidimensional scaling of genome-wide identity by state pairwise distances using the four HapMap populations as a reference, and then excluded. Cryptic relatedness was assessed using an IBD estimate of more than 0.125 which is expected to correspond to roughly 12.5% alleles shared IBD or a relatedness at the first cousin level. Related subjects that passed all other quality control thresholds were retained during subsequent phasing and imputation. 9048 participants and 526,688 SNPs passed these quality control filters.DNA of the ALSPAC children was extracted from blood, cell line and mouthwash samples, then genotyped using references panels and subjected to standard quality control approaches. ALSPAC children were genotyped using the Illumina HumanHap550 quad chip genotyping platforms by 23andme subcontracting the Wellcome Trust Sanger Institute, Cambridge, UK and the Laboratory Corporation of America, Burlington, NC, US. The resulting raw genome-wide data were subjected to standard quality control methods. Individuals were excluded on the basis of gender mismatches; minimal or excessive heterozygosity; disproportionate levels of individual missingness (>3%) and insufficient sample replication (<0.8). Population stratification was assessed by multidimensional scaling analysis and compared with Hapmap II (release 22) European descent (CEU), Han Chinese, Japanese and Yoruba reference populations; all individuals with non-European ancestry were removed. SNPs with a minor allele frequency of <1%, a call rate of <95% or evidence for violations of Hardy-Weinberg equilibrium  and removed a further 321 participants due to potential ID mismatches. This resulted in a dataset of 17,842 participants containing 6305 duos and 465,740 SNPs (112 were removed during liftover and 234 were out of HWE after combination). We estimated haplotypes using ShapeIT (v2.r644) which utilises relatedness during phasing. The phased haplotypes were then imputed to the Haplotype Reference Consortium  panel of approximately 31,000 phased whole genomes. The HRC panel was phased using ShapeIt v2, and the imputation was performed using the Michigan imputation server. This gave 8237 eligible children and 8196 eligible mothers with available genotype data after exclusion of related subjects using cryptic relatedness measures described previously. Principal components were generated by extracting unrelated individuals (IBS <0.05) and independent SNPs with long range LD regions removed, and then calculating using the `--pca` command in plink1.90. Only the children's genetic data was used in this paper.We use average fine graded point scores at four major Key Stages of education in the UK. These are Key Stage 1 (age 7), Key Stage 2 (age 11), Key Stage 3 (age 14), and Key Stage 4 (age 16). We use scores for performance at the end of each Key Stage and a score at entry to Key Stage 1, which represents the start of schooling. At the time the ALSPAC cohort were at school, the age 16 Key Stage 4 exams represented final compulsory schooling examinations. Scores were obtained through data linkage to the UK National Pupil Database (NPD), which represents the most accurate record of individual educational achievement available in the UK. We used data from the Key Stage 1 and Key Stage 4 files. The Key Stage 4 database provides a larger sample size than Key Stage 2 and 3 databases and contains data for each.P-value in each 250kb window was retained and all other SNPs in linkage disequilibrium with an 2 of >0.1 were removed. The first polygenic score (GWAS sig PGS) was created from the 1,271 independent SNPs that associated with years of education at genome-wide levels of significance (p<5×10−8). The second  was created from all genome-wide SNPs reported in the meta-analysis.Two educational attainment polygenic scores were generated using the software package PRSice  based upWe selected covariates that are easily available to schools in the UK. These include the study participants sex and month of birth, and their status on three pupil characteristics that are available to schools the NPD: eligibility for Free School Meals (FSM); Special Education Needs (SEN); and English as a Foreign Language (EFL). FSM is a proxy for low income as only children from low income families are eligible. We use years of parental education, coded as basic formal education (7 years), certificate of secondary education (10 years), O-levels and vocational qualifications (11 years), A-level (13 years), and degree (16 years). For dual parent families we use the average of the two parents’ years of education, while for single parent families we use the mother’s years of education. Finally, we use a continuous measure of socioeconomic position, the Cambridge Social Stratification Score (CAMSIS). For dual parent families we used the highest of either parents score, while for single parent families we use the mother’s score. Parental years of education and CAMSIS were measured when the study participants were in utero.2) in educational achievement above age and sex; pupil characteristics; and prior achievement. Bootstrapping with 1000 replications was used to estimate confidence intervals for R2 values. To compare the predictive power of polygenic scores to additional phenotypic data that schools could collect, we repeated the regression analyses controlling for parental years of education and parental socioeconomic position. Sensitivity and specificity were calculated using selection into the top 10% of educational achievers at age 16 from the whole cohort as the ‘diagnosis’. Receiver Operating Characteristic (ROC) curves were used to visually compare models and to calculate the Area Under the Curve (AUC).To examine the predictive ability of polygenic scores for educational achievement we ran a series of regression analyses of the polygenic scores on achievement each controlling for sex, month of birth, and the first 20 principal components of inferred population structure. Principal components are included to adjust estimates for population stratification; systematic differences in allele frequencies between subpopulations due to ancestral differences. Predictive ability of the polygenic scores was determined by the incremental increase in variance explained ; Kathryn Paige Harden (Reviewer #2); David Cesarini (Reviewer #3).Thank you for submitting your article "Can education be personalised using pupils' genetic data?" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:All reviewers agree that this is an interesting manuscript with clear research questions and solid methods. The paper sets out the limits of genetic prediction for aspects of educational attainment, especially as compared to the existing information supplied by readily available risk predictors .2s and the scope for personalized interventions. The title is an obvious place to start fixing this issue". One reviewer suggested a more descriptively on-point title along the lines of: "Polygenic Scores For Educational Attainment Do Not Predict Exam Performance Beyond Readily Available Phenotypic Information". All felt that the discussion about personalized interventions could use a major overhaul that takes into account the specific concerns raised.Having said that the reviewers considered that the manuscript needed to be revised to reflect the issues described below. The thrust of the argument from several of the reviewers (both in their reviews and in the subsequent inter-reviewer discussion) was a "shared concern that the paper is a bit cavalier in how it talks about the relationship between incremental REssential revisions:The major issues that need to be addressed are these:1) More complete analysis of group level predictions (see more detailed comments from R1 in particular). The key point here is that in focusing on individual level predictions (which are "far out of reach" as anticipated given the low R2), an opportunity has been lost to explore the impact on group level differences . As reviewer 1 states: "by focusing on individual prediction (which is way out of reach), we lose out of sight that there is potential for misuse on group level discrimination"2) Defend the use of cutoffs such as defining the outcome as the top 10%? Does the ROC change with different definitions of the outcome?3) Please define "personalized education". Per the comments of reviewer 2, you should spell out what you mean by this term , and give reference to the educational literature on this subject. This revision is clearly tied to the first, in terms of setting out more clearly the opportunities for use/misuse of PRS in both the individual and the group setting. As reviewer 2 states: "the authors could be more careful about delineating more specifically *which* educational policies or practices hinge on individual prediction."4) Please do more to help readers understand exactly what is being reported in a few instances. The goal is a paper clear enough that someone with access to the data set could reproduce the exact analyses run without having to make guesses or judgment calls. (see full reviews for more specific suggestions).5) Please do more to help readers compare their estimates to the previous literature.6) Please expand the paper's Discussion about the relationship between the incremental R2 of a PGS and the scope for personalized interventions (see full reviews for details).A suggestion from reviewer 1 with which we agree:7) The structure of the results can be improved by presenting three sections in line with the three research questions. The ROC analyses is discussed under the individual prediction, but it is a population evaluation equivalent to (but not the same as) R2, not for individual prediction. Essential revisions:The major issues that need to be addressed are these:1) More complete analysis of group level predictions (see more detailed comments from R1 in particular). The key point here is that in focusing on individual level predictions (which are "far out of reach" as anticipated given the low R2), an opportunity has been lost to explore the impact on group level differences . As reviewer 1 states: "by focusing on individual prediction (which is way out of reach), we lose out of sight that there is potential for misuse on group level discrimination"We have conducted additional analyses that are presented in the Materials and methods and are referenced in the Results section. Our key point is that conditional on observable phenotypes after the age of 11, the polygenic scores do not appear to be informative. Figure 6—figure supplement 1 demonstrates that even for group level analysis, at age 7 (the first Key Stage of schooling in the UK) one could not reliably differentiate future high achievers from other students better than by selecting on phenotypic achievement. In the Discussion we explain that education is already personalised to a certain extent by teachers, but that this personalisation occurs on phenotypic characteristics such as observed attainment/aptitude and attitude to school. Specifically, we have made changes to the Results section with the following passages of text:“This misclassification is similar for parental education and socioeconomic position but lower for prior attainment . In each case, as a group the pupils predicted to be in the top 10% of achievers will on average perform higher than other pupils in exams, but the large variability shows that many of the pupils in this group will underperform.”