FAM150B-ACP1, LINC00340, FBN1, DIS3L-MAP2K1, ARID2-SNAT1 and SLC14A2) associated with refractive error. In Asian populations, three genome-wide significant loci AREG, GABRR1 and PDE10A also exhibit strong interactions with education (P<8.5 × 10−5), whereas the interactions are less evident in Europeans. The discovery of these loci represents an important advance in understanding how gene and environment interactions contribute to the heterogeneity of myopia.Myopia is the most common human eye disorder and it results from complex genetic and environmental causes. The rapidly increasing prevalence of myopia poses a major public health challenge. Here, the CREAM consortium performs a joint meta-analysis to test single-nucleotide polymorphism (SNP) main effects and SNP × education interaction effects on refractive error in 40,036 adults from 25 studies of European ancestry and 10,315 adults from 9 studies of Asian ancestry. In European ancestry individuals, we identify six novel loci ( This report by the Consortium for Refractive Error and Myopia uses gene-environment-wide interaction study (GEWIS) to identify genetic loci that affect environmental influence in myopia development, and identifies ethnic specific genetic loci that attribute to eye refractive errors. Myopia, or nearsightedness, has rapidly emerged as a global health concern in the last three decades5SHISA6-DNAH9 have been shown to interact with education level and exhibit strong genetic effects for myopia among Asians with at least higher secondary educationMajor attempts undertaken in genome-wide association studies (GWAS) to elucidate the genetic determination of myopia and refractive error have recently led to the discovery of >30 distinct susceptibility loci77In the context of the aetiology of refractive errors, education attainment is generally considered a surrogate measure for accumulated near work activity114Factoring in environmental exposures may enhance power for the detection of genes, especially in circumstances where a genetic locus has a differential effect conditional on specific environment exposures17C receptor subunit ρ1 gene GABRR1.The availability of large-scale GWAS spherical equivalent data sets from the Consortium for Refractive Error And Myopia (CREAM) makes G × E interaction analyses feasible. To identify additional genetic variants for refractive error, we performed GEWIS-based analyses on 40,036 adults of European ancestry from 25 studies and 10,315 adults of Asian ancestry from 9 studies. We identified nine new loci using the JMA approach, where three loci exhibited G × E interaction on refractive error in Asians, including the GABAβ=−0.59 D; 95% confidence interval (CI): −0.64 to −0.55 D). High education level was associated with a twofold more myopic spherical equivalent in individuals of Asian as compared with European ancestry .The baseline characteristics of 50,351 participants from 34 studies in our meta-analysis are shown in PJMA<5.0 × 10−8; Phet≥0.086; FAM150B-ACP1, LINC00340, FBN1 and DIS3L-MAP2K1. The significant association for JMA testing at these loci in Europeans was primarily driven by SNP effects in both the lower and higher education strata . SNP × education interaction was not significant (Pint≥0.208). The estimated effect sizes of SNP effects on spherical equivalent were highly similar across education strata.After stringent quality control (QC) filtering, ∼6 million SNPs in each study were eligible for the genome-wide JMA test . The JMAAREG, GABRR1 and PDE10A , GABRR1  and PDE10A . The genotype and phenotype associations were highly significant in the higher education stratum  but were considerably weaker in the lower education stratum (0.008≤Pmain≤0.243). There was no evidence of inter-study heterogeneity at index SNPs within AREG, GABRR1 or PDE10A loci (Q-test: Phet≥0.122).The JMA for spherical equivalent in 10,315 individuals from the Asians cohorts identified genome-wide significant association for three genes: GABRR1 and PDE10A index SNPs were not associated with spherical equivalent in European samples, for either the JMA test, SNP main effect or SNP × education interaction  with rs12511037 in Asians (r2=0.97) was tested but not associated with spherical equivalent . The meta-regression including study-level characteristics as covariates in the model confirmed the heterogeneity between populations of European and Asian ancestry .eraction . AREG SNAREG SNP rs12511037, GABRR1 SNP rs13215566 and PDE10A SNP rs12296610, adjusting for age, gender and population stratification in Asian cohorts . Our analysis did not reveal any significant associations between these loci and education level  and DIS3L-MAP2K1 , whereas the interaction effect was not statistically significant in Europeans (Pint=0.208).We also evaluated the association for spherical equivalent in Asian cohorts for four loci identified from European populations. Two of them showed significant associations in the JMA test: ARID2-SNAT1 (PJMA=4.38 × 10−8) and SLC14A2 (PJMA=2.54 × 10−8). Both loci showed suggestive association with spherical equivalent in European cohorts, with the same direction of effect and similar effect sizes in Asian cohorts  and SHISA6-DNAH9 in Asians . In general, the index SNPs tested at 39 loci had larger SNP × education interaction effect on spherical equivalent in Asians versus Europeans .We also evaluated the interactions between education and previously reported genetic association with spherical equivalent at 39 loci identified from recent two large GWAS studies7AREG, GABRR1 and PDE10A) in paediatric cohorts , with the stronger genetic effect in children spending more hours on reading, writing or compute use. Weaker support for an interaction was noted at GABRR1 , although the direction of meta-analysed interaction effect was largely consistent across paediatric studies with that observed in adults. We did not observe the interaction at AREG .High education levels may reflect an estimator for the greater accumulative effect of near work26GABRR1, ACP1 and SNAT1 had the highest expression in the retina. The Probe Logarithmic Intensity Error-normalized messenger RNA expression levels in the retina ranged from 121.66 to 236.69. Of note, MAP2K1 was widely expressed in the retina, sclera and choroid/RPE.Using the Ocular Tissue DatabaseAREG, GABRR1 and PDE10A) showed strong interactions with education in populations of Asian descent, with larger genetic effects within participants who had a higher level of education compared with those with a lower education level; no interactions achieved statistical significance in Europeans for top JMA associations or known myopic loci. Apart from confirming known associations at 17 previous published loci, we identified six new loci  significantly associated with spherical equivalent using the combined multi-racial cohort.This study represents the most comprehensive genome-wide scan of gene and education interactions to date, for refractive error. Here we identified novel genetic loci associated with refractive error by testing the joint contribution of SNP main effects and SNP × education effects in large multi-ethnic populations. Three loci  from CREAM and a large GWAS in Europeans  have reported a total of 39 genetic loci associated with refractive phenotypesGABRR1 and SNAT1), extracellular matrix remodelling , circadian rhythm (PDE10A) and platelet-derived growth factor receptor signalling (ACP1)  . Networknd so on . Our datGABRR1 on chromosome 6q15 (53 kb), encoding GABAC receptor subunit ρ1, is an interesting functional candidate suggestive of a role in myopia development. Modulation of synaptic plasticity via GABA-mediated inhibition would be well placed to alter the ‘gain' of the visually guided feedback system controlling refractive developmentGABRR1, together with seven SNPs within the LD block (r2≥0.8), are intronic, potentially affecting regulatory motifs (such as zfp128 and gcm1) that may influence transcriptional regulation (r2=1) with rs13215566, is associated with cis-acting expression of GABRR1 (P=2.3 × 10−4) in skin tissues  and 500 kb downstream of SNAT1 . SNAT1 is a transporter of glutamine, a precursor of GABAGRIA4 ; altogether, current evidence supports the notion that retinal neurotransmitters GABA and glutamine may be involved in the refractive development.SNP rs10889855 on chromosome 6 is an intronic variant within the AREG gene (amphiregulin). AREG is a ligand of the epidermal growth factor receptor promoting the growth of normal epithelial cells, which is critical for cell differentiation and proliferation such as regrowth of the wounded cornea40The strongest association signal for gene and environment interactions was from rs12511037, located 14 kb downstream the DIS3L and MAP2K1. MAP2K1 encodes mitogen-activated protein kinase 1, which binds to muscarinic receptors during proliferationtrans retinoic acidtrans retinoic acid is a modulator of ocular growth, inhibiting the proliferation of human scleral fibroblastsAnother novel association, rs16949788 on chromosome 15, derives from a region that spans FBN1 (Fibrillin 1), a member of the fibrillin family, encodes a large extracellular matrix glycoprotein. Mutations in FBN1 cause Marfan's syndrome, a disorder of connective tissue affecting the ocular, skeletal and cardiovascular systems46FBN1 in myopia development.AREG, GABRR1 and PDE10A were only evident in Asian populations. There are a number of possible reasons for the observed differences. First, the variation of LD patterns and joint effects of genetic variants might affect the transferability of G × E signals across populations. Similar LD patterns were seen at GABRR1 and PDE10A regions across populations whereas a long stretch of LD flanking AREG was present only in Asian populations , almost all of them had completed 12 or more years of schooling. We thus chose to categorize individuals with tertiary or university education as the higher education group in these studies. Sensitivity analysis excluding these four cohorts did not appreciably change our meta-analysis results.We dichotomized education for all participants in each study. The higher education group consisted of those who had achieved the highest educational level of A-levels, high school (higher secondary education), vocational training , university degree or those with ≥12 years spent in formal education (beginning from first grade). Those who had achieved the highest educational level of O-level, middle school (lower secondary education) or those with <12 years of formal education were classified into the lower education group. If both number of formal study years and education levels were available in the cohort, we classified participants based on years of formal education. For the four cohorts of relatively young European participants . After QC filtering, the array genotypes of each study were imputed using the 1000 Genomes Project data as reference panels  with the software Minimacr2>0.5 or IMPUTE info score >0.5) and with MAF ≥5% were eligible for the meta-analysis  for directly genotyped SNPs or a continuous variable of allele dosage probability ranging from 0 to 2 for imputed SNPs. The primary analytic model included SNP, education and SNP × education interaction term, as well as age and sex as covariates. Additional adjustments for the top principal components of genomic marker variations were performed in individual studies when applicable .