Acipenser fulvescens) from Black Lake, MI, we tested whether phenotypic variation differed among families reared in two constant (10 and 18°C) and two fluctuating‐temperature treatments (10–19°C) representing temperatures experienced in the river and a simulated anthropogenic disturbance. Body length, body area, and yolk‐sac area were quantified at hatch. Family‐by‐treatment interactions explained up to 50% of the variance observed among families in offspring hatch traits. Families incubated in 18°C and the fluctuating anthropogenic treatment had 6–10 times higher variance in traits than those incubated at 10°C. Hatched larvae were placed in raceways with ambient river water. Emergence body length, emergence timing, and growth were quantified upon emergence. Families differed in time to emergence and growth with the greatest range observed in the 18°C treatment. Results demonstrate that differential responses among genotypes to changes in the mean and variability of thermal incubation regimes can affect traits at hatch as well as a subsequent ontogenetic stage.Climate change is affecting thermal conditions worldwide. Understanding organismal responses associated with predicted changes are essential for predicting population persistence. Few studies have examined the effects of both increased mean and variance in temperature on organismal traits, particularly during early life stages. Using lake sturgeon ( Lake sturgeon are long‐lived ectotherms and a threatened species in the state of Michigan that has been numerically depressed due to overharvest, habitat loss and degradation, and limited recruitment  effects quantified in a recent study on lake sturgeon responses to stressful environmental conditions . The UBR is the largest tributary of Black Lake located in Cheboygan County, Michigan Fig. . Adults 2.22) used to keep families separate. Each female's eggs were fertilized with 0.5 ml of milt from two males to create ten half‐sibling (HS) families where all ten males were represented and no males were used more than once. Fertilized eggs were widely distributed within the couplings to prevent them from touching and left undisturbed for 30 min to allow adhesion to the mesh screens.Gametes were collected from “early” spawning fish during the first major peak in spawning on May 3, 4, and 6, 2012, when mean water temperature was approximately 13°C. Eggs were taken from five spawning females, placed in sealed plastic bags, and stored with river water to maintain eggs at ambient river temperature. Milt was collected from ten spawning males using 20‐ml syringes and placed on ice. Gametes were transported to the streamside rearing facility, and fertilizations were conducted within twelve hours of collection. Approximately 1,600 eggs were collected from each female and placed on 1‐mm mesh screens within eight polymerized vinyl chloride couplings  where temperature was controlled using heating and cooling units to produce two constant and two fluctuating thermal treatments during the egg incubation period Fig. . ConstanN = 1,200 total) were removed from the heath trays, anesthetized with tricaine methanesulfonate , and photographed using a digital camera and a ruler. Photographs were analyzed using ImageJ analysis software  to quantify three phenotypic traits at hatch: body length (mm), body area (mm2), and yolk‐sac area  allowing offspring from all females to be represented, but only five males from the fertilization scheme. Larvae that were subset and monitored until emergence were unrelated ; therefore, we refer to them as full‐sibling (FS) families. Each individual larva that was subsampled from the five FS families was randomly assigned to an individual plastic rearing chamber (12.7 cm by 6.35 cm). Rearing chambers contained only one fish, gravel substrate to provide cover during the yolk‐sac utilization period, and had mesh siding to allow for continual water passage (~0.1 m/s). Chambers were randomly placed across three fiberglass raceways  and cumulative degree‐days (Degree Days) each larva experienced while in the rearing chambers. Degree Days was estimated as a sum of the time  spent at a daily temperature above the threshold temperature, T0  and the Bayesian inference package MCMCglmm  which incorporates model fit and complexity based on an expected deviance parameter and the effective number of parameters estimated in the model  represents an interaction between variables, and εijk represents the random heterogeneous residual errors which follow Gaussian distributions. Incubation treatment was fit as a fixed effect. HS Family and the HS Family‐by‐Incubation Treatment interaction terms were fit as random effects with HS Familyj∼N,(HS Family×Incubation Treatment)ij∼N, and εijk∼N. The across‐treatment covariances in family effects were set to zero. Preliminary analyses included fitting full models where covariances were estimated using the us function, but these complex models had comparable trace plots and DIC estimates (within ± 2) as simpler models with covariances set to zero using the idh function. Therefore, we used the simpler models in all of our analyses. All models contained HS family as a random effect as opposed to fitting an animal‐specific random effect  allowing us to test the variables in the same model.The correlation between Mean H2) and 95% HPD intervals were computed (Table H2) was estimated as two times the FS Family variance divided by the total phenotypic variance equivalent to the heritability estimates derived in Dammerman et al., H2) or the upper limit of a narrow‐sense heritability given that we were unable to separate out additive genetic variance from other genetic effects. The predict function was used to produce plots of the conditioned means and the 95% prediction intervals within each of the four thermal incubation treatments. The predict function is often used to estimate new values from the fitted model which are then compared to the actual values to determine model fit. In our study, we plot the conditional means using the predict function to determine the effect of our fixed and random effects in the study.For traits where the model of best fit included a FS Family effect but no FS Family‐by‐Incubation Treatment interaction, the mode of the posterior distribution for heritability in the broad‐sense H and 95% F‐ratios which were obtained by extracting the posterior distributions for each of the FS Family‐by‐Incubation Treatment terms from the model of best fit. The numerator variance (variance 1) was expected to be larger than the denominator variance (variance 2) resulting in a one‐tailed test. An empirical tail‐area probability from the F‐ratios was calculated as one minus the sum of the ratios that were greater than one divided by the total number of F‐ratios  ranged from 10.19 (±0.09) to 13.84 (±0.09) mm among families  families showed considerable variation in the three traits measured at hatch across the four treatments. Mean body length  to 8.11 (±0.14) mm2, respectively . Families reared in the variable treatment had nine to ten times higher variance in the two traits than families reared in the cold treatment  to 28.46 (±0.32) mmH2 ± 95% HPD interval) for emergence timing was estimated as 0.21  was detected for the timing of emergence (Table S1).Approximately 87% of the larvae from the five subsampled, full‐sibling (FS) families placed in the rearing chambers emerged from the substrate to begin exogenously feeding. Individuals began to emerge 10 days after being placed in the chambers. FS families differed in the mean time spent in the rearing chambers ranging from 12.67 (±0.34) to 14.21 (±0.26) days Fig.  with fisH2 distribution were estimated as 0.32  to 15.39 (±0.47) mm Fig. . Fish rep < 0.01), but weakly explained the variability observed in growth from hatch to emergence  was detected for total growth (Table S1). Variation in mean body size at the timing of emergence was low among FS families ranging from 24.57 (±0.20) to 25.45 (±0.16) mm, and no FS Family, FS Family‐by‐Incubation Treatment, Incubation Treatment, Raceway effect, or effect of temperatures experienced while in the rearing chambers (Mean T and Degree Days) was detected .Given that maternal effects can influence growth, we plot the maternally provisioned yolk‐sac area versus total growth for larvae from the five subsampled FS families. Using a linear regression, yolk‐sac area was a significant addition to the model  egg incubation treatment had the largest range in mean body length at hatch Fig.  and larg8°C egg iOncorhynchus gorbuscha and Oncorhynchus keta after rearing individuals under different thermal regimes. These results indicate that water temperature can have a significant effect on the variability of phenotypes expressed during early development.The presence of a genotype‐by‐environment interaction can be indicative of the release of cryptic variation  reared in fluctuating thermal treatments were continually underpredicted based on reaction norms constructed from individuals reared at constant rearing temperatures. Therefore, rearing individuals under fluctuating treatments provides a more accurate representation of phenotypic trait variance and any potential genotype‐by‐environment interactions that might occur in the wild in response to climatic changes.In the ambient incubation treatment where temperatures fluctuated naturally throughout the day, the HS Family variances estimated for body area and yolk‐sac area were much larger than those observed in the constant cold treatment Table . AdditioWithin the fluctuating treatments, we also observed that the HS Family variance within the variable treatment representing the anthropogenic disturbance was 2–6 times larger for body area and yolk‐sac area than observed under “natural” conditions in the ambient treatment Table . The inc4.3Thermal conditions experienced during egg incubation are known to affect phenotypic traits associated with survival such as shape, color, behavior, and size at developmental stages beyond hatch in several taxa of ectotherms . Other studies have reported narrow‐sense heritability (h2) estimates of 0.15–0.20 for emergence timing in fishes  effects have a considerable effect on phenotypic variation during early life stages. Larvae from families vary in size and growth even when experiencing the same rearing temperature. For propagation programs, these potential size differences among members of different genotypes should be considered to avoid artificial selection that could occur if stocking preferentially emphasized release of offspring of large body size. For the wild‐produced progeny, intra‐ and interannual variability in thermal conditions within a river may result in increased variability in phenotypic trait expression among individuals of differing genotype. Thus, selection may favor certain genotypes produced during different portions of the spawning season or in different years. At the population level, this differential survival has the potential to increase the relatedness among surviving individuals within a spawning season thereby increasing levels of coancestry (or identity‐by‐descent) within a year class. If selection continually favors the same genotypes across year classes, overall relatedness could also potentially increase leading to increased levels of coancestry among individuals from different year cohorts. Therefore, monitoring how thermal conditions affect traits associated with survival among genotypes is necessary for understanding potential changes to the genetic diversity of the population.4.6Our findings have important implications regarding the impact of predicted thermal changes due to climate change on phenotypic variation in ectothermic species. Understanding how variability in phenotypic trait expression due to the release of cryptic genetic variation is maintained across sequential ontogenetic stages in wild populations is vital to understanding how populations can respond to environmental change (Ledón‐Rettig et al., http://dx.doi.org/10.5061/dryad.pq35t.Data files used for the analyses in this study are available at the Dryad Digital Repository:  Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file.


