Polygenic scores (PGSs) are individual-level measures that aggregate the genome-wide genetic predisposition to a given trait. As PGS have predominantly been developed using European-ancestry samples, trait prediction using such European ancestry-derived PGS is less accurate in non-European ancestry individuals. Although there has been recent progress in combining multiple PGS trained on distinct populations, the problem of how to maximize performance given a multiple-ancestry cohort is largely unexplored. Here, we investigate the effect of sample size and ancestry composition on PGS performance for fifteen traits in UK Biobank. For some traits, PGS estimated using a relatively small African-ancestry training set outperformed, on an African-ancestry test set, PGS estimated using a much larger European-ancestry only training set. We observe similar, but not identical, results when considering other minority-ancestry groups within UK Biobank. Our results emphasise the importance of targeted data collection from underrepresented groups in order to address existing disparities in PGS performance. There are challenges with transferring genetic risk scores from ancestry in which they were generated to another. Here, the authors investigate the use of multi-ancestry versus single-ancestry training sets to construct polygenic scores and find that the optimal strategy varies across traits. Largely driven by significant increases in sample sizes, the predictive utility of PGS has improved substantially in recent years for a variety of traits3, including cardiovascular disease4, breast cancer5, and type I diabetes6.Polygenic scores (PGS) are composite, quantitative measures that aim to predict complex traits from genetic data. As well as providing insights into the genetic architecture of complex traits, PGS have considerable clinical potential for screening and prevention strategies9, reflecting the lack of diversity in genomic samples collected to date9. Moreover, predictive performance decreases with genetic distance from the training population12. The lack of transferability of PGS across ancestries may be due to a number of factors, including population differences in allele frequencies and linkage disequilibrium (LD)11. While there is some evidence that common causal variants have similar effects across ancestries13, other studies have suggested that the underlying variant effects may in fact differ across ancestries16, which may be due to gene-by-gene or gene-by-environment (GxE) interactions18. In addition, GxE interactions for people of African ancestry may be different between those living in the UK and those living in South Africa, say. This lack of transferability raises one of the most important technical and ethical challenges in the clinical utility and applications of PGS due to their potential to exacerbate health inequalities9.These improvements, however, have largely been limited to populations of European ancestry19, that aim to address the lack of global genetic diversity in research data. However, it may take many years to collect sufficient data to reduce the disparities in PGS performance. Statistical methods may provide an alternative, short-term, cost-effective and complementary potential solution to mitigate against the negative effects of the lack of diversity in genomic datasets, by using modelling techniques to make use of all the existing data available, while allowing for some differences between groups.There are major, ongoing initiatives to collect genomic data from traditionally under-represented groups, such H3Africa20. Márquez-Luna et al. propose a ‘multi-ethnic’ PGS by combining scores trained separately on different populations21. Weissbrod et al. expand on this approach by further leveraging functionally informed fine-mapping to estimate the PGS weights22. In a related approach, Ruan et al. incorporate LD information to directly estimate effect sizes using GWAS results from two or more populations23. To account for admixture, Cavazos & Witte propose local ancestry weighting to construct individualised PGS24. These efforts have yielded promising improvements in PGS performance, though there remains a significant gap in predictive accuracy between European and non European target populations.There has been a growing interest in statistical methods to improve the transferability of PGS, which have thus far focused on GWAS-derived PGS, i.e. PGS based on summary statistics from a genome-wide association study (GWAS). These integrate results from GWAS trained on distinct populations at different stages of the PGS estimation. For example, Grinde et al. use European GWAS results to select variants, and then estimate the variant weights using the non-European GWAS results25, to estimate PGS for a range of anthropometric, blood-sample, and disease traits, with the explicit objective of improving predictive accuracy for under-represented ancestries. Specifically, we ask whether there are consistent optimal strategies for borrowing information across ancestry groups to maximize prediction accuracy in groups that have small sample sizes in available resources. For each trait, we construct training sets with varying numbers of individuals from each ancestry to assess the effect of sample size and composition on PGS accuracy, using both simulated data and data from UK Biobank25. Moreover, and to counteract the imbalance of ancestries in a multiple-ancestry training set, we investigate the use of an importance reweighting approach that places more weight on underrepresented ancestries during training. Importance reweighting is a standard statistical technique used in survey sampling that aims to account for differences between the sampling population and the population of interest26. Given the availability of individual-level information in biobanks, we estimate PGS using regularised regression applied to full genotype and covariate data (as opposed to genome-wide association summary statistics) to avoid introducing additional artefacts into our analysis via the reliance on assumptions about genotype and covariate correlation structure (including LD) and GWAS methodology.Here, we investigate the use of multiple-ancestry datasets, such as UK BiobankOur results show that the impact of sample size and composition on predictive performance is highly variable across traits. For some traits, polygenic scores estimated using a relatively small number of minority-ancestry individuals outperformed on a minority-ancestry test set scores estimated using a much larger number of European-ancestry individuals. Moreover, adding European-ancestry individuals to the training set did not always improve performance and in some cases even led to poorer performance. Although importance weighting yields moderate improvement in performance for some traits, we find that sample size is a much more prominent factor, highlighting the limitations of statistical corrections and the importance of collecting more data from a more diverse range of participants.25. We initially focus on PGS strategy for African-ancestry groups, given that predictive accuracy using European-ancestry PGS is consistently worst out of all the major ancestry groups12. Simulated data was generated using the simulation engine msprime27 in the standard library of population genetic simulation models stdpopsim v0.1.228 to generate African-ancestry and European-ancestry genotypes. We also considered a range of quantitative and binary traits from UK Biobank, using imputed genotypes along with inferred genetic ancestry labels made available by the Pan-UKBB initiative29.To investigate the effect of sample size and ancestry composition on polygenic score performance, we used both simulated data and real data from UK BiobankXYZ—for example PGSEUR. Similarly, we refer to a PGS trained on a dual-ancestry (respectively minority-ancestry) training set as PGSdual (respectively PGSmin).For both the simulated and real data, we constructed a range of training sets controlling the number of European-ancestry and minority-ancestry individuals. We considered three types of training sets: a single-ancestry set consisting only of European-ancestry individuals, a single-ancestry set consisting of minority-ancestry individuals, and a dual-ancestry set consisting of both European-ancestry and minority-ancestry individuals. We denote a PGS trained on a XYZ-ancestry training set as PGS30, which has previously been used in the context of genetic risk prediction (see for example34). To account for the imbalance in sample size numbers in the dual-ancestry training sets, we also estimated PGS using an importance reweighted LASSO, upweighting the non-European-ancestry individuals. Following Martin et al.9, we assessed the predictive performance of a PGS using partial r2 relative to a covariate-only model. See Fig. For each training set, we estimated PGS using L1-regularised regression, also known as the LASSO11, with the correlation of causal effect sizes between ancestry groups, ρ, has been estimated to be significantly less than one across a range of common traits16. We simulated traits by randomly selecting p0 = 100 SNPs to be causal and then generating effect sizes for these SNPs such that that overall heritability across the entire population was h2 = 0.3. To assess the impact of differences in causal effect sizes on the relative predictive performance of PGS strategies, we varied the trans-ancestry causal effect correlation, ρ = 0.5, 0.6, …, 1.0, generating 10 quantitative traits for each value. We assume that all causal variants are genotyped, thus avoiding any differences in PGS accuracy that may arise from imperfect tagging11. We note that in practice imputation does not fully address the issue of imperfect tagging, due to differences in imputation quality across ancestry groups9.We first set out to evaluate the relative performance of single-ancestry PGS versus dual-ancestry PGS through simulation. An important factor in the lack of transferability of PGS across ancestries is the difference in causal effect sizesnAFR = 2000, 4500, 7714, 12,000, 18,000 African-ancestry individuals. We also created five dual-ancestry training sets made up of the corresponding African-ancestry training set supplemented with nEUR = 18,000 European-ancestry individuals. To obtain PGS from the African-ancestry training sets, we used unweighted LASSO regression, while for the dual-ancestry training sets, we used the importance reweighted LASSO with γ = 0, 0.1, …, 1.5. The case γ = 0 corresponds to no reweighting, that is, the standard LASSO. The case γ = 1 corresponds to inverse proportion reweighting, so that in total, African-ancestry individuals and European-ancestry individuals have equal weight. Note that the African-ancestry training set is equivalent to the limiting case γ → ∞ whereby zero weight is placed on European-ancestry individuals. We quantified predictive performance of a PGS for a given ancestry group in terms of the predictive gap: the difference between variance explained by the PGS, r2, and SNP heritability h2 . See  “Simulation study” for full details.For each trait we created five African-ancestry training sets with AFR and PGSdual, the predictive gap for African-ancestry individuals decreased substantially as the number of African-ancestry individuals in the training sets increased  was just over 0.21 for the African-ancestry test sets, compared to 0.03 for the European-ancestry test sets. While the performance on Europeans did not change markedly as the number of African-ancestry training set individuals increased, the African-ancestry predictive gap fell to ~0.11 and 0.06 when nAFR = 7 714 and nAFR = 18,000 