βSNP) and SNP × education interaction (βSNP × education) on mean spherical equivalent:We used the following additive genetic model to test for a joint effect of SNP ; cov is a set of covariates such as age, sex and first top five principal components when applicable. For family-based studies, the kinship matrix was estimated empirically from the SNP data and included as a random effect in the generalized mixed modelβSNP × education from where βSNP and βSNP × education, and error covariance of β, to correct the potential inflation of false positive rate for the interaction P-valueThe linear regression analyses in each study were conducted with Quickes or ProbABEL for the unrelated samples and MixABEL for family-based data (see URLs). The command ‘robust' was used in the above software to calculate the robust  s.e. of In addition, each study also tested the main effect of education on spherical equivalent by adjusting for age and gender using the linear regression model:where the definition of each variable is the same as in βSNP and βSNP × education, respectively) and a β's covariance matrix from each study. A Wald's statistic, following a χ2-distribution with two degrees of freedom, was used to test the joint significance of the βSNP and βSNP × education. The JMA was performed with METALet al.Q-test was used to assess heterogeneity of the β-coefficients across studies for the SNP and interaction effects. To test for interaction between the SNP and education, we conducted a secondary meta-analysis of the SNP × education interaction effects for spherical equivalent , with a fixed-effects model using inverse-variance weighting in METAL; this is a traditional meta-analysis to investigate SNP × education interactions per se. Effects and s.e. of the SNP effect on spherical equivalent in the lower education group (βSNP) and higher education group (βSNP+βSNP × education) were derived from the JMA outputP-value of 5 × 10−8 as a significant threshold for JMA test. For the SNP and SNP × education effects for the identified top loci, the P-value threshold for significance was set at 0.0055=0.05/9 .We adopted the JMA approach17β-coefficients in Asians versus Europeans for the 39 known myopia loci.We performed a meta-regression to explore sources of heterogeneity in our meta-analysis for three loci showing G × E interactions (R package ‘metafor'). Meta-regression included the following study-specific variables as covariates: study sample size, proportion of individuals in the higher education group, average spherical equivalent, education main effects on spherical equivalent (higher education level versus lower), ethnicity (Asian versus European), study design (independent samples versus family-based studies), study year and average age. Meta-regression was also conducted to test the fold changes of the interaction λgc for the joint test for SNP and interaction terms ranged from 1.009 to 1.125 with an average of 1.019 (χ2 divided by the expected median of the 2df χ2-distribution (1.382). Genomic control correction was applied to each individual studyn<500) with λgc >1.05, we further, before starting the meta-analysis, excluded SNPs showing significant joint P-value <1 × 10−5 but neither the SNP nor SNP × education effects supported such an association. Quantile–quantile plots showed only modest inflation of the test statistics in the JMA test  in European and Asian populations of the 1000 Genomes Project (100 kb flanking the top SNP at each locus), to apply functional annotations of transcription regulation using HaploReg7The coordinates and variant identifiers are reported on the NCBI B37 (hg19) genome build and annotated using UCSC Genome Browsercis regulation of gene expression levels .Supplementary Figures 1-5, Supplementary Tables 1-10, Supplementary Notes 1-2 and Supplementary References


The allele frequency spectrum of sequence-identified variants is very different from common variants, and the identified rare genetic variation is usually jointly analyzed in a series of genomic windows or regions. In nearby or overlapping windows, these test statistics will be correlated, and the degree of correlation is likely to depend on the choice of window size, overlap, and the test statistic. Furthermore, multiple analyses may be performed using different windows or test statistics. Here we propose an empirical approach for estimating genome-wide significance thresholds for data arising from WGS studies, and we demonstrate that the empirical threshold can be efficiently estimated by extrapolating from calculations performed on a small genomic region. Because analysis of WGS may need to be repeated with different choices of test statistics or windows, this prediction approach makes it computationally feasible to estimate genome-wide significance thresholds for different analysis choices. Based on UK10K whole-genome sequence data, we derive genome-wide significance thresholds ranging between 2.5 × 10 The field of complex-trait genetics has thus far focused on the study of common  variants through candidate gene studies and, in recent years, through genome-wide association scans (GWAS). The candidate gene study era was unsuccessful in identifying many reproducible associations, partly due to the liberal thresholds used to declare statistical significance, and the issue of multiple testing became even more pronounced with the advent of GWAS. To guard against lenient significance thresholds, a genome-wide significance level was estimated, based on a Bonferroni correction for the number of independent  common variants across the genome: 5×10Common-frequency variants explain only a small proportion of complex-trait heritability. Following advances in large-scale genotyping and next-generation sequencing technologies, low-frequency (0.01 < MAF < 0.05) and rare (MAF < 0.01) variants are increasingly becoming the the focus of genetic association studies, as they are hypothesized to have larger effect sizes, more readily interpretable functions and possible translational potential. Whole-exome sequencing (WES) and whole-genome sequencing (WGS) studies identify almost all sequence variation in the targeted genomic regions, and the variants identified are often extremely rare or unique; hence, the number of variants observed increases with sample size.Analysis of WGS and WES studies usually includes not only single-variant tests, but also region-based tests, which aggregate information across multiple rare variants in order to boost power lost to the combination of low frequency and modest sample size. Numerous region-based tests for rare genetic variation have been proposed. These rely on the initial definition of an interesting region or “functional unit,” which is intuitive for WES but can be defined in various different ways for WGS . Calculations to estimate the significance thresholds then need to be based not only on the correlations between single-point (variant-specific) tests but also on the dependence between window-based tests. Although rare variants are known to display lower levels of linkage disequilibrium than common variants, for test statistics applied to regions or windows, especially partially overlapping windows, the dependence structure is not well understood.Therefore, in association studies of sequencing data, the number and frequency of variants tested are very different from the GWAS era, and the choice of potential test statistics is large. Therefore, it is currently unclear what the respective WES and WGS genome-wide significance thresholds should be. Although a simple and commonly used significance threshold for WES is simply (0.05/#genes), it is likely that the thresholds which accurately control the type 1 error should be study-specific, taking into account the analysis choices as well as key study design parameters including the size of the sequenced regions and the sample size, in order to identify the total number of independent tests carried out.cα, which has been adjusted for the number of independent tests performed, such that cα = 1 − (1 − α)me), where almost 10,000 individuals are undergoing WGS. The UK10K project is the largest WGS study to date generating data one order of magnitude deeper compared to the 1000 Genomes Project. Sequencing data on chromosome 3 were obtained, consisting of 2,577,674 genetic variants in 2,432 individuals. There were 23,096 sites where no minor alleles were observed after data cleaning; these variants were excluded. Rare genetic variants were defined using three thresholds MAF <0.005, MAF <0.01, and MAF <0.05 leading to 1,779,499 variants for MAF <0.005, 1,853,923 variants for MAF <0.01, and 2,046,466 for MAF <0.05.Performance and results are illustrated with an interim release of sequencing data from the UK10K project  can be analytically derived for a given set of genotypes, under the null hypothesis. The SKAT test statistic isThe expected correlation between pairs of SKAT [Wu et al., y is a vector of phenotypes, y under null hypothesis, K = (GW) (GW)' is the SKAT kernel matrix, which depends on the genotype matrix G, assumed to be centered, and a choice of variant weights W. Let iT and jT be two SKAT test statistics. Let iQ = e'ieK, where iK = (i WiG) (i WiG)'. Under the null hypothesis, e ∼ N and where G within a window, let x be the count of the number of minor alleles at rare variants in the window (or the row sum of G). For a simple linear regression test, the burden test statistic is given byExpected correlations between burden tests can also be written analytically. For the genotype matrix n is the sample size, H is the hat matrix of the regression test, and 1 is a vector of ones. Let iT and jT be two burden test statistics, and let where Obtaining an explicit expression for correlation between the SKAT-O statistics is not straightforward. Therefore, we have calculated expected correlations between window-based test statistics for burden and SKAT tests only. These calculations were performed for the genotype data on chromosome 3 from UK10K, using the sets of windows defined for rare variant thresholds of MAF = 0.01 and MAF = 0.05.Several different approaches have been proposed for estimating the effective number of independent tests given a correlation matrix [Chen and Liu, m be the number of tests performed in a chosen genomic region or section, and let iλ, i = 1, … m be the eigenvalues of the matrix of correlations for all tests in this region. The two methods we have used for calculating the effective number of independent tests, em, are the method of Li and Ji [Let i and Ji and the method of Li et al. , which iCalculation of correlations and eigenvalues becomes computationally infeasible for large numbers of tests. Hence, we also undertook a complementary approach based on simulation of phenotypes, also using the WGS data from chromosome 3 in the UK10K project. One thousand sets of normally distributed phenotypes were generated (under the null hypothesis of no association), and both single-marker (linear regression) and window-based tests  were performed across the chromosome 3 data for each set of phenotypes.P-values and all window test P-values for MAF thresholds of 0.005, 0.01, and 0.05. We then partitioned the chromosome into a series of sections of equal size, ranging from 1,024 equally sized sections up to the entire length of chromosome 3. For example, for a MAF threshold of 0.01, the smallest sections contained m = 72 or 73 window tests each . For each section, we calculated the minimum P-value for the window tests, for the single-SNP tests, and for both windows and single SNPs