Epistatic genomic relationship matrices for interactions of any-order can be constructed using the Hadamard products of orthogonal additive and dominance genomic relationship matrices and standardization based on the trace of the resulting matrices. Variance components for litter size in pigs were estimated by Bayesian methods for five nested models with additive, dominance, and pairwise epistatic effects in a pig dataset, and including genomic inbreeding as a covariate.Estimates of additive and non-additive (dominance and epistatic) variance components were obtained for litter size. The variance component estimates were empirically orthogonal, i.e. they did not change when fitting increasingly complex models. Most of the genetic variance was captured by non-epistatic effects, as expected. In the full model, estimates of dominance and total epistatic variances (additive-by-additive plus additive-by-dominance plus dominance-by-dominance), expressed as a proportion of the total phenotypic variance, were equal to 0.02 and 0.04, respectively. The estimate of broad-sense heritability for litter size (0.15) was almost twice that of the narrow-sense heritability (0.09). Ignoring inbreeding depression yielded upward biased estimates of dominance variance, while estimates of epistatic variances were only slightly affected.Epistatic variance components can be easily computed using genomic relationship matrices. Correct orthogonal definition of the relationship matrices resulted in orthogonal partition of genetic variance into additive, dominance, and epistatic components, but obtaining accurate variance component estimates remains an issue. Genomic models that include non-additive effects must also consider inbreeding depression in order to avoid upward bias of estimates of dominance variance. Inclusion of epistasis did not improve the accuracy of prediction of breeding values. Genomics provides tools to understand the effects of genes and their interactions and new approaches for genetic improvement . In quanWithin-breed non-additive effects, and in particular epistasis, are often ignored in genetic improvement programs. However, the total genetic value of an animal is a function of both additive and non-additive effects and, taken together, these effects could result in better predictors of future phenotypes  and infoThe additive genetic effect is the part of an individual’s total genetic effect that is transmissible across generations from parents to offspring. In contrast, non-additive genetic effects (dominance and epistasis) can be seen as the residual genetic effect after fitting additive substitution effects. Although most of the genetic variance is additive , 7 and cSeveral authors have proposed the inclusion of dominance and epistatic effects in genetic evaluation using high-density marker genotypes  , 9–12. MXiang et al.  proved aIn current pig production systems, the number of pigs weaned is a key factor to increase productivity, and litter size  is one of the most important traits under selection, in maternal line breeding programs . AlthougThe objectives of this work were to estimate additive and non-additive (dominance and epistasis) variance components for litter size for a real pig population, by considering or not inbreeding depression and to determine whether the accuracy of prediction of breeding values and total genetic values increases with the inclusion of dominance and epistatic effects.Data for this study were provided by Genus plc . Animal Care and Use Committee approval was not necessary for this study because the data were obtained from an existing database. Data on litter size  were from a pig pure line. The average litter size was equal to 12.7 ± 3.1 and 13,369 records were available for 3619 sows. Genotypes for all sows were generated using the Illumina PorcineSNP60 BeadChip . After quality control using default parameters by preGSf90   (mixed) model. Parity number and the combined effect farm-year-month of farrowing were included as fixed effects. The model also included a random permanent environmental effect for each sow. The linear model including additive, dominant and interaction terms can be written as:gligible  or too dVanRaden : \documeectively . CovariarGD⊙GD/n .In these analyses, we implicitly assume that allele substitution effects of quantitative trait loci (QTL) are distributed as a et al.  that acca et al. , which ia et al. . Note tha et al. . The NOIa et al. . For insa et al.  achievesa et al.  proved tStatistically, orthogonality means that inclusion of new terms in the model does not change estimates of already included effects in an infinitely large population. For instance, in practice, going from an additive to an additive plus dominant model should not change the estimates of additive variance components much. The advantage of using orthogonality in genetics and breeding is that it is the only way to carry out the estimation of breeding values  in an unambiguous manner i.e. such that they do not depend on other genetic terms that are fitted in the model.http://nce.ads.uga.edu/wiki/. In total, 200,000 iterations were run, discarding the first 10,000 and keeping every 100th sample. Convergence was checked by visual inspection of trace plots for the chains. Post-Gibbs analysis included estimation of the effective sample size and the deviance information criteria (DIC) as a goodness-of-fit criterion [Variance components were estimated for five nested models that added, in succession, additive effects  by fixing the variance components that were estimated. Predictive ability of total genetic values for lowly heritable traits is difficult to ascertain, thus for the comparison of models, we proceeded as follows. EBV proaches , 28 to dproaches :\documenFor comparison purposes, we also investigated the predicted ability of phenotypes of “new” sows for the three models as the correlation cory∗,y^  where \dEstimates of additive and dominance genetic variances for litter size ranged from 0.81 ± 0.12 to 0.84 ± 0.12, and from 0.17 ± 0.11 to 0.20 ± 0.11, respectively for all models  effects in the model did not have a large effect on estimates of residual variance, but they reduced the permanent environmental variance Table , which sOnly second-order epistatic effects (e.g. additive-by-additive) were included in this study. Although it is tempting to fit high-order epistasis terms given the relative ease of computing the Hadamar products of relationship matrices, caution is needed. First, the products entclass1pt{minimaThe estimate of inbreeding depression, based on the inbreeding coefficient calculated as the proportion of homozygosity, was equal to − 12.33 ± 2.29 piglets born per litter for this population. Inbreeding depression expressed as a change in phenotypic mean per 10% increase in inbreeding was equal to − 1.23 piglets born. This result shows the importance of inbreeding depression in fitness traits such as total number of piglets born. Estimates of non-additive variance components when inbreeding depression is not fitted in the model are rarely reported but, in our analyses, yielded an upward biased estimate of the dominance variance (i.e. GDI model in Fig. The global fit of the models was studied using DIC. Models with smaller DIC exhibit a better fit after accounting for model complexity. Differences in DIC between models of less than 7 units are considered as irrelevant . The valThe predictive ability of the models for selection candidates was assessed using two approaches: the three statistics based on method R and by conventional cross-validation. The method R statistics of bias Based on conventional cross-validation Table , models Using orthogonal relationship matrices, empirically orthogonal estimates of additive, dominance and epistatic variances were obtained for litter size in a pig dataset. The broad-sense heritability for litter size was almost twice the narrow-sense heritability. Genomic models that include non-additive effects must consider simultaneously inbreeding depression based on inbreeding in order to obtain unbiased estimates of variance components. Inclusion of epistasis or dominance did not improve the accuracy of prediction of breeding or genotypic values.


