Genomic prediction accuracy can be significantly increased by model calibration across multiple breeding cycles as long as selection cycles are connected by common ancestors.2 lines were genotyped with 16 k SNPs and each year testcrosses of 260 S2 lines were phenotyped in seven or eight locations. The performance gap between GBLUP and PBLUP increased significantly for all traits when model calibration was performed on aggregated data from several cycles. Prediction accuracies obtained from cross-validation were in the order of 0.70 for all traits when data from all cycles (NCS = 832) were used for model training and exceeded within-cycle accuracies in all cases. As long as selection cycles are connected by a sufficient number of common ancestors and prediction accuracy has not reached a plateau when increasing sample size, aggregating data from several preceding cycles is recommended for predicting genetic values in subsequent cycles despite decreasing relatedness over time.In hybrid rye breeding, application of genome-based prediction is expected to increase selection gain because of long selection cycles in population improvement and development of hybrid components. Essentially two prediction scenarios arise: (1) prediction of the genetic value of lines from the same breeding cycle in which model training is performed and (2) prediction of lines from subsequent cycles. It is the latter from which a reduction in cycle length and consequently the strongest impact on selection gain is expected. We empirically investigated genome-based prediction of grain yield, plant height and thousand kernel weight within and across four selection cycles of a hybrid rye breeding program. Prediction performance was assessed using genomic and pedigree-based best linear unbiased prediction (GBLUP and PBLUP). A total of 1040 SThe online version of this article (doi:10.1007/s00122-016-2756-5) contains supplementary material, which is available to authorized users. Secale cereale L.) is a small grain cereal used for food, feed and in growing demands also for ethanol and biomethane production (Geiger and Miedaner Rye (®) are available. A comprehensive expressed sequence tag (EST) resource was generated  within breeding cycles, i.e., predictionof genetic values of progeny derived from the same or related crosses within the breeding cycle in which model training is performed and (2) across breeding cycles, i.e., prediction of consecutive generations of progeny generated from crosses with variable levels of relatedness to current genetic material. Various studies have reported prediction performance that encourages the implementation of genome-based prediction in breeding programs. In a wide range of crops, prediction accuracies ranged from intermediate to high  showed that across-cycle prediction accuracy depended on the trait under study and the authors pointed out that within-cycle prediction accuracy was not suited as indicator for the performance of across-cycle prediction , prediction accuracies across subsequent cycles of selection were only slightly reduced for grain yield and dry matter content, compared to accuracies obtained with cross-validation within the same cycle when effects arising from population structure and choice of tester were modeled appropriately  to comparatively assess the prediction performance of pedigree-based and genomic best linear unbiased prediction within and across breeding cycles, (2) to gain insight into the main components driving prediction performance across subsequent breeding cycles, and (3) to develop recommendations for model training to obtain maximum across-cycle prediction accuracies.2) from subsequent cycles (Cycle 1 to Cycle 4) of a commercial hybrid rye breeding program. The four data sets comprised a total of 1416 S2 lines for which up to ten generations of pedigree information was available. To represent each selection cycle by the same number of progenies, 260 S2 lines were randomly chosen from each of the four data sets, resulting in 1040 S2 inbred lines and all subsequent representations of results are based on these 1040 S2 lines representing progenies from 430 crosses of 203 parental lines. Genetic relatedness between the four data sets is given through a minimum of eight and a maximum of 21 common parental lines . On average, two inbred lines  were derived per cross, with 400 crosses yielding five or fewer inbred lines. To obtain testcross seed, each S2 line was crossed to two out of eight F1 pollen-sterile testers  showing different levels of relatedness. Testers represent a gametic sample of the complementary heterotic seed parent pool. Plant materials described in this study are proprietary to KWS LOCHOW GMBH.The genetic material used in this study consists of four data sets of advanced-cycle inbred lines , plant height , and thousand kernel weight , with TKW measured in all trials with one replication only. Phenotypic data were analyzed following a two-stage approach. In the first stage, adjusted entry means for genotypes (testcrosses of S2 lines) were calculated separately for each location and for each of the two testers by standard lattice analysis (Utz h2) were calculated on a progeny-mean basis as described in method 1 of Estaghvirou et al. . Only high-quality SNPs with a GenTrain score ≥0.7 and a call rate ≥0.9 were used. SNPs with a minor allele frequency (MAF) < 0.01 or >10 % missing values were discarded, resulting in 10,416 useful SNPs. For 5607 SNPs the genetic map position was available . Missing values of mapped SNPs were imputed based on flanking markers using Beagle (Browning and Browning r2 (Hill and Robertson S2 lines we applied pedigree (PBLUP) and genomic (GBLUP) best linear unbiased prediction which differ in the variance–covariance structure used to model random testcross effects. The two models can be written asi using g and h) of individual 0, i.e., before selfing. For S2 lines derived from S1 plants we set To predict the testcross performance of SNCS = 208, 416, 624, and 832 (the latter only in CV3). CV2 and CV3 scenarios include all possible forward, as well as backward predictions in time. Variance components of PBLUP and GBLUP models were estimated by REML for each calibration set. For each CV scenario, prediction accuracy in validation set v was obtained by v was sampled . As rye is an outcrossing species with low ancestral LD, a rapid decline of LD was expected in this data set of S2 lines derived from many crosses of at least partially unrelated parents. Heatmaps of the expected (K) and realized (U) kinship coefficients of the 1040 S2 lines are given in Figure S3. Within each cycle, family substructures are visible, but the principal coordinate analysis based on marker data indicated no major population substructure except for one large family in Cycle 1 . The 5607 mapped SNP markers were equally distributed across the genome with SNP numbers varying between 457 on chromosome 7R to 1091 on chromosome 5R . LD decayed rapidly with 68 % of the marker pairs showing p < 0.01) between breeding cycles (Table g×l2) variance components were highly significant (p < 0.01) and estimates of σg×l2 were always smaller than the genotypic variance component. Trait heritabilities (h2) on a progeny-mean basis were intermediate to high . Averaged across the six possible single-cycle forward predictions in CV2.1 with sample size p < 0.01) was observed but it was mainly driven by the low relatedness and prediction accuracies of Cycle 1 and Cycle 4. For traits PHT and TKW correlations were not significant.The effect of relatedness of the calibration and validation set in the 12 possible single-cycle CV2.1 scenarios was assessed by calculating the Pearson correlation between ies Fig. . For GDYNCS = 208. Mean prediction accuracies increased slightly for all three traits when sampling was performed from multiple cycles compared to sampling from one cycle only . PBLUP accuracies were substantially lower  compared to average accuracies obtained with single-cycle CV2.1 scenarios and similar as (GDY and PHT) or higher than (TKW) the best of the 12 single-cycle CV2.1 predictions given in Fig. A major advantage of combining data from multiple cycles for training the prediction model lies in the increased sample size of the aggregated calibration set as compared to data from the most recent preceding cycle only. By increasing the calibration set size from its Fig. . At maxiNCS = 624 could not reach average within-cycle accuracies for any of the three traits, prediction accuracies in CV3 outperformed those of CV1 with NCS = 624 and even more so using the maximum possible population size NCS = 832.The effect of combining within- and across-cycle data for model calibration is shown in Table Evaluation of the potential of genome-wide prediction in plant breeding programs requires data sets that account for the specific properties of the employed selection schemes and populations. The data set employed here represents four advanced-cycle breeding populations of small effective population size with similar allele frequency spectra and extent of linkage disequilibrium. As the required time from recombination to the first performance test is five years, none of the four selection cycles comprised direct descendants of lines tested in earlier cycles. In contrast to recurrent selection on closed populations where pedigree relationships are reduced by half each generation, the relatedness of subsequent advanced-cycle plant populations depends on decisions made by the breeder with respect to the number of common parents and the influx of new genetic material. Thus, the relative advantage of genome- over pedigree-based prediction methods is difficult to assess theoretically and needs to be investigated with experimental data.We showed that the performance gap between GBLUP and PBLUP increased significantly for all three traits when model training was performed on aggregated data from several selection cycles, indicating that accuracy of prediction will increase as information accumulates over time. For GDY, both prediction models (PBLUP and GBLUP) yielded intermediate prediction accuracies within and across cycles. As the average family size was rather small for many crosses, the moderate difference between PBLUP and GBLUP accuracies for GDY was not surprising. When decreasing the number of markers in the GBLUP model from 10,416 to 500, prediction accuracies were quite stable for GDY (data not shown) indicating that genome-wide relatedness and not so much marker-trait associations in specific genomic regions had a strong influence on prediction accuracy of this trait. This was supported by a significant correlation between the level of relatedness of the validation and calibration set with the corresponding across-cycle prediction accuracies for GDY in CV2.1 . By increasing the sample size of the calibration set and modeling marker effects over several testers and years through data aggregation, not only an increase in mean prediction accuracy was achieved but also a slight reduction in prediction variance . Uncertainty of prediction is an important factor in optimization of breeding schemes but is often neglected in the discussion on the potential of genome-based selection. We conclude that the reduced variance of prediction is a further argument in favor of model training across several selection cycles.p < 0.01) and not significant for the other traits. This is in contrast to other studies where a strong linear relationship between average maximum kinship and prediction accuracy was found . When the breeding program advances, it can be assumed that selection cycles share fewer common ancestors. This was the case here with 8 (11) common parents of crosses for Cycle 4 and Cycle 1 (Cycle 4 and Cycle 2) compared to 18–21 common parents for the other pairwise combinations. This decrease in common ancestors over time was reflected in reduced kinship and significantly reduced accuracy when predicting lines from Cycle 4 with a model trained in Cycle 1. However, the relationship between average maximum kinship  and cumulated sample size of the calibration set . Mean prediction accuracies were very similar when sampling the same number of lines from one, two or three cycles, respectively. This indicates that the increase in prediction accuracy over cycles was mainly driven by an increase in sample size of the calibration set and that estimating marker effects based on testcrosses with more testers and evaluated in more years was of minor importance. With the given data it was not possible to separate the effects of across-cycle relatedness, genotype × year and genotype × tester interaction on prediction accuracy. We hypothesize that when averaging across two single-cross testers, specific combining ability effects can be assumed to be negligible. In addition, all S2 lines were evaluated in seven to eight locations in each year yielding very high progeny-mean heritabilities. Thus, we assume that genotype × location interactions within cycles could account to a large extent also for genotype × year interactions. The high precision of phenotypic data in our study might explain some of the discrepancies to studies on genome-based prediction in self-pollinating crops where merging data sets from subsequent progeny sets was rarely advantageous  larger sample size of the calibration set and ii) replication of alleles over years and testers, CV2 was performed with constant . Thus, our data provide an excellent base for investigating the effect of allocation of resources for maximizing selection gain from genome-based selection per unit time and budget.The effect of sample size and replication on GBLUP prediction accuracy was investigated in a simulation study by Lorenz  and a hiNCS = 624, CV2.3) and could be increased to 0.69–0.70 in CV3 (NCS = 832). Based on these results we conclude that genome-based prediction will be an important instrument in hybrid rye breeding to increase selection gain. How to implement genome-based prediction with maximum efficiency requires further research. The data employed here were taken from the first stage of a multi-stage selection scheme with strong priority on precision phenotypes and risk prevention in first selection steps Below is the link to the electronic supplementary material.