respectively. As expected, the discrepancy between the two ancestry groups decreased as the correlation ρ between the ancestry-specific genetic effects increased.For both PGSsed Fig. . For exaγ = 0), PGSAFR generally outperformed PGSdual, despite the latter being trained on more individuals—the dual-ancestry training sets consist of the African-ancestry training sets along with 18,000 European-ancestry individuals. This was particularly evident when the correlation between ancestry-specific genetic effects was lower (ρ = 0.5).In the absence of reweighting , the importance-reweighted PGSdual outperformed PGSAFR when the correlation between ancestry-specific genetic effects was relatively high (ρ ≥ 0.7). When ρ = 0.7, the relative amount of improvement with reweighting was stable as nAFR increased: for nAFR = 2000, the predictive gap was reduced by 27% , while for nAFR = 18,000, the predictive gap was reduced by 29% . In contrast, when ρ = 1, the relative amount of improvement with reweighting was decreased as nAFR increased: for nAFR = 2000, the predictive gap was reduced by 16% , while for nAFR = 18,000, the predictive gap was only reduced by 7% . We highlight that importance reweighting reduced the predictive gap even when the effect sizes were the same across ancestries (ρ = 1), indicating that the procedure can partially correct for ancestry-specific differences in allele frequencies and LD structure.Importance reweighting generally had a positive impact on predictive performance, reducing the difference between PGSγ. As γ increased from 0 to 1.5, the predictive gap typically decreased. When the correlation between ancestry-specific genetic effects was high (ρ ≥ 0.9) and the number of African-ancestry samples low (nAFR = 2000), the predictive gap increased again for larger values of γ. This reflects a crucial trade-off of importance reweighting in this context: while the bias of African-ancestry genetic effect estimates may be lower with more reweighting, the increased variance of the weights results in a lower effective sample size. The effect of reweighting was relatively small compared to the effect of increased sample size. For nAFR = 2000 and ρ = 0.7, reweighting reduced the predictive gap from 0.21 to 0.15. The same improvement for the unweighted PGSdual was seen when increasing the number of African-ancestry individuals to nAFR = 4500, though we note that the PGSAFR with nAFR = 4500 had an even lower predictive gap of 0.10.The effect on predictive performance depended on the degree of reweighting, quantified by h2 = 0.1, 0.3, 0.5, and the polygenicity  p0 = 10, 100, 1000  the number of minority-ancestry individuals in the respective training sets and (ii) the correlation of genetic effects between ancestries. For both PGSAFR and PGSdual, the between-ancestry disparity in predictive performance decreased as the number of minority-ancestry individuals in the training set increased. Despite being trained on fewer individuals, the PGSAFR tended to outperform PGSdual, particularly when the correlation between ancestry-specific genetic effects was low. Importance reweighting generally reduced the predictive gap of PGSdual, especially when the sample size imbalance between ancestries was high. As this imbalance decreased, however, the reweighted PGSdual did not outperform PGSAFR.This simulation study illustrates the relative performance of PGSNext, we sought to examine whether, even without reweighting, prediction performance in an underrepresented ancestry group can be boosted by including individuals from a different ancestry among the training samples. To do so, we used data from UK Biobank, estimating a range of PGS based on varying numbers of training individuals for a variety of traits Table . For exaFirst, we held the number of European-ancestry individuals fixed, and constructed six training sets by varying the number of African-ancestry individuals from 0% to 80% of the total number of African-ancestry individuals with non-missing data for the trait in question. The number of European-ancestry individuals was chosen such that the largest training set had a 90-10 split between European- and African-ancestry individuals. Considering height again as an example, this corresponded to keeping the number of European-ancestry individuals fixed at 44,487 and varying the number of African-ancestry individuals from 0 to 4 942. For each training set, we used the unweighted LASSO to generate PGSs, and evaluated predictive performance in terms of variance explained on held-out test sets for each ancestry.The predictive performance on African-ancestry individuals increased for five traits: height, mean corpuscular volume (MCV), female genital prolapse (FGP), high light scatter reticulocyte count (reticulocyte), and platelet crit (platelet) Fig. a. For thNext, we performed complementary analyses in which we held the number of African-ancestry individuals fixed at 80% of the total number of African-ancestry individuals with non-missing data for the trait in question. We again constructed six training sets, now varying the number of European-ancestry individuals so that the proportion of European-ancestry individuals in the training set ranged from 0% to 90%.Predictive performance on African-ancestry individuals only increased markedly for height and mean platelet volume (MPV), with the improvement for MPV appearing to tail off between the two largest training sets. For three traits , predictive performance worsened as European-ancestry individuals were added to the training set. For the remainder of the traits, predictive performance stayed mostly constant.These results demonstrate that, for some traits, the potential for increasing prediction performance by including samples from a different population can be limited. They also highlight substantial between-trait heterogeneity in response, suggestive of major differences in genetic architecture.γ = 0, 0.2, …, 1 to construct PGSdual, while for the single-ancestry training sets we just considered the standard, unweighted LASSO. In a supplementary analysis on a subset of the traits, we also estimated dual-ancestry PGS trained on the combination of the European-ancestry training set and the African-ancestry training set, using both the unweighted and reweighted LASSO  a European-ancestry training set of ~300,000 European-ancestry individuals, (ii) a African-ancestry training set of ~5000 African-ancestry individuals, and (iii) a dual-ancestry training set made up of the African-ancestry training set combined with European-ancestry individuals so that the proportion of African-ancestry individuals was 10%. For the latter, we opted for this 90-10 split—thus not using all the available European-ancestry individuals—following the previous analysis that indicated the limited benefit to African-ancestry predictive performance of adding European-ancestry individuals to the training set. A secondary motivation was to limit the imbalance between the two ancestries in order to evaluate the effect of importance weighting. We used the importance weighted LASSO with AFR outperformed PGSEUR on two traits—MCV, and erythrocyte distribution width (erythrocyte)—despite the former sample size being orders of magnitude smaller . For both of these traits, the unweighted PGSdual performed the same as or slightly worse than PGSAFR. While importance reweighting yielded a moderate improvement, the reweighted PGSdual did not outperform PGSAFR.Figure EUR performed best. We note that predictive accuracy of PGSEUR for European-ancestry individuals was the same or higher than any of the PGS for African-ancestry individuals, consistent with previous investigations into the between-ancestry disparities of polygenic scores9.For four other traits—high light scatter reticulocyte count (reticulocyte), hypothyroidism, atrial fibrillation (AFib), and and diverticular disease of intestine (DDI)—the predictive performance of all three PGS was largely similar. For the remaining traits—height, MPV, body mass index (BMI), eosinophill percentage, monocyte count, asthma and lymphocyte count—PGSTo explore whether the variability in optimal PGS strategy extended to other subpopulations, we focused in on four of the above traits  and ran the above analyses using different minority-ancestry groups: Admixed American ancestry (AMR), Central/South Asian ancestry (CSA), East Asian ancestry (EAS), and Middle Eastern ancestry (MID).EUR had the best predictive performance for each of ancestry groups, with partial r2 for height varying from r2 = 0.08 for the African-ancestry group to r2 = 0.25 for the Admixed American ancestry group. For both erythrocyte distribution width and mean corpuscular volume in African-ancestry individuals, the PGSmin and the reweighted PGSdual outperformed PGSEUR, which offered almost no predictive utility. With the exception of mean corpuscular volume in East Asian ancestry individuals, where performance was similar between the different PGS, PGSEUR was consistently the best strategy for the remaining minority-ancestry groups. Results were qualitatively identical when using only genotyped SNPs instead of the full imputed sequence  in a given ancestry group. For each ancestry group, we grouped variants into four sets: ‘rare’ (MAF ≤ 1%), ‘uncommon’ (1% < MAF ≤ 5%), ‘intermediate’ (5% < MAF ≤ 20%), and ‘common’ (MAF > 20%). Given a set of variants X, let X that are in r2 attributable to variant set r2 between modelsy is the vector of trait values, and M is the matrix of covariates , and interactions between sex and the ten genetic PCs) for the test set. We note that because we are considering the same set of variants for each trait, observed differences among traits in composition likely reflect differences in trait architecture, rather than differences in how the studies were performed.Finally, to investigate the reasons why optimal training approaches vary across traits, we investigated the contribution of variants at different allele frequencies to variance explained. Specifically, we measured the partial dual could be attributed to variants that have MAF < 5% in the European-ancestry subgroup . Conversely, variance explained in the European-ancestry subgroup was driven by variants that are intermediate or common in European-ancestry individuals . And approximately one quarter of the variance explained could be attributed to variants with MAF < 5% in African-ancestry individuals.Figure In contrast, for height we find that variance explained in European-ancestry individuals has an allele frequency decomposition with a slightly greater contribution of variants that are common in European-ancestry individuals . But, variance explained in African-ancestry individuals is dominated by variants that are common (MAF > 5%) in both populations . The effect of reweighting follows a similar pattern; for MCV shifting variance explained towards variants that are higher-frequency in the African-ancestry individuals  and, for height, tending to favour variants that are common in both groups.dual and PGSAFR could largely be attributed to variants that were relatively common in African-ancestry individuals but rare in European-ancestry individuals. Since the number of African-ancestry individuals in these training sets was relatively small, this suggests that the corresponding effect sizes are comparatively large. On the other hand, the variance explained by each of the height PGS could be attributed to variants that were common in both European-ancestry and African-ancestry individuals. We found similar patterns for the other minority ancestries , revealing that around 86% of all GWAS participants are of European descent. In the context of polygenic scores, this