“If a school headteacher or principal wanted to use polygenic scores as a selection criterion to select the highest performing students, would they identify a group that has higher educational attainment at age 16 than when that selection had been made on other criteria? If they selected the students with the top 10% of polygenic scores, they would on average only sample 24% of the top 10% highest achievers at age 16, and 76% of those not in the top 10%. In contrast, if the principal or policy maker used phenotypic measures from age 11, they would sample 51% of the top 10% highest achievers at age 16, and 49% of those not in the top 10%. This suggests that polygenic scores cannot be used to identify high achieving students more accurately than available phenotypic measures. The group of pupils with the highest polygenic scores do – on average – have higher achievement, but the predictive information provided from the polygenic scores is inferior to that provided by phenotypic predictors. Figure 4—figure supplement 1 demonstrates the variability in age 16 educational achievement for pupils predicted to be in the top 10% from each of the genotypic and phenotypic predictors”.2) Defend the use of cutoffs such as defining the outcome as the top 10%? Does the ROC change with different definitions of the outcome?To assess whether polygenic scores could be used to correctly identify a pupil as being in an actionable group (whether that be predicted low attainer in need of support or a predicted high attainer to be streamed for advanced classes) we require a cut-off for this group. This requirement for a binary outcome for use in the ROC analysis is what motivated our use of cut-offs. Given that our choice of the top 10% may seem arbitrary we have now repeated the analyses at a range of cut-offs . These are presented in the Materials and methods  and show that our results are consistent across the group definitions. These results are presented in the Materials and methods and discussed in the main body of text, with the following inclusions:“These results were consistent when other cut-offs were used to determine the high attaining group , suggesting that the results do not reflect our definition of high-attainers.”“As with achievement at age 7, these results were consistent when other cut-offs were used to determine the high attaining group .”3) Please define "personalized education". Per the comments of reviewer 2, you should spell out what you mean by this term , and give reference to the educational literature on this subject. This revision is clearly tied to the first, in terms of setting out more clearly the opportunities for use/misuse of PRS in both the individual and the group setting. As reviewer 2 states: "the authors could be more careful about delineating more specifically *which* educational policies or practices hinge on individual prediction."We have now expanded upon “personalised education” and have clearly defined this in the Introduction, as follows:“The definition of personalised education has been inconsistent, generally referring to either the tailoring of educational curriculums, learning environments and teaching styles for individual students, or for groups of students within a classroom. Personalised learning was adopted in national policy statements in England in 2004 with a focus on the needs of individual students. However, it was not mandated and was seen as being conceptually ambiguous, leading to inconsistency in its implementation across schools. Throughout, we refer to personalised education as administered at the individual level. There are currently no policies in place that rely on educational prediction, but calls are increasingly being made for genetic data to be used to personalise education.”We appreciate reviewer #2’s comments that potential policy implications could in theory be based on the average PGS of a classroom rather than the PGS of an individual . We have chosen not to discuss this in the manuscript as we are unable to think of a scenario where a class average PGS could provide actionable information. Children are streamed into classes based on performance, which on this evidence will provide more useful and accurate information of future attainment than a PGS.4) Please do more to help readers understand exactly what is being reported in a few instances. The goal is a paper clear enough that someone with access to the data set could reproduce the exact analyses run without having to make guesses or judgment calls. (see full reviews for more specific suggestions).We have edited the manuscript throughout to improve the narrative and make our analyses clearer to the reader. We have also now referred to our measure of educational performance as achievement rather than attainment, and we have made clearer what terms such as “incremental R2” refer to.5) Please do more to help readers compare their estimates to the previous literature.We have tied our results into the previous literature as best we can, now referring to the prediction in the Lee et al., 2018, GWAS as it refers to high school GPA which we feel makes a better comparison than years of education. We have also drawn comparisons to the Lee et al., 2018, incremental R2 analysis which reviewer #3 helpfully pointed us towards. We feel it pertinent to note that while personalised education has been discussed previously in papers, other than the analysis performed by Lee et al., 2018, we are aware of little for us to compare our results to.In response to reviewer #3, the figure of 13.8% was erroneous and has now been corrected.6) Please expand the paper's Discussion about the relationship between the incremental R2 of a PGS and the scope for personalized interventions (see full reviews for details).We have now expanded upon this issue in our Discussion. We have added the following text:“While future studies may lead to polygenic scores that explain a greater amount of variation in education, these may still not provide useful returns to personalised interventions. High incremental variance explained is a necessary pre-requisite for successful intervention, but it is not a guarantee that an actionable intervention will have a large effect. Furthermore, to provide actionable evidence for personalisation at a given age, polygenic scores need to explain variation in educational outcomes over and above available phenotypic at that age. If most or all the educational differences associated with the polygenic score are phenotypically expressed at a given age, then the score is unlikely to be useful for personalisation”.A suggestion from reviewer 1 with which we agree:7) The structure of the results can be improved by presenting three sections in line with the three research questions. The ROC analyses is discussed under the individual prediction, but it is a population evaluation equivalent to (but not the same as) R2, not for individual prediction.Thanks for this suggestion, we have now restructured the results as suggested with a third section titled “Using polygenic scores to identify future pupil performance”.