Caligus rogercresseyi are a main concern to the salmon farming industry due to associated economic losses. Resistance to this parasite was shown to have low to moderate genetic variation and its genetic architecture was suggested to be polygenic. The aim of this study was to compare accuracies of breeding value predictions obtained with pedigree-based best linear unbiased prediction (P-BLUP) methodology against different genomic prediction approaches: genomic BLUP (G-BLUP), Bayesian Lasso, and Bayes C. To achieve this, 2404 individuals from 118 families were measured for C. rogercresseyi count after a challenge and genotyped using 37 K single nucleotide polymorphisms. Accuracies were assessed using fivefold cross-validation and SNP densities of 0.5, 1, 5, 10, 25 and 37 K. Accuracy of genomic predictions increased with increasing SNP density and was higher than pedigree-based BLUP predictions by up to 22%. Both Bayesian and G-BLUP methods can predict breeding values with higher accuracies than pedigree-based BLUP, however, G-BLUP may be the preferred method because of reduced computation time and ease of implementation. A relatively low marker density (i.e. 10 K) is sufficient for maximal increase in accuracy when using G-BLUP or Bayesian methods for genomic prediction of C. rogercresseyi resistance in Atlantic salmon.Sea lice infestations caused by  Caligus rogercresseyi is the major sea lice species of interest in the southern hemisphere, while Lepeophtheirus salmonis is the major species of interest in the northern hemisphere. Both species affect Atlantic salmon  and rainbow trout (Oncorhynchus mykiss) [C. rogercresseyi parasitize farmed salmonids and wild fish in Chile and constitute one of the main threats for salmon aquaculture in one of the major salmon producing countries [Sea lice are common marine external parasites that belong to the order of Copepoda.  mykiss) . C. rogeountries , 3.Sea lice can cause skin lesions, osmotic imbalance, and increased susceptibility to bacterial and viral infections through suppression of host immune responses and damage to the host skin , 5. Sea C. rogercresseyi resistance in Atlantic salmon. Lhorente et al. [h2) of 0.32 for sessile C. rogercresseyi count on fins in Atlantic salmon, while Yáñez et al. [h2 of 0.12 for the same trait using pedigree and molecular information, respectively. These low to moderate heritabilities indicate that it is feasible to include these traits in the breeding program for Atlantic salmon.Different chemicals are used to control sea lice, but increasing resistance to antiparasitic drugs has been reported . An altee et al.  estimatez et al.  and Corrz et al.  estimateC. rogercresseyi. Similarly, Houston et al. [L. salmonis and observed polygenic inheritance for this trait also. The polygenic nature of these traits suggests that major quantitative trait loci (QTL) contributing to the genetic variance are unlikely and thus, that marker-assisted selection (MAS) may not be the most appropriate way to include molecular information for selection [Using a 50 K genotyping array, a recent study conducted by Correa et al.  providedn et al. , 18 usedelection . In suchelection . The difelection . Geneticelection –23.Several GS methodologies to predict GEBV have been proposed, which differ in prior assumptions on the distribution of the effects of the SNPs . For exaC. rogercresseyi resistance, using data from 2404 individuals and a 50 K genotyping array.Genomic selection has been tested with real data in salmonid species in a few studies –29 that C. rogercresseyi. The average number of fish per family was 22 and ranged from 9 to 24, and the average weight of fish was 274.9 g (SD = 90.6 g). The fish were tagged with passive integrated transponders, acclimated, and then distributed to three replicate tanks. The challenge test was carried out as described previously [Phenotype data were available for 2404 Atlantic salmon smolts from 118 families (i.e. progeny of 118 dams and 40 sires) from the breeding population of Salmones Chaicas, Xth Region, Chile. These individuals were experimentally challenged with eviously –16. Brieeviously . Experim® Axiom® myDesign™ Genotyping Array designed by Aquainnovo and the University of Chile. More details about the SNPs included in the 50 K array are in Correa et al. [Genotype data were available from a previous study . Brieflya et al.  and Yáñea et al. , 32.® Genotyping Solution Data Analysis Guide [p value less than 0.00001, an SNP call rate lower than 0.95 and a minor allele frequency lower than 0.01.The genotypes were quality controlled using the Affymetrix Genotyping Console and the SNPolisher R package following the Axiomis Guide . Additioy is a vector of phenotypes (lice count on fins), β is a vector of fixed effects , g is a vector of random additive polygenic genetic effects that follows a normal distribution ~X and T are incidence matrices, A is the pedigree additive relationship matrix, and e is the residual [The conventional pedigree-based approach, P-BLUP, was used as the control for genomic evaluations, and EBV for each individual were obtained using a linear mixed model implemented in BLUPF90 . The modresidual .A is replaced by a genomic relationship matrix G, as described by VanRaden [The genomic EBV (GEBV) for each individual were estimated using three different GS models: G-BLUP, Bayesian Lasso and Bayes C. G-BLUP was as implemented in the BLUPF90 software . G-BLUP VanRaden .α is a vector of random marker allele substitution effects and Z is the corresponding incidence matrix. The Gibbs sampler was run using 100,000 iterations with a burn-in of 20,000 iterations. Priors were drawn from double—exponential and scaled—inverse χ2 distributions, for Bayesian Lasso and Bayes C, respectively. Bayesian GEBV were estimated as the sum of the polygenic and marker effects.For Bayesian methods, marker and additive polygenic effects were estimated jointly using the following model implemented in the GS3 software :\documenPedigree (P-BLUP) and genomic (G-BLUP) heritabilities were calculated using the AIREMLF90 software  as folloh is the square root of the pedigree-based estimate of heritability [2) less than 0.2 and were homogeneously distributed across the genome were selected among the SNPs that passed quality control. Then, SNPs with a homogeneous distribution across the genome were added to the first 500 SNPs to create the 1 K panel. The same procedure was reiterated to create the 5, 10 and 25 K panels. Accuracies were then calculated for each model and SNP density, compared to those obtained with the P-BLUP model, and the relative increase in accuracy was assessed.The different models were compared using a fivefold cross validation scheme. Briefly, all genotyped and phenotyped animals were randomly separated into five validations sets, which were predicted one at a time by masking their phenotypes and using the remaining animals as training set to estimate the marker effects. Thus, for each validation run, the dataset was split into a training set (80%) and a validation set (20%). To reduce the stochastic effects, this cross-validation analysis was replicated 10 times. Accuracy was used to assess the performance of each model and was estimated as:tability , 38. To A total of 36,616 SNPs passed the genotyping quality control. An average lice count on fins of 5.1 (SD = 4.4) and an average final body weight of 281 g (SD = 92.8) were obtained. The average lice number per family ranged from 2.3 to 11.3. The pedigree-based estimate of heritability of lice count on fins was equal to 0.10, which is consistent with a previous study on the same population , while tL. salmonis resistance, for example, Tsai et al. [In all cases, prediction accuracies obtained with the GS models were higher than those obtained with the pedigree-based model, which had an accuracy of 0.41 (Table i et al.  reportedi et al. .Table 1AC. rogercresseyi resistance in Atlantic salmon. Moreover, it is the first study that evaluates Bayesian method performance for sea lice resistance using a high-density SNP array and different SNP densities in this species. We demonstrate that it is possible to increase the accuracy of breeding value predictions for C. rogercresseyi resistance using SNP information.We found that the three GS methods had similar GEBV prediction accuracies, in spite of the different priors used in each model. This is the first study that aims at evaluating the performance of GS methods for L. salmonis resistance and fillet color when using 22 K SNPs in an admixed population. For growth traits, Tsai et al. [L. salmonis resistance. A recent study in rainbow trout [Prediction accuracies obtained by using genome-wide marker information were higher than those obtained by using only pedigree information to account for the relationship between individuals. These results are in line with other studies that evaluated the performance of GS for different traits in Atlantic salmon , 27. Fori et al.  achievedow trout  reportedOur results show that SNP density had a moderate impact on prediction accuracy for all GS methods tested in this study, and that as few as 500 SNPs were sufficient to increase EBV accuracy over P-BLUP. Moreover, 10 K may suffice to obtain maximum increases in accuracy for this trait and this population.This study used real data from a breeding population and the results suggest that GS may be effective in improving resistance to this sea lice species. Further studies aimed at evaluating the use of low-density panels and imputation strategies are necessary to determine the minimum required SNP density for GS and thus reduce genotyping costs.C. rogercresseyi resistance in Atlantic salmon by using different densities of SNPs selected from a 37 K panel. By applying different genomic prediction approaches, we showed that as few as 500 SNPs were sufficient to increase the accuracy of EBV to a higher value than that obtained from pedigree-based methods. We found that the maximum increase in accuracy was obtained with 10 K SNPs when using G-BLUP and Bayesian methods.It is possible to improve prediction accuracy for