combined, for each of the 1,000 simulations. The fifth percentile of the minimum P-values was identified within each section, and then the −log10(P) values for this percentile were averaged across all sections containing the same number of tests. These numbers are then empirical estimates of the (−log of the) necessary significance thresholds for FWER = 5%, for genomic pieces of varying sizes corresponding to the different sections; equivalently, these are empirical estimates of 0.05/em (after antilog transformation), where em is the effective number of independent tests.For each simulated phenotype, we calculated and stored all single-SNP test 10(0.05/m), for m tests. To estimate the number of tests that would be performed genome-wide, we assumed that the density of variants is approximately equally distributed across all chromosomes. Because the whole genome is approximately 15.6 times longer than chromosome 3, we therefore created a new point on the x-axis at x* = −log10(0.05/(15.6maxm3)), where maxm3 is the total number of tests on chromosome 3 . Let the predicted value from the linear regression be y* = b0 + b1x*; hence, the predicted significance threshold is therefore cα = 10y*)− plotted against the Bonferroni equivalent (using m instead of em). The means are averages of the estimated values for all genomic sections of the same size. For each method of estimation, the estimated values of em increase linearly with the number of tests performed, m, and furthermore all estimates are below the diagonal line, implying that the effective number of independent tests is smaller than the total number of tests performed, as expected.In Figureem lead to slightly different estimates; the method of Li et al. [Examining the estimates derived from expected correlations between SKAT and burden tests, it can be seen that the stronger dependence between SKAT statistics  as the size of the genomic region analyzed increases. However, for a genomic region of a chosen size, there can be quite a lot of variability in the estimated significance thresholds, especially for smaller sizes. FigureIn Figurey = x, demonstrating the well-known effect of linkage disequilibrium between common variants.The simulation approach also enables us to study the significance thresholds for a combination of window-based tests of rare genetic variation and single-marker tests of common variation. In Figureem and significance thresholds based on this extrapolation for window-based tests alone, and Table We have used the apparent linear relationships in FiguresWe have not provided standard errors of these estimates, because each point used for calculation of the regression parameters is based on subdivision of the same chromosome 3 data in different ways. We cannot therefore argue that the points are independent. However, the intervals (±1.96* standard error) shown in Figure−8 would be a reasonable choice for our data.For window-based tests, the largest influencing factor is the chosen test statistic. The SKAT test does not require as small a significance threshold as the other two methods. In contrast, for the combined analytic strategy of Table We have presented an empirical approach for estimating genome-wide significance thresholds for the analysis of sequencing data and rare genetic variation. Here, we have explored the impact of the choice of MAF threshold and the choice of test statistic on the necessary thresholds for window-based tests, and have shown that these factors have different patterns of dependence and will impact necessary genome-wide thresholds.Therefore, for a chosen analytic strategy, the necessary threshold is likely to depend on the analysis plan, as well as on the design parameters such as ethnicity, sample size, or sequencing depth (because increased depth could identify more rare variants). If region-based tests are repeated under a large series of different models and assumptions, alteration of the significance thresholds would be necessary. In contrast, we believe that effects of sample size and depth on genome-wide significance thresholds will be small. Supplementary Figures S2 and S3 show that in our data, altering the sample size made no visible difference to the estimated significance thresholds. If sequence data are first imputed against a large population reference panel [Wood et al., However, the magnitude of effect of ethnic origin is currently unclear. Our data are based on UK individuals of European descent. Sequence variant correlation structure is dramatically different in more heterogeneous populations, for example, from sub-Saharan Africa. Reduced levels of linkage disequilibrium translate into higher numbers of uncorrelated variants, more independent tests and, hence a lower genome-wide significance threshold, and this would definitely be of interest to examine.http://www.1000genomes.org, Supplementary −8. This is a little smaller than previous estimates for genotyping arrays  can be expected to be between 0.6 × 10−8 and 1.5 × 10−8.We recommend that each study perform simulations to investigate the impact of their own analytic strategy on significance levels, and we suggest that sufficiently accurate predictions can be obtained by performing the simulations on a small portion of the whole genome and extrapolating to the full genome, thereby making such investigations feasible. An R package, QW signif, is available at


Plants rely on the root system for anchorage to the ground and the acquisition and absorption of nutrients critical to sustaining productivity. A genome wide association analysis enables one to analyze allelic diversity of complex traits and identify superior alleles. 384 inbred lines from the Ames panel were genotyped with 681,257 single nucleotide polymorphism markers using Genotyping-by-Sequencing technology and 22 seedling root architecture traits were phenotyped.-7). Analysis of significant SNP markers for multiple traits showed that several were located within gene models with some SNP markers localized within regions of previously identified root quantitative trait loci. Gene model GRMZM2G153722 located on chromosome 4 contained nine significant markers. This predicted gene is expressed in roots and shoots.Utilizing both a general linear model and mixed linear model, a GWAS study was conducted identifying 268 marker trait associations (p ≤ 5.3×10This study identifies putatively associated SNP markers associated with root traits at the seedling stage. Some SNPs were located within or near (<1 kb) gene models. These gene models identify possible candidate genes involved in root development at the seedling stage. These and respective linked or functional markers could be targets for breeders for marker assisted selection of seedling root traits.The online version of this article (doi:10.1186/s12864-015-1226-9) contains supplementary material, which is available to authorized users. In an effort to increase crop production, farmers and producers apply millions of tons of fertilizers such as Nitrogen (N) each year. In 2010, demand for N fertilizer was 103.9 million tons and is expected to steadily increase to 111 million tons by 2014 worldwide [Zea mays L.) have two general mechanisms to increase nutrient acquisition: 1) develop a larger root system that allows plants to come into contact with a larger soil volume, and 2) increase the trans-membrane nutrient-uptake rate. Increased root size allows plants to increase available nutrient uptake based on demand within a limited time frame [The root system is essential for plant species to absorb and acquire mineral nutrients such as N. Plant species such as maize , Rth1 (roothairless1), Rth3 (roothairless 3), and Rum1 (rootless with undetectable meristems1). Rtcs controls crown root and seminal root formation; Rtcn and Rtcl are thought to be paralogs of Rtcs. Rth1 and Rth3 control root hair elongation with Rth3 being shown to affect grain yield in maize [Maize has five main types of roots: crown, seminal, primary, lateral, and brace roots . The priin maize ,16. WhilRtcl, Rth3, Rum1, and Rul1 [Rtcs. They too found extensive variation between lines at the gene sequence level. The advent of more economic sequencing technologies facilitates genome-wide studies. Using markers covering the entire genome increases the chance of identifying additional regions of the genome associated with seedling root traits, and establishing relevance of above mentioned candidate genes to other genes affecting root development. In this study, a panel of 384 inbred lines derived from the Ames panel [A useful method for analyzing the genetic diversity of complex traits and identification of superior alleles is association mapping or linkage disequilibrium (LD) mapping . Unlike and Rul1 . Severaland Rul1  used 73 es panel  was used2) estimates for all traits were low to moderate and ranged from 0.12 to 0.49  between both methods with values of r = 0.85 for TRL and r = 0.75 for TPB (data not shown).Pearson correlations were calculated comparing the same traits  (TBP) measured in a previous association panel  that useCorrelation coefficients were calculated for the 22 traits listed in Table 2 = 0.2) within approximately 10 kb throughout the genome. Chromosome 8 showed the slowest decay with an r2 value of 0.2 reached at approximately 15 kb  was calculated. Based on the ad hoc statistic values in Structure 2.3.4 the mapping population was sorted into two subpopulation (K = 2). One subpopulation comprised of 319 lines or 83% of the total 384 lines used for GWAS  located on chromosome 2 . Chromosome 2 also contained the SNP marker with the highest significance. Most significant markers on chromosome 2 were located in bins 2.00–2.02 and 2.07-2.08. Clusters on chromosome 3 were located within bins 3.01 and 3.06-3.09 while clusters on chromosome 4 were within bin 4.05. On chromosomes 2 and 8, four markers in total were significantly associated with multiple traits. Chromosome 2 had 3 markers; marker S2_20263530 was significant for PRL, PER, Diameter (DIA), Depth (DEP), Shoot Dry Weight (SDW), TBP, and SUA. Marker S2_202178253 on chromosome 2 is associated with traits SUA, SDW, SL, and TPB. The third and final marker on chromosome 2 was marker S2_20252886; this marker is associated with both SUA and TBP. These three significant markers are found within gene models GRMZM2G002879, GRMZM2G154864, and GRMZM2G087254. The final marker is S8_146152722 and was associated with both PER and DEP. This marker on chromosome 8 is located in gene model GRMZM2G070837. On chromosome 4, 13 markers were found significantly associated with multiple traits. All 13 markers on chromosome 4 are located within 250 kb. Nine of these markers are located within the same gene model, GRMZM2G153722. Of the remaining four markers on chromosome 4, two are located in the same gene model GRMZMZG427409; one is located in another gene model GRMZM2G053511 while the remaining marker is located in an intergenic region. Four of the previously listed gene models have hypothetical protein products. An earlier expression analysis [Rtcs, Rtcl, Rul1, Rum1, and Rth1), one significant SNP marker at position 205,392,941 on chromosome 3 is located a little more than 3 Mbs from Rum1. No other significant markers were located in or near previously reported root development genes. A list of all significant marker trait associations is found in Additional file Using the GLM model, an additional 263 significant markers were found using the same threshold of P = 5.36 × 10-7 for root