Sample size and minor allele frequency had a major influence on SPAEML’s ability to distinguish between additive and epistatic signals, while the number of markers tested did not. We conclude that SPAEML is a useful approach for providing further elucidation of the additive and epistatic sources contributing to trait variability when applied to a small subset of genome-wide markers located within specific genomic regions identified using a priori analyses.Association studies have been successful at identifying genomic regions associated with important traits, but routinely employ models that only consider the additive contribution of an individual marker. Because quantitative trait variability typically arises from multiple additive and non-additive sources, utilization of statistical approaches that include main and two-way interaction marker effects of several loci in one model could lead to unprecedented characterization of these sources. Here we examine the ability of one such approach, called the Stepwise Procedure for constructing an Additive and Epistatic Multi-Locus model (SPAEML), to detect additive and epistatic signals simulated using maize and human marker data. Our results revealed that SPAEML was capable of detecting quantitative trait nucleotides (QTNs) at sample sizes as low as  The ability to identify genomic regions containing gene(s) associated with quantitative phenotypes has great potential for elucidating the genetic architecture of traits , as well as identifying targets for marker-assisted selection in plants and animals and therapy in humans. One analysis that seeks to identify such regions is the genome-wide association study (GWAS), in which statistical analyses are conducted on a set of markers spanning a species’ entire genome to determine which marker subsets exhibit the strongest associations with a trait of interest  panel  as a function of sample size and number of markers. To achieve this, we used genomic data from 2648 individuals from the North Central Regional Plant Introduction Station (NCRPIS) maize diversity panel ; μ is the grand mean; βj is the additive effect of the jth marker; xij is the observed genotype of the jth marker of the ith individual, numerically coded as, e.g., 0 for aa, 1 for Aa/aA, and 2 for AA; γuv is the two-way epistatic term between the uth and the vth marker;xiu and xiv are the observed genotypes for the uth and the vth markers, both of which are numerically coded in the same manner as xij; I is a subset of the m markers with additive effects included in the model; U is another subset of markers with two-way epistatic effects included in the model; and εi represents a normally distributed random error term. A stepwise model selection procedure is used to determine the optimal sets of markers belonging to I and U.The statistical approach implemented for SPAEML is similar to those previously described  cases and 1255 controls , or the same random subset of n = 300 individuals in each species. Similarly, the test data sets included either a random subset of m = 15,000 SNPs or a random subset of m = 5000 SNPs. For both species, all SNPs in the 5000-marker set were also included in the 15,000-marker set.Within each species, we constructed multiple test data sets varying in sample size and number of markers. All test data sets consisted of either the full set of individuals (H2). To empirically evaluate the false positive detection rate of SPAEML in the absence of genomic signals, the traits simulated in the first setting had zero QTN and H2 = 0. The genomic sources of variation underlying the traits in the next setting consisted of four markers that were randomly selected to be additive QTN and four additional marker pairs that were randomly selected to be epistatic QTN. The additive and epistatic QTN both followed a geometric series; that is, the QTN with the jth largest effect size was 0.95j. Since the purpose of this setting was to evaluate the ability of SPAEML to identify signals for a trait with an ideal genetic architecture, the heritability was set at H2 = 0.99. To assess whether SPAEML can distinguish between additive and epistatic signals, the next setting consisted of two simulated QTN containing both non-zero additive and non-zero epistatic effects. Thus, the additive effects of these two QTN were 0.90 and 0.81, and the epistatic effect of these two QTN was 0.9. All traits simulated at this setting had a broad-sense heritability of H2 = 0.95.Traits were simulated as previously described in scheme 2 of Zhang et al.  for eachjth QTN set to 0.45j, and a broad-sense heritability of H2 = 0.92. In a similar vein, the next setting was based on the genetic architecture of Alzheimer’s disease in humans ; a flowchart of this implementation of SPAEML is provided in Supplementary Figure http://www.vital-it.ch/software/FastEpistasis, and Bonferroni correction was applied to control for multiple testing. FastEpistasis only tests one pair of markers at a time and constructs a model that includes additive effects for each marker and a two-way interaction term that models their epistatic effect.For each trait that was generated in the simulation study, SPAEML, JL analysis, and FastEpistasis were conducted to identify markers exhibiting peak associations with additive and epistatic QTN. For each of the five simulation settings, sample sizes, species, and number of markers, two separate permutation procedures  detection rate of a QTN was defined to be the proportion of the corresponding 100 simulated traits in which a QTN was detected. A similar metric specific to SPAEML, the specification rate of a QTN, was defined as the proportion of 100 traits where an additive QTN was correctly identified by SPAEML as additive, and both loci contributing to an epistatic QTN were correctly identified by SPAEML as epistatic. A window size of ±250 kb has been previously used in maize diversity panels to designate local regions of genomic proximity in maize  included as a main (additive) effect in SPAEML or JL analysis, (ii) included as part of a two-way interaction (epistatic) effect by SPAEML, or (iii) included as part of a two-way interaction effect with a A false positive (FP) detection was said to occur for (i) each main effect detected by SPAEML or JL analysis corresponding to a marker located outside of the ±250 kb windows surrounding all QTN, (ii) each two-way interaction effect detected in SPAEML where both corresponding markers were located outside of the ±250 kb windows surrounding all QTN, or when (iii) a statistically significant association outside of these windows was identified by FastEpistasis. Hence the FP rate of a given approach was defined to be the proportion of 100 traits simulated at a given sample size, marker number, species, and setting with at least one FP.We conducted a simulation study to explore the impact of sample size and number of markers on the ability of SPAEML to identify additive and epistatic QTN. To enable a thorough investigation, traits with different genetic architectures ranging in complexity were simulated using genotypic data from a maize diversity panel and then again with genotypic data from a human case–control cohort Table . Figure α = 0.05. The observed empirical FP rates across species, number of markers, and sample sizes suggest that these procedures are controlling for type I errors reasonably well, with SPAEML having empirical FP rates that are most consistently close to α = 0.05  and the Bonferroni procedure (used for FastEpistasis results) to control the type I error rate at .05 Fig. . The FP n = 300 individuals. One of the most detrimental impacts of small sample size on the accuracy of SPAEML appeared to be on the FP rate; substantially high FP rates from SPAEML were observed only at n = 300  minimal FP rates, (ii) QTN detection rates that were comparable to JL analysis, (iii) greater capability to identify both loci underlying epistatic QTN, and (iv) the capacity to distinguish between additive and epistatic signals in traits simulated in the human data set. In light of this contrast and the negligible impact of the number of tested markers on the simulation results, the remaining sections present findings based on n = max individuals and m = 15,000 markers.The results from these simulation studies show that sample size has a substantially greater impact on QTN detection than the number of markers, underscoring the well-established importance of having sufficient sample sizes when conducting quantitative genetics analysis Doerge . Neverthsis Fig. . FinallyQTN Fig. -18. In cAmong the three approaches that were evaluated, only the output of SPAEML provide results for both additive and epistatic terms fitted to one model. To characterize the ability of SPAEML to distinguish between additive and epistatic signals, both of the QTNs considered in the “Additive vs. Epistatic” setting harbored non-zero additive and epistatic effects. At this setting, we observed contrasting results between the two species. In maize, SPAEML classified the signals at these QTNs as epistatic 100% of the time, suggesting that SPAEML was unable to distinguish between these additive and epistatic effects  while “AD-like” was not (H2 = 0.34). Secondly, the effect size of the epistatic QTN was substantially higher relative to those of the additive QTN in the “Inflorescence-like” setting, whereas the strength of the epistatic QTN in the “AD-like” setting was not.We compared the accuracy of the three approaches in simulation settings 4 and 5, which approximate the polygenic underpinnings of maize inflorescence . However, the accuracy improves dramatically at larger sample sizes. Although this result is unsurprising, direct quantification of SPAEML’s ability to identify additive and epistatic QTN at different sample sizes is informative, as it is useful to know how a model will behave on a smaller data set when desired sample sizes are unavailable. Our results show that even in those cases SPAEML will find many significant SNPs and epistatic pairs, although they may be misspecified in the final model.Our study confirmed the common expectation that sample size positively affects the accuracy of SPAEML. We also demonstrated that SPAEML is capable of true positive detection and even correct specification of additive and epistatic QTN at the smaller sample size that we explored (In contrast to the substantial impact of sample size on the accuracy of SPAEML, we observed similar true and false positive rates at the two marker sizes that were tested. From a statistical perspective, these results suggest that for these simulated data, the conservativeness of the multiple testing problem is similar for both 5000 and 15,000 markers. Thus, the larger marker set does not decrease the accuracy of SPAEML. This is important, as our marker sets are orders of magnitude smaller than those currently available on a genome-wide scale in heavily researched species. We hope the usefulness of SPAEML holds for larger sets, although direct extrapolation is not recommended. We believe this method is best used on a set