We estimate α for 25 UK Biobank diseases and complex traits. All traits produce negative α estimates, with best-fit mean of –0.38 (s.e. 0.02) across traits. Despite larger rare variant effect sizes, rare variants (MAF < 1%) explain less than 10% of total SNP-heritability for most traits analyzed. Using evolutionary modeling and forward simulations, we validate the α model of MAF-dependent trait effects and assess plausible values of relevant evolutionary parameters.Understanding the role of rare variants is important in elucidating the genetic basis of human disease. Negative selection can cause rare variants to have larger per-allele effect sizes than common variants. Here, we develop a method to estimate the minor allele frequency (MAF) dependence of SNP effect sizes. We use a model in which per-allele effect sizes have variance proportional to [ Negative selection removes deleterious genetic variation, and can influence genetic architectures and evolution of complex traits. Here, the authors analyze data from 25 UK Biobank diseases and complex traits, and quantify frequency-dependent genetic architectures which suggests actions of negative selection. Recently, several studies have investigated the relationship between minor allele frequency (MAF) and trait effects6. However, these studies have analyzed a small number of traits and have not evaluated the genome-wide contribution of rare variants (MAF < 1%), which remains unknown7.The contribution of rare variants to the genetic architecture of human diseases and complex traits is a question of fundamental interest, which can inform the design of genetic association studies and shed light on the action of negative selectionHere we develop a profile likelihood-based mixed model method to infer MAF-dependent architectures from genotype and phenotype data. We apply our method to 25 complex traits and diseases from the UK Biobank data set, analyzing data from 113,851 individuals and 11,062,620 SNPs, including rare variants (MAF > 0.07%). Our analysis shows that rare variants have significantly increased per-allele effect sizes for most traits, with significant heterogeneity across traits. For each of these traits we also estimate the phenotypic variance explained by variants in different frequency ranges, including rare variants.11. Specifically, if SNPs that affect a trait are more likely to be under negative selection, they will be enriched in the lower-frequency spectrum, so that lower-frequency SNPs will on average have larger trait effects. Thus, MAF-dependent architectures estimated from genotype and phenotype data can shed light on evolutionary parameters. Previous studies have used MAF-dependent architectures or related information to estimate a coupling parameter9 between fitness effects and their trait effects for prostate cancer6 and type 2 diabetes13. In this work, we use evolutionary modeling and forward simulations to investigate whether our parameterization of MAF-dependent effects  is consistent with evolutionary models, estimate the coupling between fitness effects and trait effects, and draw inferences about the average genome-wide strength of negative selection.It is widely believed that frequency-dependence of SNP effect sizes is due to increased negative selection on variants that affect complex traits15 (here referred to as the α model), in which the per-allele trait effect β of a SNP depends on its MAF p via:We assume a previously proposed random-effect modelα implies that lower-frequency SNPs have larger per-allele effect sizes, whereas α = 0 implies no dependence, and α model is simple and convenient, but has not previously been validated by evolutionary modeling.A negative value of mentclass2pt{minimα using a linear mixed model framework16. The model likelihood depends on α, α by maximizing the likelihood with respect to α. Our estimate 15. We include linkage disequilibrium (LD)-dependent SNP weights17 in our model, to avoid biases due to LD-dependent architectures19. Details of the method are described in the Methods section; we have released open-source software implementing the method (see URLs).For a given set of genotype and phenotype data, we estimate 20 and simulated phenotypes, using N = 5000 individuals and M = 100,000 consecutive SNPs from a 25 Mb block of chromosome 1 (see Methods). We used default parameter settings of α = − 0.3, 17, but we also considered other parameter settings for each of these. Imputation noise was introduced by randomly sampling the genotypes used to simulate phenotypes from imputed genotype probabilities, while still using the expected dosage values for inference (see Methods).We evaluated our method using simulations based on imputed UK Biobank genotypesα estimates at default and other parameter settings, both using LD-dependent weights α when LD is correctly modeled, and only modestly biased estimates of α when LD is not correctly modeled. Importantly, imputation noise does not induce bias, indicating that our method is unbiased even if causal SNPs are not perfectly tagged. Although values of N and M in our main simulations were chosen to approximately match the power of the UK Biobank traits analyzed , similar results were obtained when N was reduced to 2500, a setting with lower power , but were well-calibrated in simulations at larger values of N and M .In Table mentclass2pt{minimmentclass2pt{minimα, we also used our simulation framework to evaluate the effectiveness of our method in obtaining SNP-heritability estimates that avoid biases due to MAF-dependent and LD-dependent architectures. In Supplementary Table 22. 14. Other methods of avoiding bias due to MAF-dependent and LD-dependent architectures have recently been proposed, including GREML-LDMS4 and LDAK19; a complete benchmarking of SNP-heritability estimation methods is provided in ref. 23.Although the main focus of this paper is on obtaining and interpreting estimates of α are likely to be robust.We applied our method to 113,851 British-ancestry individuals from the UK Biobank with 1000 Genomes- and UK10K-imputed genotypes at 11,062,620 SNPs with at least 5 minor alleles in the UK10K reference panel . We analyzed 25 heritable, polygenic traits with at least 50% of individuals phenotyped , and 20 traits had significantly negative estimates , implying that lower-frequency SNPs have larger per-allele effect sizes. We observed statistically significant heterogeneity in estimates of α across the 25 traits (P = 0.0014), consistent with different levels of (direct and/or pleiotropic) negative selection across traits (see Discussion); our test for heterogeneity accounts for estimation noise, which varies across traits depending on heritability and sample size (see Methods). We estimated the underlying distribution of true (unobserved) values of α to have mean −0.38 (s.e. 0.02) and standard deviation 0.08 (s.e. 0.03), assuming a normal distribution (see Methods). We obtained very similar results when repeating the entire analysis using 9,336,687 SNPs with MAF > 0.3% in the UK10K reference panel . Results are reported in Fig. α estimate of −0.38, and a relatively small proportion of SNP-heritability even for the most negative α estimate of −0.60. Specifically, at α = −0.38 (s.d. 0.08), only 8.9% (s.d. 2.7%) of SNP-heritability is explained by SNPs with MAF < 1%. We also used We estimated the proportion of SNP-heritability explained by SNPs in each part of the MAF spectrum, for different values of 17, with an LD-dependent architecture parameter of τ* = −0.3.  We also performed an analysis in which MAF-dependent and LD-dependent effects are estimated jointly, maximizing the profile likelihood over values of both α and τ* for each of the 25 UK Biobank traits (see Methods). Results are reported in Supplementary Table τ* was generally close to τ* = −0.3. Although a different value of τ* provided the best fit for some traits, the overall impact on α estimates was small, with the best-fit distribution of true (unobserved) values of α across traits changing from −0.38 (s.d. 0.08) to −0.35 (s.d. 0.11).The above analysis used LD-dependent weights based on a model of ref. 11. Here we use evolutionary modeling to predict the frequency-dependent architecture of a trait, given the coupling between fitness effects and trait effects. The aim of this analysis was to investigate whether the α model (Eq. α across 25 UK Biobank traits.Frequency-dependent trait effect sizes have been widely attributed to negative (purifying) selection on variants that affect complex traits, which causes them to be enriched for lower-frequency variants, so that lower-frequency SNPs will have larger traits effects9, which introduces a parameter τ quantifying the coupling between a SNP’s fitness effect (selection coefficient s) and target trait effect size (β); τ > 0 implies that SNPs under negative selection have larger trait effect sizes on average, whereas τ = 0 corresponds to no coupling. Using this model, we derived two analytical results. First, it is straightforward to show thatp is minor allele frequency (see Methods). This implies that increased trait effects for lower-frequency variants requires both that lower-frequency variants have significantly larger selection coefficients s and that τ > 0. Second, based on Eq. (sτ2|p) to quantify the MAF-dependence of SNP effects under the Eyre-Walker model (see Methods). In this derivation, we ignored LD between selected SNPs, assumed a constant effective population size Ne, and assumed that selection coefficients s of SNP loci across the genome are drawn from a gamma distribution, with mean k (ref. 24).  