Behavioral traits of interest are often measured by questionnaires and analyzed as sum scores on the items. However, statistical results on genotype by environment interaction based on sum scores can be biased due to the properties of a scale. This article presents a method that makes it possible to analyze the actually observed (phenotypic) item data rather than a sum score by simultaneously estimating the genetic model and an item response theory (IRT) model. In the proposed model, the estimation of genotype by environment interaction is based on an alternative parametrization that is uniquely identified and therefore to be preferred over standard parametrizations. A simulation study shows good performance of our method compared to analyzing sum scores in terms of bias. Next, we analyzed data of 2,110 12-year-old Dutch twin pairs on mathematical ability. Genetic models were evaluated and genetic and environmental variance components estimated as a function of a family's socio-economic status (SES). Results suggested that common environmental influences are less important in creating individual differences in mathematical ability in families with a high SES than in creating individual differences in mathematical ability in twin pairs with a low or average SES.Genotype by environment interaction in behavioral traits may be assessed by estimating the proportion of variance that is explained by genetic and environmental influences  This approach does not take into account the possible existence of genotype — environment interaction: Different genotypes might respond differently to the same environment, or conversely, some genotypes may be more sensitive to changes in the environment than others. Genotype by environment interaction can be assessed in the case that the common and unique environment feature are latent  variables , one can test not only for interaction effects with additive genetic influences (A × M), but also with common environmental influences (C × M) or unique environmental influences (E × M) — that is, moderation of variance components (henceforth referred to as ACE × M). This approach was applied by, among others, Heath et al. , analyzi0a + βaMij), (β0c + βcMij), and (β0e + βeMij) respectively, where Mij represents a moderator variable for individual j from twin family i. β0a, β0c, and β0e, are intercepts estimating influences of all components  independent of M and βa, βc, and βe represent regression coefficients that express the respective interaction effects .Purcell  implemenThe aim of the current article was to incorporate a measurement model into the univariate analysis of ACE × M. This is important since statistical findings regarding non-linear effects such as ACE × M interaction effects are dependent on the scale at which the analysis takes place — a simple non-linear transformation can obscure or reveal interaction effects 2 for twin j from family i). It can, however, be shown that this parametrization is ill determined in the sense that there is no unique maximum likelihood (ML) solution for a given data set. This means that the model is not identified, as it can result in multiple parameter estimates with an equally good fit . This makes the interpretation of results non-trivial: For instance, confidence intervals (CI) for the moderation effects cannot be interpreted meaningfully nor the sign of the sign of the β0a, β0c, β0e, and βa, βc, and βe, parameters.Purcell  estimatei , this makes variance components different for families with a different value on the moderator variable. For example, to model C × M, we have for every twin family i:M denotes a vector consisting of the moderator values for every twin family i of one moderator variable. β0c represents the intercept  and β1c represents the C × M interaction effect. Note that in case of a bivariate moderator variable , this results in two possible values for σ2Ci  when Mi = 0 and σ2Ci = exp(β0c + β1c), but depending on the distribution of the moderator variable, this can result in a different variance component for every family. The underlying idea behind this parametrization is that a variance cannot be negative. Contrary to Purcell's  and that there is a ceiling effect in the IQ data in the sense that there is more measurement error at the right tail of IQ scores, then consequently there is less information on high scoring twins and these pairs will seem more alike in a biometric analysis that is not corrected for measurement error. If IQ levels increase with SES, the correlation of the first and second twin of a family will be lower at higher SES levels, leading to higher estimates of genetic variance — and therefore to a positive A × SES interaction effect. Note that this effect is spurious in the sense that they are due to scale properties rather than biological mechanisms.Tests or questionnaires that consist of multiple items may not be equally reliable across the entire range of sum scores — that is, measurement error can be heterogeneous across the trait continuum. For example, cognitive ability tests show little measurement error for average performing participants, but can become less informative for highly able participants as they usually contain only a few very difficult items. Likewise, a depression scale that contains mostly extreme items may be highly informative for depressed participants but less so in the assessment of healthy controls. It has been shown that if phenotypes are heterogeneous across the trait continuum, this can lead to spurious interaction effects in GE interaction models when environmental variables are unmeasured  by twin j from family i, p(ijkY = 1), is modeled as a logistic function of the difference between the twin's latent traits score  and the difficulty of the item:ij refers to the latent trait score of individual twin j from family i, kb denotes the difficulty of item k, which represents the trait level associated with a 50% chance of endorsing an item. This IRT model is suitable for dichotomous items , as is, for example, collected from mathematical ability tests. An underlying assumption of the Rasch model is that all items discriminate equally well between varying abilities: How rapidly the probabilities of a correct answer change with trait level is the same for all items. An extension of the Rasch model, the two-parameter logistic model (2PLM), also estimates discrimination parameters that differ across items. The change in probabilities of a correct answer with trait level can then be different  among the different items  is estimated based on performance  and on test item properties . The simplest IRT model is the Rasch model, also known as the one-parameter logistic model (1PLM), where the probability of a correct answer to item Tucker-Drob et al.  proposedAs sum score data were available for 12 separate cognitive tests, they tested whether there was a single factor common to all tests, using Mplus. Subsequently, the ACE × M analysis and a non-linear factor structure were modeled using the Markov chain Monte Carlo (MCMC) estimation program WinBUGS  while keeping the number of twin pairs constant.Next, we applied the new methodology to the data of Dutch twin pairs on mathematical ability and estimated genetic and non-genetic variance components in 12-year-olds for mathematical ability as a function of a family's SES.The full model, consisting of a biometric and psychometric part, is presented in more detail for MZ and DZ twins separately.i, the effect of common environmental influences is perfectly correlated within the pair and normally distributed with an expected value consisting of the phenotypic population mean, μ, and the main effect of the moderator variable M. Familial influences F, consisting of additive genetic influences (A) and common environment (C), were assumed to be normally distributed for every family i:1m represents a regression coefficient that expresses the estimated main effect of the moderator variable. In order to model A × M and C × M, for every twin MZ family i, variance components were divided into an intercept (representing variance components when Mi = 0) and a linear interaction term (denoting A × M and C × M respectively):0c (β0a) represents common-environmental (additive genetic) variance when Mi = 0 and β1c band β1a represent A × M and C × M, respectively.For each twin pair ij of individual twin j from family i then consisted of the familial effect:The expected value of the phenotypic trait, θ2E, was different for every MZ family i with a different value on the moderator variable and divided into an intercept  and an interaction term:In order to model E × M, variance due to unique-environmental influences, σk of twin j from family i, ijkP, were then modeled conditional on θij in the Rasch model:kb refers to the difficulty parameter of item k. In the simulation studies, it was assumed that item parameters were known.In the psychometric part of the model, the probabilities for correct item response i that is perfectly correlated within a twin pair with an expected value consisting of the phenotypic mean and the main effect of the moderator variable M:Similar to MZ twin pairs, a normal distribution was used to model a common environmental effect for every DZ family 2Ci = exp(βc0 + βc1Mi), . This yielded a genetic effect A3ij that was unique for every individual twin j from DZ family i:The genetic value was scaled by multiplying it with the standard deviation σij, then consisted of the common environmental effect for every DZ family i and the additive genetic effect for every individual twin j:2Ei was divided into an intercept  and an interaction term  was set to 0.25, exp(β0c) was 0.25 and exp(β0e) was fixed to 0.5. All interaction effects  were set to zero. For every MZ and DZ family, a dichotomous moderator value was simulated such that the moderator explained approximately 11% of the total phenotypic variance (with β1m fixed to 0.7). The simulated datasets were then analyzed using the above described method and a sum score approach. In the sum score approach, all scores were divided by the standard deviation of the sum score of those twins who scored 1 on the moderator value in order to set both the IRT and sum score analysis on the same scale and make results comparable. To estimate the power of both models, the 95% highest posterior density interval  suggests an increased  false positive rate.In each scenario, 250 datasets were simulated, each consisting of 2,000 twin pairs where the percentage of MZ twins was fixed to 28% of all pairs. The phenotypic population mean, μ, was fixed to 0. Using similar values as Purcell , exp was investigated by varying the number of items  while fixing the number of twin pairs at 1,000. Details and results of this simulation study can be seen in the online supplementary material.All simulations were carried out using the software package R , exp(β0c), and exp(β0e) were equal to 1 under both models and are therefore not tabulated here.The true parameter values, posterior means and the means of posterior standard deviations, averaged over 250 replications, can be found in 1m as well as exp(β0a) and exp(β0c) were underestimated. More importantly, the analysis resulted in relatively high interaction parameters . exp(β0a) and exp(β1e). Power estimates for the IRT model were either equal to or only slightly above (0.06 for β1a) the 5% that can be expected when an interaction would be found simply due to chance. In other words, the IRT approach did not result in the finding of spurious interaction effects.In the first scenario, a negatively skewed sum score distributed was mimicked, resulting in a slight ceiling effect, which resulted in biased parameter