of markers that has been whittled down by using prior biological information, such as linkage disequilibrium analysis, hypothetical relations between markers and cellular pathways, or other preliminary analyses that remove markers that do not contribute to the final model. This will bring the problem into the setting of optimal performance for SPAEML, and also reduce the computational burden from testing both additive and epistatic effects, which grows binomially with the marker set size.We found SPAEML to be much more capable of distinguishing between additive and epistatic signals for traits simulated in the human data set, despite that the same number of markers, similar number of individuals, and the same simulated genetic architectures were evaluated in the maize and human data sets. We propose two distinct but not mutually exclusive hypotheses to explain these results. First, differences between the underlying characteristics of the maize and human genomes could result in LD-related properties being more favorable for SPAEML to work optimally in the human data set. The second hypothesis is that the differences in accuracy are a downstream ramification of the difference in MAF distribution across the two data sets Fig. , potentiTo ensure that the most appropriate biological conclusions are made by breeding, medical, and quantitative genetics research communities, it is imperative that statistical models which approximate the genetic architecture of traits are accurate. By design, both JL analysis and FastEpistasis oversimplify the intricate patterns of main effects and multifaceted interactions between loci contributing to phenotypic variability. While JL is designed to only consider additive effects in a multi-locus model, FastEpistasis is designed to only test for epistasis, one pair of markers at a time. In contrast, we demonstrate that SPAEML is a sensitive and accurate approach capable of identifying and distinguishing between additive and epistatic genomic signals, at least for data sets of several thousand samples and markers. We suggest that SPAEML, which conducts model selection for all possible main effects and two-way interaction effects of a set of markers, is best used for constructing an accurate model on a limited set of markers identified through an a priori analysis, once markers in genomic regions with no contributions to phenotypic variation have already been eliminated. We hypothesize that utilizing as much a priori information as possible on both the target trait and data set, particularly transcriptomic, metabolomic and genomic relatedness between individuals, could theoretically expedite the identification of such genomic regions.https://bitbucket.org/wdmetcalf/tassel-5-threaded-model-fitter. The genotypic data, simulated trait data, and code to simulate the traits are available at: https://github.com/ncsa/EpiQuant_GWAS_Simulations.The Java code used to perform SPAEML is available for download at Supplementary Figure CaptionsSupplementary Figure 1Supplementary Figure 2Supplementary Figure 3Supplementary Figure 4Supplementary Figure 5Supplementary Figure 6Supplementary Figure 7Supplementary Figure 8Supplementary Figure 9Supplementary Figure 10Supplementary Figure 11Supplementary Figure 12Supplementary Figure 13Supplementary Figure 14Supplementary Figure 15Supplementary Figure 16Supplementary Figure 17Supplementary Figure 18


Currently, numerous papers are published reporting analysis of biological data at different omics levels by making statisticalinferences. Of note, many studies, as those published in this Journal, report association of gene(s) at the genomic andtranscriptomic levels by undertaking appropriate statistical tests. For instance, genotype, allele or haplotype frequencies atthe genomic level or normalized expression levels at the transcriptomic level are compared between the case and controlgroups using the Chi-square/Fisher’s exact test or independent (i.e. two-sampled) t-test respectively, with this culminating intoa single numeric, namely the P value , which is used to make or break the outcome ofthe association test. This approach has flaws but nevertheless remains a standard and convenient approach in associationstudies. However, what becomes a critical issue is that the same cut-off is used when ‘multiple’ tests are undertaken on thesame case-control (or any pairwise) comparison. Here, in brevity, we present what the P value represents, and why and whenit should be adjusted. We also show, with worked examples, how to adjust P values for multiple testing in the R environmentfor statistical computing (http://www.R-project.org). Biological data is currently being generated ona massive scale, which has resulted not only in anavalanche of raw data, but has also led to the testingof multiple hypotheses. To test these hypotheses,inferential statistics is applied to relevant sampledatasets, leading to further biological insights andpossible discoveries. Essentially, hypothesis testing isa statistical method which computes the probability ofthe strength of evidence based on the sampled data foror against the null (i.e. no difference or no change)hypothesis, which is culminated in a single numeric,namely the P value. Here, we discuss P values, butmore importantly, with a focus on association studies,discuss why, when and how they should be adjusted.We hope that this short guide results in more accuratereporting of P values and the respective inferences.1, µ2) is <0.05, one would say(absolutely arbitrarily) that it is their eureka momentby shrugging off (reject) the null hypothesis (µ1=µ2),and embracing (accept) the alternative hypothesis(µ1.µ2). However, what we are actually quantifying isthe probability of observing data as or more extremethan what we have observed given the null hypothesisis true  is 0.05 . Accordiis true . Meanwhiis true . There is a matter of considerable controversysurrounding the position of Pvalue in scientific inferenceand this has become even more heightened by theemergence of big data analysis, which mainly revolvesaround its misunderstanding and misuse , 10. Thesingle=5×10-2. The probability of not observing a typeI error in a single test is then psingle=1-α=1-5×10-2=0.95.Accordingly, the probability of not observing a typeI error in multiple (e.g. 20) tests is pmultiple=(1-α)m=(1-5×10-2)20≈3.6e-01 and thus αmultiple=1-(1-α)m ≈ 0.64,therefore showing the substantial increase in typeI error after multiple testing. If the number of testsincreases dramatically, the inflated type I error rate(αmultiple) would reach 1. For instance, αmultiple= 0.9941if α=0.05 and m=100.Assuming that all the flaws mentioned are addressed,the last but the most important issue that remains in Pvalue quantification is when multiple testing occurs,but what constitutes multiplicity? Imagine a scenariowhere the expression of twenty genes at the transcriptlevel have been compared between a fixed set of casesand controls or, at the genomic level, genotype/allelefrequencies of twenty single nucleotide polymorphisms(SNPs) have been compared. By pure chance,assuming independence of tests, one would expect,on average, one in twenty of transcripts or SNPs toappear significant at the 5% level. This is because the‘probability’ of a false positive in this scenario is nowinflated and clearly requires adjusting the originalsingle test significance level of 0.05. In other words,the probability of observing a false positive (i.e. typeI error) generated by all tests undertaken should notexceed the 5% level . This issingle=α´. The probabilityof not observing a type I error in a single test is thenpsingle=1-α´. For independent tests, this probabilitywould be pmultiple=(1-α´)m. Next, the probability oftype I error for multiple tests is αmultiple=1-(1-α´)m.Rearrangment of the equation leads to the approximatedBonferroni correction for multiple testing α´≈ α/m.Following the same scenario, the α´ for each of thetwenty tests would be 0.05/20=2.5×10-3. By applyingthe same rule, when 1,000,000 SNPs are tested in agenome-wide association study (GWAS) αˊ would be5×10-8 and when expression dysregulation is examinedfor 20,000 genes on a whole-transcriptome microarray,αˊ would be 2.5×10-6. So how one ought to correct this inflation of thefalse positive rate? The first solution is to control typeI error by minimising the significance threshold . Say the probability of a type I error ina single test is the standard αHere we provide worked examples for the twomost commonly used methods without in-depthmathematical detail and formulae. This approach isanalytically more convenient compared with the firstmethod, in which, after setting an adjusted threshold,raw P values have to be checked against a' one at atime. The function used here is p.adjust from the statspackage in R. Imagine you have tested the level ofgene dysregulation between two groups (e.g. casesand controls) for ten genes at the transcript leveland below is the vector of raw P values obtainedby implementing the independent t test .P_value <- c.The simplest way to adjust your P values is to usethe conservative Bonferroni correction method whichmultiplies the raw P values by the number of tests m. Using the p.adjustfunction and the ‘method’ argument set to "bonferroni",we get a vector of same length but with adjusted Pvalues. This adjustment approach corrects accordingto the family-wise error rate of at least one falsepositive (FamilywiseErrorRate (FWER)=Probability). p.adjust ## [1] 0.001 0.010 0.060 0.300 0.950 1.000 1.000 1.0001.000 1.000 The results show that only two out of ten genes remainsignificantly dysregulated. Had we not undertaken thismultiple testing correction, we would have reportedsignificant dysregulation for another two genes. Thiscorrection method is the most conservative of all anddue to its strict filtering, potentially increases the falsenegative rate  which siA philosophically different and more powerfuladjustment method is that proposed by Benjamini andHochberg . This mep.adjust   ## [1] 0.001 0.005 0.02 0.075 0.19 0.195## [7] 0.334 0.690 0.834 0.985 A quick comparison of the results show that FDRidentifies one more dysregulated gene compared with theBonferroni method. This third gene (corrected P=0.02)is what would be called a false negative as it shows nosignificance when the conservative Bonferroni method isused but remains significant under FDR. To better compare these two multiple testing correctionmethods, a large array of random P values (n=500) wereadjusted . The freThe take home message is that it does not matterwhether you are interested in identifying a significantassociation with SNPs, differentially expressedgenes (DEG) or enriched gene ontology (GO) terms,the moment you conduct multiple tests on the samesamples or gene sets respectively, it would be essentialto address the multiple testing issue by adjusting theoverall false positive rate through calculating a´ oradjusting your raw P values (as shown here based onBonferroni or FDR) for true positives to be teasedout. This will in no doubt enhance reliability andreproducibility of research findings.