Under these assumptions, we derived the result that there exists a MAF threshold T such that for p > T the α model approximately holds, but for p < T trait effects are approximately independent of frequency (see Methods). The threshold isWe used an evolutionary model of Eyre-WalkerT is independent of the trait analyzed, since k parametrize the distribution of genome-wide selection coefficients.Intuitively, this threshold corresponds to the maximum frequency at which even the most strongly selected SNPs are still only affected by genetic drift, with their frequency being too low to be significantly affected by selection. We note that 25, using a European demographic model26 and realistic LD patterns (see Methods). Specifically, for a given τ we computed E(sτ2|p) in Eq. , so that T = 0.006  values of T with less MAF-dependent effects would be ignored. However, Tsim of 0%, 5% and 10% and genome-wide UK Biobank genotypes (see Methods), in order to assess which value of Tsim was most consistent with T.) Specifically, we simulated traits mimicking UK Biobank height in heritability, sample size and α. Due to computational constraints, we did not simulate traits other than height; however, since T is the same across traits (see Eq. α model with threshold Tsim and UK Biobank imputed genotypes.) We determined that the Tsim = 0% (−0.10 (s.d. 0.02); p = 0.01 for difference), and very significantly different from values for Tsim = 5% (−0.16 (s.d. 0.01); p = 0.0002 for difference) and Tsim = 10% (−0.19 (s.d. 0.02); p = 0.0007 for difference) (see Supplementary Table Tsim = 0% only (−0.01 (s.d. 0.07); p = 0.7 for difference) (see Supplementary Table 9 (see Discussion and refs. 28) or of the assumption of gamma distributed SNP fitness effects. In summary, our results are somewhat supportive of T < 5%, i.e., the α model provides a good fit for common SNPs (MAF ≥ 5%) but may overestimate SNP effect magnitudes of SNPs with MAF < 5%, but this should not be viewed as a conclusive finding.We sought to draw inferences about the threshold τ. First, a threshold T < 5% would imply an average selection coefficient Ne = 10,000 (ref. 29) and k = 0.25 (ref. 24), −4 or stronger. We caution that this bound on T, which should not be viewed as a conclusive finding. Second, we determined that the best-fit estimate of τ value in the range  , α model using SNPs above the threshold T from Eq. . First, a value of k ≥ 0.0625 would imply that −5 or stronger. Second, the best-fit estimate of τ value in the range   and standard deviation 0.08 (s.e. 0.03), implying that only 8.9% (s.d. 2.7%) of SNP-heritability is explained by rare SNPs (MAF < 1%), despite significantly larger effects for rare variants. Although rare variants explain relatively little heritability, rare variant association studies may still identify variants of large effect that reveal interesting biology and actionable drug targets30. On the other hand, rare variants will likely play only a limited role in polygenic risk prediction, which will be largely driven by common variants.We have quantified the MAF-dependent architectures of 25 diseases and complex traits under the T < 5%, i.e., the α model provides a good fit for common SNPs (MAF ≥ 5%) but may overestimate effect magnitudes of rare and low-frequency SNPs; our estimate of 8.9% (s.d. 2.7%) of SNP-heritability explained by rare SNPs (MAF < 1%) should therefore be viewed as a suggestive upper bound. This would imply an average genome-wide negative selection coefficient on the order of 10−4 or stronger, given the MAF-dependent architectures that we inferred. The best-fit α estimate across 25 traits implies an Eyre-Walker9τ parameter between 0.3 and 0.5, quantifying the coupling between fitness effects and trait effects. These findings are conditional on the assumption that the shape parameter k of the fitness effect distribution of genome-wide SNPs does not substantially differ from the value inferred for coding variants by ref. 24. Under a broader range of possible values of k, −5 or stronger, and the best-fit α estimate across 25 traits implies a τ value between 0.3 and 0.8. We caution that these results may be impacted by violations of model assumptions, such as the Eyre-Walker fitness-trait coupling model9 (see discussion below) or the gamma distribution of SNP fitness effects; these assumptions have been frequently employed13, but may not perfectly fit UK Biobank traits. Our finding that estimates of α (and hence τ) vary only modestly across traits is consistent with the action of pleiotropic selection, in which SNPs that affect the target trait also affect other selected traits31; under direct selection, greater variation in τ would be expected, and traits that are not directly selected would have τ = 0.Using evolutionary modeling and simulations, we determined that our results are somewhat supportive of 5, as well as height and BMI4. These studies analyzed a small number of traits, and either did not analyze rare variants5 or aggregated all MAF < 10% variants into a single MAF bin4, underscoring the difficulty of obtaining precise estimates of rare variant heritability using the MAF bin approach. Another study used targeted sequencing of 63 prostate cancer risk regions to conclude that 42% (s.e. 11%) of the prostate cancer SNP-heritability attributable to these regions in African Americans is due to rare SNPs (MAF < 1%), although rare variant heritability in Europeans was non-significant6.Recent studies have investigated MAF-dependent architectures in genome-wide analyses of schizophrenia19 (revising an earlier LDAK method14) and estimated a parameter that it referred to as α. We refer to this parameter as αLDAK, because it is different from the parameter α that was previously described in refs. 15 and that is defined and estimated in this paper. Specifically, the Discussion section of ref. 19 states that the SNP effect size variance is proportional to 19, the SNP effect size variance is proportional to wj is an LD-dependent weight (see Eq. (19). Unlike the LD-dependent weights that we use17, wj is dependent on MAF, with lower frequency SNPs having higher values of wj. Thus, SNP effect size is specifically not proportional to αLDAK is a parameter that is different from α. Indeed, our simulations confirmed that estimates of αLDAK obtained using the LDAK software were upward biased by roughly 0.4 compared to the true α as defined in previous work15 and this paper  is independent of the number of SNPs. However, we determined here that inclusion or exclusion of rare variants does not significantly affect our results  in their analysis of prostate cancer to simulation results, inferring 27 used a different modeling approach to estimate the mutational target load.In addition, several recent studies have drawn inferences about evolutionary parameters that affect complex traits. Refs. 34, meriting further investigation. Second, we use the Eyre-Walker model9 to parameterize the coupling between fitness effects and trait effects. The Eyre-Walker model has previously proven useful in a variety of settings13, but other coupling models are also possible28 and merit further exploration. One limitation of the Eyre-Walker model is that it does not allow for signed correlations between SNP trait effect and selection coefficient, i.e., the damaging allele is equally likely to reduce or increase the trait value. This assumption is violated when the target trait is under direct selection, but is plausible if selection on the SNP is mainly pleiotropic, which appears to be the dominant form of selection for the traits analyzed here (see above). Third, we assume that the distribution of selection coefficients follows a gamma distribution. This assumption implies that there are no outlier SNPs under exceptionally strong negative selection. Such extremely selected SNPs would stay at very low frequencies and only affect our results if they had extreme effects on the target trait. However, such SNPs have not been identified for most complex traits2. Fourth, our analytic derivations ignore LD and assume a constant population size. Our derivations imply that α = −2τ (see Methods), but our forward simulations, which include realistic LD patterns and demography, suggest that α = −τ. The direction of this change is consistent with the action of background selection due to LD, since strong LD leads to a SNP’s frequency being influenced not only by its own selection coefficient but also by the selection coefficients of many other correlated SNPs, leading to a less negative α value for a given τ. However, this difference could potentially also be due to demography35. The impact of LD and demography on α could potentially be investigated further using forward simulations. Finally, our forward simulations assume that negative (purifying) selection is the dominant mode of selection affecting complex traits. Although positive selection is likely to affect some loci, recent work has suggested that selective sweeps were rare in human evolution36 and hence unlikely to have substantial genome-wide effects on MAF-dependent trait architectures. We also did not investigate the potential effects of stabilizing selection27. Despite these limitations, our quantification of MAF-dependent effect sizes and investigation of the underlying evolutionary parameters is broadly informative for the genetic architectures of diseases and complex traits.We note several limitations in our work. First, our analyses are restricted to high-prevalence diseases and quantitative traits, as low-prevalence diseases are not well-represented in the UK Biobank due to random ascertainment. This motivates additional analyses of low-prevalence diseases, which could potentially be subject to stronger direct selection. However, we caution that our method might be susceptible to biases when used to analyze ascertained case-control traits, as previously described for linear mixed model based heritability estimation methodsN individuals and M SNPs withWe assume a linear complex trait model for y is a vector of N phenotype values with mean zero, X is the mean-centered genotype matrix, β is the vector of M SNP effects and ε is a vector of environmental effects . Furthermore we assume the effect size of SNP j to be a random variable that follows a distribution depending on its minor allele frequency (MAF) pj:α value indicates larger trait effects on average for lower-frequency SNPs, whereas α model, has been used in previous analyses of complex traits15. We note that β defines the per-allele SNP effect which is distinct from the heritability explained by a SNP. Under Hardy-Weinberg equilibrium and given Eq. ]α1+.Here, y is a multivariate normal distribution withFrom Eqs.  and 5)  5) it foX, SNP frequency vector p and phenotype vector y, the likelihood over the three parameters α is fully defined by Eq.  was derived in the following way: for some α′, XDα′XT was calculated. Given phenotype values y and for a given α′, we inferred maximum likelihood estimates for 37, using the GCTA software implementation37. This procedure was repeated for a range of α′. Here we used a minimal range of α′∈{−1.00, −0.95,…,0.00} for all traits, but extended the range to higher values if necessary, such that there is a minimal difference of 5 in log profile likelihood between the mode and the boundary. This ensures that the part of the curve that is significantly above zero is sampled. These data points were then interpolated with a natural cubic spline, yielding the final profile likelihood curve. Credible intervals for 38.In practice, the profile likelihood α values across n traits by comparing α values across traits, was calculated by assuming normally distributed true α with mean α estimates most closely. We note that by accounting for the standard errors in our estimates of α, our approach ensures that any heterogeneity that is detected reflects true differences in frequency-dependent architectures and not merely differences due to estimation noise, which varies across traits depending on heritability and sample size.Given 17 showed that for a