Geum triflorum to quantify the scale over which genetic differences for quantitative traits important to adaptation have evolved, comparing the proportion of variance attributed to broad regional- and local population-level effects. Geum triflorum is a widely distributed species spanning a range of environments, including alvar and prairie habitats, which have extreme regional differences in soil-moisture availability. Alvar habitats are regions of thin soil over limestone that experience substantial seasonal variation in water availability, from flooding to desiccation annually. This contrasts with prairie habitats, whose deeper soils mitigate irregular flood–desiccation cycles. Using a common garden experiment, we evaluated 15 traits broadly grouped into three trait classes: resource allocation, stomatal characteristics, and leaf morphological traits for individuals sourced from prairie and alvar environments. We quantified the proportion of trait variance explained by regional- and population-scale effects and compared the proportion of regional- and population-trait variances explained across trait classes. Significant regional differentiation was observed for the majority of quantitative traits; however, population-scale effects were equal or greater than regional effects, suggesting that important genetic differences may have evolved across the finer population scale. Stomatal and resource allocation trait classes exhibited substantial regional differentiation relative to morphological traits, which may indicate increased strength of selection for stomatal and resource allocation traits relative to morphological traits. These patterns point towards the value in considering the scale over which genetic differences may have evolved for widely distributed species and identify different functional trait classes that may be valuable in establishing seed transfer guidelines.For widely distributed species, understanding the scale over which genetic variation correlates to landscape structure and composition is critical. Particularly within the context of restoration, the evolution of genetic differences may impact success if seeds are maladapted to the restoration environment. In this study, we used  Geum triflorum, to examine the proportion of trait differences attributable to regional or population environments. Environmental differences associated with regional climate differences significantly influenced the distribution of functional trait variation across seed sources, pointing towards the importance of understanding climate adaptation when recommending seed transfer for restoration.Restoration aims to source appropriate seed for success in the restoration environment. However, genetic differences in traits important to plant function may have evolved influencing success of different seed sources when planted in different environments. In this study, we established a common garden experiment using the widespread perennial,  Understanding the scale over which phenotypic traits evolve is crucial to successful habitat restoration. Both macro- and microevolutionary processes contribute to the evolution of broad- and fine-scale genetic variation for traits important to adaptation . This isIdentifying the scale and extent over which genetic differences in traits important to adaptation have evolved has been a major goal of restoration ecology . QuantifGeum triflorum or Prairie Smoke, to quantify the scale(s) over which trait differences important to plant function have evolved to inform seed transfer in a restoration context.For widespread grassland species, identifying and sourcing material for restoration remains challenging, particularly where population trait differences may have evolved in response to varying selective pressures. Understanding the degree to which variance in traits associated with plant function and fitness vary across the landscape will be important to restoration programmes. In this study, we use G. triflorum has a wide distribution spanning the Great Plains of the USA and Central Canada (hereafter referred to as ‘Prairie’), as well as alvar habitats surrounding the Great Lakes Region and into Manitoba  region, 2 from the Manitoba Alvars (MBA) region and 6 from the Prairie (PRA) region  region ; Table 1) region . In addi) region ; Table 12 s−1 and temperatures between 18.3 and 23.9 °C. Plants were watered biweekly, and provided between 10–15 pellets of slow release fertilizer mix (Osmocote 14N-14P-14K) at regular intervals throughout the course of the experiment. In May 2016, surviving seedlings were transferred to a permanent outdoor research facility at the Minnesota State University Moorhead (MSUM) Regional Science Center , one leaf was randomly sampled, photographed and measured for variation in midvein length, sinus depth and mini leaflet presence and shape on a 1-cm2 grid. Midvein length was measured as the total length of the primary vein per sampled leaf. Sinus depth refers to the depth of the margin between the apex lobe and the next nearest lobe. Mini leaflets, defined as small leaflets along the midvein between lobes, were assessed as present or absent, and the shape of leaflets was assessed as lobed or non-lobed , calculated as a ratio of leaf area to dry mass, was measured over 1 day using a LI-3000C (Li-Cor Biosciences) portable area sensor for 99 individuals . The surface area of one randomly selected mature leaf was estimated alongside fresh and dry mass. Leaves were dried for 68 h at 50 °C, following which dry mass was taken. Specific leaf area is calculated as dry mass per unit leaf area. Leaf dry matter content (LDMC) was also calculated with these data, as LDMC is calculated as the ratio of fresh to dry mass.