traits above the heritability threshold of HRoot traits are difficult and laborious to measure at the adult stage in a field setting. In the current study, measurements of seedling root architectural traits in our association mapping population were used as a first step for later comparison with adult plant traits. One of the traits studied, RDW, has been shown to be positively correlated with key adult plant traits such as yield at both HN and LN conditions , suggestRoot architecture is a key plant characteristic but highly variable among maize genotypes. Table 2 = 0.281). This could be due to limitations in ARIA’s ability to identify the primary root accurately each time, or is a product of PRL sensitivity to micro environmental conditions. We included PRL in the present study, as this trait has been shown to be important in water and nutrient acquisition [Heritability values ranged from 0.12 to 0.49. Previous studies have shown similar ranges of heritabilies for root traits at various stages of growth, both under controlled environmental  and field conditions ,28. Rootuisition .Population structure analysis using the software package Structure 2.3.4  revealed2 threshold = 0.2) across the whole genome was close to 10 kb. These results agree with a LD decay of 10 kb across ExPVP, stiff stalk, and non-stiff stalk lines within the entire 2,815 inbred lines within Ames Panel [Average LD decay . Conversely, 135 SNPs markers were significantly associated with Diameter (DIA) (H2 = 0.33). Different reasons may account for this discrepancy, such as (i) tight linkage of multiple associated SNPs for a low heritability trait, (ii) absence of detectable SNPs in genome regions impacting high heritability traits, and (iii) unknown trait architecture, i.e., number of genes and distribution of gene effects with impact on traits of interest.The only two traits (SRL and BSH) for which significant SNPs were detected using MLM had low heritability estimates. Since associations were found fitting both the Q and K matrix, the risk of type I error is low. BSH and SRL are components of other traits Table . Thus, sGLM is less stringent than MLM. This explains the large discrepancy between vastly different numbers of significant associations detected by the two methods of calculation. As noted in other studies , MLM canFor the MLM analysis, gene model GRMZM26322186 contained two of the significant markers for seedling root trait SRL. This candidate gene is expressed throughout seedling development . The gen-9 and 2.66 × 10-8 respectively. This strengthens our findings at the individual SNP level. Throughout seedling development this gene model showed expression is detectable in both roots and shoots [Sorghum bicolor and Setaria italica (foxtail millet), with greater than 85% sequence identity. Both species have hypothetical protein products with currently unknown function. A homologue in Arabidopsis thaliana [The most noticeable candidate gene identified within this study is GRMZM2G153722. This gene model is located on chromosome 4 and contained 9 of 13 significant markers found for two traits, DIA and SUA. Haplotype analysis for this gene was examined with two haplotypes being identified within this region of the genome. One haplotype was found significant for both DIA and SUA at p-values of 5.22 × 10d shoots . The canthaliana  plays anSorghum bicolor, bamboo, and Setaria italica with greater than 85% sequence identity, as was previously noted for GARMZM2G153722. Results from a BLAST of GRMZM2G322186 cDNA revealed 100% identity with maize gene cef1, which codes for an aspartate aminotransferase (AAT) superfamily (fold type I) gene of pyridoxal phosphate (PLP)-dependent enzymes. No phenotypes have been linked to this putative gene and protein product. Expression of these genes was detected at V1 stage in the primary root in B73 [Gene models GRMZM2G154864 and GRMZM2G322186 contained significant SNPs for multiple traits. BLAST results for GRMZM2G154864 cDNA identified both t in B73 . These gRtcl, Rth3, Rum1, and Rul1 were studied with regard to their impact on seedling root trait expression using a candidate gene-based association mapping approach [Rum1 was putatively detected by a linked significant SNP. No SNPs within the remaining genic regions were significantly associated in this study. We used a candidate gene-based association mapping approach for those same four candidate genes in our population to determine, whether any SNP in these regions would show significance due to a less stringent multiple testing threshold. Nevertheless, we did not find significant SNPs within these root development genes. Most lines used for the previous association panel [Rtcl, 45 polymorphisms were detected. In our population only five SNPs were present within this region. Due to these discrepancies in allelic frequencies between populations, it can be expected that results can be inconsistent between association studies in different panels [Wild type alleles of root development genes approach . SNPs wion panel  were difon panel . These dt panels .The putative SNPs identified within the current study might aid in selecting lines with these particular phenotypic root characteristics. Respective SNPs can be used to breed for specific root types under various environmental conditions, thus enabling use of maize root architecture information as part of a selection strategy. The idea of an ideal root architecture or root ideotype has been presented -43. IdeoThe association mapping panel consists of 384 inbred lines obtained from the USDA-ARS North Central Regional Plant Introduction Station (NCRPIS) in Ames, Iowa  high-throughput phenotyping software [Manually evaluated traits were root dry weight (RDW), shoot dry weight (SDW), shoot length (SHL), and total plant biomass (TPB). SHL was measured manually using a ruler measuring from the base of the shoot to the tip of the primary leaf. After root and shoot measurements were conducted, roots and shoots were collected separately and dried for 48 hrs at 55°C, to determine RDW, SDW, and TPB. In addition, 22 traits (Table software . For thiOur association panel was grown in a completely random design (CRD) in three independent replications completed June 13, 2012, July 3, 2012, and October 5, 2012. Each experiment was grown in the same growth chamber under the same growing conditions. All trait data for phenotypic analysis were collected on a plot basis . The additive model for analysis of variance was:yij represents the observation from the ijth plot, μ is the overall mean, Ri is the experiment and Gj is the genotype. The interaction between the fixed effect Gj and the random effect experiment is confounded with the error (E(ij)). The statistical software package SAS 9.3 was used to obtain ANOVA table, expected mean squares, and least square means for association analyses. Function PROC GLM was implemented and type 3 sums of squares were used to account for missing data. Genotypic 2)  were all calculated on an entry mean basis. Heritability was calculated as follows:Where MSG and MSE stand for mean square of genotype and mean square error, respectively. Rep is the number of independent replications (3). Least square means across all three replications were calculated using SAS 9.3 to adjust means. Phenotypic correlations were calculated using the SAS function PROC CORR to determine the relationship between seedling traits.Genotyping-by-sequencing (GBS) , was usePopulation structure (Q matrix) was estimated from a reduced random number of unimputed SNPs  using Structure 2.3.4 software . The parTASSEL 4.0 [2 onto genetic distance in measured in base pairs using an r2 value of 0.2 as a cutoff. All markers with less than 35% missing data and a minor allele frequency greater than 0.05% were used to calculate LD decay. Once r2 values were calculated, this data was summarized using R 3.0 statistical software for each of the 10 maize chromosomes individually as well as combining all chromosomes to test a genome wide LD decay. Software SpAGeDi [The software program SSEL 4.0  was used SpAGeDi  was used2G. Where K is the kinship matrix, used to determine correlations between different individuals and determine whether they are independent, as our assumption is that all individuals are independent from one another. Both Q and K matrices were fit in the MLM to control spurious associations due to population structure and relatedness, respectively [A mixed linear model (MLM) was also used for association studies utilizing the program GAPIT (Genome Association and Prediction Integrated Tool-R package) . Statistectively .To account for multiple testing during GWAS, the statistical program simpleM was implemented using R program 3.0 . Based owww.panzea.org/lit/data_sets.html. As the GBS data used for this study is a subset of the entire GBS Ames US Inbreds data set.Phenotypic data will be available upon request from the reader. Genotypic data can be found freely available at http:\\


Maternal genetic and phenotypic characteristics  affect both the intrauterine milieu and lifelong health trajectories of their fetuses. Yet at the same time, fetal genotype may affect processes that alter pre and postnatal maternal physiology, and the subsequent health of both fetus and mother. We refer to these latter effects as ‘fetal drive.’ If fetal genotype is driving physiologic, metabolic, and behavioral phenotypic changes in the mother, there is a possibility of differential effects with different fetal genomes inducing different long-term effects on both maternal and fetal health, mediated through intrauterine environment. This proposed mechanistic path remains largely unexamined and untested. In this study, we offer a statistical method to rigorously test this hypothesis and make causal inferences in humans by relying on the  randomization inherent in the process of meiosis. For illustration, we apply this method to a dataset from the Framingham Heart Study. A common belief is that genetic, phenotypic, and behavioral characteristics of mothers affect the metabolic milieu during pregnancy, and that this in turn affects both the short and long-term metabolic health of the offspring, including the risk of obesity. This is likely true and some evidence is supportive . Yet theThe maternal–fetal relationship can and has been viewed as both one of intimate cooperation and that of intergenerational competition . FoundatIdentifying specific aspects of fetal genotypes  influence maternal phenotype may be challenging for all the reasons that studying complex genetic effects are challenging in general, but also because a statistical model for testing such hypothesized effects has not yet been offered. Except in certain situations of controlled experimental crosses, observational studies showing an association between fetal genotype at a particular genomic locus and maternal phenotype merely indicate association (correlation) and not necessarily of causation. Therefore, we offer a statistical model, adapted from one developed by one of the authors in the context of family based association  testing, to rigorously test this hypothesis in humans (and other diploid populations) and make causal inferences by relying on the randomization inherent in the process of meiosis. Although the model is adapted from genetic study, the principle has its theoretic root in the causal inference literature. We describe the method here and illustrate it with data from the Framingham Heart Study (FHS).if we condition