estimates: The main effect of the moderator variable, β1a = 0.36[0.85], β1c = 0.29[0.67], and β1e = 0.24[0.10]). To save space, the results of the second scenario are not tabulated but can be obtained from the first author.In the second scenario, a slight floor effect was mimicked, resulting in a positively skewed sum score distribution. Since the second scenario was the mirror image of the first scenario, parameter estimates were very similar to those found in the first scenario with spurious interaction effects in the opposite direction  indicate that there was only a small decrease in standard deviations and standard errors with increasing number of items. Also, the increase in precision with increasing sample size was small, suggesting that as much as 20 items are sufficient to fit the ACE × M model.incorrect, 1 = correct) of the mathematics subscale of this test.The model described above was used to investigate ACE × SES in mathematical ability of 2,110 12-year-old Dutch twin pairs. Mathematical achievement was measured with the Eindtoets Basisonderwijs, which is a Dutch national achievement test that is administered in the last year of primary education. The Eindtoets Basisonderwijs test assesses what a child has learned during primary education and consists of 290 multiple choice items in four different subjects . Here, we used the 60 dichotomous item scores  on the mathematics subscale of the Eindtoets Basisonderwijs test. The linking procedure and harmonization of different test versions is described in detail in Schwabe et al. (n twins = 52), the child was attending special education (n twins = 34), a different test was used at the school the twin was attending (n twins = 13), the child (n twins = 2), or the whole school (n twins = 1) did not attend the test, or the reason was unknown (n twins = 609).The data of 12-year-old twins from the Netherlands Twin Register from birth cohorts 1998–2000 were used to link individual twins to their dichotomous item scores  and 1 . We interpret these two categories as ‘families with average or low SES’ (coded as 0) and ‘families with high SES’ (coded as 1). Seven hundred and twenty (34%) families had a high family SES and 988 (47%) an average or low SES . On the probability π , a beta-distributed hyperprior was used, which was different for MZ and DZ twins . Note that by using prior distributions, all available data could be analyzed without missing SES values resulting in a reduction of sample size.As there were twins with missing SES data, independent Bernoulli distributed prior distributions were defined  + exp(βc0) + exp(βe0). The results suggest that the largest part of phenotypic variance could be explained by genetic influences, a substantial part by unique environmental influences and a negligibly small part by common environmental influences. A significant and negative C × SES interaction effect was found, meaning that common environmental influences are less important in creating individual differences in mathematical ability in families with a high SES than in creating individual differences in mathematical ability in twin pairs with a low or average SES.Heritability was defined as In this paper, the biometric modeling of moderation of variance decomposition  was extended with an IRT model at the phenotypic level, making it possible to analyze item data rather than sum scores. We applied the extended model to data on mathematical ability.We modeled ACE × M on the log-transformed variances, using a parametrization that is uniquely identified and therefore to be preferred over the parametrization by Purcell . Note, hTo show that in the case of heterogeneous measurement error, the sum score approach results in spurious interaction effects while the proposed method is unbiased, two scenarios were simulated. While the first scenario resulted in a situation often encountered in cognitive ability studies with gifted children , the second scenario is typical for psychopathology studies . The results showed that spurious interaction effects can be expected when the sum score approach is used, in particular in the case of an E × M interaction. On the other hand, the IRT approach was unbiased. A second simulation study suggested that 20 items are sufficient to use the IRT method.The method was applied to investigate the moderating influence of SES on variance components in mathematical ability of 2,110 12-year-old Dutch twin pairs. The results suggest that most of the phenotypic variance could be explained by genetic influences, resulting in a relatively high heritability of 71%. A substantial part of the variance in mathematical ability could be explained by unique environmental influences and a small part by common environmental influences. Furthermore, a negative C × SES interaction effect was found, meaning that common environmental influences were less important in creating individual differences in mathematical ability in families with a high SES than in creating individual differences in mathematical ability in twin pairs with a low or average SES. Children from low-SES families are generally disadvantaged. For example, they live in disadvantaged neighborhoods with poor facilities and inferior schools or have fewer books at home  are used. To correct for measurement error in the moderator level, in future research, the method will be extended to include an IRT model also at the level of the moderator variable. In case of heterogeneous measurement error in the moderator variable, it is to be expected that this to be developed method performs better than the method introduced here , but it is unclear how large the differences in the two methods are and whether heterogeneous measurement error in the moderator variables also results in the spurious finding of interaction effects. Heterogeneous measurement error in the moderator variable can, for example, occur when the moderator resembles a psychological trait. Assume, for example, that one is interested in the influences of study motivation on the importance of genetic, common environmental, and unique environmental influences on individual differences in educational achievement: A scale that measures study motivation might be very reliable for students with an average motivation, but it may be very difficult to distinguish the motivated students from the very motivated students .A drawback of the method is that it is computationally intensive and, depending on the number of items and twin pairs, can take several hours to complete. In future research, more efficient sampling algorithms will be applied to lighten the computation burden. The model can furthermore be expanded to include both linear and quadratic interactions on the paths (such that the ACE variance estimates are quadratic with respect to the moderator). Therefore, one can test whether genetic variance can be modeled as an inverted U-shaped curve, with the highest genetic variance in the ‘average’ environment. In this study, we considered only linear interaction effects. It has been shown that the integration of a curvilinear interaction effects is problematic even in the case that environmental measures are unmeasured (Schwabe & van den Berg,


With the development of the next-generation sequencing technology, the influence of rare variants on complex disease has gathered increasing attention. In this paper, we propose a clustering-based approach, the clustering sum test, to test the effects of rare variants association by using the simulated data provided by the Genetic Analysis Workshop 19 with an unbalanced case-control ratio. The control individuals are (a) clustered into several subgroups, (b) statistics of the separate subcontrol groups as compared to the case group are calculated, and (c) a combined statistic value is obtained based on a distance score. Collapsing of rare variants is used together with the proposed method. In our results, comparing the same statistical test with and without clustering, the clustering strategy increases the number of true positives identified in the top 100 markers by 17.24 %. Compared to the sequence kernel association test, the proposed method is more robust in terms of replicated frequencies in the replicates data sets. The results suggest that the clustering approach could improve the power of nonparametric tests and that the clustering sum test has the potential to serve as a practical tool when dealing with rare variants with unbalanced case-control data in genome-wide case-control studies. Genome-wide association studies have successfully detected a number of variants associated with complex traits and provided valuable insights into the genetic etiology of complex traits, but only a small portion of the total heritability has been explained . This cuThe GAW19 data set consists of the real whole genome sequencing genotype data and 200 replicates of simulated phenotypes, including the continuous systolic (SBP) and diastolic blood pressure (DBP) and hypertension status. In this study, we use the genotypes on chromosome 3, which include 48,510 single-nucleotide polymorphisms (SNPs). Quality control is conducted and SNPs are excluded if the percentage of missing value is more than 5 %, the minor allele frequency (MAF) equals zero, or an inconsistent genotype format exists. There are 1943 independent individuals and 42,825 SNPs that pass the quality control assessment with a MAF of less than 1 %.AA, Aa, aa coded as 0, 1, 2. Where a refers to the minor allele. We want to analyze the association of G with the binary phenotype Y, as well as with its continuous phenotype information. In this study, a χ2 test is used to measure this association.Suppose a marker G has 3 genotypes Step 1. K-means clustering for individuals’ classificationK groups, where K is an optimal group number determined by cross-validation [K sets of control data have different average levels of hypertension.Step 2. Clustering sum testIn this step, a K-means clustering method  is used lidation . Thus th2 test statistic is then calculated. The clustering and the χ2 test statistic are then combined with the weighted sum test.Each control data set after clustering is matched with the same case data set. The χThe form of the clustering weighted sum test is:dk is the average phenotype distance between the kth control group and the case group. D is the sum of dk and Sk is the χ2 test applied on the kth control and case data sets.Where, L are collapsed as pseudo markers. Window sizes L are chosen as 1, 10, 15, 20, 25, 30, 50, where one refers to no collapsing. CST is then applied to these pseudo markers and the optimal collapsing window size is chosen.For all rare variants, SNPs within window size n pseudo markers in 50 replicates by using 3 methods, namely, the CST based on the χ2 test, the χ2 test, and SKAT [n is set as 50, 100, 200, 300, 500, 750, 1000. Under the setting of chosen window size 15, CST-χ2 outperforms the χ2 test and SKAT in different selection criteria settings. This is especially true when the selection criteria is to be within the top 100 and 300; in those cases, the number of true positives identified is 44.7 and 35.9 % higher, respectively, than the numbers identified by SKAT.Rare variants on chromosome 3 are collapsed using different window sizes and the statistical test is conducted to detect causal variants. A “pseudo marker” is 1 collapsed marker and a corresponding “pseudo answer” is the pseudo marker that contains at least 1 functional causal variant. Table and SKAT , where np value of each table count is estimated based on a binomial distribution to describe the probability of obtaining more than the observed number of answers under the null hypothesis of no