However, the performance on an African ancestry sub-cohort was minimal. A PRS constructed with schizophrenia GWAS also explained a significant fraction of PTSD diagnosis variance , confirming previously reported genetic correlation between the two psychiatric ailments. Overall, these findings demonstrate the important role polygenic analyses of PTSD will play in risk prediction models as well as in elucidating the biology of the disorder.Post-traumatic stress disorder (PTSD) is a psychiatric illness with a highly polygenic architecture without large effect-size common single-nucleotide polymorphisms (SNPs). Thus, to capture a substantial portion of the genetic contribution, effects from many variants need to be aggregated. We investigated various aspects of one such approach that has been successfully applied to many traits, polygenic risk score (PRS) for PTSD. Theoretical analyses indicate the potential prediction ability of PRS. We used the latest summary statistics from the largest published genome-wide association study (GWAS) conducted by Psychiatric Genomics Consortium for PTSD (PGC-PTSD). We found that the PRS constructed for a cohort comprising veterans of recent wars ( It occurs in ~10% of those experiencing severe trauma, with a lifetime incidence rate of 6.8−8% in the US general public3 and up to 15% among Operation Enduring Freedom and Operation Iraqi Freedom (OEF/OIF) veterans5. The current approach to diagnosis in general clinical practice relies on clinician interviews and patient self-reports. Variation in patients’ willingness to self-disclose, as well as highly heterogeneous symptom presentations and severity levels of PTSD6, make accurate and timely diagnosis challenging. Underdiagnoses, in particular, may result in serious, and at times fatal, outcomes that could have potentially been avoidable10.Post-traumatic stress disorder (PTSD) is a debilitating mental illness that can develop following a traumatic experience, such as combat, sexual assault, or natural disaster12. Despite an international effort studying military and civilian cohorts where many molecular layers and modalities were investigated16, there are, as of yet, no validated blood-based PTSD biomarker panels. Towards this end, one of the more-promising approaches, facilitated by a recent large-scale multi-site collaborative genome-wide association study (GWAS) from the Psychiatric Genomics Consortium for PTSD (PGC-PTSD)17, is genomic profiling using single-nucleotide polymorphisms (SNP’s).The urgent need for biomarkers as an objective diagnostic and prognostic tool for PTSD cannot be overstatedPTSD genomic profiles assess the degree of genetic propensity, in probabilistic terms, for developing PTSD following a traumatic experience. This information is of great importance not only for identifying biomarkers for disease prognosis, but also for elucidating disease etiology and mechanisms. As genetic profiles can be obtained prior to trauma exposure, they can also be used to plan preventative measures in at-risk populations, including military personnel. For example, duty assignments, number of tours, and dwell times between tours can be adjusted in relation to risk and resilience profiles. Pre-deployment resilience building strategies and personalized early interventions can also be implemented, especially for those that are at a higher risk. Furthermore, in the long-term, enhanced understanding of the genetics of the disorder will inform the design and tailoring of effective therapeutics.18, is highly polygenic. Individual (or even a few dozen) common SNP variants account for only a small part of the genetic influence. For instance, the largest published PTSD GWAS to date17, done with 20,000 (25% cases) participants, could not find any novel GWAS significant variant, nor could it replicate previously identified hits. A study of this sample size had 80% power to detect a disease (causative) allele with genotype relative risk of 1.186–1.35 . This suggests that common variants have individually small effect-sizes and are not by themselves predictive of PTSD risk.The main technical challenge in building genomic profiles, besides shortage of study samples, is the fact that the genetic architecture of PTSD, not unlike most other complex psychiatric traits20. Also of note, a moderate level of heritability (30%), particularly for women, was recently confirmed with SNP array-based heritability analysis17. Hence, a sensible way of capturing the genetic liability of an individual is, instead of looking at individual genes and variants in isolation, to account for the additive effects of these small effect risk variants. The total sum of risk variants, weighted by corresponding effect-sizes, which are usually obtained from GWAS summary statistics, is commonly known as polygenic risk score (PRS)22.Despite this lack of individual large effect-size common variants, small effects from many variants accumulate to result in a moderate level of heritability. Among those exposed to trauma, twin studies indicated a PTSD heritability of ~30% in men and 70% in womenWe investigated various issues pertaining to PTSD-PRS. First, we discussed its opportunities and limitations from a theoretical performance analysis. Next, we constructed the PRS using GWAS summary statistics in a deeply phenotyped and well-curated cohort comprised of OIF/OEF veterans conducted by Systems Biology PTSD Biomarkers Consortium (SBPBC), hereafter referred to as the SysBio cohort. We then showed that ancestral makeup similarity between discovery and validation cohorts was a major performance determinant. Furthermore, as a demonstration of genetic overlap among psychiatric illnesses, we use schizophrenia GWAS summary statistics to predict PTSD phenotypes. Overall, in addition to theoretical and empirical investigation of PRS prediction performance on PTSD onset and severity, we demonstrated its use in studying genetic correlation with other psychiatric disorders.Study participants are OEF/OIF veterans recruited from New York University Langone Medical Center (NYU), the James J Peters VA Medical Center (JJPVAMC), and Icahn School of Medicine at Mount Sinai (ISMMS) as part of a multi-site consortium effort (SBPBC) to identify, validate, and deploy PTSD diagnostic biomarkers. All participants in both cases and controls had experienced combat exposure. Written informed consent was obtained from all participants before the clinical assessment was conducted. Assessment of combat-associated PTSD diagnosis and severity was based on CAPS-IV  administered by a doctoral-level clinician. Deep and extensive phenotype information was thoroughly gathered. These included, in addition to CAPS, the Structured Clinical Interview for DSM-IV for anxiety, mood, alcohol and substance use, and psychotic disorders, as well as demographics data including race/ethnicity, age, relationship-status, and anthropometric data, including BMI, weight, and height. Further details about clinical and demographic data can be found in Table 23. As pre-phasing was believed to improve imputation accuracy and speed, the study data were pre-phased with SHAPEIT24 with genetic map data for build 3725. Imputation was done for a window of 5 Mb at a time with IMPUTE226 using phased reference panel from 1000 Genome Project phase 3 data set. The imputed data were reassembled with GTOOL. The following criteria were used for QC filtering with PLINK: minimum threshold for a minor allele frequency of 0.01, maximum individual missingness rate of 0.1, and Hardy–Weinberg equilibrium p-value of 0.001. A total of 9,831,409 variants survived this QC filtering step. Of note, our target SysBio cohort participants were completely independent of the discovery GWAS cohort of the PGC-PTSD study.Blood samples were drawn at JJPVAMC or ISMMS and shipped to Emory University for SNP genotyping. The genotype data were obtained with the Infinium PsychArray BeadChip from Illumina . Genotype calling was made with GenomeStudio. Samples were processed in two batches . Per-sample genotyping rate, in each batch, was >99%, resulting in a total of 303,378 typed variants. Hence, no sample needed to be discarded due to quality–control (QC). This leaves 244 samples with genotype and phenotype data. Imputation was performed with standard steps. First, the genotype data were split into individual chromosomes. Then, strand orientation of genotyped data of each autosomal chromosome were checked and corrected with PLINK1 PTSD GWAS summary statistics data, which is the largest published PTSD study to date  with European ancestry participants17, and2 Schizophrenia GWAS summary statistics data, which is the largest psychiatric genetic study (37 K cases and 113 K controls) to date, also consisting of mostly European ancestry participants27.PRS is often trained on GWAS summary statistics data, without the need to directly access raw individual-level genotype training data, which is often not readily available. Reliable estimation of PRS parameters, however, requires a large sample