ZBTB38), 6q25.3 (RGS17), 9p22.1 (HAUS6), 9p13.3 (UBAP2), 11p11.2 (RAPSN), 14q12 (AKAP6), 15q15 (KNL1) and 18q23 (ZNF236).There is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a genome-wide association study (GWAS). The underlying methods, however, are often designed to test the global null hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying composite null hypothesis that a variant is associated with none or only one of the traits. We propose testing the null hypothesis based on the product of the Z-statistics of the genetic variants across two studies and derive a null distribution of the test statistic in the form of a mixture distribution that allows for fractions of variants to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions: 3q23 ( We propose a new approach PLACO that uses aggregate-level genotype-phenotype association statistics—commonly referred to as GWAS summary statistics—to identify genetic variants that influence risk of two traits or diseases. It allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. We demonstrate that PLACO can achieve major power gain over alternative methods that are typically used. We applied PLACO to Type 2 Diabetes and Prostate Cancer summary data from two large case-control studies. Many previous studies have reported an inverse association of these two chronic diseases suggesting shared risk factors; however, shared genetic mechanisms underlying this association is poorly understood. PLACO identified a number of novel shared genetic regions that are not detected by individual trait analysis. Many of the loci implicated by PLACO increase risk for one disease while decreasing risk for the other. PLACO can similarly be used on other traits to shed light on shared genetic risk factors. Years of genetic research on various complex human traits have implicated numerous genetic variants as risk factors for two or more traits. Pleiotropy, the phenomenon where a genetic region or locus confers risk to more than one trait , is wideTo detect potential pleiotropic effects of genetic variants, many statistical methods for jointly analyzing multiple traits in genome-wide association studies (GWAS) have been proposed , 12, 13.A number of Bayesian approaches exist that allow evaluation of pleiotropy on a genome-wide scale based on posterior probability of simultaneous association of a variant with two or more traits given GWAS summary data for each trait . HoweverIn the frequentist realm, recently a few methods have been proposed to specifically test for pleiotropy, where the rejection of the null hypothesis of no pleiotropy is driven by the significant association of a genetic variant with more than one trait –29. All pleiotropic analysis under composite null hypothesis), can be applied to summary-level data available from GWAS of two traits and can account for potential correlation across traits, such as that arising due to shared controls in case-control studies. We conduct extensive simulation experiments to study type I error and power of PLACO at stringent significance levels. We apply PLACO to summary data on common variants from two large case-control GWAS of European ancestry on Type 2 Diabetes (T2D) and on Prostate Cancer (PrCa). Many previous studies have reported an inverse association of these two chronic diseases suggesting shared risk factors; however, shared genetic mechanisms underlying this T2D-PrCa association is poorly understood. We replicate some candidate and known shared genes, and identify a number of novel shared genetic regions.In this article, we propose a formal statistical test of pleiotropy of two traits borrowing ideas from statistical mediation analysis literature. The proposed method, PLACO . For the ease of explanation, we will assume the two traits are binary ; however, our approach, being based on summary statistics, is applicable to two qualitative and/or quantitative traits. An individual’s outcome or trait can take value 0 for controls or 1 for cases. If the genetic variant under consideration is a bi-allelic single nucleotide polymorphism (SNP), an individual’s genotype can take values 0, 1 or 2 depending on the number of copies of minor alleles at the SNP. If the variant is imputed, the genotypic value will range between 0 and 2. For simplicity, we assume there is no covariate. Note, this assumption can be easily relaxed by considering trait residuals (obtained from regressing the covariates on the trait) instead of the raw trait values. Although residualizing outcome data is not standard, previous studies have shown that it does not affect validity of genetic association tests [Consider two genome-wide studies of traits on tests –32.βk is the genetic effect on the k-th trait . The null hypothesis of no association of the genetic variant with the k-th trait corresponds to βk and Z-score (Zk) has an asymptotic N distribution under the null Z1 and Z2 are expected to be independently distributed. It is to be noted that the Z-scores can also be obtained under any other genetic model , and the following methodological development is still applicable.The typical approach in a GWAS is to test for association of each genetic variant with the trait, and report the estimated genetic effect sizes, their standard errors and the corresponding p-values for all genetic variants (often referred to as ‘summary statistics’). For a given genetic variant, the marginal model for outcome data isβ1 = β2 = 0). Rejection of this global null can be due to one associated trait  or both . Here, we are interested in identifying the genetic variants that are associated with both the traits or outcomes . The effects of such a genetic variant on the traits may or may not be equal. Formally, our null hypothesis of no pleiotropy is H0: at most 1 trait is associated with the genetic variant while the alternative hypothesis is Ha: both traits are associated.The conventional cross-phenotype association methods test the global null hypothesis that none of the traits is associated with the given genetic variant . This is a special two-parameter case of the intersection-union principle of statistical hypothesis testing. A level-α intersection-union test (IUT) [H0 vs. Ha is, reject H0 if a level-α test rejects Hk0 for every k = 1, 2. Consequently, the p-value for the IUT ≤ maximum of the p-values for testing p1, p2}, where pk is the p-value corresponding to the test statistic Zk  for model in Mathematically, our null hypothesis of no pleiotropy is a composite null hypothesis st (IUT)  of H0 vsH0: β1β2 = 0 vs. the alternative hypothesis Ha: β1β2 ≠ 0. This immediately reminds us of the product of coefficients hypothesis tests for the significance of mediation effects in epidemiology [H0, the test statistic is N distribution as its null distribution.Observe that our null hypothesis of no pleiotropy can simply be written as emiology . It invoapproach , 35 is uH00 to be true for most genetic variants). As a consequence of sparse signals and hence the breakdown of condition for asymptotic normality of Sobel’s method, testing pleiotropy using Sobel’s method fails to control type I error and lacks power to detect pleiotropic effects of a genetic variant. In the mediation literature, as an alternative to Sobel’s method, [In the context of genome-wide mediation analysis, the normal approximation of Sobel’s method depends on a condition that only holds if at least one of the mediation coefficients is non-zero . In the  method,  proposed method,  from medH00 holds with probability π00 under which the single-trait test statistics Z1 and Z2 have asymptotic standard normal distributions. Further assume that the sub-null hypothesis H01 holds with probability π01 under which Z1 has a standard normal distribution and Z2 has a conditional N distribution given the mean parameter μ2. We assume a μ2. Similarly, assume that the sub-null hypothesis H02 holds with probability π02 and Z2 ∼ N while Z1|μ1 ∼ N, where Suppose the global null Z1 and Z2 are independent N variables under H00; (b) Z1 and Z2 are independent N and H01; and (c) Z1 and Z2 are independent N variables respectively under H02. Consequently, the products Z1Z2, H00, H01 and H02 respectively (assuming the parameters τ1 and τ2 are known). The (symmetric) normal product distribution is given by the probability density function (p.d.f.) x < ∞, where In other words, we are assuming (a)  order 0 .H0: β1β2 = 0 (no pleiotropy) against Ha: β1β2 ≠ 0 using the product of Z-scores as our test statistic is given byz1 and z2 are the observed Z-scores for the two traits at a given genetic variant, and u. Observe that the analytical form for PLACO p-value in π00, π01, π02, τ1 and τ2. One can estimate these parameters only once under the null using the GWAS summary statistics on the millions of genetic variants genome-wide and assume they are known. However, this p-value evaluation approach is sensitive to these parameter estimates and can be quite conservative at genome-wide levels  for testing Z2) are the estimated marginal variances of the Z-scores under the hierarchical model we assumed [R [PLACO (https://github.com/RayDebashree/PLACO). Details of the estimation of parameters needed for calculating this approximate p-value are provided in Section A of μ1 and μ2 (under H02 and H01 respectively) are assumed [The PLACO p-value in  assumed . This casumed [R  program  assumed .Z-scores for the two traits are independent. While the independence of the effects Z-scores, is guaranteed in a mediation analysis assuming there is no unmeasured confounding [Z-scores will be correlated [The above formulation of PLACO assumes that the founding , it is nfounding , 41) or rrelated  and may Z-scores is nk, case and nk, control are respectively the number of cases and the number of controls in the study for k-th outcome, and n12, control  is the number of shared controls (cases) between the two studies [ρ, thus, ranges between 0 and 0.5, where the maximum is reached when there are equal number of cases and controls in each study, both studies have the same sample size and all the controls are shared  and n1, n2 are the respective sample sizes of the two traits [For two outcomes from two case-control studies, the correlation between the  studies . In realo traits .