associations. Window size 15 has been demonstrated to be the most significant window size when the criteria setting is top 100 markers (Fig. 2 test and SKAT, the optimal window sizes are 15 and 10, respectively.The 2 test, the main difference between CST and the χ2 test is the clustering information. We use the results obtained using optimal window size 15 to compare the performance of the CST approach to the χ2 test. The numbers of pseudo answers identified in the top 100 and 300 markers are 2.72 and 7.04 using CST and 2.32 and 5.78using the χ2 test. In addition, we compare the general performance across different window sizes, that is, sizes other than 15. The significant levels of CST are still stronger than the χ2 test in most cases (see Fig. 2 test. This result indicates that involving more continuous phenotype information by clustering could increase the power of nonparametric tests.In this study, because CST is based on an χIn this part, we compare the number of causal markers identified by CST and SKAT under their optimal window sizes. Table In the top 2 pseudo answers detected, the replication frequencies of CST are as high as 22 and 16 out of the total 50 replicates, whereas they are 10 and 6 using SKAT. In the top 5 pseudo answers, the replication frequency is 96.3 % higher than it is for SKAT. These results show that CST is a more robust approach than SKAT for identifying rare variants. This may be because of the nonparametric nature of the CST, which could weaken the influence of noise from different types of underlying genetic architecture.MAP4 shows the strongest effect among causal genes in chromosome 3. Both the CST and the SKAT could detect MAP4 in the top 5 markers, although the detected SNPs in MAP4 are not the same. MAP4 ranks first by the CST, and this pseudo marker includes seven answer SNPs with cumulative effects of −114.19 and −53.134 in SBP and DBP, respectively. Cumulative effects in MAP4 identified by SKAT are −18.180 and −8.459 in SBP and DBP. The cumulative effect is calculated by the sum of SBP and DBP effects within the same collapsing window. In addition, CST identifies the pseudo marker containing more than three causal SNPs, whereas in the SKAT result, 4 of the top 5 pseudo answers contain only 1 causal SNP. From this perspective, CST can detect causal markers with the largest cumulative effect size in a robust manner whereas SKAT tends to detect markers containing a single SNP with a different effect size rather than with a large cumulative effect.Information on causal markers for hypertension in the simulated data is provided by GAW19. The gene ZBTB38. One gene, MAP4, could be detected in different regions by both methods. Findings of these two genes could further validate the effectiveness and accuracy of CST: the top marker identified is supported to have the strongest effect on hypertension and the second marker is the only overlapped variant identified and ranked as the topmost by SKAT. The small-overlapping pattern might be a result of the difference between the theoretically based hypothesis of the definition to measure the causal relationship between markers and disease of interest. One assumption behind collapsing is that the genetic probability distribution is similar within the same collapsing region. CST could match the assumption to enlarge the collapsed signals in the same effect direction. For SKAT, it is a kernel regression to detect the effect in each region and an inverse weight score is given to rare SNPs. SKAT is more useful and sensitive for detecting SNPs in a region with an opposite effect direction.Surprisingly, the findings by the two methods show very little overlap: only one marker is detected by both methods at SNP position 141164276 in gene In this paper, we propose a clustering-based test to detect rare variants when continuous phenotypes are available. There are three advantages of doing this: First, the CST can make better use of phenotype information, instead of just dichotomizing continuous phenotypes in a single case-control study. Second, when the ratio of number of cases to controls is extreme, the CST can balance the number of samples in each case-control set by dividing the larger group into smaller groups. Third, CST produces more robust results than the other tests because of its nonparametric form. All of the above findings suggest that CST has the potential to become a useful method in dealing with rare variants in case-control studies and thus is worth further investigation.The CST has been shown to outperform SKAT with larger power when the collapsing region contains many causal SNPs with the same effect direction. With the collapsing strategy applied, the CST, as a burden test, combines signals of rare variants within a certain region, thus, signals of cumulative effects could be enlarged for detecting whether the effects of causal variants are in the same direction. SKAT is based on a multiple regression to directly measure the relationship between phenotypes and multiple genetic variants in a region  and it iPrevious study on a similar version of GAW19 data sets indicates that the false-positive rate is usually high, as our results show in Table


Expression quantitative trait locus (eQTL) maps are considered a valuable resource in studying complex diseases. The availability of gene expression data from the Genetic Analysis Workshop 19 (GAW19) provides a great opportunity to investigate the association of gene expression with genetic variants in blood.A total of 267 samples with gene expression and whole genome sequencing data were employed in this study. We used linear mixed models with genetic random effects along with a permutation procedure to create an eQTL map. The eQTL map was further tested in terms of functional implication, including the enrichment in disease-related variants and in regulatory regions.h2 > 0.4).We identified 22,869 significant eQTLs from the GAW19 data set. These eQTLs were highly enriched with genetic loci associated with blood pressure and DNase hypersensitive regions. In addition, the majority of genes associated with eQTLs showed moderate to high heritability (We successfully created an eQTL map from the GAW19 data set. Our study indicated that the eQTLs were enriched within regulatory regions, and tended to have relatively high heritability. Gene expression is an essential component of the central dogma of molecular biology, and is mediated by both genetic and environmental factors . ExpressFor each analysis we used real phenotype data from individuals in the Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) whole genome sequencing (WGS) families provided by GAW19, which included systolic and diastolic blood measurements, age, sex, and smoking status. These measurements were quantified in four visits, and data for at least one visit was available for 939 participants. A full description of the data can be found in Almasy, et al. .The genotype data was generated from WGS, which included 12,296,048 single-nucleotide variants (SNVs) on odd-numbered chromosomes found in at least one of 464 studied participants.The gene expression profiled was previously described in detail by Göring, et al. . Brieflycis-eQTLs as SNPs located within 1 Mb of the transcript starting sites, and trans-eQTLs as SNPs located more than 1 Mb of the transcript starting sites, or in different chromosomes.The functional annotation of genetic variants was performed using the ANNOVAR (Annotate Variation) package . We defiPc1, Pc2) as covariates. Using the subscript ij to denote the jth individual in the ith family, and defining Yij and SNPij as the gene expression and genotype dosage, respectively, we write the model as:αij is the random intercept, and εij the normally distributed error term with mean zero and variance σε2. The αij within the ith family are normally distributed with mean zero and covariance matrix σ2Φ, where Φ is the kinship matrix. The overall covariance matrix is block diagonal with one block per family. The model was fitted in R using the lmekin function from the coxme package [The association of genetic variants with gene expression (eQTL) was tested by linear mixed effects models, adjusting for random genetic effects and age, sex, smoking status and the first two components from the expression principal components analysis , we had limited power to uncover cis-eQTL for the original transcript. We repeated the above procedure for each transcript three times to obtain a p value between cis-eQTL and transcript.We ran a Shapiro-Wilk normality test for all the expression probes and we found that the test was significant after a Bonferroni correction for more than half of the probes. To reduce type I error that may arise from violating the normality assumption, we estimated significance using a modified version of the permutation procedure proposed by Iturria, et al.  that preNg) for each gene and account for linkage disequilibrium, we multiplied the p values by the factor p value from each permutation to form a null distribution of the adjusted p value statistic for each heritability bin.To obtain the significant results we split the genes into seven heritability bins. This splitting choice gave an approximately equal number of permutations per bin. To adjust for the different number of SNPs tested  <5 %). Therefore, we extended this list to nearby SNPs with distance less than 1 kb and We also examined if eQTLs were significantly enriched within DNase hypersensitive regions based on ENCODE data .h2 < 0.1), and all the other eGenes have medium to high heritability (h2 > 0.4). The ten most significant eQTLs are shown in Table Here, we report significant expression SNPs (eSNPs) controlling for a false discovery rate of 0.05 using the Benjamini-Hochberg procedure . We founp <6.1E-4) showed that the set of GWAS results contained more eSNPs than we would expect by chance.To demonstrate the usefulness of our eQTL map, we examined the distribution of blood pressure–related genetic variants from GWAS found in the literature. Our variant list contained 31 SNPs that were a part of the eQTL study, two of which were eSNPs. Even with the small numbers, a Fisher’s exact test , which contained 17 times more eQTLs than random variants.We found 386,135 variants that were part of the eQTL analysis that lie within DNase hypersensitivity regions, of which 5,679 were found to be eSNPs. Our results confirmed the enrichment of eQTLs in DNase cluster regions (Fisher’s exact test p <5.5E-9) maps to the gene TPP3 on chromosome 16, while the other (GI_42661149 with p <1.8E-6) maps to the predicted gene LOC400604.We then tested the association of gene expression with blood pressure, and found that two probes were significantly associated with blood pressure. One probe (GI_7706275.A with The identification of genetic mechanisms underlying gene expression would enable a better understanding of the biology of complex diseases. We performed a comprehensive analysis of the association between gene expression and genetic variants using GAW19 data, and successfully identified 22,869 eQTLs despite limited sample size. These eQTLs were highly enriched in genetic loci associated with blood pressure and DNase hypersensitive regions, suggesting that eQTLs might play an important role in regulatory functions. Our breakdown of eSNP results by heritability indicates that most of these eSNPs have high heritability. Future investigation with a larger sample size would further validate the association of heritability with eQTLs.We created an eQTL map that included 22,869 eQTLs from GAW19 data. We found that eQTLs were enriched within regulatory regions, and tended to have relatively high heritability.