size GWAS. GWAS summary statistics data, unlike individual-level genetic data, are often publicly available for many traits and diseases. It typically contains results from univariate association test statistics on a variant-per-row format. In this study, GWAS summary statistics data from two studies were used as base/discovery data sets:P value thresholding procedure. The LD clumping was done on windows of 250 kb with a squared correlation of allele counts r2 = 0.1. This means that within a given 250 kb window with r2 = 0.1, the SNP with the smallest p value was chosen as a representative SNP. A PTSD-PRS was constructed and its performance  was evaluated over a grid of ten equally spaced p value thresholds from 0.1 to 1 inclusive, and the nominal significance threshold of 0.05  was chosen for the final PRS calculation. For schizophrenia–PRS, a threshold of 0.05 had been shown to be the most predictive in the original publication27. Thus, this threshold was used to avoid multiple testing burden. The first five principal components were added as covariates to correct for population stratification in both analyses. Standardization was done by converting raw scores to z scores . This part of the analyses was done with a wrapper function around the R code of PRSice v1.2528.To choose the optimal predictive set of SNP’s on the target data set, we conducted the standard LD clumping followed by .05 Fig. . Each ti21. More precisely, S is a set of SNP’s that survived the clumping and thresholding steps, t is one of the two traits studied as base phenotypes, and PRS summarizes genetic liability from many variants into a single number as a weighted sum of per-loci risk allele dosage23. First variants were filtered with the QC criteria described above. The resulting set of SNP’s was LD (linkage disequilibrium) pruned with window size of 50, shift size of 5 and correction (r2) threshold of 0.2 (–indep-pairwise 50 5 0.2). Then IBS (identity-by-state) similarity between individuals was computed (–genome) with the pruned data. Clustering was performed with this similarity matrix (–cluster). This yielded the four clusters shown in Fig. The clustering was performed with PLINKR2 of the PRS was computed as the difference between the R2 of full model that contains PRS along with covariates and the R2 of null model that contains only covariates. Similarly, Nagelkerke’s pseudo-R2 of the PRS was computed as the difference in Nagelkerke’s pseudo-R2 between that of the full model and null model. The p value of the null hypothesis that the regression coefficient of PRS is zero is reported with the R2. Odds ratios and difference in mean CAPS  between quantiles were computed using the glm function in R , with the first five principal components added as covariates to control for population stratification. The power analysis for single variants in the Introduction section (for the previous largest GWAS) was done using GAS power calculator. Standardization was done by converting raw scores to z scores . All computations were done on R (version 3.2.3) statistical computing environment and PLINK (v1.90b3s 64-bit)23.Initially, we sought to provide a preview of the roadmap ahead using analytical derivation. In light of upcoming large-scale genetic studies, this approach will also set expectations for opportunities and limitations for future genetic risk prediction studies of PTSD. These projections are predicated on standard assumptions and models from quantitative genetic theory . Using the heritability estimate of 30%  and an estimated disease prevalence of 8%, the optimal panel trained on an infinite number of samples would have an AUC of a little over 80% Fig. . It shou17 one performed on European ancestry cohorts and another on African ancestry. Each study consists of ~10,000 samples with ~25% PTSD positive cases. The African ancestry summary statistics did not result in any statistically significant predictive PRS, even when considering only African–American (or cluster 3) subset of our target subjects. This might arise from several technical challenges, including the fact that the African genome is highly diverse with short LD blocks and recent admixtures31, and most commercial arrays that tag a single variant from an LD block have low genetic coverage for African ancestry genome32. For this reason, only the European (EA)-based summary statistics are used in the present study to build PTSD-PRS for all target subjects including those of African ancestry participants.We used the two GWAS summary statistics data from the largest PTSD GWAS study published to date conducted by PGC-PTSD:P value threshold  explained ~5% of PTSD onset variance  as well as PTSD severity variance  as measured by CAPS (a quantitative measure of PTSD severity that ranges from 0 to 120).The PRS was constructed with a clumping-and-thresholding approach with the first five principal components added as covariates (see Methods). The PRS constructed with the best performing n = 244), the PTSD-PRS has an AUC (area under the receiver operating characteristic curve) of 0.60 for PTSD diagnosis and a C-index of 0.58 for prediction of CAPS. Next, using the PRS values, participants are stratified into equal-sized quantiles. The odds ratio for PTSD diagnosis between the highest and lowest quartiles is 11.2 (95% CI = 5.4–23.1), and between highest and lowest deciles is 50.5 (95% CI = 15.9–160) , see Methods. Having defined four genetic ancestry clusters Fig. , we exam36. To demonstrate this point for PTSD, we chose the largest (n = 150 K) and most successful (108 significant hits) PGC study to date conducted in schizophrenia27, and showed evidence of polygenic overlap with PTSD. For schizophrenia–PRS, the step of choosing the optimal p value threshold  is skipped in order to avoid multiple testing burden. Instead, a threshold of nominal significance (PT = 0.05) has been shown to be the most predictive in the original publication27, and that threshold is used here.One of the most-profound findings emerging from recent psychiatric genomic studies is the degree to which psychiatric disorders, as defined and classified based on conventional diagnostic nosologies, overlap at a genetic levelR2 of 2.96%, p = 0.0175). The corresponding AUC and C-index are 0.57 for both. For stratification, odds ratio for PTSD diagnosis between the highest and lowest quartiles is 4.5 (95% CI = −4.4–60.8), and between highest and lowest deciles is 12.6 (95% CI = 3.9–40.9). The difference in mean CAPS between the highest and lowest quartiles is 28.2 (95% CI = −4.4–60.8), and between the highest and lowest deciles is 53.6 (95% CI = 12.3–94.98).The resulting PRS explains ~3% of the variance in predicting PTSD onset . Given the rapidly evolving technological developments in whole genome and exome sequencing, this is an avenue that will become possible in the very near future. Once identified, these rare variants are likely to have larger effect-sizes (negative selection), and have potential to substantially improve prediction accuracy. Integrating other modalities, including neuroimaging biomarkers and other omics panels such as epigenomics, transcriptomics, metabolomics, and proteomics, is also promising.Second, future polygenic risk prediction models, in addition to common single-nucleotide variants studied in this article, can incorporate rare and low frequency variantsThird, the PRS predicted phenotype is an important factor to consider for future studies. PTSD is characterized by a heterogeneous set of distinct symptoms. PTSD-PRS, as applied in the current study, attempts to predict genetic influences on the overall diagnosis, ignoring heterogeneity in the clinical presentation. As larger genotyped samples that are more deeply phenotyped become available, it will be possible to create genetic scores for clinical subtypes  and sub-phenotypes  as well as specific traits, some of which might be shared with other disorders. This is particularly valuable for PTSD, and psychiatric illnesses in general, where comorbidity is prevalent and the boundaries around symptom-based diagnostic criteria are a moving target. This approach may also unearth pleiotropic patterns and help explain the widespread genetic correlations among psychiatric disorders and behavioral traits.46. On the other hand, genetic predictors trained on a GWAS conducted on a given ancestral group is less predictive in samples from a different ancestral group. As most genetic studies are conducted with European ancestry participants47, the prediction for non-Europeans is more difficult, particularly for African ancestry individuals, as is seen in the present study.Ethnic diversity in genetic study cohorts  presents both unique challenges and opportunities. On one hand, beyond the mere proportional representation of the diverse US military service men and women, a genetically diverse study sample facilitates identification of trans-ethnic and population-specific causal variants48.Going forward, it is important to keep both pros and cons of genetic biomarkers