given MAF, SNPs with higher LD have lower per-allele effects on average. Specifically, they use level of LD (LLD), defined as the rank-based inverse normal transform of the LD score. LLD is transformed separately in each part of the MAF spectrum, ensuring that it is independent of MAF. Ref. 17 reported that SNPs that have LLD one standard deviation above the mean have a squared per-allele effect size reduced by (30 ± 2)% on average. This violates our assumption that, at a given MAF, all SNP effects are independent and identically distributed.Ref. To avoid bias in our estimation due model misspecification, we incorporated LD-dependent SNP effects by changing Eq.  to7\docu17, however, since LLD has mean zero and is independent of MAF, β are not i.i.d. given p. To remove the LD dependence in the effect size distribution, we calculated a renormalized genotype matrix p. Unless otherwise stated, we hence estimated α using X to avoid biases due to LD-dependent architectures.This expression incorporates the LD dependence of ref. l in Eq.  to \docuτ*, similar to ref. 17. We assume thatWhen estimating LD-dependent architectures, we used an LD-weight parameter α and τ* by identifying the pair of values  that maximizes the profile likelihood using a 2D grid, with τ* = −0.60, −0.45, −0.30, −0.15, 0.00 and α = −1.00, −0.95, −0.90,….We jointly estimated 39: individuals were selected to have self-reported and confirmed British ancestry and related individuals were removed from the analysis such that the pairwise genetic relatedness is < 5% (after LD-pruning SNPs). Individuals that had withdrawn consent to participate in the UK Biobank project after initial publication were removed from the analysis. We used imputed genotype data as provided by UK Biobank. These genotypes were imputed using the IMPUTE2 software40 and a joint reference panel from the UK10K project41 and 1000 Genomes Phase 3 (ref. 42). The resulting imputed genotype data includes roughly 70,000,000 SNP loci across the 22 autosomal chromosomes. The data was downloaded in the BGEN file format (see URLs), a compressed file format that includes—for each individual and variant site—the probability of being homozygous reference, heterozygous, or homozygous alternative. Due to imputation uncertainty, the genotype matrix X and the allele frequencies p are not known precisely. Instead, we use the expected genotypes given these probabilities (genotype dosages). To exclude large-effect SNP loci from human leukocyte antigen genes, SNPs on chromosome 6 in the 30–31 Mb region were masked and we verified that no significant associations were found in nearby regions after masking. Due to memory constraints, GCTA could not be run using a GRM of all 113,851 individuals at once. Instead, we divided all individuals into three equally sized batches, calculating the profile likelihood of α for each batch and using the sum of the resulting log likelihoods to compute the final likelihood curve.We use the UK Biobank phase 1 data release (see URLs), which comprises of data from 152,729 individuals genotyped at 847,131 SNP loci. Here, we only used data from 113,851 individuals following selection criteria previously used by ref. α estimation only using SNPs of MAF > 0.3% did not lead to significantly different results, implying that our results are not significantly affected  in our main analysis. To further assess calibration of imputation noise, we compared the uncertainty implied by the genotype probabilities with an empirical assessment of imputation accuracy performed by the UK Biobank study (see URLs). Supplementary Figure N = 5000 random subset of the 113,851 unrelated British UK Biobank individuals. We used M = 100,000 consecutive SNPs from a 25 Mb block of chromosome 1. N and M where chosen to approximately match the power of the UK Biobank traits analyzed . As in the main analysis of UK Biobank traits, only SNPs with at least 5 minor alleles (MAF > 0.07%) in the UK10K reference panel were included. Phenotype values were generated using the linear model described in Eq.  than in their study . Due to computational constraints we did not use their workflow for imputed genotypes, but rather used the same hard-called genotypes for both phenotype simulations and estimation, an option available in LDAK.Simulations to estimate Tsim = 0%, Tsim = 5% and Tsim = 10%, we used genome-wide SNPs  and set the number of samples , α = −0.45 and h2 = 0.61, to match UK Biobank height. We randomly selected 1% of SNPs to be causal. In simulations with Tsim = 0%, causal effect sizes were sampled from Tsim = 5%, causal effect sizes were sampled from Tsim = 10%.When simulating trait values with 16 require that all SNP effects are i.i.d. distributed in order to avoid biases. In the case of MAF-dependent SNP effects, this assumption is clearly broken. This issue has been addressed in previous work and several solutions to this problem have been suggested19. Here we show that knowing α for a given trait can provide another way to avoid heritability estimation biases due to MAF-dependent architectures. As previously stated, our model assumes y = Xβ + ε, with βj is the per-allele effect, the average effect on the phenotype of having one minor allele. However, one can define renormalized genotypes y using REML. The variance in the phenotype explained by M SNPs can be calculated in the following way:α = −1, as has been used in many previous methods16, A is simply equal to M.Heritability estimation methods based on standard restricted maximum likelihood (REML) estimation in a linear mixed model framework37. Our SNP heritability estimate In practice, heritability estimation was performed in the following way: the renormalized genotype matrix 38), as well as at least 50% of the 113,851 British ancestry individuals to be phenotyped. We also removed phenotypes for which the top 10 SNPs explained 10% or more of the trait variance, so as to avoid α estimates that are dominated by a few top SNPs, as our goal is to study polygenic architectures.  The 25 traits that we chose include 21 quantitative traits and 4 case–control traits. Eleven of the quantitative traits are blood cell traits, whereas the remaining 14 include a wider range of physiological measurements and diseases. Since the number of available blood cell traits was large and many of them were highly correlated, we additionally required blood cell traits to have a pairwise phenotypic correlation of r2 < 0.5, removing the less heritable trait for any correlated pair.In this analysis we investigated 25 highly heritable and polygenic human traits  were removed from the analysis. Sex and ten principal components of the GRM were included as fixed effects for all traits, with additional trait specific covariates also included for some traits  = E|p). The main assumption of this analysis is that, at a given selection coefficient, the effect size of the SNP is independent of its frequency, i.e., E = E(β2|s). This is equivalent to the statement that the frequency dynamics of a SNP is influenced by β2 only through s. We then use the model of Eyre-Walker9, where the absolute value of β is proportional to sτ(1 + ε), with ε ~ N and τ indicating how strongly β depends on s. It follows that E(β2|s) ∝ sτ2 and from above, for some constant c,We aimed to use the frequency dependence of SNP effects to draw conclusions about the fitness effects of SNPs, as well as the coupling between fitness and the target trait effects. Let τ, this equation shows that increased average effects of lower-frequency SNPs requires lower-frequency SNPs having increased s and hence implies significant negative selection. Some previous analyses32 have argued that in the absence of selection, SNPs of MAF ranges of equal width  are expected to explain an equal fraction of heritability. However, even in the absence of selection, population expansion can lead to excess rare variants, leading to increased rare variant heritability43. Increased rare variant heritability is therefore not necessarily a sign of selection.Given a positive τ and the joint distribution of s and p, E(β2|p) can be derived from Eq. (25). Simulations were run with a European demographic model inferred by ref. 26, a burn-in of 3880 generations before the bottleneck, a mutation rate of 44, and a recombination rate of 10−8 per base pair per individual per generation45. These simulations also require assumptions about the distribution of fitness effects (DFE), i.e., the distribution of s for de novo mutations, but the DFE for genome-wide SNPs in humans is currently not known. We assumed a gamma distributed DFE, using a plausible range of average fitness effects, T close to or greater than 0.5 and hence no or almost no frequency dependence; see Supplementary Figure k = 0.125 and 0.25 which includes the range of plausible values derived by ref. 24. In the analyses reported in Supplementary Figure k = 1, 0.5, 0.25, 0.125, 0.0625). Although the gamma distribution does not include variants with exactly zero effect size, k effectively parametrizes the polygenicity of fitness effects. For example, at k = 0.0625, the mean SNP fitness effect is almost 7000 times larger than the median SNP fitness effect, indicating that fitness effects are extremely sparse. At k = 1, the mean is only 1.4 times larger than the median, indicating that fitness effects are extremely polygenic. Since SNPs with negligible fitness effects also have negligible effects on the target trait under the Eyre-Walker model9, the shape parameter k determines the polygenicity of both fitness and the target trait.Assuming we know from Eq. . We simurom Eq. 2. Simulatσ2, was set to zero. This parameter does not change SNP effects on average and is therefore negligible in the limit of large SNP numbers. This was also noted in original analysis by ref. 9.For each choice of DFE we simulated 25 independent replicates over a 4 Mb block each, for a total of 100 Mb with each DFE. In all simulations the Eyre-Walker noise parameter, Ne, E(β2|p) can also be derived analytically. Under these assumptions and assuming mutation rate per base pair μ ≪ 1/Ne (ref. 44), it is known that 46). Given s is drawn from a gamma distribution with mean k, we obtainIn the absence of LD between selected SNPs and assuming a constant effective population size β2|p) is constant, whereas for pτ−2. We note that these calculations imply α ≈ −2τ, whereas α is significantly less negative in simulations , results are generally similar, although they differ for very common SNPs. Specifically, when using MAF, E(β2|p) ∝ ([p + T]τ−k−2 + [1−p + T]τ−k−2)/([p + T]k− + [1−p + T]k−), with threshold frequency α model more closely (though not perfectly), as the correction terms for very common SNPs match the (1 − p) factor in the E(β2|p) ∝ [p(1 − p)]α model.This result shows that for see Fig. , with thα to SNP effects from a simulation with a given k and τ in Fig. c = 1. When estimating τ from α over  and on τ over , in which case k = 0.25. Using k = 0.125 lead to similar results, e.g., α = −0.38 then corresponds to k = 0.25.When fitting t in Eq.  does nothttps://github.com/arminschoech/GRM-MAF-LD; UK Biobank website, http://www.ukbiobank.ac.uk/; BGEN file format, http://www.well.ox.ac.uk/~gav/bgen_format/; UK Biobank genotype imputation manual, http://www.ukbiobank.ac.uk/wp-content/uploads/2014/04/imputation_documentation_May2015.pdfOpen-source software package implementing our method, https://github.com/arminschoech/GRM-MAF-LD.Source code of the GRM-MAF-LD software developed for this analysis is publicly available at Further information on experimental design is available in the Supplementary InformationPeer Review FileReporting SummarySource Data