−2.Chlorophyll content was quantified over a single 90-min period in the field common garden using a CCM-300 (Opti-Sciences) on 98 individuals, ~5 individuals per population for a total of 33 PRA, 56 GLA and 9 MBA individuals. The CCM-300 records emission ratios of 700 and 735 nm (red and far red wavelengths), which is linearly correlated to chlorophyll content  at UC Davis Stable Isotope Facility . To assess the repeatability of isotope measurements across samples, 23 technical replicates were evaluated. A correlation of r = 0.793 across technical replicates provides confidence in the repeatability and precision of the assay. Reported δ 13C values are expressed as relative to the Vienna Pee Dee Belemnite.To quantify integrated water-use efficiency (WUE), we used carbon isotope composition as measured by δ 13C . Leaf saseeStomatal density and size were measured for adaxial and abaxial leaf surface impressions for individuals within the common garden experiment. Newskin ‘liquid bandage’ was applied to either adaxial or abaxial surfaces for two leaves per individual within the common garden for a total of 650 leaf surface impressions  exiting through the stomata of a defined leaf section over a 30-s period. Five individuals were sampled per population [see], with one individual within each population measured per day to minimize effects of temporal environmental variation on population-level estimates. A subset of 10 individuals were measured daily over the course of the experiment. The aim of the repeated measures was to account for possible influence of temporal variation in temperature and humidity on stomatal conductance. We used a linear model to assess repeatability, with individual as a fixed effect, and temperature and humidity as random effects. Temperature and humidity had little effect on stomatal conductance measurements , and repeatability within individuals was fairly low (R2 = 0.372).Stomatal conductance was measured using a Decagon SC-100 Porometer (METER Group) between 09:00 a.m. and 11:30 a.m. over the course of 5 days (8 August 2018 to 12 August 2018) for 99 individuals in the common garden experiment  was classified as a fixed effect and population as a random effect, as populations represent a random selection of the number of populations (pj) within each region. Interaction terms were not included in the model because no population occurred in more than one region. Normality of residuals was visually assessed for all traits. All statistical tests were conducted in R  effects, regional differences were accounted for by including fixed effect estimates in the denominator of the R2 , with residual variation representing differences in trait values from effects not evaluated in this study.To determine the impact of ecogeographic scale on trait differentiation, we estimated the proportion of variance explained by fixed (region) or random  effects for each trait using the rptGaussian function in the rptR package . The rptR2 . We estin = 1000) to provide a 95 % confidence interval for variance explained for each trait dependent on the predictor variable. P-values for random effects (population) were obtained from likelihood-ratio tests.To determine the significance of fixed (region) effect estimates, an analysis of variance (ANOVA) was conducted on the linear mixed effect model . The pro[see]. A Dunn test post hoc evaluation was conducted using the Dunn.test . However, regional differences did not have a significant effect on variability observed for other morphological traits, including leaf sinus depth , presence of mini leaflets (R2 = 0.009) and the presence of lobed or unlobed leaflets (R2 = 0.008)  (R2 = 0.047 (P < 0.001) and R2 = 0.161 (P < 0.001), respectively.The proportion of variance for midvein length explained by region was significant (= 0.008) ; Fig. 3.ctively) . In addiR2 = 0.014, P = 0.718). This contrasts with carbon isotope discrimination where we observed a significant proportion of variability explained by regional differences . Other resource allocation traits exhibited a similar pattern, including leaf dry matter content and chlorophyll content  (The proportion of variance explained for specific leaf area (SLA) by region was negligible and insignificant (ctively) ; Fig. 3.R2 = 0.292, P = 0.001). Region and population explained the same proportion of variance for chlorophyll content . Region explained a greater proportion of variation in carbon isotope discrimination relative to population-level differences, though both were significant .A significant proportion of trait variation was explained by region for stomatal density and SAI . Resource allocation and stomatal