In recent years pleiotropy, the phenomenon of one genetic locus influencing several traits, has become a widely researched field in human genetics. With the increasing availability of genome-wide association study summary statistics, as well as the establishment of deeply phenotyped sample collections, it is now possible to systematically assess the genetic overlap between multiple traits and diseases. In addition to increasing power to detect associated variants, multi-trait methods can also aid our understanding of how different disorders are aetiologically linked by highlighting relevant biological pathways. A plethora of available tools to perform such analyses exists, each with their own advantages and limitations. In this review, we outline some of the currently available methods to conduct multi-trait analyses. First, we briefly introduce the concept of pleiotropy and outline the current landscape of pleiotropy research in human genetics; second, we describe analytical considerations and analysis methods; finally, we discuss future directions for the field. Most complex phenotypes are highly polygenic . Since 1.1.The term ‘pleiotropy’ was coined over 100 years ago by German scientist Ludwig Plate to describe the phenomenon of a hereditary unit affecting more than one trait of an organism . Since ta,b). In practice, fine-mapping and molecular studies are required to confidently distinguish between these different scenarios [In the case of biological pleiotropy, causal variants of different traits fall into the same gene or regulatory unit (e.g. transcription factor binding sites) . In GWASfigure 1cenarios .Figure c). GWAS will still pick up an association of the variant with the second trait, but this association will disappear when conditioned on the first. Causal inference can be achieved through Mendelian randomization studies, which have been widely used in genetic epidemiology [FTO gene with osteoarthritis (OA) [Mediated pleiotropy refers to the case where a variant directly affects one trait, which in turn affects another c. GWAS wemiology ,10–12. Atis (OA) , which wtis (OA) .d). A classic example of this is the human leucocyte antigen (HLA) region on chromosome 6. Due to its high gene density and extensive linkage disequilibrium (LD), GWAS signals within the HLA region are difficult to map finely. While the HLA locus has been associated with a range of diseases [Finally, cross-phenotype associations can also arise due to spurious pleiotropy. At the planning stage of a study, design artefacts may lead to inaccurate results. For example, ascertainment bias or misclassification of cases can both inflate genetic overlap estimates. At the analysis stage, causal variants in different genes may be tagged by the same GWAS variant d. A clasdiseases ,15–20, m1.2.In 2011, a systematic evaluation of associations reported in the NIHGR GWAS catalogue found that 4.6% of variants were associated with more than one trait . This nuDSP gene are associated with chronic obstructive pulmonary disease, as well as pulmonary fibrosis and lung function traits [ASTN2 gene have been shown to affect both risk to osteoarthritis [Many cross-phenotype effects are not surprising. For example, variants in the n traits . Others rthritis  and migrrthritis ,24. ThesUntil a few years ago, the focus of many consortial efforts was to combine datasets of one phenotype for large-scale GWAS and meta-analyses ,25,26. FThe establishment of genome-wide genotyped biobanks  and cohoOne challenge of the PheWAS approach is the high multiple-testing burden that grows as the number of traits and variants tested increases . AlthougInvestigating pleiotropy in human traits not only holds the potential to uncover additional associations, but could additionally help to redefine disease classifications. This is of particular interest in disorders for which the aetiopathology is unclear, and for which current diagnostic tools might be inadequate. For example, psychiatric conditions are highly comorbid, and until recently ,39 have 2.2.1.There are some practical considerations to be taken into account when selecting an appropriate method for multi-trait analysis.First, the type of data available will determine which statistical approach is applicable. Due to limitations of data sharing policies it might not be possible to obtain individual-level genotype data for all traits analysed.Second, the type and number of traits to include must be considered: some approaches require all traits to be continuous, while others also allow for dichotomous traits or a combination of both. Several methods, such as colocalization tests ,43 or geZ-scores of all independent, non-associated variants from two studies [Finally, if each trait is measured on a different set of individuals, sample overlap between each dataset will need to be accounted for. This has been implemented in several methods ,44,46. I studies , althoug studies –49.2.2.Pleiotropy analyses can be broadly classified into three categories according to the level at which they assess genetic overlap: genome-wide, regional and single variant.Genome-wide methods are currently only available for pairwise trait comparisons, and can be used as an initial assessment of the global genetic overlap between two traits.The latter two approaches aim to detect cross-phenotype effects at distinct genomic regions and at a single variant, respectively.Region-based methods bin variants into groups based on pre-defined criteria, such as LD-blocks or gene boundaries, and then test for cross-phenotype effects within each group. An advantage of such approaches is that they alleviate the multiple testing penalty incurred by single-point analyses; furthermore, they can increase power by combining information across biologically meaningful units.Since variant-level methods test each variant separately, they provide the highest resolution. On the other hand, they are less powerful in situations where each trait is associated with a different variant in the same functional unit, and might fail to identify these cross-phenotype effects unless all relevant variants are in at least moderate LD.The above analysis approaches can be further sub-divided based on their underlying statistical framework into univariate and multivariate. Univariate methods combine summary statistics of single-trait GWAS to search for cross-phenotype effects. This means that analyses can be carried out with each trait measured on a distinct set of individuals. Multivariate methods, on the other hand, jointly model all traits in a statistical framework, which requires that all individuals included in the study have phenotype information for all traits analysed. The statistical difference between uni- and multivariate methods is best illustrated by the example of linear regression analysis: for univariate regression, the response variable (i.e. the phenotype) will be a vector, with one data point for each individual in the study; for multivariate regression, the response variable will be a matrix, where each row represents an individual and each column represents one phenotype. Although there are exceptions, these categories are often analogous to distinguishing between methods requiring only summary data and individual-level information, respectively.2.3.Polygenic risk scores  were initially used in genetic epidemiology to test how well a set of variables could predict, or distinguish between, case-control status in a study sample –53. In tp-value threshold for variant inclusion (rather than using only genome-wide significant variants). One reason for this could be that many variants with a true effect on the phenotype did not reach genome-wide significance in the base study. This is especially likely for highly polygenic traits, for which only a fraction of the heritability can be explained by currently known risk variants.This framework can also be applied to two different traits ,36,54,55Genetic correlation (rg) captures the extent to which genetic factors influence the covariance of two traits. Multivariate methods for genetic correlation analysis include GCTA ,56, BOLTTCF2, for which the C allele confers increased risk for prostate cancer and decreased risk for type 2 diabetes [g. Conversely, in the case of disease traits, genetic correlation could be inflated due to ascertainment bias or misclassification of cases [More recently, a univariate method for genetic correlation analysis, cross-trait LD score regression (LDSC), requiring only summary statistics, has been developed ,59. Likediabetes . As for of cases .2.4.p-values below some threshold in that region. The statistical significance of the index can be calculated using two separate approaches for traits measured on overlapping or non-overlapping datasets, respectively.The pleiotropic region identification method (PRIMe)  defines gwas-pw) to enable simplicity of use for the pairwise comparison of GWAS summary statistics [both traits being associated with a given region, thus making it possible to distinguish from the scenario of one trait driving an observed signal.In 2013 Giambartolomei and colleagues described a Bayesian colocalization model to identify genomic regions of colocalizing expression quantitative trait loci (eQTL) and GWAS signals . This meatistics . The modatistics . It geneMultivariate methods for locus-based analysis also exist: Tang & Ferreira  extended2.4.1.The substantial drop in sequencing costs over the past decade together with the establishment of better reference panels for imputation have made association studies of low frequency and rare variants feasible ,71. MethWhile some of the multi-trait methods described above are applicable to both common and low-frequency markers –69, apprWu and Pankow extended univariate SKAT for the application to multiple continuous traits . AnotherIn adaptive weighting reverse regression (AWRR) , the gen2.5.p-value threshold and declare all variants that fall below this threshold for a group of traits as cross-phenotype associations [p-values will be missed. Consequently, a number of methods to statistically combine summary data for multiple traits have been developed  method that tests for the presence of two or more trait associations at a variant . This haZ-statistic at a variant [In a generalization of fixed-effects meta-analysis, all possible subsets of traits are evaluated to identify the one with the maximum absolute  variant . The app variant . The met variant .TOX gene missed by conventional meta-analysis [Zhu and colleagues developed two meta-analysis test statistics to detect cross-phenotype associations assuming homogeneous and heterogeneous effects across studies, respectively . The tesanalysis .A recently published method, MultiMeta, enables the joint analysis of summary statistics obtained from multivariate GWAS, such as multivariate LMM analysis (see §2.6) . MultiMeeach trait separately [The Multi-Trait Analysis of GWAS (MTAG) tool takes a slightly different approach to the above-mentioned methods: in a generalization of inverse variance weighted meta-analysis, it incorporates effect estimates from multiple traits and outputs adjusted effect estimates for parately . Sample 2.5.2.p-values of association with both the ‘principal’ and the ‘conditional’ trait fall below a certain p-value threshold [Conditional false discovery rate (cFDR) can detect variants associated with one ‘principal’ trait, given its hreshold . An extehreshold . Conditihreshold .p-values from two input studies, the method tests for an excess of shared signals and can be used to identify a list of variants with evidence of association for both traits.Asimit and colleagues developed a Bayesian approach that adjusts for sample size  differences between studies . Based o2.5.3.In metaCCA, a method based on canonical correlation analysis (CCA), single-trait summary statistics together with genotype data from a reference panel are used to reconstruct the genotype–phenotype covariance matrix for each study . Weighte2.5.4.In order to aid variant prioritization and fine-mapping, the integration of GWAS data and functional annotations (such as chromatin marks) as well as transcriptomic data has become popular –96. SomeThe first tool allowing for the simultaneous modelling of multiple GWAS and annotation data was GPA . The modFastPAINTOR, an extension to the single-trait fine-mapping algorithm PAINTOR , additio2.6.As the availability of large-scale genetic datasets with multiple phenotype measurements increases, the focus of method development for multi-trait analyses has shifted towards multivariate methods that use individual-level data rather than summary statistics .Table 2These approaches are generally more powerful than combining test statistics from univariate GWAS, as the inter-trait covariance can be accounted for ,118. In 2.6.1.One efficient way to deal with multivariate phenotypes is to first apply a dimension reduction technique that collapses the individual trait values, and then perform an association between genotype and this new set of variables. Principal component analysis (PCA) derives linear combinations of the phenotypes that explain the greatest possible covariance between them . This apRecently, it has been shown that PCs can also be combined across individual multi-trait studies for meta-analysis. Average PCs are derived from the weighted means of the loadings (i.e. the linear combination of traits) in each study .In contrast to PCA, CCA derives linear combinations of the traits that explain the greatest amount of covariance between a given variant and the traits. The first implementation of CCA for multivariate phenotypes was developed by Ferreira & Purcell , and lat2.6.2.Linear mixed models (LMMs) are an extension of standard regression analysis incorporating both fixed and random effects, and have gained popularity in GWAS due to their ability to handle relatedness among individuals ,122. MulKorte and colleagues first applied multivariate LMMs to pairwise quantitative trait measurements in a human cohort . The metFitting multivariate LMMs requires a computationally intensive parameter estimation step, which until recently impeded their application to more than two traits ,102,103.2.6.3.Generalized estimating equations (GEEs) are a multivariate method to jointly analyse non-normally distributed phenotypes ,123. As 2.6.4.Bayesian statistics allow for a model comparison between several alternative hypotheses, making them an attractive tool for pleiotropy analysis ,107,126.mvBIMBAM and has been used to identify variants associated with low- and intermediate-density lipoprotein subfractions [A model-selection framework proposed by Stephens returns Bayes factors for each possible partitioning of phenotypes into one of three categories: unassociated, directly associated, or indirectly associated with a genetic marker . The weiractions . While iA Bayesian multivariate regression framework was also implemented in the widely used GWAS software SNPTEST .2.6.5.A non-parametric score test based on Kendall's tau makes no assumption about the distribution of traits being analysed, and can thus incorporate any type of trait . A limitAnother way to allow for the inclusion of traits with mixed distribution is to reverse the regression of standard GWAS. MultiPhen performs ordinal regression of the genotype  on multiple phenotypes and tests for association using a likelihood ratio test . Alternap-values of different traits while taking into account the correlation between the traits [Trait-based Association Test that uses Extended Simes procedure (TATES) is a model-free approach that combines univariate e traits . Even thBased on a univariate method developed by O'Brien , which drinculo [Multinomial models are a generalization of logistic regression, where the outcome variable (in this context the phenotype) can take more than two possible outcomes . Such morinculo . The Bayrinculo .2.6.6.Model selection procedures are effective tools to discern associated from non-associated traits. A log-linear framework proposed by Lee and colleagues  distinguThe pleiotropy estimation and test (PET) tool determines the pleiotropic effect of a variant on two continuous traits as the proportion of inter-trait correlation explained . This qup-values to the permutation-derived ones. The method tests for evidence against the null hypothesis of no association with all included phenotypes, and thus excludes the possibility of a signal being driven by one trait only. Therefore, if all but one of the analysed traits are associated with a variant or gene, the method will not reject the null.Lutz and colleagues extended the above method for non-continuous traits and for more than two phenotypes, as well as for rare variant or region-based tests  . The app2.7.Several comparisons of different multi-trait methods have been conducted to date, testing power and type I error rates, as well as computational performance under different scenarios ,136–138.Multivariate approaches are generally more powerful than univariate methods , unless When combining summary statistics across multiple traits in a univariate fashion, an important consideration is the power of individual studies. As for regional or genome-wide methods, single-point methods will fail to detect cross-phenotype associations if the input datasets are underpowered. Another important aspect is the ancestry of input study samples, especially for methods requiring the specification of reference panels , for whin < 5000), making it hard to predict their performance on large datasets. For example, methods implemented in the programming language R will generally be less memory-efficient than programs implemented in C or C++.The implementation and computational efficiency of different methods are additional important considerations. This is especially relevant to multivariate methods using individual-level genotype data, which generally require more memory and processing power. Most of the multivariate approaches outlined above have been tested on small to moderate sample sizes  or due to confounding factors such as environmental exposures can be achieved through Mendelian randomization (MR). Notably, while most methods outlined in this review aim to detect biological pleiotropy and are confounded by mediated pleiotropy, the opposite is true for MR. MR uses information on the association of one or several genetic markers—instrumental variables (IVs)—with each trait to infer whether or not trait 1 causally influences trait 2 ,139–142 a priori. Consequently, MR is not a method to detect new genotype–phenotype associations [In order to be a valid IV, three key assumptions about the genetic marker must be met: first, the marker is associated with trait 1; second, the marker is not associated with any confounding variables, such as environmental exposures; and third, the marker is not associated with trait 2 when conditioning on trait 1. The first two assumptions are usually easy to fulfil in a GWAS context. The first assumption also implies that the function of the gene or marker used as an IV is known ciations . Some cociations ,144. ArgTo overcome this limitation, several approaches have been proposed to both detect and subsequently adjust for pleiotropy in MR settings –147. TheI2 index can be used to test for heterogeneity between individual IV estimates [If individual-level data are available and both traits have been measured on the same sample, the Sargan test can be used to assess evidence against the null of all MR estimates being the same . For twostimates . In Eggestimates . An intestimates . By appl2.9.In addition to methods for detecting cross-phenotype effects, a recently published tool (BUHMBOX) aims to distinguish heterogeneity in disease cases from true pleiotropy between two diseases . It compTo our knowledge, BUHMBOX is currently the only method aimed at identifying spurious pleiotropy. BUHMBOX is not agnostic (i.e. D1 and D2 need to be specified by the user) and it is only applicable to disease traits.3.Pleiotropy will continue to grow as a key research area of human genetics as data availability increases.A key question that has been the subject of debate in evolutionary biology  and is lA further consideration is whether functional measurements, such as gene or protein expression, constitute traits in themselves or simply intermediate steps between genes and phenotype. This is especially important when attempting to draw biological conclusions from multi-trait analyses. MR approaches will be necessary to correctly infer causality, and indeed some work has already been done with regard to this question .It is increasingly common for researchers to be confronted with sample numbers in the hundreds of thousands, and an important next step will be to develop fast and efficient algorithms with good scalability. In contrast to single-trait GWAS, where analysis approaches are now fairly standardized, multi-trait methods vary considerably in the statistical approaches they employ. Ensuring comparability and replicability of results will be a key challenge in pleiotropy research moving forward.As data on cross-phenotype associations accumulate and our understanding of molecular links between diseases grows, these insights will be invaluable for drug development and repurposing, and for personalized medicine.