Health and survival are key goals for selective breeding in farm animals. Progress, however, is often limited by the low heritability of these animal fitness traits in addition to measurement difficulties. In this respect, relevant early-life biomarkers may be useful for breeding purposes. Telomere length (TL), measured in leukocytes, is a good candidate biomarker since TL has been associated with health, ageing, and stress in humans and other species. However, telomere studies are very limited in farm animals. Here, we examined the genetic background, genomic architecture, and factors affecting bovine TL measurements in early life, and the association of the latter with animal fitness traits expressed later in life associated with survival, longevity, health, and reproduction. We studied two TL measurements, one at birth (TLB) and another during the first lactation (TLFL) of a cow. We performed a genome-wide association study of dairy cattle TL, the first in a non-human species, and found that TLB and TLFL are complex, polygenic, moderately heritable, and highly correlated traits. However, genomic associations with distinct chromosomal regions were identified for the two traits suggesting that their genomic architecture is not identical. This is reflected in changes in TL throughout an individual’s life. TLB had a significant association with survival, length of productive life and future health status of the animal, and could be potentially used as an early-life biomarker for disease predisposition and longevity in dairy cattle. Telomeres are evolutionarily conserved, tandemly repeated DNA sequences, which protect the ends of chromosomes during cell division . Due to in vitro studies at cellular level and on model organisms have led to a hypothesis that telomere length (TL) could be used as a predictor of the individual organism’s lifespan. Indeed, this hypothesis has found support in studies on wild birds  examine the genetic architecture of early-life leukocyte TL measurements in dairy cattle using pedigree and genomic data and ii) determine the association of early-life bovine TL with future animal fitness traits, linked with health, reproduction, survival and longevity. We used the largest population of farm animals with telomere measurements published to date and conducted variance component analyses to estimate genetic parameters, and GWAS to identify genomic regions and candidate genes controlling TL. We also investigated the predictive capacity of TL with regards to animal health, reproduction, survival and longevity using mixed linear models.Blood sample collection was conducted in accordance with UK Home Office regulations , and procedures were approved by the Scotland’s Rural College (SRUC) Animal Experimentation Committee. The other data used in the analyses were obtained from a database of records collected routinely at the experimental farm.vs. control group maintained at the UK national average level) and two feeding groups (low forage diet based mainly on concentrated feed with cows housed throughout the year vs. high forage diet with cows turned out to pastures during summer). All animals are closely monitored and recorded for a range of traits and events . Since 2004, a routine blood sampling protocol for experimental animals has been established, with the first sample being collected within the first 2 weeks from birth and repeat sampling carried out annually.The population used in the present study consisted of female Holstein–Friesian cattle raised at the SRUC Dairy Research Centre at Crichton Royal Farm in Scotland, UK. The herd was established more than three decades ago to study the effects of long-term selection and the interactions between animal genotype and diet . The cowThe dataset used for the present study included 2,202 blood samples collected from 702 animals, born between 2008 and 2015. Animals were approximately equally split between genetic and feeding groups. A complete pedigree of 11,598 animals was extracted from the farm database.DNA was extracted from frozen whole blood samples using the DNeasy Blood & Tissue spin column protocol (QIAGEN) and had to pass the following quality control steps to be considered for TL measurement with qPCR: DNA yield, measured on a NanoDrop ND-1000 Spectrophotometer (Thermo Scientific), had to be greater than 20 ng/μl, and DNA purity, expressed as ratios of absorbance at 260nm/280nm and 260nm/230nm, had to be greater than 1.7 and 1.8, respectively. Furthermore, each sample had to pass a DNA integrity gel test described in The amount of telomeric DNA was measured in relation to the amount of the reference gene beta-2-microglobulin (B2M) that is constant in copy number and has been used before in telomere studies on ruminant species such as the Soay sheep , roe deeThe following qPCR protocol was used on a LightCycler 480 (Roche): 15 min at 95°C (enzyme activation) followed by 50 cycles of 15 s at 95°C (denaturation), 30 s at 58°C , and 30 s at 72°C . The melting curve was acquired as follows: 1 min at 95°C was followed by 30 s at 58°C and a continuous increase of 0.11°C/s to 95°C with continuous signal acquisition.TEL and EB2M for the telomere and the B2M reaction, respectively). The following formula was used for TL calculation  and CqB2M for the telomere and the B2M reaction, respectively; and Cq values of the individual samples were CqTEL(Sample) and CqB2M(Sample).where the Cq value describes the number of cycles of a qPCR that is required for an amplification curve to cross a set fluorescence threshold; the Cq values of the calibrator sample were CqSamples had to pass the following qPCR quality control to be considered in the statistical analysis: the coefficient of variation calculated for the Cq values across triplicate had to be smaller than 5%, and individual amplicon efficiencies had to be within 5% of the reaction specific mean efficiency calculated using LinReg PCR.Two telomere measurements were calculated: TL at birth (TLB), based on the first sample collected within 2 weeks after birth, and TL in first lactation (TLFL), based on the first sample collected within the milking period following the cow’s first calving. The records were log-transformed to ensure normality of the data distribution. All analyses and results reported henceforth are based on log-transformed TL measurements. DNA was extracted from whole blood using the DNeasy Blood & Tissue kit (QIAGEN) as described in - Illumina BovineSNP50 BeadChip —246 animals- GGP Bovine 50K (Neogen/GeneSeek)—161 animals- GGP Bovine HD 150K (Neogen/GeneSeek)—295 animalsThe genotypes obtained from the GGP chips 50K and 150K were subsequently imputed to the SNPs found on the 50K Illumina chip using the method of A range of variables was extracted from the farm database to test their possible effect on TLB and TLFL , where V is the (co)variance matrix of the two traits. The null hypotheses were that the genetic correlation between TLB and TLFL is equal to unity and residual correlation is equal to zero. The hypotheses were tested using the log-likelihood ratio test, with the likelihoods compared to the ones obtained from the analyses where the correlations were fixed as defined by the null hypothesis.Subsequently, bivariate analyses between TLB and TLFL were conducted using the same models in order to derive estimates of the genetic, residual and phenotypic correlations between the two traits. Vector of the random effects was assumed to be MVN . After quality control, 44,160 SNP markers remained for further analysis.The SNP genotype data were subjected to quality control measures using PLINK v1.09 : minor aPopulation stratification was investigated using a genomic relatedness matrix generated from all genotyped individuals. This matrix was converted to a distance matrix that was used to carry out classical multidimensional scaling analysis with the GenABEL package in R , in orde−6 and P ≤ 2.26 × 10−5 for genome-wide significant  and suggestive  levels, respectively, corresponding to −log10(P) of 5.94 and 4.64. In addition, a search for SNPs significant at the chromosome-wide level  was performed. The extent of linkage disequilibrium between significant SNPs located on the same chromosome was calculated using the r-square statistic of PLINK v1.09 /2; dominance effect, d = AB − [(AA + BB)/2]; proportion of phenotypic variance due to SNP = [2pq (a + d(q − p))2]/VP, where AA, BB, and AB represent the predicted trait values for the corresponding genotype ; p and q, the SNP allele frequencies; and VP, the total phenotypic variance of each trait derived in the genetic parameter estimation step. These analyses were performed using ASReml 4.0 software http://www.ensembl.org/Tools/VEP) tool within the Ensembl database and the Bos_taurus_UMD3.1 assembly. Moreover, genes located around the significant markers, in 0.5 Mb upstream and downstream windows, were annotated using the BioMart data-mining tool (http://www.ensembl.org/biomart/martview/) and the Bos_taurus_UMD3.1 assembly.All genome-wide significant (post-Bonferroni correction) and suggestive significant SNPs identified in the genomic analysis for TLB and TLFL were mapped to the reference genome and annotated using the variant effect predictor , which is not significantly different from unity. The phenotypic correlation was close to the correlation between raw values Figure 1Multidimensional scaling analysis revealed the presence of two principal components in the population corresponding to the two genetic groups, which were subsequently included in the GWAS model to account for population stratification.GWAS results identified distinct genomic associations with the log-transformed TLB and TLFL measurements Table 2.All significant SNP markers that were identified in the GWAS were also found to have a significant effect on TLB and TLFL in the ensuing mixed model analyses based on the numerator relationship matrix. The additive and dominance genetic effects, and the proportion of the total phenotypic variance