on parental mating types at the locus under study , we can reasonably draw causal inferences about the effects of fetus genotype on mother’s pregnancy because of the aforementioned randomization, er study . Note thX, and random factors then causal inference can be made and in addition, causal effects of treatments can be estimated without bias. The assignment to treatment group means that if two units have the same value of X, then they either must receive the same treatment or must be randomly assigned to treatments (not necessarily with the same probability). The critical point is that the probability that a study unit is assigned to one treatment rather than others is a function only of the values of X in the sample and purely random factors. Here, X can either be univariate or multivariate. The principle has been further explored for observational data explicitly in F,gM), are the X in k, is the treatment although we have three groups here ; mother’s phenotype is the dependent variable Y using Rubin’s notation. Therefore conditional on parents’ mating types at a locus, then the offspring are randomly assigned to genotypes at that locus. Equivalently, the study unit, the parents–child trio, is randomly assigned to the genotypes of offspring solely based on the parental mating types. Based on the aforementioned previous work, causal inference can be made on the effect of offspring’s genotype  on mother’s phenotype . Note that the causal inference is to ‘treatment assignment’ which in this case is the offspring’s genotype at the locus under study and/or the other loci physically linked to and correlated (in disequilibrium) with it , by use of a link function  from Framingham, Massachusetts, and is now on its third generation of participants. The Offspring Study  was initiated in 1971. A sample of 5,124 men and women, consisting of the offspring of the Original Cohort and their spouses was recruited. The recruitment of the third generation participants who had at least one parent in the Offspring Study and would be at least 20 years old by the close of the first exam cycle was started in 2001. A recruitment target of 4,095 Gen III participants was achieved by July of 2005. In order to draw causal inference using the model as described above, we need information from both parents and offspring , and moAlthough information on gestational hypertension, diabetes, and weight gain is available in FHS, in the final dataset we obtained, the number of observations of hypertension and diabetes are small. Therefore we only focus on weight gain, which is binary with value 1 if the mother reported to have >30 pounds weight gain during pregnancy and 0 otherwise, that is:where I is the indicator function.FTO is a gene located in chromosome region 16q12.2. Studies have revealed association of single nucleotide polymorphisms (SNPs) in this gene with obesity. The genotype we tested are four SNPs  in FTO gene which have been shown to be associated with obesity . We perfTable 1 depicts the results from the logistic regression for SNP rs9930506. The results from additional analyses are summarized in Table 2. P-values for the genotypes are from two degrees of freedom test of the two dummy variables for each genotype. Neither of the results is significant at α level of 0.05. This may indicate that the variants of these four SNPs carried by children do not have effect on mothers’ weight gain during pregnancy. Of course, given the small sample size, there is a possibility that there is not enough power to detect such effect. Given that this is an illustration of the application of a previously validated method, and the small sample size, we did not intend to arrive at any biological conclusions from this analysis.To analyze the data, we used logistic regression. We performed analyses including and excluding mother’s age at children’s birth in the model. For the analyses we conducted, none of the mother’s age at children’s birth was significant (at α = 0.05). Therefore they were not included in the final models. The hypothesis that the fetal genotype affects maternal physiology and behavior represents a complementary view about not only some gestational diseases  of mothers, but also long-term effects on metabolic health of both mother and offspring. In addition, the effects of this process may be cyclic over generations . This hyBoth animal studies and human studies have shown the effect of fetal genotype on mother’s physiology during pregnancy . This prif we condition on parental mating types at that locus under Mendelian theory  and assumes samples with unrelated study units. The model can be extended to handle data with related study units, such as biological siblings, by the use of a linear mixed model . The correlation between the related individuals can be dealt with via a random effect by using a matrix of kinship coefficients (a kinship coefficient is a measure of degree of genetic correlation between two individuals; There are no significant findings in our data analysis. This may be because that the four SNPs we tested did not have deleterious effects on maternal metabolic function, or our analysis lacked the requisite power to detect an effect. Statistical power is influenced by many factors including effect size and sample size. Metabolic function is a complex phenotype, and we did not expect a large effect size for any of its risk factors. We only tested four SNPs in FTO gene due to its relationship with obesity, in a small sample, and think that a genome-wide scan in a much larger sample is warranted for more reliable inferences.Although our statistical method makes the direct test of our hypothesis possible in human studies, it should be noted that conducting such studies necessitate a great deal of time and effort because both parents and offspring need to be included in the study and relevant physiological measurements must be made in the mothers during pregnancy. The effort is worthwhile because if the hypothesis is validated, our understanding of some gestational metabolic conditions may be shifted to a new level. New strategies may be developed to prevent and reduce morbidity and possibly mortality in both the mother and offspring and their future descendants.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Admixture mapping and association testing have been successfully applied to the detection of genes for complex diseases. Methods have also been developed to combine these approaches. As an initial step to determine the feasibility of combining admixture and association mapping in the context of whole genome sequencing, we have applied several methods to data from the Genetic Analysis Workshop 18. Here, we describe the steps necessary to carry out such a study from selection of reference populations and preprocessing of data through to the testing itself. We detected one significant result with a Bonferroni corrected p-value of 0.032 at single nucleotide polymorphism rs12639065. Computing local ancestry for Hispanic populations was challenging because there are relatively few methods by which to handle 3-way admixture, and publicly available Native American reference panels are scarce. However, combining admixture and association is a promising approach for detection of quantitative trait loci because it might be able to elevate the power of detection by combining 2 different sources of genetic signal. Whole genome sequencing (WGS) is fast becoming a feasible technology for use in genetic studies of complex traits. Such a rich source of data allows for many methodological approaches; however, with the sheer increase in volume of data, alternatives must be evaluated with regard to their validity and power. For example, in the context of marker panels, methods for admixture mapping and association testing have been used for detection of genes for complex traits -3. CombiThe GAW18 data set consists of WGS data that were obtained for Mexican American families sampled from San Antonio, Texas, as a part of the Type 2 Diabetes Genetic Exploration by Next-Generation Sequencing in Ethnic Samples (T2D-GENES) consortium . The genThe ancestry estimates in this article were produced for all individuals using chromosome 3 markers. The regression analysis was performed on chromosome 3 on a set of 132 unrelated individuals with genotype, SBP, and DBP data as measured at their first examination. Simulated Q1 traits not influenced by individual genotypes were used for type I error rate assessment.Local ancestry is defined as the number of copies of chromosomes inherited from a parental population at a given genomic location, resulting in a mosaic of segments of distinct ancestry across the chromosome and, equivalently, ancestry switches between those segments . HistoriSeveral newer methods allow for higher density marker panels and background LD, but most do not readily allow for multiple-way admixture. The method that we used, LAMP-LD, combines window-based processing within a hierarchical Hidden Markov Model and takes as an input the genotypes of the admixed individuals as well as phased haplotype reference panels representative of the ancestral populations . We prodg, with 0 ≤ g ≤ 2. Because of imputation, g is not always an integer. For each marker, local ancestry was coded into dummy variables representing each unique combination of ancestry: EE, DAA, DNN, DEA, DEND, and NA Dwhere E, N, and A represent European, Native American, and African ancestry, respectively, for the allele. Four tests were conducted over chromosome 3 for the logarithm of each of the 2 blood pressure measurements, denoted by y, based on the following models:Multiple linear regression models were fit to individual log-transformed blood pressure measurements with global ancestry proportions of European, Native American, and African descent as explanatory variables. Additional covariates were selected based on forward stepwise selection with a 0.05 significance level, resulting in log(SBP) with global ancestry, age, and blood pressure medication used as explanatory variables and log(DBP) with global ancestry and blood pressure medication used as explanatory variables. We assumed an additive genetic model using counts of minor alleles, Model 1 (null): y = α + X'β + εModel 2 (association): y = α + X'β + βgg + εModel 3 (admixture): y = α + X'β + [βAADAA + βNNDNN + βEADEA + βENDEN + βNADNA] + εModel 4 (heterogeneous association and admixture):β + [βAADAA + βNNDNN + βEADEA + βENDEN + βNADNA]    + βg,EE(g × DEE) + βg,AA(g × DAA) + β g,NN(g × DNN) + β g,EA(g × DEA) + β g,EN(g × DEN) + β g, NA(g × DNA) + ε. Here, X represents baseline covariates. Both Wald and likelihood ratio tests were used to test for admixture (model 3 vs. model 1), association (model 2 vs. model 1), association adjusted for admixture (model 4 vs. model 3), and admixture and/or association (model 4 vs. model 1). Wald and likelihood ratio test statistics (LRTS) are asymptotically chi-squared distributed under the standard assumption of a normally distributed error, ε. Local ancestry and genotype at a marker are not independent; hence, genetic effects in the full model (model 4) were stratified by individual local ancestry  + βgg + εy = α + X'The current trend toward studying local admixture focuses on continental origin as opposed to finer scale identification to region of origin within a continent. It is widely accepted that modern Hispanic populations, such as the GAW18 population, are the result of recent admixture of 3 continental-level