ρ by the Pearson correlation of the Z-scores for the genetic variants with “no effect” on any trait. For a real dataset, the truth about which genetic variants have “no effect” is unknown. We choose the genetic variants that do not exceed a pre-defined significance threshold  for any trait to estimate the correlation ρ between Z-scores [ρ; however we did not find appreciable differences between GWAS results obtained using estimates from these two approaches [PLACO software, before applying PLACO genome-wide. If Z = ′ be the vector of Z-scores for a given genetic variant and Z-scores as Zdecor = R−1/2Z so that Z-scores to test for pleiotropy of two correlated traits. However, we found from our simulation experiments that PLACO is an appropriate test of pleiotropy of two independent or moderately correlated traits, and may show inflated type I error for strongly correlated traits or when studies share more than half of their subjects.The number of overlapping samples between studies/traits may not be known when only GWAS summary data are available. In such a situation, one can estimate the correlation parameter Z-scores . One mayZ-scores  to estimproaches . IrrespeR [α.To evaluate operating characteristics of PLACO as a test for pleiotropy, we conduct simulation experiments in R . We consH00 , 0.5% variants under the sub-null H01 , 0.4% variants under the sub-null H02 , and 0.1% variants under the alternative Ha . Thus, our simulated dataset has 9.99 million null variants to estimate type I error and 10, 000 non-null variants to estimate statistical power. Note, we have explored additional simulation settings such as those with higher proportion of variants associated with at least one trait or with larger MAF of variants; the details and results of which are provided in Section C of Out of the 10 million genetic variants, we assume 99% of variants to be under the global null of no association n1 = n2 = 2000) or the first study on the first trait is 4 times larger than the second study on the second trait . We assume a case-control ratio of 1:1 in each study, and a baseline disease prevalence of 15% and 10% for the first and the second disease trait respectively. Our generative model, described in Section C of We simulate the two case-control studies such that the individuals in one study are independent of the other. We consider situations where the two studies have either comparable (1:1) or unbalanced (4:1) sample sizes. In other words, either the two studies have equal sample sizes  or the first trait is measured on many additional individuals . We vary both the strength and the direction of pairwise trait correlation: ρtrait = {−0.9, −0.4, 0, 0.4, 0.9}. The null genetic variants with non-zero effect on one trait only are assumed to explain 0.1% of the variance of the associated trait. The generative model is the same as before except that a bivariate normal model with means 0, variances 1, and pairwise correlation ρtrait is used to simulate the quantitative traits. In this scenario too, we only compare type I error of Sobel’s approach, maxP, and PLACO (with and without correction for correlation), and do not evaluate power.We simulate a single study with measurements on two correlated quantitative traits measured either on the same individuals  across the autosomes and the X chromosome.Schumacher et al.  meta-anaZ-scores from the two datasets can be jointly analyzed appropriately using PLACO. From the effect estimates and the standard errors, we calculate the Z-scores, and remove SNPs with Z2>80 [Z-scores from T2D and those from PrCa is approximately 0 as well.In this paper, we use the two sets of meta-analysis summary statistics of genetic association with T2D and with PrCa to detect shared common SNPs. Sources of these summary statistics are provided under Web resources. We remove any SNP with allele mismatch between the two datasets, and focus on the remaining 5, 041, 948 autosomal SNPs with MAF ≥1% that are available in both the studies. For a given SNP, we harmonize the same effect allele across the two studies so that th Z2>80 , 63 sincpPLACO<5 × 10-8) in ±500 Kb radius and linkage disequilibrium (LD) threshold of r2>0.2 into a single genetic locus using FUMA [SNP2GENE function, v1.3.5e). The gene annotations for all loci are based on proximity to the most significant/lead SNPs as mapped by FUMA. We perform different gene-set enrichment analyses using the GENE2FUNC function, where the genes were prioritized by FUMA based on the loci identified by PLACO. To provide additional evidence of sharing at these loci, we perform Bayesian colocalization test [coloc (v3.2.1). This test computes 5 different overall posterior probabilities of the chosen region: coloc.abf function with default parameters and priors on the effect estimates and their variance estimates for the SNPs in the chosen region for each of T2D and PrCa. For the significant loci with convincing evidence of colocalization, we manually look up Open Targets Genetics platform [cis expression quantitative trait locus (eQTL) analysis in FUMA using data from the eQTLGen Consortium [cis-eQTL analysis, we additionally consider T2D-relevant tissues  [To characterize the findings from PLACO, we clump all the significantly associated SNPs . Foplatform  to gathensortium , the lar muscle)  and PrCa muscle) .Irrespective of whether the sample sizes of the two studies are same or widely different, PLACO has well-calibrated type I error at stringent significance levels . In compZ-scores are not decorrelated for studies with overlapping samples, pleiotropy analysis will likely show spurious association signals as indicated by the inflated ‘PLACO (no overlap correction)’ curve. The other approaches are still very conservative across all scenarios of overlap.Regardless of the extent of control overlap in the two studies, PLACO exhibits appropriate type I error when correlation is accounted for in the analysis . We alsoWe find PLACO has well-calibrated type I error for moderately correlated traits irrespective of the direction of correlation between the traits, and has inflated type I error for strongly correlated traits . ApplicapTrait1<5 × 10-8, pTrait2<5 × 10-5 and the other pTrait1<5 × 10-8, pTrait2<5 × 10-3 (‘Naive-1’ and ‘Naive-2’ respectively in our figures). As reasoned before, comparing power under Scenario I is sufficient. Regardless of the magnitude and directions of pleiotropic association and the sample size differences between studies, PLACO has dramatically improved statistical power to detect pleiotropy compared to the naive approaches  with our index SNP, the GWAS peak, from that locus. To define ‘previously associated SNP’ in our context of pleiotropy of T2D and PrCa, we looked for any SNP within each locus that is associated with both T2D-related trait  and PrCa-related trait (either of PrCa or prostate-specific antigen levels). Since GWAS catalog includes exome-wide studies, we chose a slightly liberal exome-wide significance threshold of p<5 × 10−7 to define previously reported associations. We discovered 38 potentially novel loci, after liftover of GRCh38 genomic coordinates in GWAS catalog to hg19 using R package liftOver [PLACO identified 1, 329 genome-wide significant SNPs that mapped to 44 distinct loci . The lealiftOver .THADA, BCL2L11, AC005355.2, PBX2 (in the major histo-compatibility complex or MHC region of 6p21), JAZF1 and CDKN2A/B have been previously implicated in studies of both T2D and PrCa. In particular, THADA [JAZF1 [HNF1B, also known as TCF2, is another recognized shared gene [HNF1B), which may have weakened any signal in this region. Signals from PLACO point to candidate shared genes such as PPARG [CDKN2A [KCNQ1 [MTNR1B [GWAS catalog search reveals that 6 out of 44 loci near genes r, THADA  S3 Fig)THADA, BCred gene , which wred gene , 63 THADA, BC [MTNR1B  S8 Fig)THADA, BCFUMA are significantly enriched in GWAS catalog reported genes for PrCa, T2D and other T2D related traits , and both have similar PLACO p-value of pleiotropic association.Bayesian colocalization tests of ±200 Kb region around the lead SNPs of the 43 loci reveal 26 lead SNPs as having the highest posterior probability of being associated with both PrCa and T2D . Eight lcis-eQTLs in multiple T2D-relevant tissues . The RGS17 locus show associations with various cancers, including PrCa and prostate neoplasm, and body mass index (BMI) but has no known associations with any T2D-related trait (no relevant mouse data available). Of particular interest are the HAUS6 and the RAPSN loci. While HAUS6 and its nearby genes RRAGA and PLIN2 have various cancers (including PrCa) as associated diseases in Open Targets Genetics, one or more of them are related to metabolism phenotype, abnormal gluconeogenesis and hypoglycemia in mice. GWAS catalog search of these genes did not yield any known association result with any T2D-related trait. Similarly, the nearby gene MADD for the RAPSN locus has various cancers, neoplasms and glucose-related phenotypes as associated diseases in Open Targets Genetics; and is a recognized T2D gene, which when knocked out in mice, show impaired glucose tolerance, hyperglycemia and abnormal pancreatic beta cell morphology.The lead SNPs of 6 of the 8 potentially novel pleiotropic loci with convincing evidence from the colocalization analyses have effect alleles that increase risk for one disease while protecting from the other . While t tissues –S16 Figss , RGS17 (6q25.3), HAUS6 (9p22.1), UBAP2 (9p13.3), RAPSN (11p11.2), AKAP6 (14q12), KNL1 (15q15) and ZNF236 (18q23). A recent study [We use the most recent publicly available case-control GWAS summary data on T2D and on PrCa in individuals of European ancestry to determine variants that influence risk to both these diseases. We identify several known and candidate shared genes, and detect a number of novel shared genetic regions near nt study  showed ant study . Effect https://www.nih.gov/research-training/environmental-influences-child-health-outcomes-echo-program), to understand genetic underpinnings of pediatric outcomes. One important scientific question will be to identify genetic overlap of such outcomes , which PLACO can conveniently address, that too without having to pool individual-level data.The key advantage of PLACO among existing frequentist approaches is not requiring individual-level data which makes it easily applicable to datasets for which only GWAS summary data are available. It does not require compute intensive permutations or Monte Carlo simulations to calculate p-value of simultaneous association of two traits with one genetic variant. We are conveniently using the asymptotic normality of MLE of genetic effects to get at the null distribution of the PLACO test statistic. The existence of an analytical form for PLACO p-value  and its H01 or H02 is small [PLACO may be inflated and indicate a genome-wide significant result. We suggest that SNPs with marginal Z2>80 be removed before analysis, similar to suggestion for LD-score regression approaches. PLACO is a single-variant association test that is not expected to control type I error for genetic variants with low minor allele counts since the asymptotic normality of MLE assumption may be violated [Our study and our statistical approach are not without limitations. PLACO requires genome-wide summary data to infer pleiotropic association of each variant, and cannot be used when summary data on only a handful of candidate genetic variants are available. Calculation of PLACO p-value requires parameter estimation using variants across the genome, and hence cannot be used to test pleiotropy of a set of variants known to be significantly associated with one trait. PLACO shows inflated type I error when the traits are strongly correlated even after using our decorrelation approach. The approximate PLACO p-value Click here for additional data file.S1 Fig10p-values) are plotted on the y-axis and Expected on the x-axis. Unequal study sample size, and equal case-control size assumed in each study. Study 1 has 4, 000 unrelated cases and 4, 000 unrelated controls. Study 2 has 1, 000 unrelated cases and 1, 000 unrelated controls, of which either 20%, 40%, 80% or 100% of the controls are shared between the two studies. Type I error performance of tests of pleiotropic effect of a genetic variant on the 2 traits is based on 9.99 million null variants with genetic effects that are either {β1 = 0 = β2} or {β1 = 0, β2 = log(1.15)} or {β1 = log(1.15), β2 = 0}. The gray shaded region represents a conservative 95% confidence interval for the expected distribution of p-values.Observed(−log(PDF)Click here for additional data file.S2 Fig10p-values) are plotted on the y-axis and Expected on the x-axis. Type I error performance of tests of pleiotropic effect of a genetic variant on the 2 traits is based on 9.99 million null variants with genetic effects that are either {β1 = 0 = β2} or {β1 = 0, β2 explains 0.1% of Trait 2 variance} or {β1 explains 0.1% of Trait 1 variance, β2 = 0}. The gray shaded region represents a conservative 95% confidence interval for the expected distribution of p-values. P-values ≥10−12 are shown here.Observed(−log(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 Fig(PDF)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig(PDF)Click here for additional data file.S7 Fig(PDF)Click here for additional data file.S8 Fig(PDF)Click here for additional data file.S9 Fig(PDF)Click here for additional data file.S10 Fig(PDF)Click here for additional data file.S11 FigTissues considered are whole blood from eQTLGen Consortium; and adipose, liver, muscle-skeletal, pancreas, and prostate tissues from GTEx v8.