We estimated genotype by environment interaction (G × E) on later cognitive performance and educational attainment across four unique environments, i.e. 1) breastfed without maternal smoking, 2) breastfed with maternal smoking, 3) non-breastfed without maternal smoking and 4) non-breastfed with maternal smoking, using a novel design and statistical approach that was facilitated by the availability of datasets with the genome-wide single nucleotide polymorphisms (SNPs). There was significant G × E for both fluid intelligence  and educational attainment  when comparing genetic effects in the group of individuals who were breastfed without maternal smoking with those not breastfed without maternal smoking. There was also significant G × E for fluid intelligence  when comparing the group of individuals who were breastfed with maternal smoking with those not breastfed without maternal smoking. Genome-wide significant SNPs were different between different environmental groups. Genomic prediction accuracies were significantly higher when using the target and discovery sample from the same environmental group than when using those from the different environmental groups. This finding demonstrates G × E has important implications for future studies on the genetic architecture, genome-wide association studies and genomic predictions. On the other hand, there are reports that breastfeeding has little effect on intelligence in children after stringent correction for socio-demographic factors5. There are also a number of studies reporting that maternal smoking around birth has negative effects on intelligence and later performance9 whereas some studies show no such effects after adjusting for confounding effects such as socio economic status11. There is an interesting study by Batstra et al. (2003) demonstrating that the adverse effects of maternal smoking on children’s cognitive functions and performance were limited to those who had not been breastfed12, which is one of few studies accounting for the combined effects of breastfeeding and maternal smoking around birth. However, there are no studies into a genotype by environment interaction (G × E) for later cognitive performance conditional on the maternal environment as determined by breastfeeding or/and maternal smoking around birth. Hence, it is unknown whether the genetic expression for these traits differs between these maternal environments.There has been considerable interest in effects of breastfeeding and maternal smoking around birth on cognitive function and later performance such as intelligence, memory and educational attainment. Many studies have suggested breastfeeding influences cognitive function and intelligence16. G × E can be estimated in an experiment where individual or relatives’ phenotypes can be measured in different environments. However, measurement of relatives across environments is not feasible in human populations as family sizes are small and often confounded with environments and limited data exists on genetically related individuals measured across environments. The limited focus on G × E in human genetic studies is therefore unsurprising. However, when using genomic information it becomes much easier to obtain information about the same genotypes measured in different environments. Therefore, genomic data provides opportunities to estimate G × E in human data.Genes have the ability to react and produce alternative phenotypes in response to the environment. Genetic variation in response to environmental conditions has been described as phenotypic plasticity, reaction norms or G × E. The phenomenon is widespread and one of the fundamental factors in biology and evolution20. In the approach, two individuals who are not related in the conventional sense can be compared experimentally, because they share part of their genome by descent and this information can be derived from genome wide SNP genotypes. Since the unrelated individuals do not share common environments, any covariance between their shared genome and their phenotype is most likely genetic and not environmental. Genetic data create links between individuals in the population so that the estimation of G × E and testing of related hypotheses do not require measures of relatives in different environments, or longitudinal data on the same individuals. The proposed approach can be applied whenever phenotypes are recorded and genotype data are collected across known environmental conditions, in this case, breastfeeding and maternal smoking status. We use a multivariate linear mixed model22 to estimate genetic variance and covariance based on relatedness derived from genome-wide SNP genotypes. A genetic correlation  between the phenotypic expression of genotypes in different environments, which is significantly different from 1, indicates evidence of G × E24.In this study, we estimate G × E on later cognitive performance and educational attainment across the maternal environments for breastfeeding and smoking using a novel statistical approach that is facilitated by the availability of datasets with the genome-wide single nucleotide polymorphisms (SNPs). The use of genome-wide SNP data on unrelated individuals to determine genotype effects across environments presents a paradigm-shifting approach to dissect the genetic architecture of complex traitshttp://www.ukbiobank.ac.uk)25 where there were genotyped individuals measured for cognitive traits and environmental variables (see Methods). We preliminarily analysed the phenotypic data using a multi-trait genomic residual maximum likelihood (GREML) to dissect shared genetic architecture between the cognitive traits. Then, it was primarily focused to estimate G × E explained by the genome-wide SNPs using a whole genome approach. In the approach, we used a multi-variate GREML to estimate genetic variance and covariance explained by the genome-wide SNPs for each cognitive trait across different environmental conditions of breastfeeding and maternal smoking status (see Methods). We carried out the analyses on the four unique environmental groups, i.e. 1) breastfed without maternal smoking, 2) breastfed with maternal smoking, 3) non-breastfed without maternal smoking and 4) non-breastfed with maternal smoking. The rationale for such grouping is that the environmental effects of breastfeeding and maternal smoking are not likely to be additive12. Therefore, the combination of breastfeeding and maternal smoking status would generate four distinct environments that could be used to test our hypothesis with a novel approach to estimate G × E.We used the UK Biobank database , a sample of 25,445, 78,283, 77,919 and 77,750 genotyped and phenotyped individuals was available for respective analysis of fluid intelligence, memory, reaction time and educational attainment. The distribution of samples classified by breastfeeding and maternal smoking status is shown in Table 21 that explicitly modelled the genetic as well as residual covariance structure, as there were multiple phenotypes for each individual (see Methods). Adjusted phenotypes controlled for non-genetic confounders were used (see Methods). All of the estimates were significantly different from zero, indicating that there were significant genetic factors underlying those traits. The estimated SNP-heritability ranged from 0.067 to 0.219, and the estimated genetic correlations ranged from −0.338 to 0.674. The estimates agreed approximately with those in Davies et al.26 although we used a different subsets of the sample of phenotypes, different SNPs, and a different model for analysis (see Methods).In a preliminary analysis, we estimated the proportion of the phenotypic variance and the genetic correlation explained by genome-wide SNPs for fluid intelligence, memory, reaction time and educational attainment Table . We usedWe further partitioned the genetic variance and covariance into three functional categories; SNPs in genes that were differentially expressed in the central nervous system (CNS); SNPs in the other genes; and the remaining SNPs (see Methods). Figure Next, we stratified the individuals according to the status of breastfeeding and maternal smoking around birth, i.e. breastfeeding and non-smoking (B&NS), breastfeeding and smoking (B&S), non-breastfeeding and non-smoking (NB&NS), non-breastfeeding and smoking (NB&S) as in Table To estimate genome-wide G × E we used a four-variate GREML to estimate genetic variance and covariance between the four environmental groups, i.e. B&NS, B&S, NB&NS and NB&S. We found that there was significant G × E between B&NS and NB&NS for both fluid intelligence  and educational attainment  Tables . The genFor fluid intelligence and educational attainment that showed a significant G × E signal, we further estimated genome-wide G × E in a sex-stratified analyses to see if there was any significant sex difference in each environment, i.e. to test if genetic correlation between males and females was significantly different from 1. We found no significant difference between males and females in the same environment for all cases except that there was a weak signal of difference between male and female for NB&S group for fluid intelligence  (Supplementary Tables We compared genome-wide association studies (GWAS) based on the different environmental groups for fluid intelligence or educational attainment between which there was significant G × E. In the GWAS based on B&NS, there were no genome-wide significant SNP whereas GWAS based on NB&NS detected a significant locus in chromosome 22 for fluid intelligence . For the analyses of G × E for each trait, we tested if the different environment groups were heterogeneous . In our G × E analyses, there was no need to model residual covariance structure because it was not possible for the same individual to have multiple measures across the environments.The analyses of the four traits Table  or thoseFor fluid intelligence and educational attainment, although we found evidence for G × E between B&NS and NB&NS, and B&S and NB&NS, there was no signal for that between B&NS and NB & S, even though these environments showed the highest contrast in mean effects Figs . This waWe carried out the analyses on the four environments classified by the combined effects of breastfeeding and maternal smoking status Tables  and 4. WTo ensure that socio-economic status were not affecting our results, we also undertook the analyses with phenotypes additionally adjusted for average total household income. Supplementary Tables 27, could be significantly decreased if there was G × E and the discovery and target samples had different environmental conditions  using a regression with the sex or year-of-birth information as a dependent variable and the ‘known’ and ‘unknown’ answer as an explanatory variable. Supplementary Table 30, which approximately conform with the pattern of the rate from the UK Biobank data , all of the cognitive phenotypes in the UK Biobank data have been reported to have a reasonable reliability from re-test data9. A limitation of our study was that we did not explicitly adjust for maternal intelligence due to lack of information. A number of studies reported that significant effects of breastfeeding or maternal smoking disappeared after adjusting maternal intelligence11. However, it is also possible that a stringent adjustment of confounding effects such as maternal intelligence can over-correct the true effects of breastfeeding or maternal smoking. Indeed, breastfeeding effects on cognitive function or brain development have been evidenced in experimental species32 and brain image analyses34 using experiments without such confounding. Some studies reported significant breastfeeding effects even after correcting for confounding36. Maternal smoking effects on cognitive function or brain development have also been demonstrated in experimental species37 and brain image analyses38 that were without confounding effects. Another limitation was that we did not consider gestational age in the analyses because the information was not available. There are a number of studies reporting gestational age is a risk factor for later cognitive development40. A further study is required to confirm the combined