explained by each of these SNPs, are summarized in NUP93) gene. All the above-mentioned variants were not coding variants and had a predicted modifier impact, meaning that prediction of impact may be difficult to make and can vary considerably (https://www.ensembl.org/info/genome/variation/prediction/predicted_data.html)Most significant SNPs identified in the GWAS were located in intronic, intergenic, and downstream gene regions. Only one of the SNPs (Hapmap52077-ss46526963) associated with TLB was localized in the 3’UTR region of the Nucleoporin 93  heritability estimates of 0.36 and 0.46 found for TLB and TLFL, respectively, confirmed earlier estimates in cattle  and fellGWAS results shed more light on the genetic architecture of TL in dairy cows, highlighting specific genes that might underlie TL control. This is the first study, to our knowledge, that GWAS for TL traits were performed in a non-human mammal population. There are many previous GWAS of leukocyte TL in humans . HoweverNUD93 gene. The product encoded by NUD93 is an important component of the nuclear pore complex in eukaryotic cells and a target of caspase cysteine proteases that play a central role in programmed cell death by apoptosis  gene. Deficiency of the coiled-coil serine rich protein 1 has been already associated with a cell division defect in humans and several human cancers  were identified in close proximity with the SNP markers on chromosomes 29 and 24 associated with TLB and TLFL in the present study, respectively. All the above discussed genes are putative good candidates for TLB and TLFL in dairy cattle; however, further studies on independent datasets are needed to validate these results and identify the causative mutations.Specifically for TLB, the SNP marker on chromosome 18 was located in the 3’ UTR of the poptosis . A recenpoptosis . The SNP cancers . The SNP nucleus  and seve nucleus . The onln humans . Finallyn humans , includin humans . Interes2 = 0.36)  had detected a significant maternal permanent environment effect, explaining 33% of the total variance, which is of similar magnitude to the direct heritability estimate (h = 0.36) . However = 0.36) , recentl = 0.36)  after a  = 0.36) .in utero conditions would have the highest impact on the trait in the calf. Previous studies in other species have indicated that maternal diet  could accelerate genetic selection for enhanced cattle longevity. While we also detected significant and positive phenotypic correlations between TLB and survival to 12, 24, and 36 months, more research is needed to further dissect the associations of TB with survival to later ages, which can determine the profitability of the cow and sustainability of the farm. In general, long TL was associated with enhanced longevity and survival at either the genetic or phenotypic level. Previously published associations of TL with longevity are inconclusive and depend on the species and population studied, the animal age at TL measurement, and the definition of longevity. The associations between longevity and TL in dairy cows are likely to be different to those detected in humans and wild animals, as the longevity of a dairy cow does not represent her biological limits but instead depends on her productivity and reproduction—both of which carry high oxidative stress . Brown eThe present study focused on specific early life TL measurements. Future studies should examine the genetic background of the rate of telomere shortening over time, also known as attrition rate, and the association with animal performance and fitness in later life.In conclusion, the present study examined the genetic and genomic architecture of bovine TL at birth and in first lactation and found them to be moderately heritable, complex polygenic and highly correlated traits. A comprehensive examination of the associations between TL and animal fitness traits expressed at both early and mature age provided evidence of an association of TLB with survival, longevity and mastitis resistance. These findings may be used to inform breeding programs and strengthen the interest for further studies to fully understand the reported associations and the underlying mechanism of TL changes over time.https://www.egenes.co.uk/langhillUP/) where all requests to access the datasets can be made for research purposes. All reasonable research-focused requests are normally accepted.The datasets for this manuscript are not publicly available because the animals, and associated records and sampling, are part of a long term (50 years) genetic selection experiment supported by a range of funders including commercial and confidential in nature. As such the data in their entirety are not available to upload to a public database. Instead, we have established a publically facing interface  and procedures were approved by the SRUC Animal Experimentation Committee.JI-W performed the genetic parameter and trait association analyses. AP performed the genomic and post-genomic analysis. LS, RW, SU, JF and DN performed the telomere length measurements. JI-W collated the blood sample catalogue, curated the samples, and constructed the database of phenotypic and telomere length records for the purpose of the experiment. JI-W, GB and AP collated and edited the genotyping data. All authors met routinely during the project and contributed to the analysis design and interpretation of results. JI-W and AP wrote the manuscript with input from GB. All other co-authors provided manuscript editing and feedback. All authors read and approved the final manuscript. GB, MC, DN, BW and AP conceived and designed the genetic and genomic studies and secured funding.http://www.bbsrc.ac.uk/), the Rural & Environment Science & Analytical Services Division of the Scottish Government, and Scotland’s Rural College (http://www.sruc.ac.uk/).The authors gratefully acknowledge funding from the Biotechnology and Biological Sciences Research Council (BB/L007312/1 and BBS/E/D/30002276; 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.


Triticum aestivum L.) yield, but processing and end-use quality are critical components when considering its use in feeding the rising population of the next century. The challenges with end-use quality trait improvements are high cost and seed amounts for testing, the latter making selection in early breeding populations impossible. Here we describe a novel approach to identify marker-trait associations within a breeding program using a meta-genome wide association study (GWAS), which combines GWAS analysis from multi-year unbalanced breeding nurseries, in a manner reflecting meta-GWAS in humans. This method facilitated mapping of processing and end-use quality phenotypes from advanced breeding lines  of the CIMMYT bread wheat breeding program from 2009 to 2014. Using the meta-GWAS we identified marker-trait associations, allele effects, candidate genes, and can select using markers generated in this process. Finally, the scope of this approach can be broadly applied in ‘breeding-assisted genomics’ across many crops to greatly increase our functional understanding of plant genomes.One of the biggest challenges for genetic studies on natural or unstructured populations is the unbalanced datasets where individuals are measured at different times and environments. This problem is also common in crop and animal breeding where many individuals are only evaluated for a single year and large but unbalanced datasets can be generated over multiple years. Many wheat breeding programs have focused on increasing bread wheat ( Triticum aestivum L.) consumption supplies nearly 16 g of protein per capita daily and is quickly increasing in urban areas and least developed countries, which are predicted to have the largest population increases [The human population is growing exponentially with projections predicting greater than 9 billion people by the year 2050. Currently global bread wheat , and pup loaf volume (LOFVOL), were measured according to AACC [Wheat processing and end-use quality phenotypes for thousand kernel weight (TKW) grain protein (GRNPRO), Alveograph W (ALVW) and PL to AACC  methodol to AACC . GRNPRO  to AACC . These m to AACC . Dough s to AACC . Pup loa to AACC  adjustme to AACC . Phenoty to AACC .Pst1 and Msp1, ligated with barcoded adapters, amplified, and then sequenced as in the protocol of Poland, et al. [Triticum aestivum IWGSC genome assembly version 2.25 [very-sensitive-local option. SNPs were named by chromosome pseudo base pair position from the IWGSC 2.25 and numerically coded for major, minor, heterozygous, or missing classes. SNPs were then curated in JMP-Genomics 7.1  to maintain maximum data accuracy with the large amounts of missing data found using genotyping-by-sequencing. Individuals with greater than 35% missing data were removed from further analysis. Markers with greater than 25% missing data, greater than 20% percent heterozygous, or less than 5% minor allele frequency were also removed. Polymorphism information content was calculated for each marker , and statistical significance was declared at p < 0.001. All significant marker-trait associations are reported in Association mapping for processing and end-use quality phenotypes was conducted using a Q-K mixed model  in JMP-Gp-values were corrected with FDR [Haplotype analyses were conducted for multiple significant markers present in narrow genetic distances with similar impact on trait of interest. Haplotype phases and probabilities for each individual within years were estimated using JMP-Genomics 7.1, and the haplotype probabilities were regressed against all traits within each year. Estimated haplotype trait means and standard errors from haplotype trend regressions for each year were combined using an inverse-variance and fixed effects meta-analysis model and with FDR .Candidate genes were identified through previous literature reports with named genes in the wheat gene catalog. If no named wheat quality QTL were identified in a region, a BLAST search was conducted within the haplotype boundaries. Predicted annotations most likely to have impact on grain fill, protein deposition, or grain storage proteins were reported.To apply genomic tools to the CIMMYT wheat breeding program we utilized genotyping-by-sequencing (GBS)  and discp < 0.001) covering 40 unique SNPs  gene [Final LOFVOL is a complex, but heritable trait that is impacted by quality and quantity of the storage proteins present in the flour, as well as by non-protein factors . Here webm) gene . The allbm) gene and MAS cMeta-GWAS is a powerful, novel method, which allowed the largest genetic study of wheat quality to date . Using meta-GWAS GBS markers associated with major processing and end-use quality traits were discovered for all traits examined. However, the more applicable outcome was combining single marker trait