By splitting the cohort into a discovery sample of 40,000 and target sample of 12,000, we developed a prediction algorithm based entirely on common genetic variants that discriminated  those with no hair loss from those with severe hair loss. The results of this study might help identify those at greatest risk of hair loss, and also potential genetic targets for intervention.Male pattern baldness can have substantial psychosocial effects, and it has been phenotypically linked to adverse health outcomes such as prostate cancer and cardiovascular disease. We explored the genetic architecture of the trait using data from over 52,000 male participants of UK Biobank, aged 40–69 years. We identified over 250 independent genetic loci associated with severe hair loss (P<5x10 Living with male pattern baldness can be stressful and embarrassing. Previous studies have shown baldness to have a complex genetic architecture, with particularly strong signals on the X chromosome. However, these studies have been limited by small sample sizes. Here, we present the largest genome-wide study of baldness to date, using data from over 52,000 male participants in the UK Biobank study. We identify over 200 novel findings. We also split our dataset in two to build and apply a genetic predictor of baldness. Of those with a polygenic score below the median, 14% had severe hair loss and 39% no hair loss. By contrast, of those with a polygenic score in the top 10%, 58% reported moderate-to-severe hair loss. Male pattern baldness affects around 80% of men by the age of 80 years , and it The total proportion of variance in male pattern baldness that can be attributed to genetic factors has been estimated in twin studies to be approximately 80% for both early- and late-onset hair loss , 12. NewAR gene showing the strongest association. The largest published genome-wide association study (GWAS) to date highlighted eight independent genetic loci that were linked to baldness; the top AR SNP yielded an odds ratio of 2.2 in a case-control meta-analysis of 12,806 individuals of European ancestry [-8) with baldness; two of these were located on the X chromosome [A number of studies have identified specific genetic variants linked to variations in baldness, usually with the ancestry . One of romosome .Several attempts have been made to build predictors of male pattern baldness using polygenic risk scores. Heilmann et al. found, using a case-control design with ~600 per arm, that a predictor based on 34,186 SNPs explained 4.5% of the variance on the liability scale . Marcińshttp://www.ukbiobank.ac.uk) is a large, population-based genetic epidemiology cohort. At its baseline assessment (2006–2010), around 500,000 individuals aged between 40 and 70 years and living in the UK completed health and lifestyle questionnaires and provided biological samples for research.The UK Biobank study  . 16,724 (31.6%) reported no hair loss, 12,135 (23.0%) had slight hair loss, 14,234 (26.9%) had moderate hair loss, and 9,781 (18.5%) had severe hair loss.-8), in addition to 117 hits  on the X chromosome . The QQ plot for the autosomal GWAS is shown in S1 Fig. An LD clumping analysis indicated that these hits can be attributed to 247 independent autosomal regions. All previously reported autosomal hits [-8, S1 Table). The previously reported X chromosome variant from Li et al. [S1 Table). The chromosome 6 hit (rs4959410) from Liu et al. [Table 1. The top 10 independent X chromosome hits are presented in Table 2; rs140488081 and rs7061504 are intronic SNPs in the OPHN1 gene. After conditioning on the top SNP (rs73221556), 47 SNPs (including the two lead X chromosome SNPs from the literature: rs2497938 and rs6625163) remained significant at P<5x10-8. In the UK Biobank data, the two lead SNPs from the literature were in very high LD (R2 = 0.98). Summary output for all of the SNPs is available at the following URL: http://www.ccace.ed.ac.uk/node/335. A list of the 287 independent loci are reported in S2 Table.The genome-wide association study of the four-category self-reported baldness measure in 52,874 White British men from UK Biobank yielded 13,029 autosomal hits from the imputed data P<5x10-8, in admal hits  that mapi et al.  and the -269). A full list of the autosomal significant gene-based hits is provided in S3 Table and significant genes on the X chromosome are shown in S4 Table. A significant enrichment (FDR <0.05) was found for 143 gene sets; the full results are presented in S5 Table.The gene-based analysis identified 112 autosomal genes and 13 X chromosome genes that were associated with baldness after a Bonferroni correction . The top gene-based hit was, as expected, the androgen receptor on the X chromosome  of the variance in baldness can be explained by common autosomal genetic variants, while 4.6% (SE 0.3%) can be explained by common X chromosome variants.S6 Table).Genetic correlations were examined between male pattern baldness and 24 cognitive, health, and anthropometric traits using LD Score regression. No significant associations were found; all estimates were close to zero . The optimal autosomal polygenic score yielded an AUC of 0.75 for discriminating between those with no hair loss  and those with severe hair loss . The corresponding AUC for the optimal X chromosome polygenic score was 0.62. An additive combination of the autosomal and X chromosome polygenic scores gave an AUC of 0.78  for severe hair loss, 0.68  for moderate hair loss, and 0.61  for slight hair loss . Adding age as a covariate boosted the AUC to 0.79 for severe hair loss (P<2x10-16), 0.70 for moderate hair loss (P<2x10-16), and 0.61 for slight hair loss (P = 0.019). Fig 3 shows the proportion of participants in the four baldness groups for each polygenic risk decile of male pattern baldness. Of those with a baldness polygenic score below the median, 14% reported severe hair loss and 39% no hair loss. By contrast, of those with a polygenic score in the top 10%, 58% reported moderate-to-severe hair loss.The GWAS for self-reported baldness was re-run on a sub-sample of 40,000 individuals—retaining an equal proportion of each of the four baldness patterns as observed in the full cohort—to allow a polygenic prediction score to be built and applied to the remaining, independent sample of 12,874 individuals. The most powerful predictions from comparing the extreme phenotype groups were observed at the P<1x10S2 Fig and S7 Table). These significant annotations included a broad array of functional elements including histone marks, enhancer regions, conserved regions, and DNaseI hypersensitivity sites (DHS). The ten tissue types were then tested for significance after controlling for the baseline model. Following correction for multiple testing, all ten of the tissue groups showed significant enrichment .The results of the partitioned heritability analysis indicated that 27 of the functional annotations from the baseline model were statistically significant  [IRF4) [MEMO1 [SLC14A2 [HDAC9), and frontotemporal dementia (MAPT) [IRF4 with both hair colour and hair greying, but not with male pattern baldness [HDAC9 has been identified as a baldness susceptibility gene in a previous study [OPHN1, a gene previously associated with X-linked mental retardation [As mentioned above, the GWAS identified 247 independent autosomal loci and 40 independent X chromosome loci. The top 20 hits from the autosomes were located in or near to genes that have been associated with, for example, hair growth/length in mice  [IRF4) , cancer ) [MEMO1 , bladder[SLC14A2 ), histonbaldness . HDAC9 hus study . Two of ardation .-15), RSPO2 has been linked to hair growth in dogs. PGDFA has been linked to hair follicle development [EBF1 is expressed in dermal papillae in mature hair follicles [PRR23B is proximal to a GWAS hit for eyebrow thickness [WNT10A has been linked to both straight hair [Of the top autosomal gene-based findings , which has been well established as a baldness associated gene [EDA2R) and downstream (OPHN1) genes. EDA2R plays a role in the maintenance of hair and teeth as part of the tumor necrosis factor receptor. Onset of male pattern baldness could be influenced by EDA2R via activation of nuclear proto-oncoprotein c-Jun, which is linked to transcription activation of AR [OPHN1 and ZC4H2, have previously been associated with X-linked mental retardation [The top X chromosome gene-based findings included the androgen receptor . GO:000r growth . GO:0003alopecia . MP:0000air loss . It is iS1 Fig), this is likely to be a result of genuine polygenic effects. We have used identical analysis protocols for other traits with far lower SNP-based heritabilities in the same UK Biobank cohort and observed no evidence of inflation [The main strength of this study is its large sample size and phenotypic homogeneity. Many meta-analytic studies of complex traits are weakened by different cohorts collecting data at different time-points, under different protocols, in different populations. The present study replicated all of the previously identified autosomal hits for baldness from Li et al.  and Heilnflation .We identified over two hundred independent, novel genetic correlates of male pattern baldness—an order of magnitude greater than the list of previous genome-wide hits. Our top SNP and gene-based hits were in genes that have previously been associated with hair growth and development. We also generated a polygenic predictor that discriminated between those with no hair loss and those with severe hair loss. Whereas accurate predictions for an individual are still relatively crude, of those with a genetic score in the top 10% of the distribution, 58% reported moderate-to-severe hair loss. The release of genetic data on the full UK Biobank cohort will further refine these predictions and increase our understanding of the genetic architecture of male pattern baldness.Data came from the first release of genetic data of the UK Biobank study and analyses were performed under the data application 10279. Ethical approval for UK Biobank was granted by the Research Ethics Committee (11/NW/0382).http://biobank.ctsu.ox.ac.uk/crystal/refer.cgi?id=157020). Imputed data were not available for the X chromosome, hence only genotyped variants were considered. X chromosome quality control steps included a minor allele frequency cut-off of 1% and a genotyping call rate cut-off of 98% [Genotyping details including quality control steps have been reported previously . Brieflyf of 98% . For theFig 4 shows a screenshot of the four options.From the sample of 112,151 unrelated White British participants with genetic data, we identified 52,874 men with a self-reported response to UK Biobank question 2395, which was adapted from the Hamilton-Norwood scale , 46. TheA genome-wide association study was conducted using baldness pattern residuals as the dependent variable. The residuals were obtained from a linear regression model of baldness pattern on age, assessment centre, genotyping batch and array, and 10 principal components to correct for population stratification.The GWAS for the imputed autosomal dataset was performed in SNPTest v2.5.1  via an a-8) and clumps were formed for SNPs with P<1x10-5 that were in LD (R2>0.1) and within 500kb of the index SNP. SNPs were assigned to no more than one clump.The number of independent signals from the GWAS was determined using LD-clumping , 49 baseGWAS lookups were performed for the top hits reported in Richards et al. , Li et aGene-based analyses were performed using MAGMA . SNPs we-20, <5x10-8, <1x10-5, <0.01, <0.05, <0.1, <0.2, <0.5, <1 using PRSice software [2>0.25. Thereafter, each threshold was used to discriminate between those with no hair loss and those with severe hair loss via logistic regression with results being reported for the optimal predictor only. A predictor for both the autosomes and X chromosome were built and assessed independently and additively. Receiver operator characteristic (ROC) curves were plotted and areas under the curve (AUC) were calculated using the pROC package in R [For the prediction analysis, the GWAS was re-run on a randomly selected cohort of 40,000 individuals to give regression weights for prediction, leaving an independent cohort of 12,874 in which to test the polygenic predictor. The methods for the GWAS were identical to those reported for the full sample. The regression weights from the GWAS on the 40,000 cohort were used to construct polygenic scores in the target dataset at P value thresholds of <1x10software . PRSice age in R , 55.SNP-based heritability of baldness was estimated using GCTA-GREML  after apS7 Table). Due to the large effects in the APOE region for Alzheimer's disease, 500kb was removed from around each side of this region and the analysis was repeated for the Alzheimer's—male pattern baldness analysis. The Alzheimer’s data set without this region is referred to as 'Alzheimer’s 500kb'. In total, we carried out 25 hypothesis tests. Multiple testing was controlled for using a false discovery rate (FDR) correction [S1 Appendix.Linkage disequilibrium score (LDS) regression analyses  were userrection . An overStratified linkage disequilibrium score (SLDS) regression  was usedS1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 TableNSNPS is the number of SNPs in the gene.(XLSX)Click here for additional data file.S4 TableNSNPS is the number of SNPs in the gene.(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table2 indicate the level of power to detect association where a heritability Z-score of >4 and a mean χ2 >1.02 being considered well powered [The heritability Z-score and the mean χ powered . None of(XLSX)Click here for additional data file.S7 TableProp._SNPs refers to the proportion of SNPs from the data set that were a part of the corresponding functional annotation. Statistical significance indicated in bold. Tissue groups are listed in the first ten rows followed by the functional annotation groups.(XLSX)Click here for additional data file.S8 TableVerbal-numerical reasoning and childhood intelligence were examined as educational attainment  can be (XLSX)Click here for additional data file.S1 Appendix(DOCX)Click here for additional data file.S1 Fig(PDF)Click here for additional data file.S2 Fig2)/Pr(SNPs)). Error bars are jackknife standard errors around the estimate of enrichment. The dashed line indicates no enrichment found when Pr(h2)/Pr(SNPs) = 1. FDR correction indicated significance at P = 0.011 indicated by asteriskThe enrichment statistic is the proportion of heritability found in each functional group divided by the proportion of SNPs in each group (Pr(h(TIF)Click here for additional data file.S3 Fig2)/Pr(SNPs). Error bars are jackknife standard errors around the estimate of enrichment. The dashed line indicates no enrichment found when Pr(h2)/Pr(SNPs) = 1. FDR correction indicated significance at P = 0.037 indicated by asterisk.In each functional group divided by the proportion of SNPs in each group (Pr(h(TIF)Click here for additional data file.