bias has been reflected in the lack of transferability of scores across ancestries: PGS developed using European-ancestry samples tend to perform poorly in non-European ancestry test sets9. Correspondingly, our results found that, for a range of traits, PGS estimated using European-ancestry individuals performed relatively poorly on other non-European ancestry groups. Although recent improvements in predictive performance across a number of traits indicate the potential clinical utility of PGS6, the disparity in PGS accuracy across ancestry groups, raises serious technical, clinical and ethical issues, with likely substantial impacts on health inequalities if left unaddressed9.The lack of diversity in human genetic studies has been brought into focus by a number of articles . A potential drawback of using an individual-level approach was the considerable computational cost associated with constructing the PGS, which may be impractical in the context of large-scale biobanks of increasing diversity.However, the question of how to optimally construct PGS directly from multiple-ancestry training data has largely been unexplored. That is, to maximise predictive accuracy for a minority-ancestry group, is it better to employ a PGS trained on just the minority-ancestry individuals or a combination of the minority-ancestry individuals and the majority-ancestry individuals? To investigate this, we compared the prediction accuracy of PGS trained on different subsets of the available data. This was possible due to the availability of individual-level genetic data in UK Biobank, accompanied by a wide range of phenotypic measurements. This in turn allowed us to vary the number of individuals of each ancestry in each training set and thus to assess the effect of sample size and composition on PGS predictive performance for a range of quantitative and binary traits. Moreover, the use of individual-level data to estimate PGS, as opposed to the more standard approach of using external GWAS summary statistics, avoids making any assumptions such as common LD structure or phenotype definition from the GWAS population and target population . For those in the second category (such as height), the best performance in the underrepresented group was achieved by training in the much larger majority group, though note this still represented a substantial decrease in absolute performance relative to the majority European-ancestry group. When the minority group was African-ancestry individuals, the first category, though smaller, included important biomarkers such as MCV. Moreover, for a given trait, the optimal strategy varied by ancestry. For MCV for example, PGS15. We found that the variability across traits could be at least partially explained by differences in the allele frequency pattern of causal variants or, more precisely, variants in LD with a causal variant. Specifically, we found that for some traits, such as height, most predictive utility could be attributed to variants that were relatively common (MAF > 5%) in both European- and African-ancestry individuals. For other traits, such as MCV, the predictive utility could be attributed to variants that were common in African-ancestry individuals but rare in European-ancestry individuals. This points to why PGSEUR for MCV performed much worse than the corresponding PGSAFR, despite being trained on a much larger number of individuals. We also note that the minority-ancestry PGS and reweighted dual-ancestry PGS performed particularly well for blood cell traits. This may be due to the influence of relatively few loci that have large phenotypic effects and strong differences in allele frequency between populations indicative of strong evolutionary selective pressure (such as has been shown for the DARC (Duffy) locus46). For such traits, a strategy that emphasises the minority-ancestry data may be favoured. Further work is needed, however, to determine the precise nature of differences in optimal strategy and the relation with trans-ancestry differences in genetic architecture.These findings raise the question of why the optimal strategy varies across traits and ancestry groups. Recent studies have ascribed the overall lack of PGS transferability to a number of factors, including population-level differences in allele frequencies, LD patterns, location of causal variants, and effect sizes47. Therefore, statistical solutions must be considered in combination with efforts to address the global health research funding gap48, diversity of the bioinformatics workforce49 and assessing the impact and translation of analyses to real-world data50 in addition to efforts to increase the number of non-European-ancestry participants in genetic research. Each of these partial solutions, in combination, provide essential contributions to reduce and remove opportunities for negative effects on health inequalities, particular amongst those from different ancestry groups51.Our findings highlight the limitations of statistical corrections alone in reducing the disparities of PGS performance between ancestries. There are numerous sources of potential bias that adversely affect the application of an analytical pipeline to individuals of minority and/or underrepresented groups, including problem selection, data collection, outcome definition, model development and lack of real-world impact assessments and considerations9. An important consideration surrounds future sampling strategy: whose genomes should we aim to sequence to reduce existing disparities in polygenic prediction accuracy? Our findings indicate that increasing the number of samples from minority-ancestry groups can lead to significant improvements in prediction performance. Moreover, even within the same ancestry group, PGSs do not always generalise across other characteristics such as age, sex and socio-economic status52, pointing to the need of more diversity across multiple axes both alongside and within genetic ancestry.It is becoming increasingly clear that the vast disparities in PGS performance can only be bridged by improving the diversity of human genetic datasets54. The categorisation of individuals into discrete ancestry groups to explain differences between behaviours and exposures may be unhelpful55, whereas continuous representations of genetic ancestry57 enable identification of areas of genetic ancestry where performance is stronger or weaker as well as how the trait itself varies across ancestry. Ultimately, approaches to genetic prediction must acknowledge both the many similarities of human biology, but also the differences in history, cultural heritage, exposure, and behaviour that can lead to certain factors being of greater relevance for particular groups of individuals.Perhaps counter-intuitively, with more diverse data, statistical tools such as importance reweighting may eventually play a more important role as we seek to boost predictive utility by using all the available data. Reweighting strategies have the benefit of overcoming the lack of universal definitions of race, ethnicity and ancestry, which causes considerable confusion and imprecision30. The LASSO has previously been used in the context of genetic prediction (see for example refs. 34 and references therein) and is suitable for high-dimensional problems where one expects the number of non-zero predictors to be small relative to the number of total predictors. Although there exist other full genotype PGS methods such as linear mixed models (see e.g. ref. 58), we focus on the LASSO largely for its computational efficiency. We provide an analysis of predictive performance versus sample size, focusing on differences in predictive performance between European-ancestry individuals and non-European-ancestry individuals.To construct PGSs from full genotype data, we use L1-penalised regression, also known as the LASSOn be the number of individuals in the training set. Denote q covariates, X to be the n × p genotype matrix, and y to be the n-vector of observed phenotype values. We assume a linear relationship between the phenotype and predictors,θ is a q-vector of covariate effects, β is a p-vector of variant effects, and ϵ is an environmental noise term with mean 0.We first briefly recap the LASSO algorithm for constructing polygenic scores. Let θ, β), where λ is a regularisation parameter. The purpose of the ∣∣β∣∣1 term is to penalise large values of ∣β∣ and thus encourage sparse solutions, that is, solutions with a relatively low number of non-zero coefficients. Note that the parameters θ are not penalised. The choice of λ controls the degree of penalisation with higher values of λ encouraging smaller values of β. To select λ, we applied an 80-20 training-validation split to the training set, generating a path of solutions for a range of values of λ using the training split, and then selecting the value of λ that maximises r2 (for quantitative traits) or the Area Under the Curve  on the validation split.The LASSO aims to minimise the objective function,59 and snpnet34 on simulated and real data respectively. The snpnet package is an extension of glmnet designed to interface directly with the PLINK software61 to handle large-scale single nucleotide polymorphism datasets such as the genotype data in UK Biobank. Using the default package settings and following the guidance in34, we did not standardise the genotypes before fitting.We optimise  using thβ are the same for all individuals. While this assumption may be reasonable within a single ancestry group, it is unlikely to hold more generally. We consider a hypothetical model that allows genetic effects to vary among individuals. To this end, we introduce a low-dimensional latent variable z representing the ancestry of a given individual. For an individual i,θ( ⋅ ), β( ⋅ )) are now vector-valued functions parameterised by z. The only assumption we make about these functions is one of continuity, so that individuals with similar ancestry have similar covariate and genetic effects. Otherwise, we do not make any explicit statements regarding the form of the functions.The above description assumes that the genetic effects J = 2 ancestry groups, such that θ(zi), β(zi)) = (θj) for an individual i in ancestry group j. Using superscripts to denote the ancestry group ( is the vector of observed phenotypes for group j),In this paper, we consider the special case with nj to be the number of individuals of ancestry j in the training set, we assume n1 > n2 to reflect a European-ancestry dominated training set. Applying the standard LASSO to such a training set, we would expect the estimate θ(1), β(1)) than to (θ(2), β(2)). All else being equal, this would result in better predictive performance for test individuals in group 1.Denoting πTE(z) given a training set of observations z1, …, zn, how should one obtain a single estimate for ? Our proposed approach is to use importance reweighting, a statistical technique commonly used in survey sampling26. Importance reweighting aims to account for distributional differences between the sampling population and the population of interest by assigning weights to each of the samples in the training data. Here, we assign each of the training individuals a weight wi that quantifies the similarity of the ancestry variable zi to the test set ancestries, with individuals who have a similar ancestry to the test set assigned a higher weight. More concretely, assuming an ancestry distribution πTR( ⋅ ) on the training set, we setπTR, πTE so in practice we must approximate , we minimise the following weighted LASSO objective function:We return for a moment to the more general model in Equation . Supposew1, w2 such that w2 ≥ w1 with