associations into haplotype makers. Haplotype QTL facilitated the ability to reliably test for presence or absence, designate a window where candidate genes should be explored, and allowed for tests of QTL effect on all other traits.GluD1, is well known for majorly impacting dough strength, and is commonly selected using marker assisted selection in breeding programs [Here we demonstrate the implications of this methodology on seven meta-haplotypes which impact wheat processing and end-use quality as well as grain thousand kernel weight. In the CIMMYT bread wheat breeding program, all QTL, except one, had been selected where the more frequent allele favored increased TKW, but decreased final loaf volume. This is unsurprising as the primary goal of the breeding program is to increase grain yield while continuing to make acceptable food products. The one exception of QTL predominantly selected for increased ALVW with decreased TKW, programs , 9.wbm QTL remains protein and grain size neutral, while selection impact gluten extensibility and loaf volume [As many QTL documented in this study impact TKW, there is potential for use as selection targets for breeding or gene editing for increased yield potential. The majority of these QTL seem to impact starch synthesis or grain filling –38. So, f volume . As the f volume .In this study we show that meta-GWAS can be used as a powerful approach for insight to the genetic basis of important traits in a breeding program. This will enable more robust and genetically informed breeding approaches to compliment QTLs with designed crossing strategies and marker-assisted selection. Given the unbalanced testing and highly dynamic nature of breeding programs, this approach to ‘breeding-assisted genomics’ can be applied to other traits and species, allowing for immediate breeding for beneficial alleles in parallel to uncovering the genetic basis of important traits. This advantage of decreased time from marker-trait association to implementation in breeding could assist in the rapid development of crop varieties adapted to changing climates while simultaneously possessing quality characteristics for existing and emerging food markets.S1 FigFor each chromosome the physical position of the marker in base pairs shown with the respective PIC value on color scale.(TIF)Click here for additional data file.S2 Fig2) on y-axis.Pairwise LD among all markers used in this study grouped by chromosome with physical distance in bp between pairs of markers on x-axis and correlation coefficient (R(TIF)Click here for additional data file.S3 FigThree-dimensional display of principle components for a) population structure and b) cryptic relationship structure, also presented with two-dimensional outline of principle components for c) population structure and d) cryptic relationship structure. Scree plots demonstrate variation explained by each principle component in e) population structure and f) cryptic relationship structure.(TIF)Click here for additional data file.S1 TableGBS tags were aligned to Chapman, et al. population to identify chromosome and cM positions. MarkerName: given name of the respective marker based on the IWGSC draft sequence 2.25 position; Strand: forward (+) or reverse (-) strand; Tag: DNA sequence of genotyping-by-sequencing tag where SNP was identified; POPSEQ Chrom: chromosome designation based on PopSeq position assignment; POPSEQ cM: genetic position in centiMorgans based on PopSeq position assignment.(CSV)Click here for additional data file.S2 TableMarker ID is the GBS SNP name in this study. Chromosome and position are listed as identified by Bowtie 2 aligned to IWGSC 2.25. POPSEQ chromosome and position are from markers which aligned to the Chapman, et al. population. Trait is the phenotypic trait of interest. Significant effect and standard error of the effect are listed along with the negative log10 probability of the significant marker-trait association corrected with False Discovery Rate.(PDF)Click here for additional data file.S3 Tablep < 0.001; ** p < 0.01; * p < 0.05.TKW: thousand kernel weight; GRNPRO: grain protein; ALVW: Alveograph W; ALVPL: Alveograph P/L; LOFVOL; loaf volume. Significance levels: *** (PDF)Click here for additional data file.


TP53, with 0.5 cm wider heads in increaser-allele carriers versus non-carriers during mid-childhood, suggesting a previously unrecognized role of TP53 transcripts in human cranial development.Cranial growth and development is a complex process which affects the closely related traits of head circumference (HC) and intracranial volume (ICV). The underlying genetic influences shaping these traits during the transition from childhood to adulthood are little understood, but might include both age-specific genetic factors and low-frequency genetic variation. Here, we model the developmental genetic architecture of HC, showing this is genetically stable and correlated with genetic determinants of ICV. Investigating up to 46,000 children and adults of European descent, we identify association with final HC and/or final ICV + HC at 9 novel common and low-frequency loci, illustrating that genetic variation from a wide allele frequency spectrum contributes to cranial growth. The largest effects are reported for low-frequency variants within  Size and shape of the brain are, among others, influenced by the dimensions of the skull. Here, the authors report genome-wide association studies for head circumference and intracranial volume in children and adults and the identification of nine common or low-frequency variants associated with these traits. This is also true within the lifespan of an individual, where developmental changes in brain size and shape must be reflected in changing cranial phenotypes.The size and shape of the vertebrate brain is governed by the internal dimensions of the skull. Across vertebrate evolutionary history, major changes to brain size and proportion have been accompanied by modifications to skull morphology3. In infants and children, HC is highly correlated with brain volume as measured by MRI studies5, especially in 1.7- to 6-year-old children, although its predictive accuracy decreases with progressing age5. Healthy children from around the world, who are raised in healthy environments and follow recommended feeding practices, have strikingly similar patterns of growth6. The observation that final HC is largely determined by the age of 6 years in a large study from the UK7 is therefore likely to be valid in multiple populations. In addition, nutritional status, body size, and HC are closely correlated for healthy children during early life, and become less related after 24 months of age8. While HC properties in early childhood have immediate medical relevance, there are also compelling reasons to study HC in adulthood. In the adult population skeletal measures continue to act as a permanent measure of peak brain size that is unaffected by subsequent atrophic brain changes9. In early childhood, HC is likely to proxy overall body size and timing of growth, tracking changes in brain size. In older individuals, HC is valuable precisely because HC is robust to soft tissue atrophy, solely reflecting an absolute measure of final HC dimension.Serial measures of maximal head circumference (HC) or occipito-frontal circumference are routinely obtained to monitor children’s cranial growth and brain development during the first years of life and abnormal trajectories may indicate a range of neurological conditions10. Reported twin-h2 estimates are 90% in infants, 85–88% in early childhood, 83–87% in adolescence and 75% in young and mid adulthood10, with evidence for strong genetic stability between mid-childhood and early adulthood10. There are arguments to support the hypothesis that some of the underlying genetic factors act by a coordinated integration of signaling pathways regulating both brain and skull morphogenesis during development11. Especially, cells of early brain and skull are sensitive to similar signaling families11. Genetic underpinning of potentially shared mechanisms is supported by the fact that genome-wide signals for both infant HC and intracranial volume (ICV) are strengthened when combined12, irrespective of their dissimilar developmental stages. However, genetic investigations studying (near) final HC and adult ICV are likely to be more informative on mechanisms underlying developmentally shared growth patterning which affect final cranial dimension. Additionally, low-frequency genetic variants, ranging between 0.5 to 5% minor allele frequency, have been poorly characterized by previous genome-wide association study (GWAS) efforts13, both due to the small size of previous studies, and the limited coverage of lower-frequency markers by the first imputation panels.HC is highly heritable and the notion of a developmentally changing, but etiologically interrelated, phenotypic expression of HC during the life course is supported by twin studies14 and the haplotype reference consortium (HRC)15, that have previously facilitated the discovery of low-frequency genetic variants for a range of traits17, we carry out GWAS for final HC. Specifically, we aim tostudy low-frequency and common variants for final HC, allowing for age-specific effects through meta-analyses of mid-childhood and/or adulthood datasets,investigate genetic variants influencing a combined phenotype of (near) final HC and ICV, termed final cranial dimension, andexplore developmental changes in the genetic architecture of HC through longitudinal modeling of genetic variances in unrelated individuals as well as growth curve modeling of HC trajectories for carriers and noncarriers of high risk variants.Exploiting whole-genome sequence data together with high-density imputation panels such as the joint UK10K and 1000 genomes (UK10K/1KGP)TP53. Collectively, these findings provide insight into the genetic effects influencing cranial growth during childhood and adolescence, while yielding additional genetic associations which enhance our understanding of the biological mechanisms underlying these complex developmental processes.Through these analyses we show that the developmental genetic architecture of HC is genetically stable during the course of childhood and adolescence and correlates with genetic determinants of ICV. Integrating information from both (near) final HC and ICV in a combined analysis including up to 46,000 children and adults of European descent, we identify nine novel common and low-frequency loci for either HC or HC + ICV, including low-frequency variation within p = 3.0 × 10−8, Supplementary Figures p = 2.2 × 10−9, Supplementary Figures p = 2.0 × 10−8, Supplementary Figures p < 3.3 × 10−8)  Table  and repl18, suggested that carriers of the T risk allele at rs35850753 developed larger heads from mid-childhood onwards  