N = 515), lateral ventricular volume (N = 798), and the cognitive measures block design , digit span , and the Ray Auditory Verbal Learning Task . Data were collected across 11 sites in Europe and Australia; all genotyping and genetic analyses were done at the same laboratory in the United Kingdom. We calculated polygenic risk scores for schizophrenia and bipolar disorder separately, and used linear regression to test whether polygenic scores influenced the endophenotypes. Results showed that higher polygenic scores for schizophrenia were associated with poorer performance on the block design task and explained 0.2% (p = 0.009) of the variance. Associations in the same direction were found for bipolar disorder scores, but this was not statistically significant at the 1% level (p = 0.02). The schizophrenia score explained 0.4% of variance in lateral ventricular volumes, the largest across all phenotypes examined, although this was not significant (p = 0.063). None of the remaining associations reached significance after correction for multiple testing . These results indicate that common genetic variants associated with schizophrenia predict performance in spatial visualization, providing additional evidence that this measure is an endophenotype for the disorder with shared genetic risk variants. The use of endophenotypes such as this will help to characterize the effects of common genetic variation in psychosis.This large multi‐center study investigates the relationships between genetic risk for schizophrenia and bipolar disorder, and multi‐modal endophenotypes for psychosis. The sample included 4,242 individuals; 1,087 patients with psychosis, 822 unaffected first‐degree relatives of patients, and 2,333 controls. Endophenotypes included the P300 event‐related potential ( They arHowever, it is still largely unknown exactly how these genetic risk variants lead to the illness, and an important goal of psychiatric genetic research is to clarify the effects and mechanisms of these variants , block design , and the Rey Auditory Verbal Learning Task (RAVLT) immediate and delayed recall  are common and persistent across psychotic disorders  between the P300 amplitude and bipolar disorder (−0.33) . See Supplementary Materials for a summary of the data collected from each site. Participants provided written informed consent, and the study was approved by the respective ethical committees at each of the 11 participating centers.2.2The Wechsler Adult Intelligence Scale, revised version . EEG data acquisition and processing varied slightly between sites and are summarized below. The full methods for each site are reported elsewhere . We applied standard quality control procedures, phasing and imputation, and adjustments for population structure as described in the Supplementary Materials and in Bramon et al. . Samples were genotyped with the Genome‐wide Human SNP Array 6.0 at the Affymetrix Services Laboratory , hence including an increasing number of SNPs the more liberal the threshold .Polygenic scores for each individual were calculated using PLINK , lateral ventricular volume, and measures of cognition .R2 between a model only including the covariates and a model including covariates plus the polygenic score is reported, which represents the additional proportion of the variance explained by the polygenic risk score.Endophenotype measures were standardized for each site separately  to control for differences between the centers. Covariates included in all analyses were clinical group , study site, the first three population structure principal components, age, and gender. Because the sample included related individuals, robust standard errors were used to account for effects of clustering within families. This specifies that the standard errors allow for intragroup correlation; that is, the observations are independent between families (clusters) but not necessarily within families. The change in Linear regression analyses were performed for each endophenotype using the entire sample—patients with psychosis, unaffected relatives of probands, and controls—examining the associations with polygenic score at the different significance thresholds of the Psychiatric Genomics Consortium's SNP list. This was done separately for both the schizophrenia and bipolar disorder polygenic scores.p‐values by seven tests through Bonferroni or other methods was deemed too stringent for a hypothesis‐driven study such as this .Although we tested seven endophenotypes, we know that measurements within domains are correlated  and thus a correction of 33.1p < 0.001) and controls , whereas relatives and controls did not differ in mean age . There were more males in the patient group compared to both the control  and relative groups . The group of relatives contained more female participants than the control group . Age and gender are included as covariates in all analyses.Demographic information and mean values of the different endophenotypes are presented in Table Mean scores on the different endophenotypes followed the expected pattern of improving performance from patients, through to relatives and controls. See Supplementary Materials for statistics of group differences and distributions across groups, after correcting for covariates of age, gender, and study site.3.2F = 86.6, p = 2.3 × 10−37; controls vs. patients p = 1.6 × 10−35, controls vs. relatives p = 3.6 × 10−4, patients vs. relatives p = 1.1 × 10−16), with patients having the highest scores, followed by relatives and lastly controls . A higher polygenic score was associated with poorer performance on the block design task. The polygenic score for schizophrenia explained 0.4% of the variance in lateral ventricular volumes, the highest percentage across all phenotypes we examined; although this result was not significant (p = 0.063). No other associations reached significance after correcting for multiple testing. These results are shown in Figure The polygenic score for schizophrenia predicted scores on the block design task at the SNP 3.3F = 21.8, p = 4.0 × 10−10; controls vs. patients p = 4.9 × 10−11, controls vs. relatives p = 6.1 × 10−4, patients vs. relatives p = 2.8 × 10−3), with patients having the highest scores, followed by relatives and lastly controls , although this did not reach significance after correction for multiple testing (p = 0.02). The proportions of variances explained by the bipolar disorder polygenic score were all <0.2% (and mostly below 0.1%), and none of the other associations were significant after correcting for multiple testing. These results are shown in Figure The polygenic score for bipolar disorder explained 0.17% of the variance in block design . This resulted in a reduction in the total sample size of 17.8% to 3489 participants. This analysis did not change the overall conclusions of the study, and has been described in the Supplementary Materials.4The aim of this study was to investigate whether polygenic risk scores for schizophrenia and bipolar disorder—based on the latest mega‐analyses from the Psychiatric Genomics Consortium—influence a range of endophenotypes for psychosis in this large international sample. This included the P300 event related potential amplitude and latency, lateral ventricular volume, and measures of cognition . Higher schizophrenia polygenic scores predicted poorer performance on the block design task, with 0.20% of the variance explained.Several studies have investigated the relationship between cognition and polygenic score for schizophrenia. Terwisscha vanScheltinga, Bakker, van Haren, Derks, Buizer‐Voskamp, Cahn et al. 2013) failed to show an association with intelligence in a sample of 672 patients with schizophrenia and controls, but McIntosh et al.  failed t saw an aHence, research suggests that there is a genetic overlap between cognitive performance and schizophrenia susceptibility  and Papiol et al.  both loop‐values approaching significance, and the question remains whether with larger samples one might see an association.Ventricular volume has a genetic basis with heritability estimates ranging from 30% to 70%  phenotypes, and environmental factors play important roles too. Furthermore, all endophenotypes are likely to have complex genetic influences, including a substantial polygenicity de Geus, , and onlThat the only endophenotype reaching significance (the block design task) was measured in larger samples suggests that power might indeed be an issue. For the EEG and MRI measures, that are more laborious to obtain, sample sizes in this study ranged from just over 500 to about 800, which means that a variance explained of 1–1.5% or higher could be detected, suggesting power was limited for these phenotypes. For the cognitive endophenotypes, however, the sample sizes were larger and variances explained of 0.25–0.55% or higher could be detected .A limitation of this study was the heterogeneity of methods between study sites in terms of endophenotype collection, processing and analysis. This might have added noise to the data and thus reduce power to detect any true effects. However, an important strength was that genotyping of all samples was done at the same laboratory using the same platform, and that all genetic analyses and quality control were completed in a unified way. Furthermore, it is precisely through this multi‐center effort that we were able to achieve a very large sample, a key strength of this study. As the Psychiatric Genomics Consortium's work shows, large international collaborations are essential in genetic studies of common diseases and traits , providing further evidence that this measure is an endophenotype for the disorder with shared genetic risk variants. No other associations between polygenic scores for schizophrenia or bipolar disorder and endophenotypes reached significance, possibly due to a lack of power, with larger samples needed to detect these small effects. As discovery samples get larger, and additional and better targeted genetic information is included, the performance of polygenic scores will be further enhanced. Larger association studies using these scores on deeply phenotyped samples may in future provide a promising approach to investigate the effects and mechanisms of genetic risk variants for psychosis.All authors declare that they have no financial interests or potential conflicts of interest.Additional Supporting Information may be found online in the supporting information tab for this article.Supporting Data S1.Click here for additional data file.