in mind. One of the reasons genetic biomarkers are attractive for psychiatric traits is the fact that samples from in vivo brain tissue, the primary disorder-relevant tissue for a psychiatric illness, is usually inaccessible. Most other “-omics” markers have tissue-specific variation, with peripheral profiles not aligning with those from the brain. Also, in addition to being a more stable marker, presently available technologies for genetic markers have a better analytical validity than other omics assays. On the other hand, information content from a single-molecular layer might be inherently limited . In order to build a robust biomarker panel, combining multiple modalities might be necessary. Addressing ethical concerns and potential misuses of genetic information also should be considered50. In addition, functional interpretation of the PRS is also difficult owing to the large number of genetic variants it comprises.Limitations of the study need to be noted. First and foremost, the current PRS has sub-optimal predictive accuracy owing in part to the fact that the discovery GWAS is still underpowered. Our target cohort is also small and comprises very well-curated samples that is not a random representative sample from the general population. Here, we almost exclusively used data from male participants. Future studies need to include larger numbers of female participants, particularly in light of the fact that women have double the rates of PTSD heritability and prevalence. Also, preliminary findings on gender-specific mechanisms of the illness have been reportedIn summary, our work contributes to the use of polygenic risk for a further understanding of PTSD risk and its underlying mechanisms, whereas also identifying areas of needed future research. Overall, these findings showed that PRS, in addition to being a powerful prognostic tool, is useful in unravelling disease etiology and mechanisms, which, in turn, will enable more personalized and novel intervention strategies. As more well-powered genetic studies become available in the near future, together with advances in whole-genome and exome sequencing, accuracy, and insight obtained from such analyses will become even more precise and useful clinically.Supplementary information - Polygenic risk associated with post-traumatic stress disorder onset and severity


Genomic selection and high-throughput phenotyping (HTP) are promising tools to accelerate breeding gains for high-yielding and climate-resilient wheat varieties. Hence, our objective was to evaluate them for predicting grain yield (GY) in drought-stressed (DS) and late-sown heat-stressed (HS) environments of the International maize and wheat improvement center’s elite yield trial nurseries. We observed that the average genomic prediction accuracies using fivefold cross-validations were 0.50 and 0.51 in the DS and HS environments, respectively. However, when a different nursery/year was used to predict another nursery/year, the average genomic prediction accuracies in the DS and HS environments decreased to 0.18 and 0.23, respectively. While genomic predictions clearly outperformed pedigree-based predictions across nurseries, they were similar to pedigree-based predictions within nurseries due to small family sizes. In populations with some full-sibs in the training population, the genomic and pedigree-based prediction accuracies were on average 0.27 and 0.35 higher than the accuracies in populations with only one progeny per cross, indicating the importance of genetic relatedness between the training and validation populations for good predictions. We also evaluated the item-based collaborative filtering approach for multivariate prediction of GY using the green normalized difference vegetation index from HTP. This approach proved to be the best strategy for across-nursery predictions, with average accuracies of 0.56 and 0.62 in the DS and HS environments, respectively. We conclude that GY is a challenging trait for across-year predictions, but GS and HTP can be integrated in increasing the size of populations screened and evaluating unphenotyped large nurseries for stress–resilience within years.The online version of this article (10.1007/s00122-018-3206-3) contains supplementary material, which is available to authorized users. Triticum aestivum L.) with high-yield potential and improved resilience to stressed environments is crucial  in response to stress .Indirect selection using correlated responses of high heritability for a target trait of low heritability is an effective breeding strategy in achieving rapid progress for traits of low heritability Falconer . In thisThe integration of cutting-edge technologies like GS and HTP has the potential to accelerate gains in breeding for high-yielding climate-resilient wheat varieties. Hence, the goal of this study was to evaluate these tools for potential application in sparse testing GY (minimize one or more years of testing) in the advanced yield-testing stage. For this purpose, we used the elite (second-year) yield trial nurseries (EYT) of CIMMYT’s spring bread wheat for GY evaluated in DS, and late-sown heat-stressed (HS) environments. In addition, our specific objectives were: (1) to assess the phenotypic and genetic correlations of GY in stressed environments with days to heading (DTHD), plant height and green NDVI (GNDVI) (2) to compare genomic and pedigree-based prediction accuracies for GY within and across nurseries/years (3) to compare genomic and pedigree-based predictions in populations with and without full-sibs, and gain a better understanding of the relative advantage of genomic predictions over the pedigree in populations with different family structures (4) to evaluate multivariate predictions of GY using GNDVI with the IBCF approach (5) to evaluate multivariate predictions of GY from GNDVI and relationships (genomic or pedigree) (6) to compare pedigree, genomic, and HTP-based predictions and identify the best approach for practical implementation in various stages of a breeding program.F6:F7 derived lines. They were planted at the Norman E. Borlaug Research station, Ciudad Obregon, Sonora, Mexico, in the 2013–2014 (EYT 13–14), 2014–2015 (EYT 14–15), 2015–2016 (EYT 15–16) and 2016–2017 (EYT 16–17) growing seasons. Each of these nurseries was sown in 39 trials, and each trial comprised 28 lines and two checks in an alpha lattice design, with three replications and six blocks. For the DS environment, the trials were sown at the optimum planting date (around the last week of November) in raised beds that received 250 mm of water in two irrigations. The late-sown HS environment was simulated by sowing later than the optimal time (around the last week of February) and naturally exposing the lines to high-temperature stress, particularly during the critical grain-filling period. This environment received an optimum of 500 mm of water in five irrigations.We used four different EYT nurseries comprising 4368 lines that were developed using the selected bulk breeding method and each EYT nursery comprised 1092 The DTHD (number of days from germination to 50% of spike emergence) and the height of the plant from the ground to the top of the spike in centimeters were recorded for all the lines. Harvested grain weight was calculated on a plot basis and used as a measure of GY. High-throughput phenotyping data were collected with a hyperspectral camera  from the Alava Remote Sensing Spectral Solution , that was mounted in a Piper PA-16 Clipper aircraft . The camera’s sensor had a 12-bit radiometric resolution, covered the light spectrum in the 400–850 nm region with a 7.5-nm full width at half maximum and the integration time was set to 18 ms. The flights were done around noontime and aligned to the solar azimuth angle at 300 m above the ground, resulting in a ground sampling distance of 30 cm. For each stressed environment, the aerial imageries were taken several days from heading through maturity. The observations were spaced at approximately seven to 10-day intervals, depending on the weather condition and cloudy or windy days were avoided. In the DS environment, HTP data were collected on the EYT 15–16 and EYT 16–17 nurseries and in the HS environment, data was collected on the EYT 14–15 and EYT 15–16 nurseries.http://www.grupoalava.com). Radiometric calibration of the sensor was done using coefficients derived from a calibrated uniform light source and an integrating sphere . Dark frame correction was performed for each flight dataset. Atmospheric calibration was performed using irradiance measurements acquired at the beginning and end of each flight using the aerosol optical depth from sun-photometer measurements  based on the SMARTS (A Simple Model of the Atmospheric Radiative Transfer of Sunshine) simulation model (Gueymard http://www.rese.ch/) based on data from the inertial navigation system attached to the camera , as described in Zarco-Tejada et al. (R780 − R550)/(R780 + R550)  ɛijkl is the residual with IID The best linear unbiased