ancestral populations, namely European, Native American, and African ,13.HapMap phase 3 release 2 genotypes for 112 unrelated CEU (Utah residents with ancestry from Northern and Western Europe) and 113 unrelated YRI  individuals were used as proxy reference panels for European and African ancestral components, respectively . For theTo avoid possible bias as a result of different pipelines and phasing methods, HGDP and HapMap data sets were phased using the segmented haplotype estimation and imputation tool (SHAPEIT) method .Whereas HapMap and HGDP reference data sets are based on NCBI Build 36.3 genomic coordinates, the GAW18 data set uses Build 37.3 coordinates. To allow for full confidence in the mapping between the 2, only markers in the genome-wide data set with available rs numbers in the VCF GAW18 data files were used. Chromosome 3 markers present in the 3 data sets were extracted. This resulted in a set of 40098 SNPs (denoted by SNP40098) with an average intermarker distance of 4932 bp.et al give estimated average global ancestry proportions for the HapMap Mexican sample in Los Angeles (MXL) and for a cohort of 492 parent-offspring trios recruited from Mexico City (MEX1) [Johnson y (MEX1) . Those pB = (2 × 2 × 0.01) TLz(1-z) where T is generations since admixture, L is the total chromosome length (224.6cM for chromosome 3 for the genetic map used), and z is global proportion for one of the ancestral components [Assuming a 2-way admixed population, an estimate for the number of ancestry switches in a diploid genome is given by the formula mponents . The samBesides SNP40098, 2 smaller subsets constructed by selecting AIMs were also used. First, marker information content for ancestry using the f value for all 40098 markers between each pair of the 3 reference populations  was estiWe first present results of ancestry estimation. Then we provide findings from the statistical tests proposed. Last, we interpret the regression model at a marker found to have significant association and/or admixture.z = 0.49, we estimated B = 26.9 average number of ancestry switches and 27.9 average ancestry blocks in chromosome 3 for the GAW18 population. We used this result together with the global ancestry proportions estimated for MXL to evaluate different parameters for the LAMP-LD method and different SNP subsets on which to base the local ancestry estimation.Assuming 12 generations since admixture and Ancestry estimates produced with LAMP-LD are summarized in Table Local ancestry estimates based on the LAMP-LD run for the SNP40098 marker set with window size 70 were used in the subsequent linear regression models. This run produced close to the desired number of ancestry switches and global ancestry proportions. The slightly higher average African ancestry can be explained by 2 individuals with close to 50% estimated African global ancestry (51% and 53%). In summary, there were 2462 unique local ancestry vectors for the sample of 132 unrelated individuals.The LAMP-LD method used ignores family structure; however, using all family members for estimation of local ancestry may improve the estimates because LAMP-LD builds virtual reference populations at the training phase upon which it produces its estimates. As validation, local ancestry was estimated with the set of unrelated individuals only. For a marker (rs12639065) found to have significant association and/or admixture, the resulting ancestry vector was identical to that of the full analysis.Permutation-based significance thresholds were computed for a FWER of 0.05. Using these thresholds, no significant results were found for the test of admixture, test of association, and test of association adjusting for admixture; however, one SNP remained significant for the combined test of admixture and/or association for the log(DBP) trait. All models, fit under both null and alternative hypotheses included effects for global ancestry proportions and the selected covariates. Table LSM3 and SLC6A genes. The minor allele frequency at this marker is 0.364; a Pearson chi-square goodness-of-fit test for departure from Hardy-Weinberg equilibrium gave a p-value of 0.190. Testing the residuals for the full model, the Shapiro-Wilk test for departure of normality gave a p-value of 0.479. As expected, local ancestry estimates do not change for any individual in the sample for a region around the significant marker, from 14,317,580 bp to 14,513,695 bp .The SNP is located in an intergenic region between the -7, which corresponds to a Bonferroni adjusted p-value of 0.032 . The permutation-estimated p-value is closer to the Wald-based p-value of 9.974 × 10-7 and greater than the LRTS- produced p-value of 2.118 × 10-7. This is in line with our observations from the permutation threshold runs, where the LRTS produced smaller p-values and a not entirely uniform distribution but the Wald-based permutation p-values were uniform as expected under the null (data not shown).LRTS and Wald tests resulted in the same rank for the admixture and/or association test, producing a permutation p-value of 8.068 × 10To further evaluate the FWER, the admixture and/or association statistics were computed on all markers in SNP40098 for all 200 simulated data sets for the Q1 trait. Sex and age were used as covariates and the minimum p-values for each data set were retained. This resulted in estimated FWERs of 0.05 and 0.04 compared with the thresholds derived for the LRTS and Wald test statistic, respectively . Adjusting for the genotype at the marker, a Native American local ancestry at this region is related to a 15% higher DBP on average (e0.14 ≈1.15). Two of these parameters are significant , and although the parameter estimate for the indicator for Native American and African local ancestry, NAD, is not significant , this is likely a result of the small NA sample size.Linear regression parameter estimates for model 4 for the log(DBP) trait at rs12639065 are presented in Table e0.123 ≈1.13), and is also highly significant, with a p-value of 9 × 10-5. Also significant is the parameter estimate for the genotype stratified on Native American and European local ancestry at the region; DBP is expected to increase by 5% per minor allele carried at the marker (e0.049 ≈1.05). Interestingly, although marginally nonsignificant with a p-value of 0.064, given a Native American local ancestry at the region, the minor allele has a negative effect for the trait . All parameters for stratified genotype effects with an African local ancestral component were nonsignificant, possibly because of small sample sizes.Although the model suggests that for entirely European local ancestry at this region, DBP is expected to be lower compared with other local ancestries, a minor allele at the marker seems to have a positive effect in such a case, with DBP expected to increase by 13% per minor allele carried at the SNP  presented in Table Combining admixture and association information is a promising approach for detection of quantitative trait loci. Local ancestry estimation must be performed before such combined tests are conducted; however, producing quality local ancestry estimates is challenging in a multiway admixed population such as the one used in GAW18. To the best of our knowledge, all proposed methods use some form of reference panels, which serve as proxies for the ancestral populations in the admixture. Although good reference panels exist for many populations, we found that obtaining such a proxy for the Native American ancestral component present in Hispanic populations is particularly difficult. Furthermore, using 3 different data sources increases the complexity of the process because it necessarily involves aligning and intersecting the sets used. We did find the use of benchmarks to be helpful in evaluating the ancestry estimates produced. Possible benchmarks for assessing quality are global ancestry proportions for similar populations as well as model-based estimates for the expected number of ancestral blocks in a chromosome. We did not use the family structure in our local ancestry estimates. Methods for local ancestry estimation that exploit the family structure should improve on the quality of the estimates.Although no significant results were detected for tests of admixture, association, and association adjusted for admixture, we did find a significant marker from a combined admixture and/or association test. This may indicate increased power of quantitative trait loci detection when aggregating 2 different sources of genetic signal. Simulation studies are necessary to evaluate the power of a combined approach; however, it seems that the results from our analysis demonstrate promise and the need for further studies of such a method.Finally, the regression model at the significant SNP suggests that the genetic signal at the SNP does not act in the same direction for different local ancestral backgrounds. More work is needed to investigate the source of heterogeneity in the association effect. Although it is tempting to think of potential sources of heterogeneity as a result of ancestry or environment, another possible explanation may relate to differences in LD between the ancestral populations. A more extensive study would be needed to evaluate such differences and their effects.The authors declare that they have no competing interests.SAS, KLE, and DY designed the overall study, and DY and SAS conducted statistical analyses and drafted the manuscript. All authors read and approved the final manuscript.


Plant-model-assisted phenotyping and metabolomics enable phenotypic and genetic dissection of early vigour traits in a rice diversity panel. P <1×10–4 and 64 at P <5×10–4. Associations for NSC and model parameters revealed new regions related to early vigour that had greater significance than morphological traits, providing additional information on the genetic control of early vigour. Plant model parameters were used to characterize physiological and genetic trade-offs among component traits. Twelve associations were related to loci for cloned genes, with nine related to organogenesis, plant height, cell size or cell number. The potential use of these associations as markers for breeding is discussed.Early vigour of rice, defined as seedling capacity to accumulate shoot dry weight (SDW) rapidly, is a complex trait. It depends on a genotype propensity to assimilate, store, and/or use non-structural carbohydrates (NSC) for producing large and/or numerous leaves, involving physiological trade-offs in the expression of component traits and, possibly, physiological and genetic linkages. This study explores a plant-model-assisted phenotyping approach to dissect the genetic architecture of rice early vigour, applying the Genome Wide Association Study (GWAS) to morphological and NSC measurements, as well as fitted parameters for the functional–structural plant model, Ecomeristem. Leaf size, number, SDW, and source-leaf NSC concentration were measured on a panel of 123 japonica accessions. The data were used to estimate Ecomeristem genotypic parameters driving organ appearance rate, size, and carbon dynamics. GWAS was performed based on 12 221 single-nucleotide polymorphisms (SNP). Twenty-three associations were detected at  O. sativa L.) is the most important staple food crop worldwide. In 2011, rice crops occupied 164.1M ha [http://faostat.fao.org (accessed 28/01/2013)]. Rice is grown in a variety of environments, covering a wide range of latitudes, altitudes, and