R2 of 0.239 and 0.082 using GIANT summary association statistics for height and BMI in the UK Biobank study , explaining 46.9% and 32.7% of the overall polygenic variance, respectively. For diabetes status, the area under the receiver operating characteristic curve was 0.602 in the UK Biobank study using summary-level association statistics from the DIAGRAM consortium. GraBLD outperformed other polygenic score heuristics for the prediction of height (p < 2.2 × 10−16) and BMI (p < 1.57 × 10−4), and was equivalent to LDpred for diabetes. Results were independently validated in the Health and Retirement Study . Our report demonstrates the use of machine-learning techniques, coupled with summary-level data from large genome-wide meta-analyses to improve the prediction of polygenic traits.Machine-learning techniques have helped solve a broad range of prediction problems, yet are not widely used to build polygenic risk scores for the prediction of complex traits. We propose a novel heuristic based on machine-learning techniques (GraBLD) to boost the predictive performance of polygenic risk scores. Gradient boosted regression trees were first used to optimize the weights of SNPs included in the score, followed by a novel regional adjustment for linkage disequilibrium. A calibration set with sample size of ~200 individuals was sufficient for optimal performance. GraBLD yielded prediction  Consistent with this hypothesis, polygenic risk scores that include both strongly and weakly associated variants are vastly superior than those including only genome-wide significant variants. For example, a recent study by Abraham et al. showed that a polygenic risk score incorporating 49,310 variants had a discrimination ability that was similar and complementary to the widely used clinical Framingham risk score for the prediction of coronary artery disease (CAD)2. Thus, there is a need for polygenic risk score methods that can integrate a large number of genetic variants.The advent of precision medicine depends in large part on the availability of accurate and highly predictive polygenic risk scores. While progress has been made identifying genetic determinants of polygenic traits, the amount of phenotypic variance explained by polygenic risk scores derived from genome-wide significant associations remains modest. On the other hand, moderate to high narrow-sense heritability has been established for many human traits. It has been proposed that weak, yet undetected, associations underlie polygenic trait heritabilityp-value threshold, and pruning the remaining SNPs based on LD3. This “pruning and thresholding” (P+T) approach has the advantage of being simple and computationally efficient, but discards some information because of LD pruning. To remediate this issue, a novel method, LDpred, which uses LD information from an external reference panel, was recently proposed to infer the mean causal effect size using a Bayesian approach4. While the latter method has been shown to improve prediction R2, it depends on estimates of polygenic heritability and causal fraction, and can be sensitive to the misspecification of LD. We hypothesized that a further gain in prediction R2 could be made by tuning the weights of SNPs included in polygenic risk scores using principles of machine-learning.The most popular heuristic for polygenic risk score is based on linkage disequilibrium (LD) pruning of SNPs, prioritizing the most significant associations up to an empirically determined 5, and thus, are ideal for updating the SNP weights in polygenic risk scores. Tree-based models partition the predictor space according to simple rules by identifying regions having the most homogeneous responses to predictors and fitting the mean response for observations in that region. Gradient boosting6 is an efficient algorithm that sequentially combines a large number of weakly predictive models to optimize performance.Machine-learning encompasses a wide-ranging class of algorithms widely used to solve complex prediction problems. It has proven particularly useful when prediction is dependent on the integration of a large number of predictors, including higher-order interactions, and when sizeable training datasets are available for model fitting. In particular, gradient boosted regression trees are powerful and versatile methods for continuous outcome predictionhttps://github.com/GMELab/GraBLD), involves two steps and uses the univariate regression coefficients from external meta-analysis9 summary association statistics as the starting point  to calibrate the weights of SNPs contributing to the polygenic risk score, adjusting for LD instead of pruning. Our heuristic, gradient boosted and LD adjusted , LDpred (0.207), or an unadjusted polygenic risk score (0.165) . The inputs for the gradient boosted regression trees were obtained from the Genetic Investigation of Anthropometric Traits (GIANT) consortium summary association statistics14 for diabetes, respectively. The resulting score for BMI had a prediction R2 of 0.082, outperforming the prediction R2 of the unadjusted polygenic risk score (0.069), P+T (0.069), and LDpred (0.074) , and compared favorably to the unadjusted polygenic risk score (0.583), as well as P+T (0.576)  and diabetes in the UKB using summary association statistics from the GIANT consortium for BMI, and the DIAbetes Genetics Replication And Meta-analysis (DIAGRAM) consortiumcore 0.58, as wellp < 10−52 for all pairwise comparisons with GraBLD). We tested for calibration for diabetes using the Hosmer-Lemeshow test15, partitioning the UKB validation set by deciles of the predicted trait .Calibration, or the ability of a gene score to accurately predict real observations, is as important as predictiveness when gene scores are used to infer unobserved traits. To evaluate calibration, we calculated the average absolute difference between the predicted trait and the actual trait for height and BMI in the validation set. For all methods, polygenic risk scores were first calibrated in the training set through the use of a linear regression model . The average absolute difference was the smallest for GraBLD for height (0.690 SD) and BMI 0.742 SD), compared to other polygenic scores . Only directly genotyped SNPs were used for this analysis and 683 K SNPs overlapped with both the UKB and consortia associations. For each method, the optimal GraBLD derived in the UKB calibration set was tested in the HRS without any further fitting or adjustment. Consistent with the UKB results, our machine-learning heuristic produced superior polygenic risk scores for height and BMI, compared to all others methods, and was a close second to LDpred for diabetes  participants of European descent N = 8,92. Only R2, compared to existing methods. Furthermore, we showed that GraBLD risk scores were well calibrated, requiring only a small “tuning” set sample size (N~200) to achieve satisfactory performance. This latter characteristic makes our method advantageous for the prediction of unobserved traits, and stems from the fact that our heuristic leverages the large number of genetic variants reported in GWAS to train gradient boosted regression tree models through genome partitioning. Overall, our results demonstrate that machine-learning techniques coupled with summary-level data from large genome-wide meta-analysis improve the prediction of polygenic traits.Our proposed machine-learning heuristic led to significant improvements of polygenic risk scores in prediction R2 in a target population. Summary association statistics obtained from large external meta-analyses are implicitly assumed to provide the best initial estimates and regression trees “adapt” them to the regression coefficients observed in the target population. To avoid over-fitting, SNPs were divided into five distinct contiguous sets  and the weights of SNPs in each set were calculated using the prediction models trained on the remaining four sets. For example, the first set comprised SNPs from chromosomes 1, 2, and part of 3 such that SNPs from the remaining part of chromosome 3, as well as those on chromosomes 4 to 22 were used to derive prediction models for SNPs in the first set. Thus, the observed regression coefficients of any single SNP in the target population was never used directly or indirectly to derive its own weight in the polygenic score. In addition, we used a small learning rate for the boosting algorithm to reduce the risk of overfitting as it has been suggested that boosting is quite robust to overfit16. We also explored alternative machine-learning techniques to tune the SNP weights, with bagging being a close second to gradient boosted regression trees in terms of prediction R2 (0.229 for height and 0.080 for BMI) as it is based on a similar principle of subsampling. Neural net produced inferior results and slower computation. Support vector machine and random forest proved to be computationally prohibitive with run times exceeding 7 days for the same analyses done in 8.25 hours by GraBLD.The regression trees approach we used can capture nonlinear effects and higher-order interactions, while the gradient boosting algorithm combines individually weak predictors to produce a strong classifier that enables a better prediction of genetic effects. The gradient boosted regression trees adaptively reweight the contribution of each SNP in order to maximize the prediction r2 of each SNP over neighboring SNPs. The polygenic risk score weights of each SNP were divided by the corresponding sum of r2. To illustrate with a simple example, if five SNPs are in perfect LD (r2 = 1) with each other, but in linkage equilibrium with all other SNPs (r2 = 0), then the polygenic score weights of those five SNPs would be divided by five. Since all five SNPs are included in the score and the effect of all five SNPs are summed, the corrected weight contributions are equivalent to including a single SNP without correction. Thus, it is necessary to apply the LD correction only after adjusting SNP weights with gradient boosted regression trees as otherwise important information on the strength of association of individual SNPs would be lost.It is advantageous to correct the derived weights for LD when including multiple SNPs in a score, unless SNPs were first LD pruned. The novel correction we propose is based on the sum of pairwise LD R2 = R2true in simple cases where the pairwise r2 LD is either 0 or 1 and the summary association statistics are derived from an asymptotically large sample. In more common scenarios with partial LD, the variance explained by R2 < R2true reflects the loss of information when, for example, two SNPs are in partial LD and have true genetic effects with opposite directions. Using simulations, we estimated this loss of information at ~12% as the prediction R2 explained ~88% of the true genetic variance, on average (see Methods).LD is only summed over SNPs included in the polygenic risk score such that our correction is specific to the set of SNPs included in a given score. When the genetic effects were strictly additive , the resulting polygenic score provided an unbiased estimate of the underlying genetic variance although at a tradeoff of increased polygenic score variance as compared to the “true” unobserved genetic model (see Methods). It can be shown that the variance explained by the polygenic risk score 4. Second, there is a possibility that the polygenic risk scores derived using our method are inherently population-specific. However, with the exception of unadjusted polygenic risk scores, all methods require a determination of parameters in the target population and ours is no exception. Furthermore, if the genetic architecture varies between populations, then no polygenic risk score will perform