(PDF)Click here for additional data file.S12 FigTissues considered are whole blood from eQTLGen Consortium; and adipose, liver, muscle-skeletal, pancreas, and prostate tissues from GTEx v8.(PDF)Click here for additional data file.S13 FigTissues considered are whole blood from eQTLGen Consortium; and adipose, liver, muscle-skeletal, pancreas, and prostate tissues from GTEx v8.(PDF)Click here for additional data file.S14 FigTissues considered are whole blood from eQTLGen Consortium; and adipose, liver, muscle-skeletal, pancreas, and prostate tissues from GTEx v8.(PDF)Click here for additional data file.S15 FigTissues considered are whole blood from eQTLGen Consortium; and adipose, liver, muscle-skeletal, pancreas, and prostate tissues from GTEx v8.(PDF)Click here for additional data file.S16 FigTissues considered are whole blood from eQTLGen Consortium; and adipose, liver, muscle-skeletal, pancreas, and prostate tissues from GTEx v8.(PDF)Click here for additional data file.S1 Table6 null variants  and m non-null (pleiotropic) variants, where m takes values 0, 100, 300, 500, 1000, 3000, 5000 or 10000. Five different choices of odds ratios of association of m non-null variants with Traits 1 and 2 are considered. The total number of true positives (non-null variants) detected (#TP) and the total number of false positives detected (#FP) are reported. PLACO’s performance for both genome-wide threshold 5 × 10−8  of 5%) and global false discovery rate (FDR) of 5% are reported, while GPA’s performance is based on global FDR of 5%.Each study has 9.9 × 10(PDF)Click here for additional data file.S2 Table6 null variants  and m non-null (pleiotropic) variants, where m takes values 0, 100, 300, 500, 1000, 3000, 5000 or 10000. Five different choices of odds ratios of association of m non-null variants with Traits 1 and 2 are considered. The total number of true positives (non-null variants) detected (#TP) and the total number of false positives detected (#FP) are reported. PLACO’s performance for both genome-wide threshold 5 × 10−8  of 5%) and global false discovery rate (FDR) of 5% are reported, while GPA’s performance is based on global FDR of 5%.Each study has 9.9 × 10(PDF)Click here for additional data file.


Many traits and diseases are thought to be driven by >1 gene (polygenic). Polygenic risk scores (PRS) hence expand on genome-wide association studies by taking multiple genes into account when risk models are built. However, PRS only considers the additive effect of individual genes but not epistatic interactions or the combination of individual and interacting drivers. While evidence of epistatic interactions ais found in small datasets, large datasets have not been processed yet owing to the high computational complexity of the search for epistatic interactions.We have developed VariantSpark, a distributed machine learning framework able to perform association analysis for complex phenotypes that are polygenic and potentially involve a large number of epistatic interactions. Efficient multi-layer parallelization allows VariantSpark to scale to the whole genome of population-scale datasets with 100,000,000 genomic variants and 100,000 samples.Compared with traditional monogenic genome-wide association studies, VariantSpark better identifies genomic variants associated with complex phenotypes. VariantSpark is 3.6 times faster than ReForeSt and the only method able to scale to ultra-high-dimensional genomic data in a manageable time. Traditional genome-wide association studies (GWAS) evaluate genomic variants (referred to hereinafter as “variants") across the genomes of many samples for statistical association with the phenotype in question. These studies are aimed at detecting variants associated with common and complex traits and diseases, such as heart disease, diabetes, and height . GWAS haOne possible explanation is that these phenotypes are driven by an additive effect of several variants (“polygenic phenotype"), resulting in a small association power for each variant . PolygenAnother explanation is the existence of epistatic interaction (referred to hereinafter as “interaction") between sets of variants   , which iThere are 2 layers of parallelization to speed up an algorithm: multi-threading and distributed computing. The former is a common approach that allows programmers to use all processors and memory available in a single computer, usually a high-performance computer (HPC). The latter allows a program to be executed in parallel on multiple independent computers connected by a network . Given that the network is far slower than processors and memory, it is critical to implement the program in a way that reduces network operation and avoid a potential bottleneck. Apache Spark  The wider VariantSpark software suite implements k-means clustering and is compatible with standard genomic data formats , and is integrated with Hail  to offerA cluster, on the other hand, can easily scale to hold hundreds of terabytes of data (as most cloud providers can supply). The most popular distributed implementation of RF is Google’s PLANET , which iHere, we first compare the performance of VariantSpark with the approach used in traditional GWAS, logistic regression (LR) . We consTwo different sets of synthetic datasets are used in this study, both of which are publicly available  for the We use these datasets to compare the accuracy of VariantSpark with LR. A set of phenotypes are simulated for 1KG samples using PEPS that uses real genotype data and simulates a binary phenotype associated with a subset of randomly selected variants.n-way truth-variables, which are used to simulate the phenotype. A variable could be an individual variant (1-way variable) or set of n variants with epistatic interaction (n-way variable), so 2-way variables are pairwise epistatic interactions; 3-, 4-, and 5-way variables are higher-order epistatic interactions. Each variant is involved in only 1 variable. Variants involved in truth-variables (associated with the phenotype) are called truth-variants (TVs) and are to be discovered by VariantSpark or LR.PEPS first forms Table The 1KG dataset consists of 2,504 samples and ∼80M variants with multi-allelic variants converted to multiple bi-allelic variants. We generate 4 subsets of this dataset by randomly selecting variants, 2 by adding the TVs of all phenotypes back if they were removed by this process .The phenotype is simulated using VariantSpark gen-label commands and based on 5 randomly selected variants all with equal contributions . To make a more complex phenotype, the mean and the standard deviation of the noise, For the comparison to other tools, we subset variants from the 10K-10M dataset and include the 5 TVs in all subsets. We start from 100 variants and double it at each step. These datasets are listed in Table For reproducibility, all tests are performed on Amazon Web Services (AWS) compute resources. We use AWS EC2 (Elastic Compute Cloud) and EMR (Elastic Map Reduce) for HPC and cluster compute, respectively. We use clusters of different sizes listed in Table The combination of 9 phenotypes described in Table P-value computed by LR and importance score computed by VariantSpark. We replicates the experiments 3 times (similar phenotypes are simulated but different randomly selected TVs are used to form the phenotype). In the last 2 replicates, we did not process the 1KG-80M dataset with VariantSpark owing to high computational cost. Owing to technical issues, the VariantSpark results for PIL on 1KG-80M were missed for the first replicate.We ranked the variants on the basis of VariantSpark and ReForeSt are executed on a C256 cluster while Ranger is executed on r4.16xlarge computer with 64 vCPU and 488 GB of memory, which is the practical limit of HPC. We apply maxD = 15 and minNS = 50 where applicable and build 1,000 trees  with mTry = 0.1 × nV. We build a DT with Yggdrasil 10 times. For VariantSpark we build a forest with 10 trees and set mTry = nV because this parameter setting mimics growing a DT.When testing VariantSpark’s scalability the following parameters were applied to all experiments below, unless mentioned otherwise: maxD = 15, minNS = 50, mTry = 0.1 × nV, and rbs = 100 .Dataset size: The expected runtime to build 1,000 trees for all datasets in Table Cluster size: 500 trees are built for 10K-1M dataset on clusters of different sizes : 500 trees are built for 10K-1M dataset with rbs equal to 10, 50, 100, or 500.The following experiments are performed to show the effect of different parameters on the VariantSpark runtime and out-of-bag (OOB) error rate (prediction accuracy) when processing the 10K-1M dataset.Unlimited: 500 trees are built with no limits on the depth of the tree or the node size.Maximum depth (maxD): 500 trees are built with no limits on the node size but the maxD varies as follows: 3, 5, 7, 9, 11, 13, 15, 20, 25, 100.Minimum node size (minNS): 500 trees are built with no limits on depth of the trees but the minNS varies as follows: 5, 10, 50, 100, 500, 1,000.mTry: 500 trees are built with the mTry varying as follows: 10, 50, 100, 500, 1,000, 5,000, 10,000, 100,000.nTree: Starting from 100 trees and doubling the number of trees up to 1,600 trees.We compare the performance of VariantSpark with LR using phenotypes of different complexity and different sized datasets. First, we report how many TVs, i.e., variants associated with the phenotype, can be detected by the respective approaches.r ranked-variants (RVs) for all phenotype categories . We do not consider the order of variants in the list of RVs. All experiments were replicated 3 times. We highlight results from the first replicate for 1KG-80M , 1KG-5M-T , and 1KG-500K-T here, but other results  are reported in Fig. t RVs, resulting in a maximum value of 1. VariantSpark indeed achieves this for 2 datasets  and phenotypes with low numbers of individually associated variables (PIL). LR, on the other hand, only detects all TVs in the smaller of these 2 datasets and only when expanding the list to the top 2t RVs.Ideally, all TVs are expected to be listed in the top More generally, VariantSpark detects either more TV or an equivalent proportion for most phenotypes and data set sizes. VariantSpark especially outperforms LR for epistatic (PE) and complex (PX) phenotypes where interactions are involved (achieving scores up to X times better than LR). This is because the association power gained by the interaction between variants remains invisible to LR.Conversely, LR performs ≤2.2 times better than VariantSpark on datasets withdividual TVs (PIM and PIH). This gain over VariantSpark is likely due to the need to tune hyper-parameter choices for each dataset, which has resulted in non-optimal performance in these instances (see Hyper-Parameter Tuning section).t RVs, is a difficult task.For phenotypes with a high number of TVs  the detection rate is low for both VariantSpark and LR, especially in the case of the largest dataset (1KG-80M). For such complex phenotypes, detecting all TVs, even in the top 10t RVs and plot the maximum absolute value of the Pearson correlation coefficient (γ). High γ indicates that the detected variant highly correlates with the TV and possibly identifies the same genomic region as the TV. TVs are sorted on the basis of their LR γ. The γ-values for all experiments and both methods are listed in Fig. As shown in Fig. It is worth noting that association accuracy, i.e., the ability to recover TV, is distinct from prediction