effects of breastfeeding and maternal smoking around birth after an appropriate adjustment of confounding effects such as maternal intelligence and gestational age. Nevertheless, our primary aim was to estimate G × E based on the four groups stratified according to breastfeeding and maternal smoking status in the variance component approach. Even when the dependent variable within each of the four stratified groups is standardised, i.e. a mean of zero and a variance of one, which can correct the mean difference for confounding effects, it would not affect the resulting estimated genetic correlation between environments.We showed that for fluid intelligence, memory and educational attainment, the mean score of the individuals who were breastfed and not exposed to maternal smoking around birth was significantly higher than those who were not breastfed and exposed to maternal smoking around birth Figs , which aIn summary, breastfeeding and maternal smoking status are important environmental factors in fluid intelligence, memory and educational attainment. More importantly, we showed that the genetic expression of fluid intelligence and educational attainment differs for different maternal environments, implying that these environments interact with gene action. In the presence of G × E, genome-wide significant SNPs were different between different environmental groups. Genomic prediction accuracies were significantly higher when using the target and discovery sample from the same environmental group than when using those from different environmental groups. This finding has important implications in future studies of the genetic architecture, genomic prediction and GWAS for later cognitive performances.http://www.ukbiobank.ac.uk)25. UK Biobank Research Ethics Committee (REC) approval number is 11/NW/0382. Our reference number approved by UK Biobank is 14575 and we confirm that all experiments were performed in accordance with relevant guidelines and regulations. There are 502,648 participants, who were aged from 40–69 years and recruited between 2006 and 2010, measured for various complex traits and variables including cognitive functions and environmental factors. We used three cognitive traits, fluid intelligence, memory ability and reaction time, and educational attainment for which the participants were grouped into four classes according to the status of breastfeeding and maternal smoking around birth, i.e. breastfed and non-smoking (B&NS), breastfed and smoking (B&S), non-breastfed and non-smoking (NB&NS) and non-breastfed and smoking (NB&S).We used the UK Biobank database . The participant had a limited time (2 minutes) to complete as many questions as possible from the test presented in a touchscreen computer. There were 184,487 participants measured for the trait.This measure included data on questions designed to assess the cognitive function to solve problems that require logic and reasoning ability . Participants were asked to remember the location of six matching pairs of cards. Then, the cards were then turned face down on the screen and the participant had to select correct cards that match the original pairs in the fewest tries. Number of incorrect matches was recorded. There were 498,545 participants measured for the trait.Memory test included data on ‘pairs’ matching task on a touchscreen computer . The computer screen showed two cards at a time; if both cards were the same, the participants were asked to press a button-box that was on the table in front of them as quickly as possible. This reaction time was recorded. There were 496,902 participants measured for the trait.Reaction time test involved data on a test to assess reaction time and was based on 12 rounds of the card-game ‘Snap’ . Following Guggenheim et al.41, we reduced to 4 categories to consider approximately equal years of academic education, that is (1) None; (2) O-levels or CSEs; (3) A-levels, NVQ, HND, HNC or other professional qualification; (4) College or University degree. There were 498,528 participants measured for the trait.The educational categories were divided into 7 groups: College or University degree; A-levels/AS-levels; O-levels; CSEs or equivalent; NVQ or HND or HNC or equivalent; other professional qualifications, e.g. nursing, teaching; none . By touch screen interview, breastfeeding status was recorded in response to the question “Were you breastfed when you were a baby?”. There was no detailed measure for the amount of breast-milk intake.Maternal smoking status around birth was available for 494,400 participants . Through a screen touch interview, maternal smoking status was recorded in response to the question “Did your mother smoke regularly around the time when you were born?”. There was no detailed measure for the amount of smoking.http://biobank.ctsu.ox.ac.uk/crystal/refer.cgi?id=157020). We further applied stringent quality control (QC) with an imputation r-squared > 0.6, MAF > 0.01, H-W test p-value < 0.0001, SNP missingness > 0.05 and individual missingness > 0.05. Furthermore, we selected high quality HapMap3 SNPs that were reliable in estimating genetic variance and covariance at the genome-wide level, feasible for more complicated analyses and there was no substantial difference between estimated genetic variances from HapMap3 and 1000 genome SNPs44. After QC, 931,295 HapMap3 SNPs were remained for the analyses.For 502,648 participants, 152,249 individuals were genotyped and available for ~70 millions SNPs after a standard imputation process . After QC and matching breastfeeding and maternal smoking status, a sample of 25,445, 78,283, 77,919 and 77,750 genotyped and phenotyped individuals was remained for analysing fluid intelligence, memory, reaction time and educational attainment  are assumed to be normally distributed with mean zero. X and Z are incidence matrices for the effects b and g, respectively. The variance covariance matrix is defined asA is the genomic similarity matrix based on genome-wide SNPs45, and I is an identity matrix. The terms, ith environment, and i and j. It is assumed that there is no residual covariance because individual has no repeated measures. The variance and covariance components were estimated by a multi-trait or multivariate GREML. The genetic correlation was the ratio of the covariance scaled by the square root of the product of the variances between two environmental groups. The variance of the ratio was obtained by the Delta method using the information matrix24, and used to assess the significance of the estimate being different from 1, an evidence of G × E.We propose a statistical approach that integrates a novel design of unrelated subjects across different environmental conditions in which repeated measures of the same individual are typically unavailable . In the approach, we estimate genetic variance and covariance for a trait of interest across multiple environmental conditions that are tagged by SNPs to provide estimate of genome-wide G × E, i.e. in presence of G × E, the genetic correlation between traits measured in different environments is significantly lower than oney is distributed as N , a linear model can be written asg is random genetic effects, which are distributed as N , and e is random residuals, which are from N . When the phenotype y is selected such that values less than a threshold t1 and more than another threshold t2 are selected. Then, the variables after the selection can be written asAssuming that a random variable 23, the mean and variance for the selected variable areFollowing quantitative genetic theoryThe mean and variance for the genetic values after the selection areThe heritability after the selection is46c is a constant and From Eq. , the genFrom Eq. , the genTherefore, from equation , it is cyE) that is correlated with a trait of interest, the mean and variance for the selected variable for the trait arer is phenotypic correlation between the trait and environmental variable,For estimation of genetic correlation between two groups classified by an environmental variable , we randomly selected 1000 individuals for both fluid intelligence and educational attainment. For the discovery sample (to estimate the genome-wide SNP effects), we used 3362 individuals for fluid intelligence and 12919 for educational attainment that were randomly selected either from the same environmental group as the target sample or from a different environmental group. In estimating the genome-wide SNP effects, we used GBLUP47 to obtain GWAS p-values that were plotted using qqman software48.We compared genome-wide significant SNPs based on different environmental groups between which there was significant G × E. We used plink software22. Briefly, the model is very similar to the G × E model above except that y are four column vectors of phenotypic observation, each vector belongs to each trait, and the variance covariance matrix has an additional term of residual covariance as,i and j.While our primary interest was to estimate G × E, it was of interest to dissect shared genetic architecture between the cognitive traits as preliminary analyses. We used a multi-trait GREML that fitted four traits simultaneously to estimate the genetic and residual variances and covariance between the four traits. It is noted that because individuals had multiple phenotypes, residual covariance was explicitly modelled, otherwise the genetic covariance would be inflated. The details of model can be found elsewhere49; those located within the other genes except the CNS genes; and the rest of the SNPs. We partitioned the genetic variance and covariance between the four cognitive traits using a three component model fitting genomic relations matrices constructed based on the CNS, genic and non-genic SNPs.We were also interested in finding if the central nervous system (CNS) explained a significantly larger proportion of genetic variance, compared to other genic or non-genic regions, for the cognitive traits. In the annotation analysis, we divided the genome-wide SNPs into three groups; those located within ± 50 kb from the 5’ and 3’ UTR of 2,772 genes that were differentially expressed in CNShttps://sites.google.com/site/honglee0707/mtg2.The models and methods used in this study have been fully implemented in publicly available software, MTG2. The source code, executive binary file, manual and examples are readily available to use, and can be downloaded from Supplementary File