the aim of improving estimates for group 2, i.e. the underrepresented group. Specifically, we use weights of the form:γ is a hyperparameter that controls the degree of reweighting. We normalised the weights so that n1w1 + n2w2 = n1 + n2. With these weights, we thus minimise the objective function,θ, β).In this work, we consider only the special case with two ancestry groups (Eqn. ), specif27 in the standard library of population genetic simulation models stdpopsim v0.1.228 to generate African-ancestry and European-ancestry genotypes, following a similar simulation framework to that used by Martin et al.7. For each ancestry group, we generated a total of 200,000 genotypes for chromosome 20, based on a three-population ‘out-of-Africa’ demographic model62, using a mean mutation rate of 1.29 × 10−8 and a recombination map of GRCh37. This recombination map is from the Phase II Hapmap project and is based on 3.1 million genotyped SNPs from 270 individuals across four populations 63. Note that this particular simulation model also generates genotypes for East Asian individuals but we do not use these in our analysis. To reduce the computational burden, we used only the first 10% of the chromosome, applying a minor allele frequency (MAF) threshold to filter out any SNPs that had a MAF of <1% in each ancestry group, resulting in a total of 189, 765 variants.To evaluate the effect of importance reweighting on PGS performance under various settings, we undertook a simulation study. We used the simulation engine msprimeσ2 controls the SNP heritability p0 = 100 of the p = 189, 765 variants to be causal. Motivated by Trochet et al.64, we drew the causal effect sizes from a bivariate normal distribution to model the similarity of genetic effects between ancestries. Denoting ρ is the correlation between the ancestry-specific genetic effects. We set i ∉ C. For each value of ρ = 0.5, 0.6, …, 1.0, we repeated the above procedure 5 times to generate 5 quantitative traits.We simulated phenotypes from these genotypes assuming a normal linear model,nEUR = 18,000 randomly selected individuals of European ancestry and nAFR = 2000, 4500, 7714, 12,000, 18,000 randomly selected individuals of African ancestry. For each of these training sets, we computed weights γ is a hyperparameter controlling the degree of reweighting. To investigate the impact of reweighting, we varied γ = 0, 0.1, …, 1.5. Note that γ = 1 corresponds to inverse proportion reweighting when nAFR = 2000 and nEUR = 18,000. We normalised the weights to ensure that their sum equalled n, in line with the unweighted case.To investigate the effect of sample size, for each trait we created five training sets with r2, as the measure of predictive performance,r2 relative to an intercept-only covariate model. For ρ = 0.5, 0.6, …, 1.0, we repeated the above process 5 times with different randomly selected individuals in the training and test sets to calculate a mean r2 for each trait.To assess predictive performance for each ancestry, we constructed an African-ancestry test set and a European-ancestry test set by randomly selecting 2000 individuals from each ancestry out of those not included in the training set. We used the proportion of variance explained, denoted ρ = 0.8, and varying the overall heritability h2 = 0.1, 0.3, 0.5 and the number of causal SNPs p0 = 10, 100, 1000 respectively.In supplementary studies to investigate the role of heritability and polygenicity, i.e. the number of causal SNPs, we repeated the above analyses with the correlation between the ancestry-specific genetic effects fixed at 25. We used inferred genetic ancestry labels made available by the Pan-UKBB initiative29. These labels were derived based on reference data from the 1000 Genomes Project65 and the Human Genome Diversity Project (HGDP)66. Briefly, principal component analysis (PCA) was performed on unrelated individuals in the combined reference dataset, and a random forest classifier was trained on the first 6 principal components (PCs) using continental ancestry metadata. UK Biobank individuals were then projected onto this reference PC space and given initial ancestry assignments based on the random forest classifier. These assignments were then adjusted by removing outliers. Full details can be found on the Pan-UKBB website29.The UK Biobank is a large-scale cohort study with genomic and phenotypic data collected on ~500,000 individuals aged 40-69 at the time of recruitment68. To ensure that the traits under investigation were not highly correlated with each other, we used genetic correlation estimates available on the Neale Lab UKBB Genetic Correlation Browser70. Specifically, working from the most heritable traits to the least heritable, we iteratively removed a trait if it had an estimated genetic correlation of >0.5 with any remaining trait of higher heritability. Of the remaining traits, we selected the top 10 most heritable quantitative traits: height, mean corpuscular volume (MCV), body mass index (BMI), eosinophill percentage, erythrocyte distribution width (erythrocyte), lymphocyte count, monocyte count, mean platelet volume (MPV), platelet crit, and high light scatter reticulocyte count (reticulocyte). We also selected the top 5 most heritable binary traits: asthma, female genital prolapse (FGP), atrial fibrillation (AFib), diverticular disease of the intestine (DDI), and hypothyroidism. For our African-ancestry analyses, we investigated all 15 of these traits, while for the other minority-ancestry analyses, we focused in on 4 traits: height, mean corpuscular volume, erythrocyte distribution width, and asthma.We investigated a range of quantitative and binary traits available in our UK Biobank project (UKB Application Number 12788). To select these, we applied the following procedure. We first filtered out traits with estimated SNP heritability of <5% or a ‘low’ confidence rating for the SNP heritability estimate, as reported on the Neale Lab UKB SNP-Heritability Browser29. Firstly, we removed individuals who were identified as displaying sex chromosome aneuploidy. We also removed individuals who were flagged as related by Pan-UKBB. Within each ancestry group, related individuals were identified using PC-Relate71 with k = 10 and a minimum individual MAF of 5%. We filtered out variants that were not deemed to be of ‘high quality’ according to Pan-UKBB, retaining those with an INFO score of at least 0.8 and with an allele count of at least 20 per population. We also removed variants that had a MAF of <1% in both the European-ancestry group and the minority-ancestry group under analysis. To control for population structure, we included the following covariates in our model: age, sex, the first ten genetic principal components (PCs), and interactions between sex and the ten genetic PCs.We used imputed genotypes from UK Biobank, filtering out individuals and variants according to quality-control metrics used by the Pan-UKBB initiativeEuropean-ancestry A random sample comprising 80% of the quality-controlled European-ancestry individuals.Minority-ancestry A random sample comprising 80% of the respective quality-controlled minority-ancestry individuals.Dual-ancestry This set consisted of both minority-ancestry individuals and European-ancestry individuals. The basic form of this training set was made up of the minority-ancestry training set described above, combined with European-ancestry individuals so that the proportion of minority-ancestry individuals was 10%. The European-ancestry individuals were matched to the minority-ancestry individuals on age and sex. We also considered variations of this training set by removing a proportion of either the European-ancestry individuals or the minority-ancestry individuals (see Results for more details).To assess the effect of sample size and composition on PGS performance, we used subsets of the above data as training sets, controlling the number of European-ancestry and minority-ancestry individuals. The remaining individuals were then used as a held-out test set. For each trait, we constructed three types of training sets using individuals with non-missing data for that particular trait. The first two types of training sets were single-ancestry datasets, one consisting solely of European-ancestry individuals and the other consisting solely of minority-ancestry individuals.γ = 0, 0.2, 0.4, 0.6, 0.8, 1. Note that γ = 0 corresponds to the unweighted LASSO.For each dataset, we further removed variants with a MAF of <0.1% or a missing genotype call rate of <5%. Note that, as a result, the sets of variants generally differed by training set. For the single-ancestry datasets, we used the standard, unweighted LASSO to construct the PGS. For the dual-ancestry datasets, we used the weighted LASSO with r2 attributable to the PGS, relative to a covariate-only model, following Martin et al.9. Specifically, we fit the following nested linear models ,M is the covariate matrix and r2 (or the Cox and Snell pseudo-r2 for binary traits) between models (r2, and report the mean and the range of these estimates.We evaluated predictive accuracy of each PGS by ancestry group using individuals that were not included in the corresponding training sets. To assess the genetic predictive accuracy of a PGS, we calculated the partial Further information on research design is available in the Supplementary InformationReporting Summary


To fill this gap, the Mexican Biobank project genotyped 6,057 individuals from 898 rural and urban localities across all 32 states in Mexico at a resolution of 1.8 million genome-wide markers with linked complex trait and disease information creating a valuable nationwide genotype–phenotype database. Here, using ancestry deconvolution and inference of identity-by-descent segments, we inferred ancestral population sizes across Mesoamerican regions over time, unravelling Indigenous, colonial and postcolonial demographic dynamics6. We observed variation in runs of homozygosity among genomic regions with different ancestries reflecting distinct demographic histories and, in turn, different distributions of rare deleterious variants. We conducted genome-wide association studies (GWAS) for 22 complex traits and found that several traits are better predicted using the Mexican Biobank GWAS compared to the UK Biobank GWAS8. We identified genetic and environmental factors associating with trait variation, such as the length of the genome in runs of homozygosity as a predictor for body mass index, triglycerides, glucose and height. This study provides insights into the genetic histories of individuals in Mexico and dissects their complex trait architectures, both crucial for making precision and preventive medicine initiatives accessible worldwide.Latin America continues to be severely underrepresented in genomics research, and fine-scale genetic histories and complex trait architectures remain hidden owing to insufficient data Nationwide genomic biobank in Mexico unravels demographic history and complex trait architecture from 6,057 individuals. Archaeological and anthropological approaches have been used to regionalize Mexico into the north of Mexico, the north of Mesoamerica, the centre, occident and Gulf of Mexico, Oaxaca  and the Mayan region10  project, densely genotyping 6,057 individuals from 898 localities distributed nationwide  and of the genomic burden of rare deleterious variants. We carry out GWAS analyses across 22 binary and quantitative traits, and compare the prediction performance of polygenic scores computed using our GWAS or UK Biobank (UKB) GWAS data. Last, given that evolutionary histories (captured by genetic ancestries) could associate specific trait-relevant genotypes