accuracy, i.e., predicting the correct label for a sample. As shown in Fig. We benchmark VariantSpark against the fastest HPC and distributed implementation of RF, respectively: Ranger and ReForeSt. We record the runtime of all 3 tools on synthetic datasets with 10,000 samples and doubling the number of variants, starting from 100 to 6.5 million and then 10 million.Fig. For the largest dataset that Ranger processed (1.6M), ReForeSt and VariantSpark performed 4.1 and 4.6 times faster than Ranger, respectively. Ranger advertises a special GWAS mode, but we were unable to successfully run this mode. The quoted runtime in the Ranger publication  shows that GWAS mode is twice as fast as normal mode and uses the same amount of memory as save-memory mode. Given this information, the GWAS mode would not be able to process datasets with >3.2M variants and would remain slower than VariantSpark and ReForeSt.VariantSpark and ReForeSt performed comparably for 1.6M variants ; after this point, the runtime of ReForeSt increases exponentially while VariantSpark increases sub-linearly. Note the thin unmarked black line illustrating a linear runtime increase starting from the average runtime of VariantSpark and Reforest for a dataset of 1.6M variants . VariantSpark is 3.6 times faster than ReForeSt processing a dataset with 10M variants, a difference that increases further for larger datasets owing to the exponential vs sub-linear runtime behavior.We also compare VariantSpark with Yggdrasil, as the only other vertical partitioning implementation. Because Yggdrasil only builds a single DT, we run VariantSpark with mTry equal to the number of variants to emulate building a DT and record the runtime of building DTs 10 times with each method. As shown in Fig. We test VariantSpark’s scalability by recording the runtime when increasing the number of variants 10 times at each step, with 1,000, 10,000, and 100,000 samples, respectively. As shown in Fig. VariantSpark can use distributed compute resources efficiently and scales linearly with the size of the cluster as shown in Fig. We also investigate whether high-performance compute-nodes perform better than commodity ones, by running the same job on 3 clusters of the overall same capacity but with different numbers and sizes of compute-nodes. Each cluster processes the job 3 times with minimum and maximum runtimes plotted. Fig. There are 4 important parameters to set when building an RF model:nTree: Number of trees in the forestmTry: Number of variants evaluated at each node of a treemaxD: Maximum depth of a tree to growminNS: Minimum number of samples in a node to be processedHere, we show that parameter choice substantially affects the performance and accuracy of the trained model. We varied these parameters and recorded runtime and OOB. Also, we record the average number of nodes per tree and average tree depth to show the effect of maxD and minNS on the RF model.1/2 = 1,000.As a rule of thumb, it is recommended to set mTry to the square root of nV; however, our findings show that this recommendation does not suit the analysis of genome-wide datasets. Fig. Applying limits to RF training to keep trees shallow and efficient affects the runtime and accuracy of the model. Fig. Fig. The effect of VariantSpark batch size  is recorded in VariantSpark is a distributed implementation of the original RF classification algorithm . It acceWhen processing a node of a tree, RF evaluates randomly selected variants to separate samples of a node into 2 child nodes (a binary tree). The goal is to keep samples of the same class in 1 of the child nodes. The best split is the variant that results in the highest separation of samples. The best split maximizes the “information gained," which is a metric that measures the quality of separation. VariantSpark uses Gini-Index impurity as described in  to compuThe samples in each node are selected as a result of the best split in all parent nodes. Thus the best split and information gained in each node depend on all variants selected in the upstream nodes (to the root) and the interaction between them. Given a large number of trees built in an RF model a variant can be selected as the best split in various nodes in the forest. The information gained by the variant in each of these nodes discloses part of its interactions (with variants selected in upstream nodes above it). The importance score of a variant, computed as the average information gained for the variant, represents all of its interactions discovered by the RF model.Here we describe the theoretical dependency of VariantSpark’s runtime on different parameters. The runtime of the core computation (excluding loading data to memory) is expected to be linear in nTree × nNode × mTry × nS. The nTree and mTry are directly given by the user and represent the number of trees in the forest and the number of variables to be evaluated for each node of each tree, respectively. nS represents the number of samples in the dataset. To evaluate each variant at each node of a tree, the algorithm needs to loop through all samples. nNode represents the average number of non-leaf nodes per tree.The value of nNode is determined after the RF is trained because it depends on mTry, maxD, and minNS, as well as the complexity of the phenotype and the size of the dataset. The lower mTry, the lower the chance for a node to divide into pure (leaf) nodes, thus the higher nNode. With a lower maxD or a higher minNS, trees are smaller (nNode is lower). Also, more samples in the dataset result in deeper trees (nodes get purer with more splits), which ultimately increases the nNode. If a phenotype depends only on a few strongly associated signals, trees are shallower and the nNode is smaller.17 operations to build the RF model. This massive computational requirement indicates the importance of using a distributed computing platform for such analysis.Given nV = 100M, nS = 10K, nTree = 10K, nNode = 100, and mTry = 0.1 × nV a computer should perform 10The number of classes in the phenotype and the number of different values a feature can take also affects the processing time. However, we did not consider their effect because for most analysis the phenotype is a binary value and bi-allelic genotypes are encoded to 0, 1, and 2. The time it takes to load data into memory is a linear function of nS × nV .VariantSpark is implemented on top of Apache Spark, a fast distributed computing platform. In the Spark platform, the dataset is partitioned in the memory of several computers (compute-nodes), controlled by a central computer (master-node). In most implementations of machine learning algorithms, the dataset is partitioned by samples  such that each compute-node contains the data for all features and a set of samples. This is because most machine learning datasets include a large number of samples and a small number of features. However, in genomic datasets, it is the number of features that outgrows the number of samples by several orders of magnitude. Partitioning by variants  is more effective for genomic data.Vertical partitioning helps to reduce slow networking operations. If data are partitioned by samples, to process each node of a tree, each compute-node in the cluster must partially evaluate the selected mTry variants and send back results to the master node of the cluster for aggregation. However, when partitioning by variants, each compute-node evaluates a subset of the mTry variants  and only sends the information about the best local split to the master-node Fig. .Another important optimization in VariantSpark is parallelizing the processing of several nodes from several trees in a batch such that network operations never become a bottleneck. Finally, VariantSpark uses Spark RDD, which provides the lowest level of access to the memory to deliver the highest performance.While there is evidence for polygenic and epistatic phenotypes, polygenic-epistatic phenotypes have not been studied yet, likely because the existing GWAS methods are underpowered to perform such compute-intensive association studies. VariantSpark is the first methodology to perform complex association analyses on whole-genome sequencing experiments and outperforms other state-of-the-art implementations.The results provided in this article first demonstrate the capability of VariantSpark in detecting associative signals of complex interactions, and second elaborate the performance and scalability when processing large-scale datasets. Akin to deep learning methods, VariantSpark’s hyper-parameters need to be iteratively tuned to each dataset, which is made possible by VariantSpark’s speed and scalability.VariantSpark is not a replacement for traditional association analysis but a complement. The results of traditional GWAS (LR) and VariantSpark should be considered together to gain insights into the full influence of the genome on disease and other phenotypes. Similarly, VariantSpark’s output may be usable to prioritize variants in PRS to reduce noise levels.VariantSpark source code and compilation instructions:Project name: VariantSparkhttps://github.com/aehrc/VariantSparkProject home page: Operating system(s): Platform independent Programming language: Scala with Python and Hail InterfaceOther requirements: Java 8, Apache Spark 2License: CSIRO Open Source Software Licence v1.0, based on MIT/BSDRRID:SCR_018383https://bio.tools/)BioTools: biotools:variantspark  such that a user with minimal technical knowledge can get access to a computer cluster of any size with VariantSpark, Hail, and Jupyter Notebook installed and ready to use.An archival copy of the code is also available in GigaDB . FinallySupplementary Data File 1. Provides an extended and more detailed numerical comparison for all figures.Supplementary Data File 2. Includes the maximum correlation values (γ) for all experiments.Supplementary Data File 3. Provides all PEPS simulated phenotypes for 1000-Genomes dataset with truth-variants and PEPS configuration files.Supplementary Data File 4. Explains access to raw data and output file (available on GigaScience Database ) as well1000-Genome data and subsets in vcf compressed format.Dataset simulated with VariantSpark.Complete correlation matrix between TVs and RVs for all analyses.List of RVs for all analyses.Random Forest model created by VariantSpark in JSON format (used to compute average tree depth and number of nodes).Instructions to create an AWS EMR cluster via terminal.Instructions to submit VariantSpark jobs to the cluster.1KG: 1000-Genomes; AWS: Amazon Web Services; DT: decision tree; GWAS: genome-wide association study; HPC: high-performance computer; LR: logistic regression; OOB: out-of-bag error rate; PEPS: Polygenic Epistatic Phenotype Simulator; PRS: polygenic risk score; RDD: Resilient Distributed Dataset; RF: random forest; RV: ranked variant; TV: truth variant; vCPU: virtual central processing unit.nS: Number of samples in datasetnV: Number of variants in datasetnTree: Number of treesmTry: Number of variables to evaluate at each node of a treemaxD: Maximum depth of a treeminNS: Minimum number of samples in each node to be processedrbs: Number of trees to be processed in parallelγ: Maximum absolute Pearson correlation coefficient between a truth-variant and any of the ranked-variantsFunding was from CSIRO Health and Biosecurity. The authors gratefully acknowledge AWS cloud credits that were used to fund the cloud cost of this work.A.B. and D.C.B. designed the experiment. P.S., A.B., B.H., Y.J., C.H., and A.R.O. implemented the software used in this research. A.B. and R.D. conducted the experiments. A.B., D.C.B., O.J.L., and N.T. wrote the manuscript. All authors read and approved the manuscript.giaa077_GIGA-D-19-00335_Original_SubmissionClick here for additional data file.giaa077_GIGA-D-19-00335_Revision_1Click here for additional data file.giaa077_GIGA-D-19-00335_Revision_2Click here for additional data file.giaa077_GIGA-D-19-00335_Revision_3Click here for additional data file.giaa077_GIGA-D-19-00335_Revision_4Click here for additional data file.giaa077_Response_to_Reviewer_Comments_Original_SubmissionClick here for additional data file.giaa077_Response_to_Reviewer_Comments_Revision_1Click here for additional data file.giaa077_Response_to_Reviewer_Comments_Revision_2Click here for additional data file.giaa077_Response_to_Reviewer_Comments_Revision_3Click here for additional data file.giaa077_Reviewer_1_Report_Original_SubmissionBrendan Lawlor -- 10/13/2019 ReviewedClick here for additional data file.giaa077_Reviewer_1_Report_Revision_1Brendan Lawlor -- 5/19/2020 ReviewedClick here for additional data file.giaa077_Reviewer_2_Report_Original_SubmissionJoshua W. K. Ho, PhD -- 10/18/2019 ReviewedClick here for additional data file.giaa077_Reviewer_2_Report_Revision_1Joshua W. K. Ho, PhD -- 5/12/2020 ReviewedClick here for additional data file.giaa077_Reviewer_3_Report_Original_SubmissionFaraz Faghri -- 11/4/2019 ReviewedClick here for additional data file.giaa077_Supplemental_FilesClick here for additional data file.