Recently, genetic markers rs10503253 and rs2616984 in the CUB and Sushi multiple domains-1 (CSMD1) gene have been reported to be associated with schizophrenia and cognitive functions in genome-wide association studies. We examined the associations of the above SNPs with cognitive performance evaluated by the Montreal Cognitive Assessment (MoCA) tool in a cohort of the normal elderly from the Russian population. Significant association of rs2616984 genotypes with the MoCA scores was found using nonparametric analysis. No association of rs10503253 with MoCA scores was observed using both parametric and nonparametric statistics. Significant combined effect of two-locus CSMD1 genotypes on MoCA scores was demonstrated by median test. Allele “A” and genotype “AA” of rs2616984 were significantly associated with the lower MoCA scores in comparison of 1st and 4th quartiles of MoCA total score distribution. The results suggest that genetic variants in CSMD1 gene are likely a part of genetic component of cognitive performance in the elderly. The single-nucleotide polymorphisms (SNPs) in the CUB and Sushi multiple domains-1 (CSMD1) gene were recently identified in genome-wide association studies (GWAS) as significant genetic markers for schizophrenia (SZ) and cognitive performance. CSMD1 gene spanning over 2.6 Mb on chromosome 8p23.2 is highly expressed in the central nervous system and epithelial tissues –6. A min708 elderly individuals of European Russian descent without dementia and neurological diseases were recruited from a population-based cohort study on primary prevention of Alzheimer's disease in Tomsk, Russia , 13. TheHealth characteristics are presented in In each participant, the cognitive performance was assessed using the Montreal Cognitive Assessment (MoCA). MoCA measures 8 cognitive domains: memory, attention, naming, visuospatial/executive, language, abstraction, delayed recall, and orientation domains. MoCA scores ranged between 0 and 30 points, and higher scores indicate better cognitive function.Genotyping of 2 genetic variants in CSMD1 gene, rs10503253 and rs2616984, was performed by multiplex PCR with the following iPLEX primer extension reaction and detection of allele-specific extension products by matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry on Sequenom MassARRAY 4 platform. Details of the genotyping method have been previously described elsewhere .Linkage disequilibrium (LD) between genetic variants and haplotype frequencies were estimated using Haploview 4.2 software. Statistical analysis of relationships between genetic markers and cognitive performance was performed in Statistica 7.0 (StatSoft Inc.) package using parametric  and nonparametric  statistics. For ANOVA analysis, MoCA scores were adjusted for age and education using linear regression model. Differences in allele and genotype frequencies between quartiles of MoCA distribution were estimated by chi-square test.D′ = 0.107; LOD = 0.24).Allele and haplotype frequencies of rs1050325 and rs2616984 in the total sample of 708 elderly subjects, as well as in the first (MoCa < 21) and fourth (MoCA > 24) quartiles of MoCA scores distribution, are presented in p = 0.0142), while no significant differences between lower and upper quartiles were found for rs10503253.Significantly higher frequency of the major allele of rs2616984 (“A”) was observed in a subsample of individuals with MoCA score less than 21 compared to fourth quartile's subsample  and 1.70 , respectively. Genotype “AG” of rs2616984 and haplotype “CG” of rs105032/rs2616984 were associated with higher MoCA score .One-way ANOVA demonstrates no significant differences in the mean MoCA scores among genotypes of both genetic variants in CSMD1 gene, as well as among combinations of genotypes of two SNPs . Howeverp value for median test was 0.024 and Kruskal-Wallis p was 0.020. No significant association of rs10503253 with MoCA scores was observed using both parametric and nonparametric statistics. Significant combined effect of two-locus CSMD1 genotypes on MoCA scores was demonstrated by median test .In addition, less conservative nonparametric statistics indicate that genetic variation in rs2616984 locus significantly influenced the MoCA values in the normal elderly population. Under codominant model, Current data on contribution of CSMD1 genetic variation to neuropsychiatric diseases and to cognitive performance are quite controversial. More evidence is accumulated on rs10503253, which is genome-wide significant marker for SZ in Europeans according to initial GWAS and subsequent replicative studies (see above), but is not replicated for Japanese  and Han Between-population variability in CSMD1 effects on neurocognitive phenotypes may reflect population-specific composition of genetic risk factors and/or population-specific LD patterns of associated markers with unknown functional variant(s) within CSMD1 or in adjacent genetic loci. But, nevertheless, growing amount of data on CSMD1 genetic association with various neuropsychological traits clearly indicates that structural variability at this part of the genome is likely a part of the common neurological mechanism, underlying various diseases and normal variability in neurocognitive traits. Genetic overlapping over these traits may be mediated by cognitive endophenotypes, such as variability in normal cognitive performance due to normal functional differences in brain structure and functions. This point finds support in several functional studies, demonstrating that that SZ risk variants show greater effects at the level of imaging based metrics of brain structure and function than at the level of behavior . ParticuAlong with population- and genetic background-related effects, age-related differences also may play a substantial role in the variability in genetic patterns of neurocognitive traits. Association of CSMD1 variants with Alzheimer's disease probably suggests that some part of genetic susceptibility at this locus may appear in the older age, compared to SZ susceptibility variants, but may be expressed in earlier preclinical stages as markers of cognitive and memory performance. However currently we cannot delineate possible molecular mechanisms underlying the age-related difference in CSMD1 effects on neurocognitive functions. The cohort tested in the present study is, to the best of our knowledge, the oldest sample ever used for CSMD1 genetic associations with neurocognitive phenotypes. We observed the association with MoCA performance for the genetic variant previously found to be associated with cognitive functions in younger people , as wellOur study suggests that genetic variants in CSMD1 gene are likely a part of genetic component of cognitive performance in the elderly.


Genome-wide association studies have facilitated the discovery of thousands of loci for hundreds of phenotypes. However, the issue of missing heritability remains unsolved for most complex traits. Locus discovery could be enhanced with both improved power through multi-phenotype analysis (MPA) and use of a wider allele frequency range, including rare variants (RVs). MPA methods for single-variant association have been proposed, but given their low power for RVs, more efficient approaches are required. We propose multi-phenotype analysis of rare variants (MARV), a burden test-based method for RVs extended to the joint analysis of multiple phenotypes through a powerful reverse regression technique. Specifically, MARV models the proportion of RVs at which minor alleles are carried by individuals within a genomic region as a linear combination of multiple phenotypes, which can be both binary and continuous, and the method accommodates directly the genotyped and imputed data. The full model, including all phenotypes, is tested for association for discovery, and a more thorough dissection of the phenotype combinations for any set of RVs is also enabled. We show, via simulations, that the type I error rate is well controlled under various correlations between two continuous phenotypes, and that the method outperforms a univariate burden test in all considered scenarios. Application of MARV to 4876 individuals from the Northern Finland Birth Cohort 1966 for triglycerides, high- and low-density lipoprotein cholesterols highlights known loci with stronger signals of association than those observed in univariate RV analyses and suggests novel RV effects for these lipid traits. While real-life analyses and power estimations suggest improvements for discovery with very large sample sizes, for many complex traits the numbers required are unrealistic. A cost-effective alternative for improved power is to jointly analyse multiple traits, by taking advantage of the correlation structure between them.6In the past decade, thousands of loci for hundreds of phenotypes have been identified through genome-wide association studies (GWAS). Despite these discoveries, the issue of missing heritability7 In genetics, MPA was first proposed for linkage studies,9 and recently, a plethora of methods for single-variant MPA of association has been suggested.10 MPA has been shown to provide a boost in power for locus discovery,5 as well as increased precision of parameter estimates.9 There is also a biological advantage in analysing correlated traits jointly, since detecting loci that affect a combination of phenotypes could provide suggestions of pleiotropic effects,7 that is, one locus affecting multiple phenotypes in parallel. Indeed, many of the identified loci from single-phenotype analyses overlap, especially for epidemiologically correlated traits, for example, glycaemic traits share up to a half of the loci with other cardiometabolic traits, including type 2 diabetes, lipids, measures of central obesity, height, blood pressure and hypertension.11 This overlap suggests shared genetic architecture underlying at least a part of the observed epidemiological correlations. With joint analysis of multiple correlated phenotypes, the potentially shared genetic architecture would be better addressed by direct joint modelling. In addition, current technology allows for cost-effective deep phenotyping12 such as the production of the metabolomics data including hundreds or even thousands of variables. These large-scale omics datasets will be necessary in understanding the exact relationship between genes and phenotypes. However, the great potential held by the omics data will only be achieved via integration and development of highly scalable computational and quantitative approaches.13 MPA methods will be particularly useful for the omics data in order to reduce dimensionality and avoid the penalties posed by correction for multiple testing.A number of methods for multi-phenotype analysis (MPA) have been developed, including dimension reduction, and multivariate and graphical models.14 the UK10K Project15 or the Haplotype Reference Consortium.16 For example, imputation to the UK10K reference panel including 7562 haplotypes, after re-phasing with SHAPEIT v2,17 yielded for variants with MAF as low as 0.1% an r2=0.5 with genotyped variants.18 Combining these factors has led to an increased interest in RV association analysis, resulting in the development of burden tests using collapsing techniques, variance-component tests and combinations of these two.19Another way to improve power for locus discovery is to allow for a wider allele frequency range, including low-frequency and rare variants . Development in technology to produce high-quality, low-cost sequencing data has had many positive implications for RV identification. Although whole-genome/-exome sequencing is still not feasible at a large scale, that is, sequencing hundreds of thousands of individuals, accurate RV data can be produced with imputation based on dense reference panels such as the 1000 genomes project,24 but they suffer, for example, from scalability limitations, their inability to combine continuous and binary phenotypes or to analyse different phenotype combinations, and finally, the lack of efficient computational tools . The modelling is performed via weighted linear regression with the following weights: the proportion of successfully genotyped or imputed RVs within the region of interest. Parameter estimates are obtained via least squares estimation. Then, a likelihood ratio test is constructed by comparing the weighted log likelihoods of the fitted model against a null model where β=0. The test statistic has an approximate χ2 distribution with K degrees of freedom. The method described has been implemented in a freely available software tool MARV,28 which is available at https://github.com/ImperialStatGen/MARV.where =−2•ln(L)+ K•ln(N), where L is the estimated likelihood of the model, K is the number of parameters and N is the number of observations.The methodology is flexible such that it can accommodate both quantitative and binary phenotypes, as well as directly genotyped and imputed RVs. For imputed RVs, instead of using the 0/1 indicator for the absence/presence of minor allele, we use the posterior probability that an individual is heterozygous or rare homozygous. For discovery purposes, the full model, including all the phenotypes is fitted. However, to allow further investigation of the loci reaching genome-wide significance after correction for multiple testing to take into account the number of regions tested within the analysis, we have implemented in the MARV software the possibility to analyse all phenotype combinations. For model selection purposes, MARV further calculates the Bayesian information criterion, BIC29 Specifically, we used the forward simulation software tool ForSim30 and the hybrid model for population history proposed previously.29 In brief, the ancestral population size was assumed to be 8100 for 50 000 generations, followed by a bottleneck population size of 2000. After this time the population expands with an exponential growth rate of 1.29% for over 370 generations, resulting in a modern effective population size of 