and HC growth velocity  modelrds Fig. , with ri112 Fig. .Fig. 4St20, multiple HC-associated genes were identified  and contains single variants in linkage disequilibrium (LD) with known GWAS signals for infant HC13 . The strongest gene-wide signals that did not harbor variants in LD with known or novel single GWAS variants were identified at 5q31.3 , and at 16p13.3 , using summary statistics from the HC (Pediatric + adult) meta-analysis. Gene-based analyses were complemented with studies predicting gene expression levels in multiple tissues ) than in adult samples ), although 95% confidence intervals marginally overlap. The estimated genetic correlation23 between both developmental windows was high (LDSC-rg = 1.04(SE = 0.39), p = 0.0075). The LD-score regression intercepts were consistent with one for all HC meta-analyses, suggesting little inflationary bias in GWAS (Supplementary Table Linkage-disequilibrium score regression (LDSC)ses Fig.  using ge24. Fitting a saturated Cholesky decomposition model  at the ages of 1.5, 7, and 15 years (Supplementary Table h2 estimates of 0.35 (SE = 0.07), 0.43 (SE = 0.05), and 0.39 (SE = 0.07) respectively ; 1.5−15 years, rg = 0.79 (SE = 0.09); 7−15 years, rg = 0.87 (SE = 0.04), in support of LD-score correlation analyses.To investigate developmental changes in the genetic architecture of HC scores, we carried out a multivariate analysis of genetic variances using genetic-relationship-matrix structural equation modeling (GSEM)del Fig.  to HC scFig. N = 924 at thely Fig. . More im23 identified moderate to strong positive genetic correlations (rg ≥ 0.3) with many anthropometric and cognitive/cognitive proxy traits. This includes HC scores during infancy, birth weight, birth length, height, extreme height, hip circumference, childhood obesity, waist circumference, intelligence scores, and ICV (Supplementary Table rg < 0.3) were also present for years of schooling, obesity, body mass index, overweight, and extreme height.A systematic screen for genetic correlations between HC scores and 235 complex phenotypes using LD score correlationrg = 0.91(SE = 0.16), p = 1.6 × 10−8). However, there was little evidence that SNP-h2 estimates for HC are enriched for genes that are highly expressed in brain tissues or chromatin marks in neural and bone tissue/cell types, beyond chance (Supplementary Data The strongest cross-trait genetic correlation was identified between HC (Pediatric + adult) and ICV  with ICV summary statistics from the CHARGE and ENIGMA2 consortia12  at the 17p13.1 locus, a functional variant that is in LD with rs35850753, the strongest GWAS signal for HC , p = 0.013). Reciprocally, the signal at rs78378222, conditional on rs35850753, was still detectable at the nominal level in the combined cranial dimension analysis , p = 0.0024), based on standardized regression estimates.Given the prior expectation of similar genetic architectures between HC and ICV, supported through genetic correlation analyses, we meta-analyzed both phenotypes by combining HC summary statistics from pediatric and adult cohorts  at 6p21.32 within the MHC region, which is in LD with rs9268812 (r2 = 0.41), a further signal from our HC (Pediatric + adult) meta-analysis. We also observed increased statistical evidence for association at nine known markers compared to the original studies for either HC, brain volume or ICV 27, while variation at rs35850753 is not   with an enhancer in fetal brain  with either rs35850753 or rs78378222, when adjusted for the number of loci tested (Supplementary Data TP53 was found for eQTL in modest LD with rs35850753 (r2 = 0.22), explaining variation in gene level TP53 transcript in blood, with the rare T risk allele being associated with lower full-length transcript levels  of lly Fig. . Species04) Fig. . Accordiain Fig. . Using ts CADD = .9727, whr2 with rs2168812 = 0.99) is an intronic SNP within AKT3 (CADD = 17.87) and rs112040334 (r2 with rs4513262 = 0.91) an intronic 11-bp insertion/deletion within KLF11  with eQTL in blood  with lead variants from the combined ICV and HC meta-analysis show mapped chromatin interactions within mesenchymal and human embryonic stem cells and mesoendoderm . The low-frequency allele at rs78378222 leads to a change in the TP53 polyadenylation signal that results in impaired 3′-end processing and termination of many TP53 mRNA isoforms32, including full-length TP53 isoforms, although rs78378222 is also in LD with an enhancer region in fetal brain. In contrast, rs35850753 resides in the 5′ UTR of TP53 Δ133 isoforms that are transcribed by an alternative promoter. This leads to the expression of an N-terminally truncated p53 protein, initiated at codon 133, lacking the trans activation domain33. TP53 Δ133 isoforms are known to directly and indirectly modulate p53 activity and differentially regulate cell proliferation, replicative cellular senescence, cell cycle arrest and apoptosis in response to stress such as DNA damage, including the inhibition of tumor suppressive functions of full-length p53. This mechanism is consistent with the observed link between the rs35850753 low-frequency T allele and lower full-length TP53 transcript level. Thus, rare effect alleles at both rs78378222 and rs35850753 could potentially, via different biological mechanisms, be linked to impaired p53 activity and thus heightened proliferative potential and less apoptosis of normal human cells, consistent with larger HC scores and a larger cranial dimension.34, a malignant tumor of glial tissue, possibly including neural stem cells, glial progenitors and astrocytes as cells of origin35, but also prostate cancer and colorectal adenoma32. Both rs35850753 and rs78378222 have also been robustly associated with neuroblastoma36, a sympaticoadrenal lineage neural crest-derived tumor. Evidence for neurological phenotypic consequences of TP53 variation has recently been strengthened by the discovery of TP53 as a risk locus for general cognitive function using a gene-based approach37. TP53 knockout mouse embryos show furthermore broad cranial defects involving skeletal, neural, and muscle tissues38. Similarly, mouse models for Treacher Collins syndrome  could be rescued by inhibition of p53 during embryological patterning39. In particular, there is support from animal and tissue models for a role of p53 in neural crest cell (NCC) development38 with NCCs supplementing head mesenchyme during fetal development40. NCCs also contribute to the development of a thick three-membrane layer called the meninges, that cover the telencephalon40 and directly locate underneath the skull. In particular, Pia mater, the innermost layer of the meninges, adheres closely to sulci and fissures of the cortex. During postnatal brain growth, including extensive increases in myelinated white matter41, the calvarial bones are drawn outward, partially due to the expanding meninges, triggering the production of membranous skull bone40. Moreover, meninges have been thought to play a key role in the coordinated integration of signaling pathways regulating both neural and skeletal cranial growth11. It is possible to speculate that p53 is part of these joint regulatory mechanisms, for example, via Wnt signaling regulation42. However, beneficial effects of rs35850753 and rs78378222 on growth patterning leading to an increased HC and cranial dimension might be counterbalanced by adverse outcomes such as glioblastoma, keeping both variants at a lower frequency.It is noteworthy that rs78378222 has been previously associated to risk of cancers including tumors of the nervous system such as gliomaTCF7L1 at 2p11.2, a locus encoding a transcription factor mediating Wnt signaling pathways that are known to play an important role in vertebrate neural development43. The effects of this variant were consistent for both HC and ICV, although each of the individual trait analyses was too underpowered to detect association at this variant at a genome-wide level. An additional low-frequency variant in this study, rs183336048 at 4q28.1, was identified as associated with pediatric HC only, but could not be replicated due to a lack of comparable age-matched follow-up cohorts. rs183336048 lies 5′ to INTU which encodes inturned planar cell polarity protein, a polarity effector affecting neural tube patterning and cilliation44. Common variants identified in the ICV + HC combined meta-analysis also include intronic variation in AKT3 (rs2168812) and CCND2 (rs3217870), which are related through the phosphatidylinositol 3-kinase (PI3K-AKT) pathway45. Disruption of PI3K-AKT pathway components causes megalencephaly-polymicrogyria-polydactyly-hydrocephalus syndrome and a spectrum of related megalencephaly syndromes46. This supports previous in silico pathway analysis, which nominated PI3K-AKT, an intracellular signaling pathway controlling the cell cycle, as candidate pathway for intracranial volume12. Both, rs2168812 and rs3217870, have also been associated with cancer risk, similarly to the two TP53 variants, with the AKT3 variant rs12076373 (LDr2 with rs2168812 = 0.70) being related to risk for non-glioblastoma brain tumors34 and the CCND2 variant rs3217901 (LDr2 with rs3217870 = 0.63) being related to colorectal cancer , can put the lives of both mother and fetus at risk, if left untreated. Mathematical models show that evolutionary forces such as a weak directional selection for a large neonate and/or a weak selection for a narrow pelvis can account for the considerable incidence of CPD in humans50, and predict a further rise in CPD incidence due to the frequent use of Caesarian sections during recent years.Genetic correlation analyses provided strong evidence for shared genetic determinants between HC and both anthropometric  and cognitive traits, as well as ICV. Genetic correlations with waist circumference and hip circumference recapitulate observed correlations between the size of the maternal pelvis and the size of the neonatal cranium51, and identified additional evidence for genetic correlation between HC and intelligence, especially pediatric HC. With strongly shared genetic liability (i.e. a genetic correlation coefficient near one), we considered HC and ICV to be related proxy measures of an underlying phenotype, which we termed final cranial dimension. This also suggests that estimated skeletal volume, a combination of HC, cranial height and cranial length52, might represent a more accurate, easily accessible and inexpensive measure to enhance power for future genetic analysis using a multi-trait approach53 in combination with ICV, exploiting similar volumetric properties.We also confirmed previously reported genetic links between educational attainment and infant HCh2 of HC in adult samples was lower than in pediatric samples, with only marginally overlapping 95% confidence intervals, implying that phenotypic