with certain genetic backgrounds, we study the impact of genetic ancestries, portions of the genome in ROH, polygenic scores and other sociocultural and biogeographical factors on creating variation in complex and medically relevant traits in Mexico.Here, we leverage rich archaeological and anthropological information to guide a regionalized analysis of Mexico, and harness the power of genome-wide local ancestry estimation and identity-by-descent (IBD) segments to decipher fine-scale genetic histories using ancestry-specific approaches to denote origins and historical population size changes20) in a global reference sample. We use a similar approach to label local segments across the genomes of the study individuals. We use the term ‘ancestries from the Americas’ when referring to genetic ancestries that derive from genetic ancestors living in the Americas before European colonization; these have also been referred to as Indigenous ancestries, and in some places below we also use this term  relative to the total genetic variance (T); Supplementary Figs. FST values with the other regions . The method of ref. 5 further highlights the ancestral diversity reflected by the MXB samples that are represented as mixtures of multiple sources  of these three ancestries in the MXB, we analyse IBD segments30 stratified by local ancestry inference for each Mesoamerican region4 32. For example, in the Gulf, where we observe high Ne since the preclassical period (2500 bce–250 ce), there is archaeological evidence, among a myriad of other groups, of the Olmecs in the preclassical period, the Totonacs in the classical period and the Huastecs in the postclassical period (900–1521 ce)33. In Oaxaca, we observe Ne rapidly growing in the preclassical to the classical period, in line with archaeological inferences that the Zapotecs were already starting to create sedentary settlements in the preclassical period followed by a rise in social and political structures in the classical period. The subsequent postclassical period was characterized by militarism and warfare34, and our genetic evidence suggests a population decline towards the end of the postclassical period. In the Yucatan peninsula, the Maya had a prominent civilizational spread in the classical period (peak Ne observed). They started going through a slow decline only in the postclassical period due to what archaeologists have inferred as a combination of different political and ecological factors, and this trajectory is supported in the Ne trend32.We observe fine-scale variation in ns9 Fig. . As geneNe in the postclassical right before the arrival of the Spaniards and into part of the colonial period, after which we start to see a population decline in Ne. The decrease in Ne after the arrival of the Spaniards is most prominent in the centre and north of Mesoamerica. In Oaxaca and the Mayan region, where Indigenous ancestries from the Americas are most prevalent today as evidenced by the ADMIXTURE analysis  in the MXB and observe that both the number of ROHs and the total length of ROH per individual increase as we move from north to southeast in the country . ROH patterns help further illuminate the demographic and mating histories of Mexicansρ = 0.31, P = 0.016; Fig. ρ = 0.35, P = 0.006), and small ROH found on Indigenous genomic segments  unchanged42. In particular, rare variants are lost or increase in frequency after the bottleneck.We also investigate the effects of demographic histories on the frequency distribution of genetic variants. This analysis is motivated by previous theoretical and empirical work showing that undergoing a bottleneck changes the allele frequency distribution in the group that experienced the bottleneckWe evaluate this effect by computing the genome-wide sum of intergenic, synonymous and putatively deleterious (predicted-damaging missense and loss of function) alleles per individual. When considering only rare alleles , we observe that individuals with higher ancestry proportions from the Americas carry fewer rare derived alleles across variant types (strongest effect observed for intergenic variants) Fig.  in contrP < 2.27 × 10−9) on chromosomes 1, 9, 11 and 16 associated with lipid levels in blood : rs7528419), ABCA1 (high-density lipoprotein (HDL): rs9282541 and rs2065412), the LINC02702–BUD13–ZPR1–APOA1–APOA4–APOA5–APOC3–SIK3 locus , HERPUD1–CETP  and APOE , which have all previously been associated with lipid levels in European and Hispanic groups . Restricting the GWAS cohort to individuals with >90% inferred ancestries from the Americas did not identify any genome-wide significant loci.To understand trait-associated locus transferability, we conduct GWAS analyses across 22 binary and quantitative traits  are predicted better with SNPs discovered in MXB compared to traits inferred to have larger target size (height and body mass index (BMI))45. UKB-based predictors are used in our complex trait modelling below, as these can be computed for all MXB individuals.To assess transferability in the prediction of quantitative traits using polygenic scores, we re-perform a GWAS in only 4,000 randomly selected individuals from the MXB and construct polygenic scores in the remaining 1,778 individuals  in decreasing HDL levels and shown that this allele is apparently exclusive to Indigenous genetic ancestries from the Americas 43. In the MXB, we similarly observe the ABCA1*C230 allele to be in higher frequencies in individuals with a higher proportion of ancestries from the Americas, and observe that individuals with higher ABCA1*C230 allele frequencies have lower HDL levels , and caution against using an individual’s global ancestry proportion as a predictor of the effect of a single functional variant. Our results overall support that functional variants with variable frequencies or environmental interactions are partially responsible for variation in a range of complex traits in Mexico43.Previous work has implicated the Our work demonstrates the value of generating genotype–phenotype data on underrepresented groups to reveal lesser-known genetic histories and generate findings of biomedical relevance. It is also an illustration of the joint modelling of genetic and environmental effects to reveal the aetiology of complex traits and disease. In this project, we ensure diverse Indigenous and rural presence in our sampling strategy, consider the fluidity of ancestries from different local and global regions in our analyses, and evaluate their reflection in genetic and disease-relevant complex trait variation. By leveraging the largest nationwide genomic biobank in Mexico, we find diverse sources of ancestries in Mexico in light of its unique history, and infer demographic and admixture histories and ROH using ancestry-specific haplotype identity that reveal an elaborate fine-scale structure in the country. Observing a larger number of small ROH in younger individuals in the MXB and in genomic segments of Indigenous ancestries is relevant for parsing the genetic architecture of complex traits and diseases, especially those with a recessive component. We also show that demographic history affects the frequency distribution of genetic variants, thus changing how many rare variants individuals with different ancestries carry. We demonstrate the value of GWAS carried out on a resource such as the MXB for predicting complex traits. The MXB GWAS exhibits utility for polygenic score computation in independent Mexican cohorts, as well as for meta-analysis with other GWAS cohorts to increase prediction power further. Last, we observe a significant impact of genetic ancestries at different timescales, ROH, polygenic scores and sociocultural and biogeographic variables on various complex traits implicating the importance of both genetic and environmental factors in explaining complex trait variation and in considerations of potential public health interventions. Our results exhibit the added importance of considering genetic factors for preventive and personalized medicine above and beyond environmental factors. Our results will inform the design of future genetic and complex trait studies in Mexico and Latin America, and will hopefully motivate additional efforts to strengthen local research capacity across Latin America and benefit underserved groups globally.51. Participants were randomly selected to be representative of the civilian, non-institutionalized Mexican population at the state and national levels. Trained personnel conducted the interviews. Information was collected on household and sociodemographic characteristics, current health status, healthcare service usage and behavioural aspects of participants. Sera and buffy coats were obtained from 43,085 individuals aged 20 years or older. More than fifty publications have arisen from this survey providing critical insights into the status of national health alongside some genetic traits of the sampled population52. In particular, the inclusion of individuals from remote and rural locations in Mexico makes this survey unique. Given its large volume, sophisticated sampling design, breadth of demographic sampling and extensive trait data, the ENSA 2000 represents a valuable untapped genetic resource to link genetic markers and health outcomes.Since 1988, Mexico has established periodical National Health Surveys , originally conceived as National Nutrition Surveys) for surveillance of Mexican population-based nutrition and health metrics. In this study, we use data and samples collected from the survey carried out in 2000, the ENSA 2000. This survey was a probabilistic, multi-stage, stratified, cluster household survey conducted by the Mexican Secretariat of Health from November 1999 to June 2000. Research design and methods have been described elsewhereFor each individual, we have access to a range of anthropometric, disease, lifestyle and environmental data. These variables are summarized in Supplementary Table Biometric data were filtered to remove outliers with apparent errors in data entry. Outliers were identified on the basis of distribution density over the complete dataset of >6,000 individuals, resulting in height between 100 and 200 cm and weight between 25 and 300 kg.Biochemical traits were similarly curated to remove extremes and negative values (<0). Glucose was also checked against finger prick tests taken at the time of the survey, and values that were greatly discordant were also removed. Glucose measurements were further stratified by random or fasting glucose samples based on participant questionnaire responses.54.Blood pressure was manually curated for individuals for whom values differed by more than 20 units for the two readings taken, for whom diastolic pressure was higher than systolic, or for whom values were unusually high or low (<30 or >300). In these cases, both readings were manually checked, and discordant readings were discarded. These updated values were then merged with the remaining samples. A set of adjusted blood pressure phenotypes was also generated, adjusting for treatment for hypertension. In those individuals who were reported to be receiving some form of hypertension treatment, 15 units were added to systolic blood pressure and 10 to diastolic blood pressure (SBP_adj and DBP_adj)Quantitative traits were normalized using an inverse normal transform before complex trait analyses.For each individual, we have access to data for various sociocultural factors such as access to healthcare and clean water, yearly income, educational attainment, whether they speak an Indigenous language or not, and whether they live in a rural or urban environment.Localities were assigned values of latitude, longitude and altitude (metres) using data from the National Institute of Statistics and Geography (INEGI) in Mexico.To select the subset of biobanked samples to be genotyped, we first identified the total number of localities represented in the collection of extracted DNAs . We then allocated one sample to each locality in consecutive additive rounds targeting an average sample size of 5 to 10 individuals regardless of population density. The initial rounds were enriched for individuals who reported to speak an Indigenous language, and then randomly selected samples were included until saturating budget capacity. This strategy ensured maximization of both geographic coverage and representation of Indigenous ancestries, resulting in a total of 6,144 samples distributed nationwide. A further subset of 87 samples failed DNA quality control or hybridization during genotyping, for a total of 6,057 successfully genotyped samples. Samples were genotyped on the Illumina’s Multi-Ethnic Global Array (MEGA). The design of this array was previously led by C.R.G. and G.L.W. Several properties place the MEGA array as the ideal choice for biobank genotyping. It captures 1,748,250 SNPs derived from admixed population studies, making it broadly applicable in diverse populations. The array has boosted SNP coverage in both the MHC and KIR loci, a marker set of more than 30,000 SNPs for ancestry estimation, and includes more than 17,000 medically relevant genetic variants from previous GWAS and clinical studies. Such breadth of coverage of genomic diversity provides a comprehensive quantitative resource of the genetic variability in this cohort.título.Genome Studio was used to convert raw image files to plink files with raw genotype information. All SNPs were flipped to the forward strand, and duplicate SNPs were removed. For sites with missing chromosome number, physical position or both, we updated the map using the information in the SNP name or by mapping their rsID using dbSNP Build 151.We removed all individuals with >5% missing genotype data and all genotypes with >5% missing individuals. We restricted the analyses to autosomes and removed all monomorphic SNPs. We restricted the analysis to biallelic SNPs and removed all SNPs with an ambiguous strand for all downstream analyses. All related individuals were detected using plink (--Z-genome --min 0.5) after pruning for linkage disequilibrium (--indep-pairwise 50 5 0.5). A script was written to iteratively find and remove related individuals to obtain the final quality-controlled dataset.40 and the Human Genome Diversity Project (HGDP)55, Zapotec individuals from Oaxaca from the Population Architecture using Genomics and Epidemiology Study (PAGE)56, and Indigenous individuals from across Mexico from the Native Mexican Diversity Project (NMDP)12 for the analyses of population structure and ancestry.Reference genetic panels were used for various analyses of population structure. We used global populations from the 1000 Genomes Project (1KGP)For each reference panel, we restricted the analysis to autosomes, removed all monomorphic SNPs, flipped all SNPs to the forward strand, and removed SNPs with an ambiguous strand.10. An individual’s locality was used to place them into one of the seven regions: the north of Mexico, the north of Mesoamerica, the centre, occident and Gulf of Mexico, Oaxaca and the Mayan region in the southeast10. This classification was used to visualize and regionalize some of the population structure and history analyses, especially those relating to Indigenous genetic substructure within Mexico.We used an anthropological and archaeological context to delineate different Mesoamerican regions57. In this study, we obtain proxies for genetic ancestries using ADMIXTURE20 (see below). As such, we are discretizing a continuous quantity for the purposes of understanding the effects of varying demographic histories on genetic and complex trait variation in MXB. The labelling and use of such discretized ancestry proxies remains a contentious issue58. To clarify the point that such proxies are not essentialized entities in the real world, but rather variables we use for the purposes just described, we opt to refer to our ancestry proxies as being from the region whose present-day individuals such proxies cluster with. Thus, we use, “ancestries from the Americas”, “ancestries from West Europe”, “ancestries from West Africa”, “ancestries from South Asia” and “ancestries from East Asia” in the text, and shorter versions of the same for some figures (A(Americas) and so on).Genetic ancestry arises from a set of paths through the ancestral recombination graphSuch regions are useful for our analyses only in so much as they reflect demographic and environmental histories that may affect the genetic and complex trait variation we are interested in. This is only one arbitrary scale to discretize at, and we also consider the origins and implications of ancestral variations within such regional groupings in several analyses, in which we carry out dimensionality reduction within such regional groupings ) and MDS2(A(Americas))).60. In Mexico, such categories have a similar history of racism and eugenics as in other parts of the world61. We reject fixed hierarchical categorizations of humans, as well as their use to justify the superiority of one group over another. We use ancestry proxies that are estimated from ADMIXTURE using unsupervised clustering, as well as axes of ancestry that result from dimensionality reduction within these ancestries, capturing variation among groups from the Americas, for example. Despite the confluence of genetic ancestries from around the globe in present-day Mexico, genetic ancestries in humans are continuous over time and space and should be considered only in that complexity and at different scales.Although not intended, the groupings used may seem to some as similar to racial categories that were created in the past 500 years and used to justify European superiority and colonization of global regions including present-day MexicoFor the analyses of population structure, we merged the quality-control-filtered MXB dataset and reference panels using plink. We repeated some of the quality control steps on the merged dataset, removing any monomorphic or duplicate SNPs. We also removed individuals with >5% missing genotype data, and genotypes with >5% missing individuals to obtain the clean merged dataset.20 analysis. One was carried out on the merged dataset including MXB, Zapotecs from the Population Architecture using Genomics and Epidemiology Study, and global populations from the 1000 Genomes Project and the Human Genome Diversity Project  and ADMIXTUREect Fig. , and theect Fig. . FST ana62 was used to carry out the PCA. Principal components generated by smartpca . Unless otherwise noted, given the admixed nature of the Mexican individuals, we did not remove SNPs owing to departure from Hardy–Weinberg equilibrium in the MXB, as many SNPs are expected to be out of Hardy–Weinberg equilibrium owing to admixture and population structure.5  with individuals from the quality-controlled MXB dataset and individuals from the 1000 Genomes, the Human Genome Diversity Project and the Population Architecture using Genomics and Epidemiology Study as our reference panel 3 and to carry out ancestry-specific PCA 64 were published, allowing us to use these tools for the analysis of ancestry variation within the Americas for the complex trait analysis.Analyses were carried out to obtain axes of genetic variation or ancestry among a continental group. Such analyses also help interpret the specific origins of an ancestry present in Mexico today. These analyses were carried out using rfmix64 analyses, we used GNOMIX3 for local ancestry inference using its preset ‘best’ mode and then masked the non-Indigenous segments. For the European reference, we used the cohorts Iberian populations in Spain (IBS) and British from England and Scotland (GBR) from 1KGP (198 samples)40, for ancestries from Africa, the Yoruba in Ibadan, Nigeria (YRI) cohort from 1KGP (108 samples), and for ancestries from the Americas, Peruvian in Lima, Peru (PEL) from 1KGP (only those samples with >95% ancestry from the Americas) and the 50 genomes of Indigenous individuals across Mexico generated as part of the MXB Project (79 samples)65. For the PEL, we used an unsupervised clustering analysis with ADMIXTURE (K = 3) together with IBS and YRI from the 1KGP to find those PEL samples with >95% assignment to a cluster not shared with IBS or YRI; that is, with >95% ancestries from Americas. The additional 50 genomes from MXB were selected to have high Indigenous ancestries as described previously65. The reference genomes were merged with each array resulting in 856,352 SNPs in array 1 and 967,338 in array 2. Array 1 included 10 Indigenous groups from NMDP genotyped with the Affymetrix 6.0 array: Tarahumara, Huichol, Purepecha, Nahua, Totonac, Mazatec, Northern Zapotec , Triqui, Tzotzil and Maya (from Quintana Roo state). Array 2 included the 6,051 individuals from the MXB project genotyped with MEGA. The MAAS-MDS was applied to the Indigenous American ancestry segments  in both arrays 1 and 2. The analysis was run using average pairwise genetic distances and considering only individuals with >20% Indigenous American ancestries, to generate ancestry-specific MDS axes for ancestries from the Americas in the MXB 56 to estimate local ancestry using rfmix2. The MHC region was excluded from the analysis. SNPs out of Hardy–Weinberg equilibrium were removed from each of the reference panels (10−3) and the MXB AFR (10−8) subset beforehand. This dataset was merged with a subcontinental reference panel covering a range of groups in present-day Africa21. Pcamask19 was used to mask all ancestries other than ancestries from Africa, and to generate ancestry-specific principal components for ancestries from Africa in the MXB  with Northern and Western European ancestry and YRI: Yoruba in Ibadan, Nigeria)Ne) for thousands of years into the past30. These IBD segments can be further overlapped with local ancestry tracts to obtain ancestry-specific IBD tracts to estimate population size in an ancestry-specific manner for an admixed cohort 4.Analyses of population history using an approach that uses ancestry-specific identity-by-descent (IBD) segments were carried out on the entire MXB dataset, and on individuals belonging to each of the Mesoamerican regions Fig. –29. IBD 40 and the Population Architecture using Genomics and Epidemiology Study (Zapotecs from Oaxaca)56. SNPs in each population were previously filtered for Hardy–Weinberg equilibrium (10−5 for reference groups and 10−10 for the MXB samples). The MHC region was excluded from the analysis. We repeated some of the quality control steps on the merged dataset, removing any monomorphic or duplicate SNPs. We also removed individuals with >5% missing genotype data, and genotypes with >5% missing individuals to obtain the clean merged dataset.For this analysis, the MXB was merged with populations from the 1000 Genomes Project (CEU: Utah residents (CEPH) with Northern and Western European ancestry and YRI: Yoruba in Ibadan, Nigeria)66 to phase the data, refined-ibd (refined-ibd.17Jan20.102.jar)67 to call IBD and merge-ibd-segments (merge-ibd-segments.17Jan20.102.jar) to remove breaks and short gaps in IBD segments, removing gaps between IBD segments that have at most one discordant homozygote and that are less than 0.6 cM in length. Local ancestry was estimated using rfmix. The rfmix output was rephased to match the original phasing. asIBDNe (ibdne.19Sep19.268.jar) was run to estimate ancestry-specific population sizes using a 2-cM