227 650. With a maximum number of offspring set to two, the simulation resulted in a population of about 500 000 individuals. The mutation rate was assumed to be 2.0 × 10−8 bp per generation. This hybrid model has features of two published demographic histories32 and has been shown to recapitulate the number and frequency distributions of both rare and common synonymous sites, as well as empirically observed patterns of linkage disequilibrium between common variants.29To evaluate the type I error rate and power of our method, we simulated genetic variants by using a model that results in an allele spectrum similar to that observed in the European population.29 Around each transcript, we also simulated 100 kb of neutral genomic target flanking both sides of the gene.29 The simulation resulted in 16 616 SNPs, of which 96% have a MAF<5%. We randomly sampled SNPs as causal irrespective of their functional impact such that the MAF of any individual causal SNP was <2% and the sum of the MAFs did not exceed 5%.33 This resulted in 146 causal SNPs that were used for all the tested scenarios. For the selected SNPs, we randomly sampled individuals from this final population to achieve 10 000 replicates of studies of 1000 and 5000 individuals.We modelled loci as a series of 8 exons and 7 introns , with exons of length 300 bp and introns of length 3 kb such that the total coding length is 2.4 kb and the total transcript length is 23.4 kb, which corresponds to an “average” protein-coding gene from the RefSeq database.We simulated two continuous phenotypes from a multivariate normal distribution, such thatk is the causal variant and βk the effect for each causal variant, k=1,…,146, and ε ~ MVN, ΣY=cov =34 The genetic effects βk were considered under three scenarios, including (1) no effect (for type I error rate assessment), that is, βk=0; (2) all causal genetic variants having a trait-increasing effect (βk=0.1), and (3) half of the causal variants having a trait-increasing effect (βk=0.1) and half having a trait-decreasing effect (βk=−0.1). Scenarios (2) and (3) were further considered in situations when there are effects on (a) both phenotypes in the same direction with same magnitudes, (b) both phenotypes in opposing directions with same magnitudes, (c) both phenotypes in the same direction with different magnitudes , and d) only on one of the phenotypes.where gP<0.05 for the test of association. Since we analysed only the full model and one genomic region, no correction for multiple testing was applied.We estimated the type I error rate and power of our method using the full model by calculating the proportion of the 10 000 replicate analyses, in which 23 which is based on a non-parametric distance-covariance test. This method requires a phenotype similarity matrix, either by using a projection matrix or by using user-selected linear kernel functions. For our estimates, we constructed the similarity projection matrix. The genotypic similarity matrix was calculated assuming a linear kernel for genotypes, where weights are functions of MAF, following the notation from Broadaway et al.23 The method then constructs the test and provides the P-value as the output. Similarly to MARV, we estimated the power of GAMuT by calculating the proportion of the 10 000 replicate analyses in which P<0.05 for the test of association.We compared the power of MARV to that of a recently published multi-phenotype RV method GAMuT,26 To assess power, we calculated the proportion of tests for which P<0.025, where the level of significance is Bonferroni corrected for two tests performed.In addition, we compared the power of MARV over a univariate RV test by calculating associations between the simulated RVs and the two phenotypes separately using the GRANVIL software.N=12 068 live-born children).35 The Ethics Committees of the University of Oulu and Northern Ostrobothnia Hospital District have approved the study, and the individuals used for the analyses have provided written informed consent.To examine our method with a real dataset, we analysed the data for triglycerides (TG), low-density lipoprotein (LDL) and high-density lipoprotein (HDL) cholesterol from individuals belonging to the Northern Finland Birth Cohort 1966 (NFBC1966) and having participated in the 31-year clinical examination. The cohort covers over 96% of all births in the two northernmost provinces of Finland in 1966  of the first set of data have been reported previously.37 More samples were genotyped afterwards, and after the genotyping data QC, there were 5402 subjects and 324 896 SNPs available for analysis. SNPs were imputed to the 1000 Genomes all ancestries reference panel (March 2012) with IMPUTE2,38 resulting in ~38M SNPs for analysis. Of these, 7 396 876 markers were non-monomorphic with MAF<5% and good imputation quality (info>0.4).At the clinical examination, blood samples were drawn after overnight fasting. Samples were stored at –70 °C until analysed. Enzymatic assays of fasting HDL cholesterol and TG were measured using Hitachi 911 Clinical Chemistry Analyzer and commercial reagents  in the accredited laboratory of Oulu University Hospital. LDL was obtained using a previously described method.For the phenotypes, we excluded non-fasting individuals and those known to be on lipid-lowering medication. Residuals of TG, LDL and HDL were calculated by adjusting for sex, body mass index and the first three principal components (PCs) derived from the genetic data to control for potential population structure. The residuals were further inverse-normal transformed; however, it is worth noticing that a transformation to reduce skewness is not a prerequisite for the software as the phenotypes are not the outcomes of interest here. GWAS and the phenotype data were available for 4876 individuals.39 We applied a Bonferroni correction for 30 000 genes resulting in a level of significance of 1.67 × 10−6. We analysed all variants irrespective of their annotation across autosomal chromosomes using the following thresholds: MAF<5% and imputation quality>0.4.The multi-phenotype genome-wide RV analysis using the transformed residuals was performed with MARV using the method “expected”, that is, we used the genotype dosages coming from imputation. To define gene regions across the genome, we used the gene list from the University of California Santa Cruz .N=1000). Numerical results for both sample sizes are provided in The simulation studies on 5000 individuals showed a good control of type I error rate under various correlation structures between the two continuous phenotypes . SupplemIn all the tested scenarios, when all genetic effects are trait-increasing, power is almost always higher than that of univariate analyses or the kernel-based multi-phenotype test GAMuT . When thWhen we considered the above mentioned four scenarios  under thTG_HDL=−0.32, RTG_LDL=0.31, RHDL_LDL=−0.19). The MPA of RVs for the three phenotypes revealed genome-wide significant associations  covering five gene regions: SARS, CELSR2, APOA5, FAM63B and APOE  performed. This notably decreased the power of the univariate method. We note that the Bonferroni correction applied may have been too stringent, especially when the phenotypes are highly correlated, but this approach is standard in GWAS40 and is widely applied to such traits.41We propose a novel flexible method, MARV, for MPA of RVs across the genome applicable to the sequencing, imputed and genotyping data in unrelated individuals. This method using the powerful reverse regression approach should enable novel discoveries based on the large-scale genomic data with high DNA-variant density. We show with simulations that our method has a good control of type I error rate under various scenarios, even with a sample size as small as 1000 individuals. The power of our method always exceeds that of a univariate RV burden test under the tested scenarios, and the patterns mirror those presented for a common-variant multi-phenotype method.CELSR2, SARS and FAM63B, of which common variation at CELSR2 has been previously associated with blood lipids,42 and at SARS/CELSR2 with type 2 diabetes,43 while FAM63B has no reported links with blood lipid levels. We identified two additional well-established lipid genes, APOA5 and APOE.42 A recent study reported RV associations at APOE with lipid levels,44 and another study associated RVs at APOA5 with myocardial infarction.45 Our findings are in line with previous reports of variation at APOA5 and APOE mainly affecting TG and LDL levels, respectively;42 however, we observed RV association at CELSR2 with both HDL and LDL cholesterol levels, thus extending previous reports on common variation at this locus about primary effects on LDL.42 The novel FAM63B has previously been associated with schizophrenia through methylation patterns,46 making this locus an interesting biological candidate for lipid metabolism and worth further investigation, as metabolic disturbances often co-occur with psychotic illnesses.47 Importantly, our analyses showed that the associations at this locus and at CELSR2 would not have been observed in univariate analyses, whereas RV MPA had sufficient power to detect these signals. We also observed that MARV was able to detect effects from genes with widely varying sizes and number of RVs (APOA5 with 2.5 Mbp and 3 RVs vs FAM63B with 86 Mbp and 284 RVs). It remains of future work, however, to formally assess the power of MARV under properties such as varying sets of causal variants, different gene size, mutation rate, haplotype length or degree of linkage disequilibrium between causal variants.With application of MARV to TG, HDL and LDL phenotypes, we were able to detect genome-wide significant associations with RVs even with a sample size as modest as 4876 individuals. We found evidence for novel RV associations at 48 MARV could also be adapted to focus on only the most deleterious variants, rather than all of those mapping to a gene region via extracting or excluding specific markers.The simulated scenarios presented here are for two continuous phenotypes, but the method is easily applicable to a large number of phenotypes, as the real data example showed, and to a mixture of binary and continuous phenotypes. This is due to the methodological framework used, for example, reverse regression, in which the phenotypes are treated as predictors instead of outcomes, allowing for an easy incorporation of variables with varying properties into the model, as in any other linear regression analysis. Further, we have presented an example using a gene region-based association analyses, but the method and software are flexible and allow for analyses of any regions defined by the user based on start and end positions, for example, region sets, including those encoding active enhancers from analyses of human regulome.19 However, in the presence of both trait-increasing and trait-decreasing effects, or of only a small proportion of causal variants amongst those tested, there is a loss in power.19 As MARV is a burden test, it also suffers from some loss of power when both trait-increasing and trait-decreasing effects impact phenotypes, as shown in 49 Combined burden and variance-component tests, such as SKAT-O, are claimed to be more robust than burden tests in the above mentioned scenarios.19 However, when we compared the power of MARV to a kernel-based multi-phenotype RV test GAMuT in the presence of both trait-increasing and trait-decreasing effects, the power of MARV is similar to that of GAMuT in all tested scenarios.There are limitations to our method and the current version of the software that warrant discussion. MARV is based on a burden test, which has been shown to be a powerful method for RV association testing when a large proportion of variants are causal and their effects are in the same direction.In summary, we have developed a powerful method to facilitate the discovery of RV genetic effects within the multi-phenotype framework. The method has been implemented into a freely available, easy to use software tool MARV, and should allow wide and rapid implementation in the analytical pipelines for large-scale high-dimensional datasets, therefore paving the way for novel genomic discoveries.