universally well and it will be beneficial to tailor gene scores to each population. The observation that our heuristic performed equally well in the HRS, compared to other methods, suggests this might not be the case. Moreover, the small calibration sample size required by GraBLD is an advantage over other gene score methods. Third, our correction for LD yielded advantageous results yet is expected to lead to some loss of information when truly associated SNPs are in partial LD. Nonetheless, our method has several benefits over other methods, including its simplicity, use of summary association statistics, and intrinsic robustness to minor misspecification of LD or association strength.A few limitations are worth mentioning. First, our method was based on the premise that SNPs contribute additively to genetic variance. While empirical evidence suggests this holds true in most cases, our method is not expected to perform well in genomic regions where strong genetic interactions are present (e.g. HLA). In such situations, alternative methods such as LDpred might be better suitedIn summary, we propose a novel heuristic based on machine-learning concepts to improve the prediction of polygenic traits using gene scores. Our results show that for the classic polygenic traits, height and BMI, 46.9% and 32.7% of the estimated polygenic genetic variance was captured by our GraBLD gene scores. These results demonstrate the potential of machine-learning methods to harness the considerable amount of information available from local GWAS and external genome-wide meta-analyses. This is made possible through partitioning of the genome, enabling training of regression trees over large numbers of observations. Indeed, a small training sample size (~200) was sufficient to greatly improve the predictiveness of polygenic risk scores. As with other prediction problems involving machine-learning techniques, incremental improvements are to be expected with increased sample size, the inclusion of additional predictors, and the availability of more precise summary association statistics.17 at http://portals.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files. Univariate coefficients for diabetes were obtained from DIAbetes Genetics Replication And Meta-analysis (DIAGRAM) consortium14 at www.diagram-consortium.org/.Summary association statistics were used to tune the weight of SNPs in polygenic risk scores according to the target population. Univariate regression coefficients for height and body mass index (BMI) were downloaded from the Genetic Investigation of Anthropometric Traits (GIANT) consortium18 (UKB) is a large population-based study from the United Kingdom. A total of 152,249 participants were genotyped using either the UK BiLEVE or the UK Biobank Affymetrix Axiom arrays, and a subset of 140,215 participants of European (British and Irish) Caucasian ancestry were used in the analyses. Genotypes were imputed using the UK10K reference panel using IMPUTE2, resulting in ~72 M SNPs. Height and BMI were adjusted for age and sex in all analyses. To mitigate the effects of outliers, values outside the 1st and 99th percentile were removed. All analyses were adjusted for the first 15 genetic principal components unless stated otherwise. The final sample size for height and BMI was 130,215. The UKB is not part of the GIANT meta-analysis of height and BMI20, nor of the DIAGRAM consortium for diabetes14. There are 6,746 individuals with prevalent diabetes in the subset of the UKB included in the current report. We randomly selected 6,746 individuals without diabetes as paired controls on a 1:1 ratio. We then randomly sampled 1,000 case-control pairs as the calibration set, with the remaining 5,746 pairs forming the validation set.The UK Biobankp < 1×10−6 were excluded, and (6) SNPs with minor allele frequencies lower than 0.02 were removed. The final dataset included 8,292 European participants genotyped for 688,398 SNPs. Height and BMI was adjusted for age and sex in all analyses, and to mitigate the effect of outliers, values outside the 1st and 99th percentile range were removed. All analyses were adjusted for the first 20 genetic principal components unless stated otherwise. The final sample sizes for height and BMI were 8,291 and 8,262, respectively. There were 1,815 individuals with diabetes and 6,477 controls. HRS was not part of the GIANT meta-analysis of height and BMI20, nor of the DIAGRAM consortium for diabetes14.The Health and Retirement Study (HRS) is a longitudinal study conducted on Americans over age 50. We downloaded publicly available genome-wide data that are part of the HRS (dbGaP Study Accession: phs000428.v1.p1) and were generated using the Illumina Human Omni2.5-Quad BeadChip. The following HRS quality control criteria were used to filter genotype and phenotype data: (1) SNPs and individuals with missingness higher than 2% were excluded, (2) related individuals were excluded, (3) only participants with self-reported European ancestry and genetically confirmed by principal component analysis were included, (4) individuals for whom the reported sex does not match their genetic sex were excluded, (5) SNPs with Hardy-Weinberg equilibrium n individuals at m SNPs in the target population are given by a matrixX  to be standardized to have mean 0 and variance 1. For a standardized quantitative trait y with mean 0 and variance 1, the underlying linear model can be expressed as:β is a vector of true genetic effects that are fixed across individuals, but random across SNPs, with mean 0 and covariance matrix σ2I such that the total expected genetic variance is:ε the error term with mean 0 and covariance y is I. Given xi, the genotypes of m SNPs for the ith individual, the gradient boosted and LD adjusted (GraBLD) polygenic risk score g(xi) is defined as:w is an m-dimensional vector of boosted weights and C is an m × m diagonal matrix with entries, R2), and for binary traits, performance was measured using the area under the receiver operator characteristic (ROC) curve.The genotypes for 5. They are ideally suited for improving SNP weights (w) in the polygenic risk score, without requiring individual-level genotypes since they can be used to predict continuous outcomes and can model non-linear relationships without feature selection. We also tested support vector machine (SVM), bagging, neural net, and random forest. SVM (“e1071” R package) and random forest (“randomForest” R package) took an inordinate amount of time to complete and were deemed impractical. Gradient boosted regression trees gave the best results when compared to bagging (“caret” R package) and neural net (“nnet” R package) using default parameters. Thus, all analyses were performed using gradient boosted regression trees. The fitted βext refers to the univariate regression coefficients obtained as summary-level association statistics from the external consortium , and βobs) with respect to the externally derived estimates of summary association statistics (βext). When d = 0 then βobs = βext, implicitly assuming regression coefficients from large meta-analyses provide the best initial weights. While some information is lost because of this construct, the fitted weights are more robust and expected to improve the overall performance of polygenic risk scores.Gradient boosted regression trees are powerful and versatile methods that combine otherwise weak classifiers to produce a strong learner for continuous outcome predictionZ, d). While multiple SNP annotations could be included as inputs (i.e. βobs) of an individual SNP is therefore, never used directly or indirectly to derive its own weight. Furthermore, the SNP annotations used in the regression trees model should be independent of the population in which the polygenic risk score is applied.The dependent variable used in gradient boosted regression trees is constructed as:https://CRAN.R-project.org/package=gbm) with a squared error loss function. A total of 2,000 trees were fitted with an interaction depth of 5, a shrinkage parameter of 0.001, and a bag fraction of 0.5. The final number of trees used for modeling was selected as per GBM package instructions. All other parameters were set to their default values. The run time for each of the 5 folds was 8.25 hours when performed on a single 3 GHz core.Gradient boosted regression trees models were fitted using the “GBM” R package  between the jth and kth SNPs. The LD adjustment (ηj) for the jth SNP is defined by the sum of r2 between the jth SNP and the 100 SNPs upstream and downstream:j, the LD-corrected weights are given by:wj is the weight for the jth SNP.We propose a simple method to correct weights for LD in such a way that all SNPs can be included in a gene score, irrespective of LD. Let PredictionR2of polygenic risk scoreR2 of the gene score in the target population is expressed as:R2]<R2treu, implying the expected prediction R2 must be bounded above by the true genetic variance. We derive these two relations in the following subsections and further verify with simulations , we establish the expected value of the quadratic forms in (eq. The sample covariance of the gene score with the observed g(X), y) is an unbiased estimator of the true genetic variance.This equality holds for all positive definite matrices of the form (eq. ), E[Var(g(X))], can be shown to be greater than R2true:The denominator in eq. , E[Var(gg(X))] is biased and will always be greater than or equal to the true genetic variance.From the above inequality, we can conclude that E = R2true, and (2) the variance of the gene score was indeed higher than the true genetic variance. We further estimated the loss of information at ~12%, or in other words, the polygenic risk score prediction, R2, explained ~88% of the true genetic effect variance, on average.We performed simulations to confirm the effect of LD adjustment on bias and polygenic risk score variance. A total of 5,000 individuals were simulated for 450 contiguous SNPs using phased haplotypes from the 1000 Genomes Project [19]. The genetic effect of each SNP was randomly selected from a normal distribution according to a pre-defined, unobserved, true regional genetic variance that assumed genome-wide heritability varying from 0 to 0.5. For each genetic variance set-point, 1,000 simulations were completed and a polygenic risk score incorporating LD correction was derived. The average (±SD) gene score prediction 21 with an LD r2 threshold of 0.2 and testing p-value thresholds in a continuous manner from the most to the least significant association. LDpred adjusts GWAS summary statistics for the effects of linkage disequilibrium, providing re-weighted effect estimates that are then used in polygenic risk scores4. LDpred was run as recommended by the authors, and included data synchronization and LDpred steps. LDpred requires a specification for the fraction of SNPs assumed to be causal. For each model, we tested causal fractions of 1 , 0.3, 0.1, 0.03, 0.01, 0.003, 0.001, 0.0003, and 0.0001, as recommended. The results are presented using the causal fraction of the best results. A heritability estimate was also required by the algorithm and was estimated from the summary association statistics from LDpred. As a sensitivity analysis, we additionally used heritability estimates given by the variance component models in the UKB. The results were consistent and only the default option is shown. Polygenic genetic variance  was estimated for height and BMI in the UKB using the variance components implemented in GCTA13. All LD measures or related estimates used throughout the manuscript were derived from the UKB calibration set genotypes.Pruning and thresholding (P+T) polygenic scores were derived using the “clump” function of PLINKSupplementary material