IBD length threshold.We followed a computational pipeline recommended by the developers of asIBDNe to call IBD segments and local ancestry along the genome. We used beagle (beagle.25Nov19.28d.jar)6 to generate, analyse and plot admixture graphs for a sample of 6,011 individuals from the MXB  and 20,000 (--n 20000) to ensure convergence; we also used the -slower flag, enabling the computation of the necessary information to plot the top trees, and a burn-in period corresponding to half the samples. We plotted the tree with the highest posterior probabilities, which provides a visual representation of the inferred admixture events and allows us to explore the uncertainty in the inferences. Further details of the AdmixtureBayes method and prior used can be found in the corresponding paper37. Python scripts were used to categorize ROH by length, and to overlap ROH with local ancestry calls from rfmix to obtain ancestry-specific ROH summary statistics (Supplementary Table The MXB dataset was pruned for linkage disequilibrium using plink (--indep-pairwise 50 5 0.9). ROH were estimated using plink (--homozyg) identifying 349,400 ROH. We estimated the number of ROH carried by an individual (nROH) and the total sum of ROH in an individual in kilobases (sROH or sumROH) Fig. . ROH werROH were also correlated with birth year in the MXB Fig.  and used68 was used to annotate the effect of a variant using the humdiv database, and picking one consequence (or transcript) per variant according to a criterion that includes the canonical status of the transcript, APPRIS isoform annotation, transcript support level, biotype of transcript (‘protein_coding’ preferred) and consequence rank preferring high impact.Variants were annotated according to whether they were ancestral or derived, and their functional effect depending on their location in a gene or genome. Ancestral alleles for each SNP in the MXB were inferred using the EPO pipeline from the 1000 Genomes Project. Variant Effect PredictorP value  or an overall mutation burden considering all allele frequencies. Our pipeline used the R packages matrixStats, dplyr and ggplot2. We correlated the mutation burden with the global ancestry percentage from different present-day continental origins in all individuals. The ancestry estimates were from the admixture analysis. We computed a Spearman’s correlation and lue Fig. .65. Variant effect predictor was used to annotate SNPs, and mutation burden was computed in the same manner. The deleterious category includes the following consequence terms: splice acceptor variant, splice donor variant, stop gained, stop lost and start lost.This analysis was repeated in the 1000 Genomes Project Mexican Ancestry in Los Angeles, California (MXL) cohort  based on distribution density over the dataset. Height was limited to participants with measurements between 100 and 200 cm; weight was restricted to between 25 and 300 kg. Glucose and fasting glucose levels were checked against finger prick tests taken at the time of the survey and values that were greatly discordant were removed. Fasting glucose measurements were defined on the basis of whether participants had eaten in the 8–12 h before the samples being taken.Quantitative traits were measured as previously describedBlood pressure was manually curated for individuals for whom values differed by more than 20 units for the two readings taken, for whom diastolic pressure was higher than systolic, or for whom values were unusually high or low (<30 or >300). In these cases, both readings were manually checked, and discordant readings were discarded. These updated values were then merged with the remaining samples. For GWAS, the first set of readings was used unless removed during the quality control process, in which case the second set of readings was used, if available. A set of adjusted blood pressure phenotypes was also generated, adjusting for treatment for hypertension. In those individuals who were reported to be receiving some form of hypertension treatment, 15 units were added to systolic blood pressure and 10 to diastolic blood pressure.69. Before GWAS, individuals with mismatched sex or IBD > 0.9 were removed. Quantitative traits were inverse normalized before analysis. Only case–control traits with more than 100 cases were taken forward for analysis. For all analyses, age, sex and the first four principal components were included as covariates. For cholesterol, triglycerides, HDL, LDL, hypertension and fasting glucose, BMI was also included as a covariate.GWAS analyses for both binary and quantitative traits were carried out with regenie (v3.1.3)GWAS was carried out on a random subset of 4,000 individuals with genotype data available, as described above. For quantitative traits, raw values were again normalized within the selected subset before analysis.R2 = 0.7; Bayes factor ≥ 2) of SNPs within each of these regions on the basis of summary statistics for each of the associated traits70. FUMA SNP2GENE was then used to identify the nearest genes to each locus on the basis of the linkage disequilibrium calculated using the 1000 Genomes EUR populations, and explore previously reported associations in the GWAS catalogue71 8  with the --score sum modifier . We tested the prediction performance of polygenic scores by computing the Pearson’s correlation between the trait value and the polygenic score  and only genotyped data  for each trait, genetic ancestries estimated from ADMIXTURE, continuous axes of ancestry variation estimated using MAAS-MDS, and ROH . We also considered biogeographical variables such as latitude, longitude and altitude (metres). We considered demographic variables of age and sex. Last, we considered sociocultural variables: educational attainment  not captured by the fixed predictors.75 was used to obtain principal components that capture ancestry and not relatedness  and unrelated (271) set (using kinship threshold 0.044) and carrying out PCA on the unrelated set); (2) PC-relate77 was used to obtain kinship coefficients that capture relatedness but not ancestry  to correct for population structure before calculating the kinship coefficients).The genetic relationship matrix was generated using the GENESIS R package using kinship coefficients. As kinship estimates can be inflated under the presence of population structure and admixture, we obtained kinship coefficients for the genetic relationship matrix in the following manner: (1) PC-air79 and variants in high linkage disequilibrium (r2 > 0.1 in a window of 50 kb and a sliding window of 1 variant).For this analysis, we removed rare variants (MAF < 5%), regions with known long-range linkage disequilibrium50.To account for multiple significance testing, the false discovery rate was controlled at 0.05 using the approach of Benjamini–HochbergABCA1 variant frequencies were computed using plink in individuals from the MXB stratified by ancestry proxies from ADMIXTURE or by HDL cholesterol levels , and selected samples were genotyped at the Advanced Genomics Unit of CINVESTAV  through a collaboration agreement. The data have been jointly analysed, promoting local leadership and participation of Mexican researchers and trainees. The project was reviewed and approved by the Research Ethics Committee and the Biosafety Committee of the INSP . For the present project, personally identifiable data were removed from the dataset.Samples were collected as part of the 2000 National Health Survey (ENSA 2000) conducted by the National Institute of Public Health ) across Mexico. The ENSA 2000 was carried out following the strictest ethical principles and in accordance with the Helsinki Declaration of Human Studies. Informed consent was obtained from all participants after extensive community engagement. National Health Surveys have been conducted periodically in Mexico since 1988, so the community is engaged with the study and receptive to household visits by INSP staff and fieldwork teams. As described in the original methodologyFurther information on research design is available in the Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41586-023-06560-0.Supplementary InformationSupplementary notes on the strengths and limitations of the MXB, sampling ascertainment in the MXB and an observation of gene–culture discordance in the MXB for ancestries and languages from the Americas; links to all software and R packages used in this study; Figs. 1–61 and Tables 1–9, providing further details of the dataset, and of the population genetic and complex trait analyses presented in the manuscript.Reporting SummaryPeer Review File


Sorghum bicolor (L.) is one of the oldest crops cultivated by human beings which has been used in food and wine making. To understand the genetic diversity of sorghum breeding resources and further guide molecular-marker-assisted breeding, six yield-related traits were analyzed for 214 sorghum germplasm from all over the world, and 2,811,016 single-nucleotide polymorphisms (SNPs) markers were produced by resequencing these germplasms. After controlling Q and K, QTLs were found to be related to the traits using three algorisms. Interestingly, an important QTL was found which may affect multiple traits in this study. It was the most likely candidate gene for the gene SORBI_3008G116500, which was a homolog of Arabidopsis thaliana gene-VIP5 found by analyzing the annotation of the gene in the LD block. The haplotype analysis showed that the hap3SORBI_3008G116500 was the elite haplotype, and it only existed in Chinese germplasms. The traits were proven to be more associated with the SNPs of the SORBI_3008G116500 promoter through gene association studies. Overall, the QTLs and the genes identified in this study would benefit molecular-assisted yield breeding in sorghum. Sorghum bicolor is one of the oldest crops cultivated by human beings, and it is also one of the only crops affected by artificial selection evolution , spike length was measured from the leaf scars under the spike to the top of the main spike. Lastly, mature grains of each inbred line were harvested and dried at 50 °C until the weight became constant. After drying, we collected the 100-grain weight data. The means of all phenotypic data and correlation coefficients were calculated using SAS.The heading date was collected at the heading stage. At the maturity stage, the other phenotypic data of five yield-related traits were collected. For collecting plant height trait, five plants were randomly selected to be measured. Numbers of Internode were determined after stripping leaves from the stem. The data of spike type was collected according to the “Guidelines for the conduct of tests for distinctness, uniformity and stability-Sorghum . The LD was also calculated with Plink using the SNP data of whole genomes and each chromosome. Population structure (Q) was determined using Admixture software and filtered SNP markers . The numhttps://www.gramene.org/, accessed on 29 July 2022). The gene association study was conducted using TASSEL5.0 [The GWAS for the six yield-related traits was performed for the three algorisms, including lmm, fastlmm and emmax, using GEMMA, FaST-LMM, and EMMAX programs ,54,55. TASSEL5.0 .Overall, six traits related to yield were analyzed by three different algorisms based on natural variations in 214 landraces, and many significant loci were obtained. We also analyzed the differences of the three algorisms and the detection ability for different traits. Finally, a candidate gene was obtained that could affect multiple traits and find the elite haplotype. Our results enrich the discovery of sorghum-associated SNPs, and the discovered QTLs and gene will be helpful to sorghum breeding.