estimates (BLUEs) for GY and GNDVI for each date of measurement were calculated using the ASREML statistical package Gilmour , with thwww.jmp.com). Here, any value more than ‘K’ spreads (K was set to 4) from the center was considered as missing. For the GNDVI BLUEs, we calculated the across-date heritabilities across dates of measurement and removed the dates with low heritabilities. The GNDVI measurement dates were then classified into heading, grain-filling and maturity growth stages. A heatmap illustrating the range of GNDVI at the grain-filling stage for some lines in an EYT evaluated in the HS environment is shown in Fig. Quality control of the phenotypic data was done by removing the outliers that were detected with the Huber’s robust fit outliers method  Chi-square: < 9.21 [the Chi-square value was used to check whether the number of observed genotype classes fitted the expected number of genotype classes (96%) due to inbreeding and the critical Chi-square value at two degrees of freedom and alpha of 0.01 was 9.21]. The 78,662 SNPs that passed at least one of these filters were further filtered for greater than 50% missing data, less than 5% minor allele frequency and greater than 5% percent heterozygosity, and we obtained 9285 markers. Imputation of missing marker data was done using LinkImpute   for GY and GNDVI across replicates, within each nursery on a line-mean basis using the formula,σg2 is the genetic variance, σɛ2 is the error variance, and nreps is the number of replications. The estimates of genetic and residual variances were obtained using the average information-restricted maximum likelihood algorithm ×1, where VG is the t × t additive genetic (co)variance matrix of traits, ⊗ denotes the Kronecker product and K is the known relationship matrix of order n × n. The distribution of N(0n×t)×1, where Vɛ is the residual (co)variance matrix of traits and In is the n × n identity matrix.The genetic correlations between DTHD, plant height, GY, and GNDVI were obtained using the ‘All the lines in a nursery In this design, lines from both within and across-families were considered. The lines in each EYT nursery were divided into fivefold, and four of them were used as the training population to predict the remaining lines in the fivefold or the validation population.Lines that are represented by only one progeny per cross and have no full-sibs In this design, we used a subset of each of the nurseries comprising only one progeny per cross and performed cross-validations.Lines with at least two other full-sibs in a nursery We evaluated the advantage of having full-sibs in the training population by using a subset of lines that had at least two other full-sibs in that nursery. We then used 50% of the full-sibs in the training population to predict the other 50% of full-sibs in the validation population.Lines within a narrow range of days to heading in each nursery Since DTHD was moderately correlated with GY in several datasets, we created subsets of lines in each nursery by excluding the lines that were at the tails of the DTHD distributions and including only those that were within the standard deviation for DTHD. In the DS environment, the range of DTHD in the subsets was 78–87 days (EYT 13–14), 74–81 days (EYT 14–15), 79–85 days (EYT 15–16) and 70–79 days (EYT 16–17). Similarly, in the HS environment, the range of DTHD in the subsets was 59–66 days (EYT 13–14), 52–59 days (EYT 14–15), 55–61 days (EYT 15–16) and 56–62 days (EYT 16–17).For within-nursery predictions, we used all the lines in the nurseries, subsets of lines with and without full-sibs and also lines within a narrow range of DTHD in the following designs Table :Table 1TIn predictions across nurseries, we performed both forward and backward predictions using one nursery as the training population to predict the other, for every possible nursery combination. In addition, we also used all the other three EYTs to predict any given EYT. The across-nursery predictions were done using all the lines in the nurseries and also using only a subset of lines in each nursery within a narrow range of DTHD.G-matrix) calculated from markers , where G is the additive relationship matrix and σg2 is the variance component associated with markers and εi is the error term assuming that the joint distribution of ε is N , where σe2 is the residual variance.While several models are available for genomic predictions, their similarities have been reported in previous studies  which captures the identity-by-descent relationships. In addition, we also fitted model (4) with the combined genomic and pedigree-based relationships (G- and A-matrices). The Pearson’s correlation between the GY BLUEs and the predicted breeding values was used as a measure of prediction accuracy for all the models. The prediction accuracies were not divided by the square root of the heritability, because the genotypes were not replicated across the years and the across-year heritabilities could not be estimated.For pedigree-based predictions, the genomic relationship matrix in model (4) was replaced with the pedigree relationship matrix  and pedigree-based (A-matrix) predictions using the model described in (3), along with the correlated responses (GNDVI BLUEs measured at different dates) using the ‘R’ package EMMREML (Akdemir and Okeke We performed multivariate genomic (The phenotypic means and ranges of traits in the two stressed (DS and HS) environments were analyzed (Table S1). In the DS environment, average GY was the highest in EYT 16–17 (4.8 t/ha) and ranged between 2.2 and 5.8 t/ha across the four nurseries. Similarly, DTHD ranged from 59 to 96 days, and plant height ranged from 63 to 106 cm across the different nurseries. In the HS environment, average GY was the highest in EYT 14–15 (3.8 t/ha) and ranged between 1 and 5.5 t/ha in the four nurseries. The DTHD ranged between 45 and 69 days, and plant height ranged between 48 and 88 cm in the HS environment. We also analyzed the phenotypic GY variance in the full-sib families within each nursery  and observed that the deviation of the full-sibs from the family mean was low and ranged between 0.06 and 1.34 t/ha in both the environments.The phenotypic and genetic correlations of GY with DTHD and plant height were analyzed for all the lines in the nurseries and also for the subset of lines within a narrow range of DTHD Fig. . In the p values for the test of significance of the correlations indicated that most correlations, except GY with DTHD and plant height in EYT 14–15 of the DS environment and GY with DTHD in EYT 15–16 of the HS environment were significant at the threshold level of 0.001. Overall, the phenotypic and genetic correlations of GY with DTHD and plant height in the subset of lines were lower than the correlations in the complete set of lines in both the environments.In the HS environment, phenotypic and genetic correlations of DTHD with GY were weak to moderately negative in EYT 13–14 and EYT 16–17, close to zero in EYT 15–16 and slightly positive in EYT 14–15. Plant height had positive correlations with GY in all the four nurseries that ranged from 0.16 to 0.45. The We also analyzed the phenotypic and genetic correlations of GY, DTHD, and plant height across the DS and HS environments (Table S2). For GY in the DS and HS environments, the phenotypic correlations ranged between 0.12 and 0.31, while the genetic correlations ranged between 0.16 and 0.36. But, DTHD had high genetic correlations (ranged between 0.87 and 0.91), and plant height had moderately high genetic correlations across these environments (ranged between 0.51 and 0.59).The phenotypic and genetic correlations of GNDVI measured at different dates with GY in the complete set and subset of lines were analyzed Table . In the The line-mean broad-sense heritabilities for GY ranged between 0.73 and 0.80 in the DS environment and between 0.65 and 0.91 in the HS environment (Table S3). Similarly, the line-mean broad-sense heritabilities for GNDVI in the different dates of measurement ranged between 0.77 and 0.97 in the DS environment and between 0.75 and 0.94 in the HS environment.A-matrices and G-matrices for all the 3485 lines in the different nurseries were rescaled between zero and one and visualized by heat maps . We observed a higher degree of relationships with the G-matrix compared to the A-matrix, which was most likely due to the realized relationships and the identity-by-state similarities in genomic regions under selection pressure captured by the G-matrix. In addition, there was no grouping of nurseries based on the genomic relationships indicating the existence of some genetic relatedness across the nurseries.The Genomic and pedigree-based prediction accuracies for grain yield within and across nurseriesThe GY prediction accuracies for the complete set of lines in the nurseries and the subset of lines within a narrow range of DTHD were analyzed Fig. . In the In across-nursery predictions, the average accuracies in the DS environment for the complete set and the subset