Oryza sativa, under normal and aluminum (Al) stress conditions, a trait under recent selection because it correlates with survival under drought. A dense single nucleotide polymorphism (SNP) map is available for all accessions studied. Taking advantage of this map and a set of Bayesian models, we assessed additive marker effects. While total genetic variation accounted for a large proportion of phenotypic variance, marker effects contributed little information, particularly in the Al-tolerant tropical japonica population of rice. We were unable to identify any loci associated with root growth in this population. Models estimating the aggregate effects of all measured genotypes likewise produced low estimates of marker heritability and were unable to predict total genetic values accurately. Our results support the long-standing conjecture that additive genetic variation is depleted in traits under selection. We further provide evidence that this depletion is due to the prevalence of low-frequency alleles that underlie the trait.Quantitative traits are important targets of both natural and artificial selection. The genetic architecture of these traits and its change during the adaptive process is thus of fundamental interest. The fate of the additive effects of variants underlying a trait receives particular attention because they constitute the genetic variation component that is transferred from parents to offspring and thus governs the response to selection. While estimation of this component of phenotypic variation is challenging, the increasing availability of dense molecular markers puts it within reach. Inbred plant species offer an additional advantage because phenotypes of genetically identical individuals can be measured in replicate. This makes it possible to estimate marker effects separately from the contribution of the genetic background not captured by genotyped loci. We focused on root growth in domesticated rice,  Unraveling the mechanisms of phenotypic evolution under selection is a fundamental task in biology. Among-individual variation in most traits of interest results from a collective action of multiple genes in conjunction with environmental effects . To a fie.g., seemingly unimportant morphological characteristics). Since measurement scales differ among traits, some scale factor must be used to make comparisons meaningful. A popular scaling factor is the total variance. Its use is well-motivated by theory as the ratio of additive genetic to total variance yields estimates of narrow-sense heritability, a parameter important in predicting outcomes of single-generation selection on phenotypes  traits to a control group  or experimental  crosses have been necessary in the past to partition phenotypic variance into the various genetic and environmental components . Plant sOryza sativa is a selfing species with extensive genomic resources, making it a useful model system to test quantitative genetic theory. It is a major food crop that is mostly grown under irrigated or lowland rain-fed conditions, where standing water and anaerobic soil conditions are at least intermittently present  and nutrient deficiency . These problems, in turn, exacerbate drought stress in plants. Thus, rice accessions adapted to upland conditions have been under additional selection pressure for tolerance to aluminum toxicity and nutrient deficiency.Cultivated rice  present . An addi present  that leajaponica, particularly tropical japonica, cultivars are particularly resistant (Root architecture is an important determinant of drought tolerance in rice. Accessions successfully grown under rain-fed (rather than irrigated) conditions tend to have relatively long and thick roots (esistant . AccessiO. sativa accessions and a dense set of single-nucleotide polymorphisms (SNP), aus and indica subpopulations, they did not detect any signal in tropical japonica despite significant overall variation in root growth. To determine if this result reflects a depletion of additive genetic variance under selection, we set out to build on this work. We first recapitulated the previous analyses using a new, ten-fold denser, genotyping platform  analyzed by tropical japonica accessions . The Al treatment in the latter experiment was conducted as before, but the duration was extended from three to six days, with an average of eight replicates per accession under each treatment. All plants were raised in a growth chamber .All experiments involved measuring root traits on replicates of genetically identical individuals (homozygous accessions). The plants were grown either in control or aluminum-containing media. This experimental structure informed our modeling approach. We sought to concurrently estimate contributions of genotyped SNPs, total genotypic effects, and random environmental fluctuations to overall phenotypic variance. In addition, in the analyses of the original aus and tropical japonica populations, the augmented tropical japonica, and the new single-year measurements) separately. The single-year experiment measured two root traits . We included them together in a multi-trait model, but analyzed the Al treated and control sets separately. The other experiments measured only total root length, but we modeled the treated and control measurements as separate traits. However, because the treatments were applied to different individual plants, the error covariance between the two pseudo-traits was set to exactly zero. Genetic covariances were estimated from data in all models, since the same accessions were subjected to both treatment and control conditions.We fitted multi-trait Bayesian hierarchical models  to estimt distribution with three degrees of freedom to dampen the effects of outliers  take the following form:outliers  for the t prior distribution on t). We repeated all analyses with the degrees of freedom set to 1000 (making the prior close to Gaussian) with the same results. This is likely because we work within populations, in the absence of deep population structure.The marker effects enter through the eigenvectors n method . We are ct model . In thisThe covariance matrices https://github.com/tonymugen/MuGen.Detailed model descriptions are listed in the documentation provided in the Supplemental File 1. This supplemental file also includes the raw phenotypic data, scripts we used to manage the raw data, Markov chain convergence diagnostics, and post-processing and plotting of the results. The analyses were implemented in C++. The source code is included in the Supplemental File 1. The underlying library is also available from p-th trait from the total marker effects estimated in our models:t prior, thus The hierarchical model allows us to estimate heritabilities. Narrow-sense heritability  is the fe.g., The s” e.g., . The sums” e.g., .Our models were fitted using a Markov chain Monte Carlo approach, resulting in posterior samples of parameters. We used calculated heritabilities for each sample, yielding numerical approximations of posterior distributions of these statistics. Summaries of these distributions are plotted in the relevant figures.https://github.com/tonymugen/GWAlikeMeth. This is a maximum-likelihood method, first fitting the mixed modelμ is the overall mean, Because full MCMC Bayesian model fitting is computationally demanding, we did not attempt to fit individual SNP effects within that framework. In addition, treated to control root length ratio  between the predicted and the observed values were employed as accuracy measurements. To calculate summary statistics, we transformed raw correlation values using Fisher’s z transformation . We ran Beagle v4.1 . To see if any individual SNPs are associated with either trait, we used the posterior modes of accession effects , but did not detect any new associations. We did not unearth any associations in tropical japonica , and no associations of SNPs with root length traits under Al treated or control conditions in either population.We find that the heritability contributed by all markers considered together accounts for less than half of overall genetic variance in the pulation . This dor stress  despite tropical japonica sample, bringing the total to 169. These lines were already genotyped using HDRA . To increase confidence in our estimates of accession means , we increased the number of replicates per line (eight on average). We performed all experiments at the same time, eliminating the year effect as a potential confounding variable. We measured two root traits: total and longest root length (see Methods for details) and included them together in a hierarchical Bayesian model (see Methods for details). However, we fit the model to the Al-treated and control data sets separately.The estimates on a larger panel of aus population increases the fraction of genetic variation explained by markers  interval: ) between control and treated root lengths in our initial experiment. Therefore, we increased the duration of aluminum treatment to put extra stress on the plants. The longer treatment did reduce the genetic relationships between treatment and control, although the correlations remained fairly high: 0.770  for total root length (the trait measured in the previous set of experiments) and 0.816  for longest root length, closer to the correlation observed in aus .Aluminum treatment of individuals from the  markers . This isDespite all these changes in experimental protocol and analysis, we see the same low marker heritability despite the high fraction of the phenotypic variance explained by total genetic effects . No singtropical japonica is correct, we expect that the genotyped SNPs would be poor predictors of phenotypic values. To test this, we implemented a two-step genome prediction scheme, using the posterior modes of accession means generated in the last experiment and used a separate implementation of a penalized regression on genotypes . On the other hand, if there are only one or a few loci that drive trait variation and reside in a region not tagged by our SNP collection, we should see a two or more modes in the phenotypic distribution, particularly in the last experiment where overall heritability is high . Even if these variants are in complete LD with ungenotyped low-frequency causal polymorphisms, we have no power to estimate their effects and thus such tag SNPs would not account for any phenotypic variance. This is true even if the effect of allele substitution is large, since the power to detect the contribution of the locus declines with allele frequency.Models