hydrologies. This broad adaptation as a species is associated with large genetic and phenotypic diversity (Rice (2 g–1), tillering, leaf size, leaf appearance, and leaf expansion rates were studied for rice and wheat  were related to pre-flowering growth and were associated with quantitative trait loci (QTL) for rice , wheat  or extracted by the Ecomeristem model (fitted process based parameters) and evaluate their added value in support to the phenotypic and genetic study of early vigor diversity in a rice japonica panel. The underlying morphological data, as well as NSC data for a subset of 50 accessions, have previously been reported by Supplementary Table S1 at JXB online). All were lines or varieties adapted to rainfed upland ecosystems, except three that were adapted to irrigated flooded systems and four to rainfed-lowland systems. Roughly, half of the panel consisted of improved genetic materials and the other half of traditional varieties or landraces. Seeds of the accessions were obtained either from the Centre de Ressources Biologiques Tropicales de Montpellier or from the International Rice Research Institute (IRRI) gene bank. For each accession, the seeds were produced by single seed descent over two generations in a CIRAD Montpellier greenhouse to ensure that the samples were homogeneous.The panel used in this study included 123 accessions, all belonging to the tropical japonica group except three belonging to the temperate japonica group  that were reported in three previous publications by the same authors on 202 accessions (–2 d–1. Air humidity and temperature were regulated by the adiabatic method and were set to 25/22 °C (day/night) and 50/90% air humidity. Seedlings were grown in a germination chamber at 29 °C. When seedlings had reached 3cm in height, five seedlings per pot were transplanted in 1.0 l drained pots  at CIRAD  on the panel described above. Mean daily photosynthetically active radiation (PAR) was 4.6 MJ m–1) were measured at the end of the experiment, 30–40 d after transplanting depending on the accession and its development rate. Final sampling was not performed at the same date for all accessions because of differences in phenology. Accessions had 8– 9 appeared leaves on the main stem at final sampling. In order to enable comparison among accessions, observations (tiller and leaf number) were normalized by the photo-thermal time experienced by each plant from germination to final sampling, whereas LLL was normalized by its rank , syn. phyllochron–1], defined as number of leaves appeared on the main stem per unit thermal time) and Relative Growth Rate  from germination to final sampling were computed as described by For each plant, the date of appearance of leaf 6 on the main stem was noted. Tiller number (NBT), last ligulated leaf length , appeared leaf number on the main stem, appeared leaf number on the whole plant (NBL), and shoot dry weight ; PLASTO (°Cd), SLAP (cm2 g–1), ICT (unitless), EPSIB (g MJ–1 m2). Only accessions for which the estimated parameters resulted in less than 15% deviation, on average, between simulated and observed variables were retained. This limited the GWAS study on model parameters to 123 accessions.Ecomeristem is a deterministic crop model simulating plant morphogenesis at organ level at daily time steps using weather and soil hydrological properties as input. The model version used here only simulates the vegetative growth phase of rice. It was described in detail by r=0.32, P <0.01, with the linear regression PLASTO=44.5+1.16 MGR), similar to previous reports  for starch and as soluble sugar per unit dry matter (mg g–1) for hexoses and sucrose.This work analysed NSC content in source leaves for the 123 accessions, thus for a larger panel than the one (50 accesions) described in http://www.R-project.org) and R package FactoMineR v 1.27 as previously described in Statistical analyses  of phenotypic data were performed with statistical software R (r2 >0.7) were considered as a unique region. To find consistent and significant associations between the genetic markers and phenotypic traits, a mixed model involving population structure as fixed effect and a Kinship matrix (K) as random effect) in Tassel V4.3.6 was used. Population structure was represented by the matrix of accession scores in a Principal Component Analysis (PCA) performed on markers in Tassel using six components to make it consistent with the structure analysis reported for the same tropical japonica panel by P-values below the thresholds of 1×10–4 (named in this study as significant association) and 5×10–4 (named in this study as suggestive association) were considered. The corresponding q-values for all traits were computed using the software Q-value v1.0 , using a method combining Diversity Arrays Technology (DArT Markers) and a next-generation sequencing technique based on GBS called DArTseq™ (SNPs markers). The original dataset described in lue v1.0 . Q value–1 (factor 5) and starch from 0 to 50mg g–1 on a dry weight basis. The distributions of genotypic model parameters  (see Supplementary Table S2 at JXB online). Regarding the NSC traits, SUC was the only variable having an effect in Dimension 1 (positive). This was associated with a significant positive correlation (P <0.01) between SUC and both DR and SDW (see Supplementary Table S2 at JXB online).rameters , H, I wesis MFA,  was perfiversity . DimensiSupplementary Table S2 at JXB online by positive, significant correlations between FRU and LLL, and between NSC and MGR. SDW was more explained by organ number (Dimension 1) than by organ size-related traits (Dimension 2). In general, few significant correlations were found between sugar-related traits and other types of traits.Dimension 2 (explaining 18%) was mainly composed of sugar-related traits  and organ size . This is confirmed in Supplementary Fig. S2 at JXB online shows QQ plots and Manhattan plots for the other traits. A total of 23 QTL were identified that were significantly associated with either morphological traits, sugar-related traits or model parameters at P <1×10–4. For approximately two-thirds of the significant associations, the P-values corresponded to q-values below 0.10 (low 0.10 . Five QTP <1×10–4) were found within ±20kb regions. Three QTL for the model parameter (DEV_PLASTO_MGR), the morphological variable (DR), and the metabolic variable (FRU_GLU) were associated with cloned genes having known phenotypic functions on panicle development, floral meristem size or meiosis (P <5×10–4) reported in Supplementary Table S3 at JXB online were found within the ±20kb regions. Nine suggestive QTL (P <5×10–4), related either to early vigour (SDW or RGR) or its component morphological variables (LLL), model parameters  or metabolic traits (NSC), were associated with cloned genes with a known function on vegetative organs  or reproductive organs (anther dehiscence)  .r2 >0.7) on chr 1 was observed between two markers (735 758 and 754 061) . However, no gene with known function was reported within this QTL region. DR was significantly associated at QTL12 on chr 7 at position 19 079 282  than accessions having the T allele. Only one QTL was significantly associated with LLL on chr 9 (P <5×10–4) (see Supplementary Table S3 at JXB online) were also associated with genes with known function  . 109 acc 079 282  and colo 079 282   compared with accessions with allele G . Significant associations for GLU and FRU were also observed on chr 6 at position 9 355 224 (Supplementary Table S3 at JXB online); it was within the 20kb region from the Rice S1Z1 (SUMO E3) ligase 1 protein gene that controls anther dehiscence . PLASTO colocalized with NSC on chr 7 at position 22 559 297 but this association had P <5×10–4 (see Supplementary Table S3 at JXB online). However, the phenotypic effects of these traits were located on different MFA dimensions . Allele A had a negative effect on NSC (105mg g–1 versus 120mg g–1) and a positive effect on PLASTO (62.79 °Cd versus 59.78 °Cd). No cloned gene was positioned near this marker.Among the model parameters, eight significant QTL were detected, mainly for (DEV_PLASTO_MGR) . DEV_PLASupplementary Table S3 at JXB online) and on chr 6 at position 9 355 224 (QTL8: RGR and DEV_PLASTO_MGR) . The wide distribution observed for DEV_PLASTO_MGR within each group carrying each allele explained the high standard deviation observed (data not shown).Model parameters significantly colocalized with morphological traits for only two QTL: on chr 9  , with a STO_MGR) . This QTSTO_MGR) . In thisIn spite of the considerable knowledge on traits conferring early vigour, there is little evidence on the added value of such secondary traits when explicitly included in rice breeding programmes. This may be explained by the lack of knowledge on: (i) the compensation among traits, (ii) their genotypic diversity and genetic architecture, and (iii) their behaviour in different environments. The present study aimed to combine morphological, metabolic, and model parameters for the phenotypic and genetic dissection of early vigour. It was expected from ‘hidden’ phenotypic markers  to provide further insight into underlying trait–trait correlations and trade-offs. The approach was tested on a japonica rice diversity panel by performing GWAS for these traits.The three types of traits addressed in the present study were confirmed to contribute to early vigour, characterized by biomass accumulation (SDW). SDW was significantly correlated with morphological traits , model parameters , and metabolic traits (SUC). This confirmed the results reported by Among the metabolic traits, leaf sucrose content showed the highest (positive) contribution to vigour whereas starch and hexose contents contributed strongly (positively) to leaf size (observed LLL and MGR model parameter) but did not have a significant effect on vigour.It therefore appears that early vigour was favoured first, by a high development rate associated with a high sucrose concentration in source leaves, and was further increased by large leaves which were associated with high starch and hexose concentrations in the source leaves. This was translated in the model by a combination of low PLASTO and high MGR values. In the model, effects on the phenotype of PLASTO (affecting leaf appearance rate), MGR (affecting leaf size), and ICT (affecting tillering) are subject to compensatory responses due to assimilate limitation. It is interesting that PLASTO and MGR, which act at the culm scale, together had a dominant impact on early vigour, whereas ICT, which acts on tiller number at the plant scale, had a comparatively small effect. Since these parameter effects were evaluated on the basis of parameter fitting to each of the accessions, they reflect an observed pattern across the panel.Arabidopsis  can be interpreted as a trade-off between two traits that contribute to early vigour, because both increase the sink strenght for a finite assimilate resource , relatedMetabolic traits were previously reported in rice to participate in the expression of complex traits such as early vigour . Hexose in silico extrapolation .Supplementary Table S2. The correlation matrix for all the variables studied.Supplementary Table S3. All the suggestive QTL detected at P-values <5×10–4.Supplementary Fig. S1. The distribution of other variables studied.Supplementary Fig. S2. shows the Manhattan and Q-Q Plot for other variables studied.Supplementary Fig. S3. The allele effects for significant QTl.