trait classes explained a significantly greater proportion of regional trait variance relative to morphological traits .Population climate averages were used to summarize region- and population-specific differences in climate as a potential factor contributing to trait differences. GLA, MBA and PRA habitats were clearly differentiated based on climate, with 43.1 and 27.4 % of the variation among regions and populations explained by the first and second principal component (PC) axes, respectively . SubstanG. triflorum. We found phenotypic variance was explained by regional- and population-scale differences. Consistent with previous literature, genetic variation is partitioned at broad regional and fine population scales across complex landscapes . The large amount of variation explained by region for these traits appears to be driven by environmental contrasts. Furthermore, redundancy analysis suggests that prairie populations may invest more in resource allocation traits, with greater accumulation of leaf dry matter content and chlorophyll content, while alvar populations invest in finer-scale water control via stomatal traits.In addition to resource allocation, traits related to stomatal characteristics, specifically size and number of stomata may be under differential selection at the regional scale. Alvar plants experience seasonal flood and drought cycles, which likely select for increased efficiency in managing extremely variable water availability. The most efficient stomatal arrangement for rapid response to environmental change is more stomata of smaller size  of collection sites.plaa009_suppl_Supplementary_Table_S1Click here for additional data file.plaa009_suppl_Supplementary_Table_S2Click here for additional data file.https://github.com/zeb-yoko/AoBP-quantitative-trait-differentiation.git).All data and scripts associated with this manuscript are available on GitHub (


Genebank genomics promises to unlock valuable diversity for plant breeding but first, one key question is which marker system is most suitable to fingerprint entire genebank collections. Using wheat as model species, we tested for the presence of an ascertainment bias and investigated its impact on estimates of genetic diversity and prediction ability obtained using three marker platforms: simple sequence repeat (SSR), genotyping-by-sequencing (GBS), and array-based SNP markers. We used a panel of 378 winter wheat genotypes including 190 elite lines and 188 plant genetic resources (PGR), which were phenotyped in multi-environmental trials for grain yield and plant height. We observed an ascertainment bias for the array-based SNP markers, which led to an underestimation of the molecular diversity within the population of PGR. In contrast, the marker system played only a minor role for the overall picture of the population structure and precision of genome-wide predictions. Interestingly, we found that rare markers contributed substantially to the prediction ability. This combined with the expectation that valuable novel diversity is most likely rare suggests that markers with minor allele frequency deserve careful consideration in the design of a pre-breeding program. Global agricultural production must be increased by 60% compared to 2005–2007 levels in order to supply an estimated world population of 9 billion in 2050 . The annAegilops tauschii  compare the relevance of an ascertainment bias on the genetic diversity estimated by SSR, GBS, and SNP array markers in a wheat population comprising PGRs and European elite lines, 2) contrast the prediction ability obtained using the three marker platforms, and 3) investigate the potential and limits of genome-wide prediction models exploiting the complementarity of different marker platforms.Triticum aestivum L.) genotypes: 190 lines represent the elite breeding pool exploited in Europe (Elite) and 188 genotypes represent a random sample of PGRs maintained at the genebank of the IPK Gatersleben, Germany. Details on the plant material have already been published (www.traitgenetics.com) and the SNPs represent a subset of markers from the 90,000 SNP array  GBSublished , and (3)ublished . The 90,ublished . The devNP array . The GBSNP array . BrieflyNP array  accordinNP array , reads wNP array  with BWANP array  using thNP array . NovosorNP array  with mpiIn order to compare properties between Elite and PGRs for each marker dataset, we calculated the minor allele frequency (MAF), population heterozygosity (H), and polymorphism information content (PIC). The standard deviations (SD) of these parameters were derived by means of bootstrapping with 1,000 rounds. We evaluated the genetic diversity from each group and calculated the Rogers' distances (RD) between pairs of genotypes. SDs were obtained by resampling genotypes without replacement with 1,000 rounds. Principal coordinates analysis PCoA,  was perf−1) and heading date (HD) (days since 1 January) in three field experiments , phenotypic data were available. The 339 genotypes (or subsets) were phenotyped for grain yield (GY)  (BH−MADR) at a significance level (P < 0.05) . ThereafFirst, BLUEs of each genotype within each single environment were estimated by fitting