variation in final HC is less well accounted for by genetic influences than variation in childhood HC, probably as skeletal growth processes have ceased.Multivariate analyses of genetic variance showed that genetic factors contributing to variation in HC during infancy explain the majority of genetic variance during later life, although novel genetic influences arise both during mid-childhood and adolescence. This is further reflected in strong GSEM-based genetic correlations across childhood and adolescence, and strong LDSC-based genetic correlations between infant and adult HC. The estimated LDSC-TP53, is associated with HC demonstrates the scientific value of testing for variation in the lower allele frequency spectrum and the utility of comprehensive imputation templates. Low-frequency variants identified in this study had larger effects than common variants , during adulthood  and a combination thereof  including individuals of European descent from 11 population-based cohorts , or low MAF (<1%). Individuals were removed if there were sex discordance, high heterozygosity, low call rate (<97.5%) or duplicates. For imputation, the reference panel was either joint UK10K/1000 Genomes55 or the Haplotype Reference Consortium15. Additional details can be found in Supplementary Table Within ALSPAC, we obtained low read depth (average  × 7) whole-genome sequencing data (ALSPAC WGS)56. First, variants were filtered for imputation quality score , minor allele count  and a minimum MAF of 0.0025. SNPs with MAF discrepancies (>0.30) compared to the HRC panel were also excluded. Marker names were harmonized and reported effect and noneffect alleles were compared against reference data (Build 37). Variants with missing or mismatched alleles were dropped, in addition all insertion/deletions (INDELs), duplicate SNPs and multiallelic SNPs were excluded. The reported EAF for each study was plotted against the frequency in the HRC reference data to identify possible strand alignment issues  are reported in Supplementary Tables In addition to study-specific quality control measures, central quality control was performed using the EasyQC R packagencies >0.0 compareZ-scores using a unified protocol. After the removal of outliers (±4 SD within each sample), HC was adjusted for age within males and females separately. Residuals for each sex were subsequently transformed into Z-scores and eventually combined (thus removing inherent sex-specific effects). Note that the phenotype transformation within ALSPAC was jointly carried out for both sequenced and genome-wide imputed samples.Pertinent to this study, HC measures in all individual cohorts were transformed into 24. This multivariate analysis of genetic variance combines whole-genome genotyping information with structural equation modeling techniques using a full information maximum likelihood approach24. Changes in genetic variance composition were assessed with longitudinal HC scores in ALSPAC participants . HC scores were Z-standardized at each age, as described above. Genetic-relationship matrices were constructed based on directly genotyped variants in unrelated individuals, using GCTA software57, and the phenotypic variance dissected into genetic and residual influences using a full Cholesky decomposition model24.Developmental changes in the genetic architecture of HC scores between the ages of 1.5 and 15 years were modeled using genetic-relationship structural equation modeling 58, we estimated that we analyzed 1.52 effective independent phenotypes within this study  according to the LDSC-based genetic correlations22.Using Matrix Spectral Decomposition (matSpD)Z-scores) were regressed on genotype dosage using a linear regression framework. For cohorts with unrelated subjects  utilized a linear mixed model to control for family and cryptic relatedness, implemented in GEMMA60.Single variant genome-wide association analysis, assuming an additive genetic model, was carried out independently within each cohort using standard software  with (a) HC information available in later childhood or adult samples, (b) participants of European ancestry and (c) genotype data. Studies with whole-genome sequencing or densely imputed genotype data (HRC or UK10K/1KG combined templates) were included in the HC meta-analysis, while studies with imputation to other templates were reserved for follow-up. Following this strategy, the majority of studies were included in the meta-analysis, with follow-up in a single study.p ≤ 5.0 × 10−8) were identified from previous studies on HC in infancy13, ICV64 and brain volume65 using either published or publicly available data .Known GWAS signals  meta-analysis and the largest publicly available genome-wide summary statistics on intracranial volume  based on data from Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) and the Enhancing NeuroImaging Genetics through Meta-Analysis (ENIGMA) consortium12. A weighted Z-score meta-analysis was carried out using METAL61 using standardized regression coefficients and 12,124,458 imputed or genotyped variants, assuming a genome-wide threshold of significance at p ≤ 3.3 × 10−8.We carried out a weighted Z-scores (Z) from the METAL output to calculate the standardized regression coefficient (β) for each SNP and trait66We used the j has an effect allele frequency (EAFj) and where SNPTo disentangle lead signals observed in both the HC (Pediatric + adult) and the combined ICV + HC (Pediatric + adult) meta-analysis, variants were conditioned on each other using GCTA software and summary statistics.20, which calculates gene-based test statistics from SNP-based test statistics, position-based gene annotations and a linkage disequilibrium reference panel of UK10K haplotypes using an adaptive permutation procedure. SNP-based test statistics were annotated using mapping files with a 50 kb symmetrical window around genes. For gene definition, we used all 19,151 protein-coding gene annotations from NCBI 37.3 and corrected for the number of genes and effective phenotypes tested, using an adjusted Bonferroni threshold of 1.7 × 10−6.Gene-based tests for association were performed using MAGMA21 as a summary-statistic-based implementation of PrediXcan to test for association between tissue-specific imputed gene expression levels and HC, implemented in the MetaXcan standalone software (v0.3.5). This approach first predicts the transcriptome level using publicly available transcriptome datasets. Then, it infers the association between gene and phenotype of interest, by using the SNP-based prediction of gene expression as weights (predicted from the previous step) and combines it with evidence for SNP association based on phenotype-specific GWAS summary statistics. We predicted gene expression levels for cerebellum  to phenotypic variation in HC. The method is based on GWAS summary statistics and exploits LD patterns in the genome and can distinguish confounding from polygenic influences22. To estimate LDSC-h2, genome-wide χ2-statistics are regressed on the extent of genetic variation tagged by each SNP (LD-score). The intercept of this regression minus one estimates the contribution of confounding bias to inflation in the mean χ2-statistic. LD score regression was performed with LDSC software (v1.0.0) and based on the set of well-imputed HapMap3 SNPs  and a European reference panel of LD-scores. LD-score correlation analysis can be used to estimate the genetic correlation (rg) between distinct samples by regressing the product of test statistics against the same LD-score23. Bivariate LD score correlation was performed with the LDHub platform67 v1.9.0 68 is a method for partitioning heritability from GWAS summary statistics with respect to genes that are expressed in specific tissue/cell types. We applied this method to HC summary statistics to evaluate whether the heritability of HC is enriched for genes that are highly expressed in brain tissues. GTEx v6p 25. The threshold for multiple testing for eQTL was adjusted according to the number of genes near the studied novel signals and their proxy SNPs (r2 = 0.2 and ±500 kb). For Brain xQTL, we corrected for multiple testing based on a threshold of p < 7.4 × 10−4 to account for 68 genes tested. For FUMA eQTL analysis, a multiple testing threshold of p < 7.6 × 10−4 was applied to adjust for 42 genes and, 24 blood and brain tissues/cell types . Analyses were restricted to participants of UK ancestry (UK Biobank specified variable). One from each pair of related individuals, individuals with high missingness, heterozygosity, gender mismatch and putative aneuploidies were excluded. Genotype dosage at lead single variants identified with GWAS was converted into best-guess genotypes using PLINK v1.90b3w. Linear, ordinal logistic, multinomial logistic and logistic regressions were fitted to test the association between genotype and continuous, ordered categorical, unordered categorical and binary outcomes respectively. Analyses were adjusted for age, sex and genotyping chip, and, for sensitivity analysis, 10 principal components. A conservative Bonferroni threshold was applied accounting for a total of 11,056 tests performed and two genotypes tested (p < 2.26 × 10−6).To characterize the phenotypic spectrum of identified HC signals, we conducted a phenome scan on 2143 phenotypes in the UK Biobank cohort18 (R sitar library v1.0.11). SITAR comprises a shape invariant mixed model with a single fitted curve, where individual curves are matched to the mean curve by modeling differences in mean HC, differences in timing of the pubertal growth spurt and differences in growth velocity18. Individuals with large measurement errors, i.e. with HC scores at younger ages exceeding scores at later ages (by more than 0.5 SD of the grand mean) as well as outliers  were excluded. The best fitting model was identified using likelihood ratio tests and the Bayesian Information Criterion and included four fixed effects for splines, a fixed effect for differences in mean HC and a fixed effect for sex, in addition to two random effects for differences in mean HC and growth velocity. Stratified models were fitted for carriers and noncarriers of increaser-alleles at candidate loci. To examine the relationship between genotype dosage and differences in HC and growth velocity, these random effects were regressed on genotype dosage using a linear model.Trajectories of untransformed HC (cm) spanning birth to 15 years were modeled in 6225 ALSPAC participants with up to 13 repeat measures  using a mixed effect SITAR modelSupplementary InformationPeer Review FilesDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Supplementary Data 11Supplementary Data 12Supplementary Data 13Supplementary Data 14Supplementary Data 15Supplementary Data 16Supplementary Data 17Supplementary Data 18Supplementary Data 19Supplementary Data 20