Tamiasciurus hudsonicus) to look for evidence of (1) additive genetic variance in lifetime reproductive success and (2) fitness trade-offs between fitness components, such as male and female fitness or fitness in high- and low-resource environments. “Animal model” analyses of a multigenerational pedigree revealed modest maternal effects on fitness, but very low levels of additive genetic variance in lifetime reproductive success overall as well as fitness measures within each sex and environment. It therefore appears that there are very low levels of direct genetic variance in fitness and fitness components in red squirrels to facilitate contemporary adaptation in this population.A trait must genetically correlate with fitness in order to evolve in response to natural selection, but theory suggests that strong directional selection should erode additive genetic variance in fitness and limit future evolutionary potential. Balancing selection has been proposed as a mechanism that could maintain genetic variance if fitness components trade off with one another and has been invoked to account for empirical observations of higher levels of additive genetic variance in fitness components than would be expected from mutation–selection balance. Here, we used a long-term study of an individually marked population of North American red squirrels ( The Robertson–Price identity states that a trait must be genetically correlated with fitness to evolve in response to natural selection  is surprisingly high, leading to an expectation of high evolutionary potential of fitness in these systems  are a good system in which to examine both sexual antagonism and temporal fluctuations in selection as forms of balancing selection that could maintain genetic variance in components of fitness. Red squirrels are diurnal, semi-arboreal rodents that are common throughout most of forested North America. Offspring depend on their mothers for nutrition prior to weaning at about 70 days after birth, while fathers provide no parental care  as an important food source , was monitored from 1987 to 2011. The population was completely enumerated through regular livetrapping of individuals with unique alphanumeric ear tags  as our measure of fitness. Individuals were considered to be dead if they were not trapped for more than one year or if they were found dead . Only individuals with known mothers were included in our analysis, as we knew from previous work in this system that mothers could have large effects on fitness-related traits in their offspring , maternal (Vm), and permanent environmental (Vi) effects for all models of annual reproductive success and Va and Vm for models of lifetime reproductive success  was estimated for LRS and ARS. Our bivariate models allowed for covariance between additive genetic variances and maternal effects of the two traits in question . However, we did not estimate covariances between either among-individual variances or residual variances. Phenotypic variance (Vp) was estimated as the differences between individuals in the focal trait, where Va, Vm, Vi (if applicable), and Vr were summed to estimate Vp. Heritabilities (h2), maternal effects (m2), and permanent environmental effects (pe2) were estimated as the proportion of phenotypic variance explained by the additive genetic variance, maternal variance, and individual variance, respectively. As all response variables followed a Poisson distribution, we report latent heritabilities, where the raw mean of a trait was added to the denominator of the heritability estimate  package Hadfield . We assuilities h, maternaF-test in our analysis of deviance , and ARS differed significantly between both cohorts  and years .Mean lifetime reproductive success (LRS) was 1.1 ± 3.5 pups, with a mean female LRS of 1.4 ± 3.9 pups and a mean male LRS of 0.3 ± 1.6 pups. The mean annual reproductive success (ARS) of males and females together was 1.9 ± 2.1 pups, with a mean ARS of 3.0 ± 3.0 pups in mast years and a mean ARS of 1.7 ± 1.8 pups in nonmast years. Mean LRS of individuals averaged 1.5 ± 3.9 for individuals born in mast years and 1.0 ± 3.3 for individuals born in nonmast years. LRS differed significantly between cohorts (Va) in LRS was very low and did not increase when considered separately as female LRS, male LRS  where birth weight, birth date, and natal litter size are highly correlated with fitness (Wilson et al. The maternal effects that we have demonstrated Tables –4 could


Many genetic markers have been shown to be associated with common quantitative traits in genome-wide association studies. Typically these associated genetic markers have small to modest effect sizes and individually they explain only a small amount of the variability of the phenotype. In order to build a genetic prediction model without fitting a multiple linear regression model with possibly hundreds of genetic markers as predictors, researchers often summarize the joint effect of risk alleles into a genetic score that is used as a covariate in the genetic prediction model. However, the prediction accuracy can be highly variable and selecting the optimal number of markers to be included in the genetic score is challenging. In this manuscript we present a strategy to build an ensemble of genetic prediction models from data and we show that the ensemble-based method makes the challenge of choosing the number of genetic markers more amenable. Using simulated data with varying heritability and number of genetic markers, we compare the predictive accuracy and inclusion of true positive and false positive markers of a single genetic prediction model and our proposed ensemble method. The results show that the ensemble of genetic models tends to include a larger number of genetic variants than a single genetic model and it is more likely to include all of the true genetic markers. This increased sensitivity is obtained at the price of a lower specificity that appears to minimally affect the predictive accuracy of the ensemble. Genome-wide association studies (GWAS) have been used extensively to examine the association between common single nucleotide polymorphisms (SNPs) and disease phenotypes. While many of these studies have successfully found genetic variants that have highly significant associations with phenotypes, typically their effect sizes are small and the predictive power is limited. In order to build genetic prediction models with hundreds of SNPs, investigators often combine multiple SNPs into a genetic score that is used as a single covariate  method. The prediction of the phenotype for an individual with genetic score i,NGS is then provided by the formula:where N of SNPs included in the genetic score varies, one can compute different genetic scores for each individual and therefore different genetic prediction models. The challenge is to choose the best number of SNPs to be included in the genetic score for optimal prediction. A simple approach is to randomly divide the data into a training set and a test set, use the training set to generate cumulative genetic scores by adding one SNP at a time from the sorted list of SNPs so that GSi,N+1 = GSi,N + Ri,N+1 for N = 1,…,S, and use these S models to predict the outcome in the test set. The model with the largest correlation between predicted and observed phenotype in the test set will identify the best genetic score, and therefore the best number of SNPs. In this sampling strategy, “single split,” the dataset is split into training and test sets only once.where S genetic models, one for each of the genetic scores i,NGS, N = 1,…,S. The S genetic models are used to predict the outcome in the test set and the model with the largest correlation between predicted and observed outcome is selected as the most predictive model.K-fold cross validation (CV) can also be used to determine the optimal number of SNPs  generated in the training set can be evaluated in the independent test set to identify the ensemble of M models with best prediction (the model with the largest correlation between the predicted and observed phenotype)  We tested the prediction accuracy of the single genetic model and the ensemble of genetic models on simulated data. The following simulation scheme was adapted from Yip and Lange , Bae et S = 1000 biallelic SNPs were generated with minor allele frequency (MAF) that followed a uniform distribution in the interval . The 0.05 cutoff of the uniform distribution was used to mimic a quality control process where SNPs with a MAF < 0.05 are removed from a GWAS dataset. The genotypes i,kG where i,kG is the additive genotype coding for the ith individual at the thk causal SNP, were generated using a multinomial distribution, assuming Hardy–Weinberg equilibrium for each SNP so that, for each allele frequency p, genotypes were simulated in proportions p2, 2p(1 - p) and (1 - 2p). A sample of 1000 individuals was generated for each simulated data set.m = 5, 10, and 30 causal SNPs (out of S = 1000) with a total variability σ2Total = 1. Here we define a causal SNP to be a SNP truly associated with the phenotype (a true positive). We chose three different levels of heritability: low (h2 = 0.20), medium (h2 = 0.40), and high (h2 = 0.60), and for each h2 we defined the effect size ka for each causal SNP, under a strictly additive model, as:The phenotype was generated from a linear regression model with 2Total is the total phenotypic variability, kp is the MAF of the thk causal SNP, thk causal SNP, and m is the number of causal SNPs. The effect size in Equation (4) assumes that all causal SNPs contribute to the total heritability by an equal amount. For each causal SNP, we randomly drew The formula in Equation (4) was described in Yip and Lange , Bae et The 1000 individuals in each simulated data set were randomly separated into a set of 900 individuals (discovery dataset) and 100 individuals (test dataset) that were used for model building and testing.This simulation procedure was used to generate 1000 data sets for each combination of heritability and number of causal SNPs. A single SNP analysis was performed in each discovery dataset for all of the SNPs that were then sorted by order of statistical significance. Cumulative genetic scores were then computed for each of the 900 individuals in the training set by adding one SNP at a time from the sorted list of 1000 SNPs (sorted in order of decreasing significance), thus producing 1000 genetic scores for each subject, in each group, for each simulated dataset. We then generated genetic prediction models using the genetic scores as the covariate as shown in Equation (1) and the 1000 genetic models estimated from the training set in each simulation were used to predict the phenotype for the test dataset of 100 individuals using the formula shown in Equation (2). Ensembles of these genetic prediction models were also used to predict the phenotype for the test dataset as shown in Equation (3). The Pearson correlation between the predicted and observed phenotype was computed for all these models and the model with the highest correlation between observed and predicted values in the test set was selected as the most predictive.We also randomly divided each of the 1000 simulated set into 10 partitions and used 10 fold CV to select the most predictive genetic prediction model in each simulated data set. For each of the 10 folds the correlation between the observed and predictive phenotype was computed for all genetic models. The results from the 10 folds were then averaged to produce a single estimation of the correlation between the observed and predicted phenotype for each genetic model. The model with the highest correlation was chosen to be the model with the optimal number of SNPs.We summarize the results by the correlation between observed and predicted values using the single and ensemble of genetic models, the number of overall SNPs and the proportion of causal SNPs included in each selected model.Figure The most obvious result in Figure Both the single genetic model and the ensemble of genetic models show that the prediction accuracy tends to initially increase as more and more SNPs are added to the model. The single genetic model has a faster rate of increase than the ensemble of models, and it reaches a peak of prediction accuracy followed by a decline when the genetic score includes too many SNPs. On the other hand, the ensemble of genetic models appears to require a few more SNPs than the single genetic model to reach a peak of prediction accuracy but the rate of decline is markedly slower relative to the single genetic model as more and more SNPs are added to the models. These results suggests that the best single genetic model, selected on the best predictive accuracy in the test set, should include a smaller number of SNPs than the best ensemble of genetic models.m of causal SNPs used in the simulations when m = 5 or 10, but it is an underestimate when m = 30 and the severity of the under-estimation increases with smaller heritability. The best ensemble of genetic models, on the other hand, tends to include a number of SNPs that exceeds the number of causal SNPs.Consistent with this observation, Table h2 = 0.20), and the number of causal SNPs with large (m = 30), and it was within 5% in the other scenarios. The analysis suggests that the ensemble of genetic models is more likely to capture all causal SNPs than the single genetic model at the price of including some false positive SNPs, without substantially reducing the predictive accuracy.We next investigated how the different numbers of SNPs included in the best single genetic model and the best ensemble of genetic models affect the sensitivity of the methods, that is, the selection of true positive SNPs, and the prediction accuracy. Figure We also investigated whether a different selection of the best genetic model could produce a better inclusion of true positive SNPs. We used 10 fold CV, as described in the methods, to select the best single genetic model. The results in Table −08 (Makowsky et al., One of the major goals of GWAS was to identify genetic variants that are associated with disease or measures of disease severity in order to be used for personalized medicine. However, genetic models have been of limited utility and the selection of the best SNPs to be used for prediction is challenging (Schrodi et al., Our evaluation in simulated data suggests that using an ensemble of genetic models provides a more robust solution compared to selecting a single genetic model. The analysis showed that when there are only a few causal SNPs, both the single genetic model and the ensemble of genetic models perform similarly. However, when the number of causal SNPs increases or, equivalently, when the SNP effects are small, a single genetic model tends to underestimate the number of causal SNPs, while the ensemble of genetic models tend to include a larger proportion of the causal SNPs. This increased sensitivity of the ensemble is associated with only a slight decrease in the prediction accuracy. This analysis suggests that an ensemble of genetic models would be particularly useful to identify true positive SNPs that may be ignored in other analyses. The slow decline of prediction accuracy also makes the ensemble of genetic prediction models more insensitive to the inclusion of false positive SNPs.In this manuscript we limited attention to the theoretical aspects of the ensemble of genetic models. We applied this methodology to real data in Milton et al.  to prediMany statistical methods have been developed to model complex traits and increase the prediction accuracy including multivariate regression models and machine learning type approaches such as support vector machines (Wei et al., In our analysis we assumed that SNPs that enter the analysis are not in linkage disequilibrium, as this is a commonly made assumption (Paynter et al., Finally, the approach described made assumptions about the genetic modeling that limit the generalizability of this study. We assumed in our simulations that the genetic variants have an independent additive effect on the phenotype, and that they all explain the same proportion of variability. It will be interesting to examine the effect of other modes of inheritance, of non-uniform genetic effects, and of rare and common variants in future work.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.