of directional selection on quantitative traits predict genetic architectures dominated by loci with low-frequency alleles under some parameter combinations (tropical japonica is correct, each accession should have a unique set of causal variants. Some would have a positive effect, some would be negative. The balance would then determine the overall genotypic value of the individual line. This, in turn, implies that most regions of the genome can contribute to phenotypic variance. We indeed see some evidence of this: introgressions from indica and aus populations reduce total root length of tropical japonica accessions, particularly under aluminum stress (tropical japonica into indica increase relative root length under aluminum stress, consistent with our hypothesis.If our conjecture that low-frequency alleles underlie root traits in m stress , and theAlthough the low-frequency alleles may not individually contribute much to within-population variance, they should be detectable in biparental crosses. This is because allele frequencies of the causal variants present in these lines will be 50% and thus at high enough frequency to measure. Indeed, multiple quantitative trait locus mapping studies found loci contributing to root length under various conditions (Our results shed some light on a fundamental question in quantitative genetics. They also should be taken into consideration when designing breeding strategies to improve productivity of rice grown in aerobic soils under water-limited conditions. The upland cultivation method has been historically low-yielding (Our study highlights the importance of detailed genome-enabled investigations of polygenic traits under selection to shed light on fundamental evolutionary questions and guide practical artificial selection decisions. We hope that it will stimulate further analyses of such traits in agriculturally important plants, taking advantage of sophisticated experimental designs and increasing availability of deep whole-genome DNA sequence data.


Little information is available on the application of marker-trait association (MTA) analysis for traits related to drought tolerance in smooth bromegrass. The objectives of this study were to identify marker loci associated with important agronomic traits and drought tolerance indices as well as fining stable associations in a diverse panel of polycross derived genotypes of smooth bromegrass. Phenotypic evaluations were performed at two irrigation regimes  during 2 years; and association analysis was done with 626 SRAP markers.The results of population structure analysis identified three main subpopulations possessing significant genetic differences. Under normal irrigation, 68 and 57 marker-trait associations were identified using general linear model (GLM) and mixed linear mode1 (MLM), respectively. While under deficit irrigation, 61 and 54 markers were associated with the genes controlling the studied traits, based on these two models, respectively. Some of the markers were associated with more than one trait. It was revealed that markers Me1/Em5–11, Me1/Em3–15, and Me5/Em4–7 were consistently linked with drought-tolerance indices.Following marker validation, the MTAs reported in this panel could be useful tools to initiate marker-assisted selection (MAS) and targeted trait introgression of smooth bromegrass under normal and deficit irrigation regimes, and possibly fine mapping and cloning of the underlying genes and QTLs.The online version contains supplementary material available at 10.1186/s12870-021-02891-0. Bromus inermis Leyss.) is a long-lived and cool-season grass species [Smooth bromegrass  . Two appIn order to avoid identifying spurious associations between markers and traits and also to avoid of both types of error (types I and II) in association analysis, it is necessary to evaluate the population structure and use from a mixed-model approach , 25, 26.Lolium perenne) the application of association mapping for some traits such as flowering time, leaf length, carbohydrate content, submergence tolerance, salinity and drought tolerance has been evaluated [Festuca arundinacea), SSR loci related to agronomic traits [Onobrychis viciifolia) [In recent years, the application of association analysis in forage grasses is discussed in several reports. In perennial ryegrass  . In orchiifolia) , rust reiifolia) , and heaiifolia) . Such stSignificant differences were observed between irrigation regimes for most of the measured traits. Except for flag leaf length (FLL), flag leaf width (FLW), panicle length (PL), and winter growth vigor (WGV), the magnitude of mean performance was significantly decreased for all of the evaluated traits, under water-deficit condition. Dry matter yield (DMY) was decreased by deficit irrigation 42% on average Table .Table 1Phenotypic coefficient of variation (PCV) showed a range from 4.89% for plant height (PH) to 23.77% for number of stems per plant (NS) under normal irrigation and from 6.89% for days to anthesis (DA) to 27.42% for NS under deficit irrigation Table . GeneticThe estimates of broad-sense heritability for each irrigation regime are given in Table P values, respectively . The maximum value of DK obtained at K = 3, suggested that there were three subpopulations in the smooth bromegrass panel  68 SRAP markers showed significant associations with means of the studied traits, at the 0.01 probability level (Table SR2) of an individual trait explained ranged from 11.75 to 31.32% (Table SR2) of a trait explained varied from 9.89 to 26.28%  was separately conducted based on both GLM and MLM models. Under normal irrigation, based on the GLM model . This low ractions , 47. Theractions  and Sun ractions  in tall Based on the results of GLM and MLM models, some markers had simultaneously significant associations with more than one trait. These markers may be effectively used to improve several traits, concurrently , 34. MulDetermination of the genetic basis of drought tolerance requires correlating the occurrence of molecular markers with phenotypic scores for prediction of DNA genomic regions which involves effective factors on the response of plants . Marker–Most of the MTAs were different under normal and deficit irrigations, indicating that the environmental factors have affected these associations . These rIn conclusion, the efficiency of association analysis approach as a powerful tool for identifying and detecting genes and markers linked to complex traits of agricultural and economic importance was illustrated. Satisfactory levels of polymorphism were observed for the studied traits in the polycrossed population. Three subpopulations were identified in smooth bromegrass genotypes; and 90 significant MTAs were detected using GLM and MLM models, under contrasting water conditions. Among these, three MTAs were identified for drought tolerance. Moreover, it was demonstrated that SRAP markers can be used in the future breeding programs to enhance drought tolerance of smooth bromegrass. Some SRAP markers were associated with the key agronomic traits of this species. Environmental specificity of MTAs shows that genotype × environment interactions are effective on association analysis; nevertheless, 30 and 21 MTAs showed significantly stable expression across two irrigation regimes based on GLM and MLM models, respectively. The markers identified in the present study are useful genomic resources for MAS in the future breeding programs of smooth bromegrass.A replicated nursery of smooth bromegrass (containing 1000 samples) was established at Isfahan University of Technology Research Farm in 2006. Some of these plant materials were provided by the Hungarian Institute for Agrobotany (HIFA), Tapioszele, Hungary. The Iranian ecotypes were natural ecotypes collected from wide geographical areas of Iran by a team which are specialist in the field of grass species. These samples were evaluated at first in the research center of Fozveh, Isfahan, Iran. After formal identification and verification of them, these ecotypes were used for research projects of Isfahan University of Technology (IUT).Bromus inermis). These 36 genotypes were randomly selected from polycross progenies of a set of 25 parental genotypes  during 2 years. This region has a mean annual temperature of 14.6 °C and mean annual precipitation of 141 mm, generally without rain during the summer, making supplemental irrigation necessary for growing crops during this period.During the year that plants were established (2013) no data was recorded. Days to panicle emergence (DPE), days to anthesis (DA), plant height (PH), and winter growth vigor (WGV) were measured as mentioned in our previous studies , 55. FlaFive selection indices including tolerance index (TOL) , mean prsi designates the yield of the ith genotype grown under deficit irrigation, Ypi designates that of the ith genotype grown under normal irrigation, Yms is the yield mean over all genotypes grown under deficit irrigation, and Ymp is the yield mean over all genotypes grown under normal irrigation.where YμL, using a BIO-RAD thermocycler. Each PCR reaction was consisted of 1.5 μL of DNA, 1 μL of forward primer, 1 μL of reverse primer, 5 μL of master mix (Amplicon), and 1.5 μL of distilled water. In SRAP analysis, samples were exposed to the following thermic profile: the first five cycles were run at 94 °C for 1 min (denaturing), 35 °C for 1 min , and 72 °C for 1 min (extension). Then the annealing temperature was raised to 50 °C for another 35 cycles, followed by another extension step of 10 min at 72 °C. Electrophoresis on 12% non-denatured polyacrylamide gels was used for separation of amplified products; and then the products were stained by AgNO3 solution [Genomic DNA was extracted from young leaf tissues according to the modified method of Murray and Thompson . The quasolution .2b) was estimated for both irrigation regimes as described by Nguyen and Sleper [Data were tested for normality by Kolmogorov–Smirnov test and homogeneity of variance was tested by Bartlett test. Analysis of variance was performed for the normal and water-deficit irrigations separately, based on the split-plot in time (year) model, using Proc GLM of SAS release 9.4 . Componed Sleper :\documeσ2g is the genotype, σ2gy is the genotype × year, σ2rg is the genotype × rep, and σ2e is the residual variance, y is the number of years, and r is the number of replicates. The level of genetic variation was estimated with the calculating of phenotypic coefficient of variation (PCV) and genetic coefficient of variation (GCV) as follows:In which, p is the standard deviation of the phenotypic variance, σg is the standard deviation of the genotypic variance, and μ is the phenotypic mean [where σpic mean .Polymorphic SRAP markers were scored as binary data with presence (1) or absence (0). For each of the SRAP markers, the following indices were computed. Polymorphism information content (PIC) was determined according to the formula of Roldán-Ruiz et al. :\documei is the frequency of the amplified allele, and (1-fi) is the frequency of the null allele. Resolving power (RP) was estimated as:where i is the ith primer, fMarker index (MI) was calculated according to Powell et al. :\documei is the total bands for the ith primer, and bi is the percentage polymorphic bands of the ith primer.where NK. delta k approach described by Evanno et al. [Structure analysis and stratification of the studied population into subpopulations with different genetic structures was done based on SRAP marker data in STRUCTURE software version 2.3.4 . This ano et al.  was usedo et al. .P-values for marker–trait associations, using TASSEL version 4.2.1 [Association analysis was run by both GLM and MLM  to calcuon 4.2.1 . The pheon 4.2.1  and was on 4.2.1 .Additional file 1.