Large-effect loci—those statistically significant loci discovered by genome-wide association studies or linkage mapping—associated with key traits segregate amidst a background of minor, often undetectable, genetic effects in wild and domesticated plants and animals. Accurately attributing mean differences and variance explained to the correct components in the linear mixed model analysis is vital for selecting superior progeny and parents in plant and animal breeding, gene therapy, and medical genetics in humans. Marker-assisted prediction and its successor, genomic prediction, have many advantages for selecting superior individuals and understanding disease risk. However, these two approaches are less often integrated to study complex traits with different genetic architectures. This simulation study demonstrates that the average semivariance can be applied to models incorporating Mendelian, oligogenic, and polygenic terms simultaneously and yields accurate estimates of the variance explained for all relevant variables. Our previous research focused on large-effect loci and polygenic variance separately. This work aims to synthesize and expand the average semivariance framework to various genetic architectures and the corresponding mixed models. This framework independently accounts for the effects of large-effect loci and the polygenic genetic background and is universally applicable to genetics studies in humans, plants, animals, and microbes. Today, linear mixed models (LMMs) are routinely applied in plant breeding and quantitative genetics research. They are used for the prediction of genetic values in plants and animals , and to Candidate gene discovery through genome-wide association studies (GWAS) and quantitative trait locus (QTL) mapping is prolific in plant and animal populations . DespiteBRCA2 gene can have large effects but be incompletely penetrant, interact with other genes, and may be necessary but insufficient for predicting breast, ovarian, and other cancer risks in women  provides accurate variance component estimates (VCEs) and variance component ratios for all relevant genetic terms regardless of study design or population type, e.g. outbred or inbred. We sought to provide a synthesis and extension of the previously published works on the ASV  +        GR,          rcov  = ∼ units,  data  = data)data is an Y, levels of the marker genotypes, entries, and levels of the residual genetic term, i.e. entries. The variable units is inferred by R/sommer::mmer and can be considered as a column with as many levels as rows in the data  +vsr +       GR,        rcov  = ∼ units,  data  = data)  KM is the matrix where R/MASS::mvrnorm and transformed such that the population was heterozygosity R/stats::rnorm. A single explanatory locus was simulated with a segregation ratio of approximately R/stats::rnorm. We simulated marker effects for all g. For each simulated population we expressed LMM  +        GR,        rcov  = ∼ units,    data  = data)data is an Y, seven columns corresponding to the marker effects and interactions, a factor-coding entries G, and a factor-coding levels of where Due to the similarities between our first set of experiments and this extension, we do not provide any additional simulations demonstrating the successes of this model extension. LMM  is expremmer +GR,          rcov  = ∼ units,  data  = data)data is an Y, a factor-coding levels of G, and a factor-coding levels of where We performed one set of simulations for this model extension that follows the exact parameters as the first simulation set  +        vsr +        GR,         rcov  = ∼ units,  data  = data)data is an Y, a factor-coding levels of the marker genotypes, and three equivalent factor-coding entries, to be used for the additive, dominance, and residual genetic terms.where We performed one set of simulations for this model extension that follows the exact parameters as the first simulation set data is an Y, one factor coding for the entry ID and one-factor coding for Blocks within the random = syntax. In R/sommer, R/sommer::mmer output. “VarBeta” is the name of the model estimated variance–covariance matrix among entry means in R/sommer. The R/sommer::adiag1 to obtain R/base::solve.where The LMM for stage 2  is expremmer +vsr +        G:Env + GR,         rcov = ∼ vsr,        Gtc = matrix), nIters  = 25, emWeight = rep, W     = invOmega, data   = data)data is an M, two equivalent factor-coding entries, e.g. G and Env. In this approach, we must fix the residual variance component equal to 1 so that all the scaling of the vsr argument, the Gti and Gtc arguments are used to set the initial value of the variance component equal to the inverse of the variance among adjusted entry means  for product delivery and germplasm improvement. While the variance explained is directly linked to the effect size, it is not a direct substitute. However, the random effect machinery allows researchers to obtain variance component estimates, and effect sizes  simultaneously  is heritable, but no single locus explains any appreciable amount of phenotypic or genotypic variance (g) without relying on any particular locus but instead capturing variation of a genome-wide sample of markers. The more challenging scenario is the intermediate case in which a trait is controlled by both loci that are discernible from the polygenic background and a quantitative polygenic effect.As a point of contrast, yield in maize  with the target  and shouWe believe the “phenotype” is the entry mean for a given subdivision of environments, not the individual observations that constitute that entry mean. Our discussion here is primarily predicated on plants, but does not necessarily exclude other organisms, where replicate observations may be available per entry. In the words of Dr. Rex Bernardo, “…the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments” . Howevertry mean  and varian basis . This con is the number of entries . In stagewise analysis, The ASV estimator of total variance  and the The form of the LMM for this analysis assuming only one explanatory marker iswhere We then calculated where The ASV definition of total variance from LMM  iswhere The ASV definition of genomic variance isIn general, we replace the unknown parameter values . It is possible to extend this using the approach for multilocus models as in Equation . Increasing r from 1 to 4 did not affect the precision or accuracy of genomic and marker-associated variances. However, increased numbers of replicates did improve the precision of residual variance components. This is because entries are replicated among plots (n). Our simulations, in conjunction with our previous results , it is possible to fully saturate the multilocus interaction with more levels than are observed in a given data set. Hence, it is important to consider the number of interaction terms evaluated. In this situation, packages such as H) The factor-coding of the Mendelian and oligogenic markers is a different approach than is standard in GWAS. In GWAS, markers are typically treated as fixed and coded as continuous values, e.g. the dosage model. Assuming that a researcher is working with an outbred species and the heterozygosity  for this analysis assuming only one explanatory marker isAA and aa) or heterozygous (Aa), to LSMs. For example, the where Other terms are defined in LMM . This exThe ASV estimate of the additive variance explained by a locus is obtained as in Equation  byhth marker genotype  across environments -BLUP. ASV is only used to obtain accurate VCEs. It has been demonstrated that marker coding and different strategies for scaling and centering ASV works under many model assumptions in GLMM analyses. Beyond the often-assumed variance–covariance structure in this study, e.g. e-models .As substantiated by our simulations in this study and the context of our previous studies, ASV with REML estimation of the underlying variance components yields accurate estimates for oligo- and polygenic effect, both individually and collectively, and BLUPs of the additive and dominance effects of marker loci (t design , 2010. I