the following model:P contains the phenotypic values of GY or HD for each plot, µ corresponds to the overall mean, G represents the genotype effect, R stands for the effect of the replication, B is the effect of incomplete blocks, and e refers to the error term of the model. In the model, only µ and G were treated as fixed effect, while all other components were assumed to be random effects.in which, Second, the BLUEs of genotypes across all environments were estimated fitting the following model:Y contains the genotypic effects estimated within each environment using Equation (1), µ is the fixed effect of the overall mean, G corresponds to the fixed effects of genotypes across environments, E stands for random environment effects, G×E indicates the random effects of interaction between genotype and environment, and e is a random error term. Equations (1) and (2) were fitted using the mixed model R package ASReml-R  as:Model (2) was also used to estimate the variances and heritability of each trait. During the computation for variances and heritability, r represents the average number of replications.in which, A genomic best linear unbiased prediction (GBLUP) model was implemented, with the co-variance matrix (G matrix) derived from SNP array, GBS, or SSR marker datasets. We employed single G matrix (single-kernel) or their combination (multi-kernel). The GBLUP model of the multi-kernel model was:Y contains the BLUEs for each trait, gSNP,  gGBS and gSSR are random genetic effects derived from different markers, with SNPA, GBSA and  SSRA are the numerator relationship matrix calculated using SNP array, GBS, or SSR marker datasets, respectively, according to gSNP, gGBS, and gSSR individually. The implementation of the models is described in detail in the Where We applied a random resampling method for fivefold cross validation to investigate the prediction ability. In each cross validation, the population was divided into a training (80%) and a test set (20%). We used the training set to build the mixed model function, which was then used to predict the genetic value of the test set. The prediction ability was calculated as the Pearson correlation between estimated genetic values and the observed values in the test set. We performed 1,000 rounds of cross validation and recorded the mean and SD for these 1,000 correlation coefficients. The genomic prediction model was fitted using the “BGLR” R-package . BesidesWe found for the SNP array markers ~5–6 times higher estimates of MAF, H, PIC, and RD than for the GBS markers considering the total population of 378 lines  calculated based on the SNP-array data explained 10.42%, 4.62%, and 2.95% of the molecular variation, respectively  or GBS markers (G.158), calculated the G matrices, and evaluated prediction abilities of single-kernel models applying cross validations. In general, the prediction ability of S.158 and G.158 was up to 34.4% lower than the total marker set ; second, we applied a single-kernel model for CGS. We observed for both traits that the performance of these two models was very close to that of S-G (Linkage disequilibrium (LD) between markers can impact the prediction ability for the multi-kernel models. We calculated therefore the LD between each pair of SNP array and GBS markers across the 339 lines and deleted the corresponding GBS markers if their LD was higher than r² = 0.95. After removing 2,826 (9.5%) GBS markers, which were in tight LD, we combined SNP array and remaining GBS markers to build a new dataset (CGS). We then did two Data from GBS is typically characterized by a significant proportion of missing values . We usedEntire genebank collections have been fingerprinted using different marker technologies e.g., . In ordeThe principal coordinate analyses revealed a comparable picture of the overall population structure across the three marker technologies  but also−1 (−1)². We observed four times higher genetic variance compared to elite wheat lines in Europe (More than half a million wheat genetic resources are conserved worldwide in genebanks . Detailen Europe . Althougn Europe . The comn Europe  suggestsWe observed an ascertainment bias for wheat caused by array-based SNP markers, which particularly impacts the estimates of the within population diversity. This was not the case with GBS, which makes it an interesting marker system to fingerprint entire genebank collections. In summary, our study showed the potential of genebank genomics to unlock the genetic diversity maintained in genebanks.All authors declare that this study adheres to standard biosecurity and institutional safety procedures.The datasets generated for this study are available on request to the corresponding author.All authors declare that this study adheres to ethical standards including ethics committee approval and consent procedure. All experiments were performed under the current laws of Germany.JC, YZ, and JR designed the study. NS and MR contributed to the generation of genomic data. JC, SB, AS, and NP curated phenotypic and genomic data. JC performed the analyses. JC and JR wrote the paper with input from all co-authors.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.