Manihot esculenta Crantz) is a clonally propagated staple food crop in the tropics. Genomic selection (GS) has been implemented at three breeding institutions in Africa to reduce cycle times. Initial studies provided promising estimates of predictive abilities. Here, we expand on previous analyses by assessing the accuracy of seven prediction models for seven traits in three prediction scenarios: cross-validation within populations, cross-population prediction and cross-generation prediction. We also evaluated the impact of increasing the training population (TP) size by phenotyping progenies selected either at random or with a genetic algorithm. Cross-validation results were mostly consistent across programs, with nonadditive models predicting of 10% better on average. Cross-population accuracy was generally low (mean = 0.18) but prediction of cassava mosaic disease increased up to 57% in one Nigerian population when data from another related population were combined. Accuracy across generations was poorer than within-generation accuracy, as expected, but accuracy for dry matter content and mosaic disease severity should be sufficient for rapid-cycling GS. Selection of a prediction model made some difference across generations, but increasing TP size was more important. With a genetic algorithm, selection of one-third of progeny could achieve an accuracy equivalent to phenotyping all progeny. We are in the early stages of GS for this crop but the results are promising for some traits. General guidelines that are emerging are that TPs need to continue to grow but phenotyping can be done on a cleverly selected subset of individuals, reducing the overall phenotyping burden.Cassava ( Accuracy is generally similar across breeding populations.Data sharing across programs improves predictions in some circumstances.Accuracy across generations is sufficient for rapidcycling genomic selection (GS) on several traits.Phenotyping small numbers of progeny can have a large impact on prediction accuracy.Prospects for GS in cassava are good and improving.CASSAVA, a root crop with origins in the Amazon basin  and highly heterozygous non-inbred crop that is propagated vegetatively by farmers using stem cuttings, though most genotypes flower and can be used to produce botanical seeds from either self- or cross-pollination. Among the most important traits targeted for improvement are storage root yield, dry matter content (DM), starch content, tolerance to postharvest physiological deterioration, carotenoid content, and resistance to pests or diseases   markers genome-wide  assumes an infinitesimal genetic architecture . In contrast, models like BayesB alter that assumption, putting emphasis on major-effect loci and variable selection  to increase the rate of genetic improvement in cassava and unlock the full potential of cassava production. The project is currently in the early stages of implementing GS at three African research institutes: the National Crops Resources Research Institute (NaCRRI) in Uganda, the National Root Crops Research Institute (NRCRI) in Nigeria, and the IITA, also in Nigeria.There are ongoing efforts within the Next Generation Cassava Breeding project , root number (RTNO), shoot weight (SHTWT), harvest index (HI), severity of CMD (MCMDS), and plant vigor. We compared the performance of seven GS models for these traits in each of the breeding programs.One important topic in GS concerns the feasibility of prediction across generations and across TPs from different breeding populations or programs. To increase the rate of gain achievable by GS, prediction models will need to accurately rank unevaluated progenies rather than genotypes contemporary with the TP. It is well known that recombination and divergence relative to the TP associated with recurrent selection reduces the accuracy of cross-generation prediction, making this kind of prediction a major challenge for GS Jannink, . AccuracFinally, in a typical scenario, a GS program will phenotype all selected materials and a subset of the unselected material to update the training model. We further investigated the impact of phenotyping different sized subsets of materials for the TP update. We compared random subset selections to selections based on a TP optimization algorithm  collection, which comprises 709 elite and historically important breeding clones and a few landraces that have been collected starting in the 1970s. These materials have also been previously described in Okechukwu and Dixon , Ly et aIn addition, two generations of GS progeny were analyzed . The parFinally, in 2014, a crossing block was planted with 89 selected C1 parents, which generated 1648 GS Cycle 2 (C2) seedlings in 242 full-sib families. The Cycle 2 families had a mean size of 6.8 individuals .Seven traits were analyzed in this study. Plant vigor was recorded as 3 = low, 5 = medium, and 7 = high 1 mo after planting at IITA and NRCRI and 3 mo after planting at NaCRRI. We used the across-season average MCMDS for our analyses; this was the mean of measurements taken at 1, 3, and 6 mo after planting, on a scale of 1 (no symptoms) to 5 (severe symptoms). Dry matter content was expressed as a percentage of dry root weight relative to fresh root weight (RTWT). At IITA, DM was measured by drying 100 g of fresh roots in an oven, whereas at NRCRI and NaCRRI, the specific gravity method ; the number of plants harvested per plot was included as a covariate; the vector c and the corresponding incidence matrix cloneZ represented a random effect for the clone where c ~ NZ and the random effects vector r ~ NZ effects vector b ~ N, which was nested in location–year, with s ~ NZ and the effects vector r ~ NZ and the effects vector b ~ N was used instead of the number harvested as a cofactor. This was done to correct for differences in plot sizes.ĉ), which represents an estimate of the total genetic value  for each individual, was extracted. The EGVs were de-regressed by dividing by their reliability lmer function of lme4 package .For the clone effect, the best linear unbiased prediction (BLUP)  were also removed. Only biallelic SNP markers were considered for further analyses. We used a combination of custom scripts and common variant call file  and the accumulated predicted values for that repeat.To obtain unbiased estimates of prediction accuracy, we used a  Kohavi, . In brieIn this study, we compared the accuracy of genomic prediction via seven methods that are briefly described below. These methods differ in their assumptions about genetic architecture and whether the prediction being made represents a genome estimated breeding value , including 25 replications of fivefold cross-validation, crossgeneration, and cross-population prediction.y = Xβ + gZ + ε. Here, y is a vector of the phenotype and β is a vector of fixed, nongenetic effects with the design matrix X. The vector g is a random effect, the BLUP, which represents the GEBV for each individual. Z is a design matrix indicating observations of genotype identities, and ε is a vector of residuals. The GEBV is obtained by assuming g ~ N. The genomic relationship matrix used in the GBLUP model described above can be considered as a parametric (additive genetic) kernel function and exists as a special case of RKHS  parameter that determines the rate of decay of correlations among individuals. Because this is a nonlinear function, the kernels we used for RKHS could capture nonadditive as well as additive genetic variation. Thus the BLUPs from RKHS models represent genome estimated total genetic values rather than GEBVs.where emmremlMultiKernel function in the EMMREML package . Second, we used the t and double-exponential distributions respectively, which are both distributions with thicker tails and greater density at zero. Both BayesB and BayesCpi are variable selection models because the marker variances come from a two-component mixture of a point mass at zero and either a scaled-t distribution (BayesB) or a normal distribution (BayesCpi). Fitting BayesB and BayesCpi begins by estimating a parameter pi, representing the proportion of markers with a nonzero effect. We performed Bayesian predictions with the R package BGLR  equal to 300. We implemented RF with the randomForest package in R  is a machine learning method used widely in regression and classification Breiman, . The usescale function in R and were then used to construct a matrix of Euclidean distances between models. Distance matrices were used as an input for hierarchical clustering using the Ward criterion implemented in the hclust R function . The exception was for RF, where correction for location and blocking factors is not supported. For RF prediction, we used the same de-regressed EGVs as for cross-validation. The software and parameters used were the same as already described. The design model was the same as that described for IITA above.We evaluated the impact on cross-generation prediction accuracy of phenotyping different size subsets of the unselected C1 . We selected subsets of C1 using two methods: randomly and with a genetic algorithm implemented in the R package STPGA  for selecting the “optimal” training set. The genetic algorithm implemented by STPGA is used to rapidly find the training set that minimized the selection criterion . Cross-population predictions were made with the prediction models described above and followed the two-step approach as described above.We selected optimized subsets of the combined datasets with a genetic algorithm implemented in the R package STPGA , as there was between GG and UG , as measured by the mean of the diagonal of the genomic relationship matrix, was similar for all populations, ranging from 0.933 in GG to 0.965 in C1. The mean rate of heterozygous loci was also similar between populations, ranging from 0.15 to 0.17. There was no notable decrease in heterozygosity or increase in the inbreeding coefficient from GG to C1 or from C1 to C2 , lowest for NRCRI (mean = 0.13), and similar for the IITA GG, and NaCRRI TPs. Averaging across populations, broad-sense heritability was highest for MCMDS (0.57), followed by HI (0.43) and DM (0.39). However, broad-sense heritability was generally low for yield components .We tested seven genomic prediction models that differed in their extent and the kind of shrinkage, which is relevant in modelling different genetic architectures, and in their ability to capture nonadditive effects .n = 899), the mean predictive accuracy values across methods ranged between -0.02 for plant vigor and 0.27 for HI. For NaCRRI (n = 411), the mean predictive accuracy values ranged between 0.23 for SHTWT and 0.46 for HI. Meanwhile, the predictive accuracy values for GG (n = 709) ranged between 0.22 for plant vigor and 0.66 for DM.Overall, breeding populations exhibited differences in the cross-validated prediction accuracies between methods and across traits ) and the lowest predictive accuracy was found for vigor (multi-kernel RKHS (–0.03)).r = 0.50). In this population, CMD had the overall highest predictive accuracy across traits, whereas SHTWT exhibited the lowest predictive accuracy .In the NaCRRI population, the multikernel RKHS model showed the highest predictive accuracies for all traits except for CMD, for which BayesB showed the highest value .The average predictive accuracy with the combined GG + NR full set as the training set with the GBLUP model was consistently lower for all the traits than the average GBLUP cross-validation results . Furthermore, the subsets selected by STPGA to predict the NaCRRI (UG) validation set gave, for all traits and all subset sizes, lower predictive accuracies than the GBLUP cross-validation model , the optimized STPGA datasets gave better prediction accuracies than the same sized random sets. As the optimized STPGA dataset increased in size, the predictive accuracy did not increase, except for RTNO, where the highest predictive accuracy was found when the TP size was 1200.When the combined GG + UG full training dataset was used to predict the NRCRI TP, Random Forest and RKHS prediction models performed better for RTWT, SHTWT, RTNO, and plant vigor. Bayesian models gave better predictive accuracies for MCMDS and DM. For plant vigor, MCMDS and DM, the combined UG+GG full dataset gave better predictive accuracies than the GBLUP cross-validation model . For prediction of the NRCRI TP, the optimized STPGA selected datasets gave better predictive accuracies for plant vigor, RTWT, RTNO, and SHTWT than the combined UG+ GG full training dataset.n = 900 and n = 1200) and CMD (n = 900), the optimized datasets gave higher predictive accuracies than the random datasets. For plant vigor, CMD resistance, and DM, the selection of optimized datasets with STPGA gave better predictive accuracies than the GBLUP cross-validation model.To predict the NRCRI TP for all traits except RTNO  . For all traits except MCMDS and DM, the optimized STPGA subsets gave higher predictive accuracies than the combined UG+NR full training dataset.The predictive accuracy results of traits in the GG dataset using the full training set (UG+NR) varied across methods. Whereas Bayesian methods gave better predictive accuracy values for MCMD and plant vigor, RKHS performed better for DM, HI, RTWT, and SHTWT. The combined (UG+NR) full training dataset for predicting the GG population gave lower predictive accuracies than the GBLUP cross-validation model for all traits. The GBLUP cross-validation model also gave better predictive accuracies for all the traits than the random and optimized STPGA datasets. The optimized STPGA datasets gave better predictive accuracies than the random sets for all traits except for plant vigor and for DM  in the STPGA of different sizes for the prediction of the NR set with GG + UG. Similarly, we found a significant enrichment of the NR population (p < 0.001) in the STPGA of different sizes for predicting the GG set with the UG-NR. On the contrary, we found no significant enrichment of any population in the STPGA-optimized sets predicting the UG population.Additionally, we tested if there was differential enrichment in the optimized STPGA training set of any of the populations relative to the source sets. We found a significant enrichment of the GG population  or GG + C1 (0.19 ± 0.02). The accuracy was lower on average when we predicted C2 with GG (0.11 ± 0.01) than when we predicted C1 with GG (0.17 ± 0.02). Accuracy was lowest for both plant vigor and RTWT (0.06 ± 0.005) and was highest for MCMDS (0.32 ± 0.03) and DM (0.38 ± 0.01). Most prediction models performed similarly, as shown by the averaged accuracy across traits and training–test combinations, with RF performing worst (0.08 ± 0.01) and BayesA and BayesB performing best (both 0.20 ± 0.03). For MCMDS, we found that prediction accuracy was greatest with BayesA and BayesB .Given the constraints of breeding programs described above, it was necessary to select samples of C1 that were optimized for predicting the parents of C2, rather than the C2 themselves. Despite targeting the parents of C2, we used selected training sets to predict C2, thus simulating the addition of phenotypes to the training set. Because of this, we compared the accuracy of subsets of C1 predicting C2 to the accuracy of predicting the parents of C2. As the number sampled increased from 200 to 2400, averaging across traits and methods for subset selection (STPGA and at random), accuracy increased by 120 and 105% when predicting C2 and the parents of C2, respectively. The increase in accuracy was smaller when we included the 709 GG clones in the prediction, increasing only by 43 and 36% respectively when predicting C2 and parents of C2 (Supplementary Table S4).t = 6.29, df = 4458, p < 0.0001) than random sampling. Broken down by validation set, STPGA was significantly better than random for predicting the parents of C2  but was not significantly better for predicting C2 .The STPGA approach consistently selected training datasets with a lower expected mean PEV on the test set than random sampling, across training set sizes . Further, using STPGA to select clones for phenotyping gave 13% better accuracy on average  and to the cross-validation accuracy within the test set . When predicting C2, which was our primary goal, the subsets were almost always inferior to the full set, with the exceptions of the middle sizes for RTWT, but the advantage was very small (The correlation between the selection criterion (mean PEV) used by STPGA and the training set size is strong for all traits (range = –0.57 to –0.61). Aside from simply increasing the TP size, we wanted to assess the extent to which the mean PEV could be used as a predictor of the achievable accuracy. Regression of prediction accuracies for each sample (regardless of whether it was selected randomly or by STPGA) on mean PEV explained between 8% (RTNO) and 46% (DM) of the variance in accuracy. Multiple regression including mean PEV and training set size as predictors showed PEV to be the more significant predictor . In fact, training set size was not a significant explanatory variable for RTWT or RTNO .www.nextgencassava.org, accessed 15 Aug. 2017) aims to assess the potential of genomic selection in cassava to reduce the length of the breeding cycle and increase the number of crosses and selections per unit of time. The project is implementing GS in three breeding programs from Nigeria and Uganda, with genotypic and phenotypic data from TPs and two cycles of selection available on a database dedicated to cassava .The Next Generation Cassava Breeding Project , BayesA, BayesB, BayesCpi, Bayesian LASSO, and RF for yield components  and CMD resistance data from the breeding programs.In general, the performance of predictive models is known to be conditional on the genetic architecture of the trait under consideration  could account for the observed differences. We note the estimate of zero heritability for RTWT, RTNO, and SHTWT in the IITA C2 and acknowledge this is likely to account for the quality of cross-generation prediction in that dataset.Triticum aestivum L.) for grain yield, an additive and epistatic trait, in which RKHS, radial basis function neural networks, and Bayesian regularized neural networks models clearly had a better predictive ability than additive models like BL, Bayesian ridge-regression, BayesA, and BayesB , indicating that the three breeding populations share genetic material. Despite this, our results indicate that the prospect for sharing data across Africa to assist in GS is limited to certain traits (most notably MCMDS) and populations. Indeed, obtaining a larger training set by combining TP did not always lead to higher prediction accuracies than what could already be achieved within that population, as shown by the cross-validation results.Though the cross-validation results within the breeding programs are encouraging for the use of GS, prediction values across breeding programs were fairly low. Mean FIn animal models, prediction with multibreed populations has also been shown to be poor, with most of the observed accuracy caused by population structure , our results indicated, in our judgment, that accuracy should be sufficient for DM, MCMDS, and, to a lesser extent, HI . AlthougWe noted that RF and RKHS performed poorly across generations; this is a result that makes sense, given that the predictability of epistatic and dominant interactions declines with recombination  by Endelman et al. . Predictions of total genetic value for yield traits for selection of clones that will be tested as potential varieties could then be done after clonal evaluation data become available on at least a subset of contemporary genotypes. Further trials will be necessary to determine whether there is an advantage to this type of strategy.The primary promise GS offers to cassava breeding is the ability to select and recombine germplasm more frequently and thus hopefully speed the rate of population improvement while combining a myriad of quality, disease, and yield-related traits into a single genotype that can be released as a variety. The applicability of the results from the different prediction models in cassava is then dependent on whether the goal is the prediction of breeding values of progeny or the selection of advanced lines for testing as varieties.We are still in the early stages of GS in this crop, but the results are promising, at least for some traits. The TPs need to continue to grow and quality phenotyping is more critical than ever. However, general guidelines for successful GS are emerging. Phenotyping can be done on fewer individuals, cleverly selected, making for trials that are more focused on the quality of the data collected.Click here for additional data file.Click here for additional data file.Click here for additional data file.