of lines were 0.18 ± 0.06 with genomic predictions, 0.11 ± 0.07 with pedigree-based predictions and 0.17 ± 0.07 with the combined genomic and pedigree-based predictions. Similarly, in the HS environment, the average across-nursery accuracies were 0.23 ± 0.08 with genomic predictions, 0.14 ± 0.06 with pedigree-based predictions and 0.24 ± 0.08 with the combined genomic and pedigree-based predictions. Genomic predictions outperformed pedigree-based predictions across nurseries in most datasets and the average increase in accuracies by using genomic predictions over pedigree-based predictions was 0.07 ± 0.06 (maximum increase of 0.26) in the DS environment and 0.11 ± 0.07 (maximum increase of 0.27) in the HS environment.We also observed that the combined markers and pedigree-based model did not have a significant advantage over genomic predictions across nurseries. While the accuracies were similar in many datasets, the average increase in accuracies from the combined model over genomic predictions was only 0.02 ± 0.02 and 0.03 ± 0.04 in the DS and HS environments, respectively. We also observed a decrease in accuracies using the combined marker and pedigree-based model over the GBLUP, whenever the pedigree-based model had lower accuracies than the GBLUP. When all other EYTs were used to predict a given EYT nursery, the accuracies were generally similar or slightly lower than the predictions from single nurseries in both the environments, except in a few datasets. While the average increase in accuracies with three nurseries in the training population versus a single nursery was 0.04 ± 0.03 (maximum increase of 0.13), the average decrease in accuracies was 0.08 ± 0.04 (maximum decrease of 0.17).Genomic and pedigree-based prediction accuracies for grain yield in populations with different family structuresGenomic and pedigree-based prediction accuracies in populations with and without full-sibs in the complete set of lines were analyzed Table . In popuWhen 50% of the full-sibs were included in the training population, the average genomic prediction accuracies were 0.56 ± 0.04, and the average pedigree-based prediction accuracies were 0.59 ± 0.06 in the DS environment. In the HS environment, the average genomic prediction accuracies were 0.60 ± 0.04, and the average pedigree-based prediction accuracies were 0.58 ± 0.05. Overall, the genomic prediction accuracies were similar to the pedigree-based prediction accuracies across all the datasets in this design.We also observed that the genomic prediction accuracies in populations with full-sibs in the training population were on average 0.27 ± 0.10 higher than the accuracies in populations with no full-sibs/only one progeny per cross, resulting in 24–256% increase in accuracies in both the environments. Similarly, pedigree-based prediction accuracies in populations with full-sibs in the training population were on average 0.35 ± 0.10 higher than the accuracies in populations with only one progeny per cross, resulting in 54–321% increase in accuracies in both the environments.Multivariate prediction of grain yield using the green normalized difference vegetation indexWe used GNDVI in an IBCF approach to predict GY and observed that the average cross-validation accuracies in the DS environment were 0.41 in the complete set of lines and 0.22 in the subset of lines within a narrow range of DTHD We evaluated the ability of GNDVI combined with relationships (genomic or pedigree) to predict GY Table . In the In the HS environment, the average cross-validation accuracy within nurseries was 0.59 in the complete set and subset of lines, using both genomic and pedigree-based relationships combined with GNDVI. In across-nursery predictions for the HS environment, the average accuracies were 0.27 and 0.26 using genomic relationships with GNDVI and 0.11 and 0.17 using pedigree relationships with GNDVI in the complete set and the subset of lines, respectively.We analyzed GY in four different EYT nurseries and observed that the DS environment had higher average GY (4.1 t/ha), compared to the HS environment (3.1 t/ha). Since the average GY under optimum conditions was 6.4 t/ha, it was reduced by 36% in the DS environment and 52% in the HS environment, thereby emphasizing the importance of breeding for resilience to these stresses. In the DS environment, plants headed almost at the same time as in the optimum environment but were on average 22 days earlier in the HS environment. This is due to the high temperatures and longer day length in this environment that are known to result in shorter cycles, quicker maturity, and accelerated crop development rates. These are considered as adaptations of plants to hot weather enabling them to avoid excessive stress  the full-sibs in the training population (2) the minimal phenotypic GY variance among the full-sibs resulting from phenotypic GY selection in the first-year yield trials and (3) the minimal Mendelian sampling variance among the full-sibs, because of very small family sizes. These results indicate that GS will not be advantageous over pedigree-based selections in the EYT stage, given the family structure in these nurseries, highlighting the importance of implementing GS at the appropriate stage in the breeding program, where there is sufficient Mendelian sampling variation between the sibs. Nevertheless, predictions in populations with full-sibs in the training population compared to populations with only one progeny per cross, resulted in 24–321% increase in accuracies, clearly implying that genetic relatedness between the training and validation populations is crucial for good predictions as also reported in previous studies  genomic relationships and GNDVI (2) pedigree relationships and GNDVI (3) genomic and pedigree relationships also resulted in high accuracies. However, in EYT 16–17, the GBLUP and pedigree models also performed well and resulted in accuracies that were only slightly lower than the combined models. In the HS environment, the models with genomic/pedigree relationships and GNDVI, GNDVI in an IBCF approach and the genomic and pedigree models that had 50% of full-sibs in the training population resulted in the highest within-nursery accuracies. While Rutkoski et al.  and Sun In across-nursery predictions, the best accuracies in the DS and HS environments were obtained using GNDVI in an IBCF approach. It is interesting that the relationship based predictions across years were not more advantageous than using GNDVI of the validation population in the prediction models, although the lines in the different nurseries had some genetic relatedness. This also highlights the importance of having some information on a line’s performance in a particular environment (a correlated trait like GNDVI in this case) for successfully predicting GY and sparse testing should be considered cautiously when breeding for widely adapted and stable lines for diverse target environments.Genotype × environment interactionsG × E interactions, non-homogeneity of stress conditions across years that can increase error variance, variations in management and soil heterogeneity  using a covariate or a correction factor to adjust for DTHD  grown in the same year. These nurseries are generally not phenotyped for GY under stressed environments in CIMMYT, because of the cost, labor and resource constraints. Hence, GS- and/or HTP-based predictions of GY in two stressed environments might result in cost-savings of about 180, 000 USD . However, given that the cost of genotyping 9000 samples  is almost similar, real cost-gains can be achieved only when (1) breeding programs have higher GY phenotyping costs and (2) the cost of genotyping is lower or shared for predicting other traits. Nevertheless, phenotyping large populations also requires vast land area that might not be available for many breeding programs and GS can be a powerful selection tool in such a case.Scaling-up selections to earlier generations that are not yield-testedF5:F6 derived lines that are grown in small plots and not yield-tested or are too expensive for genotyping. This could result in huge cost-savings, if the HTP measurements for lines in the small plots are well correlated with their HTP measurements and yields in large plots.While this study has applied the IBCF approach on nurseries of about 1000 lines, our ultimate objective was to scale this approach for predicting GY with HTP traits in several ten-thousands of Increasing accuracies in early-generation across-family selectionsThe HTP trait based predictions can also be used to increase the selection accuracy in early-generation across-family selections. While within-family selections are not possible in early generations, HTP traits can enable selection of the best families for GY in stressed environments, that can then be advanced.The promising cross-validation accuracies obtained in this study indicate several opportunities for implementing GS and HTP within nurseries/years, some of which are discussed below:G × E interactions. Hence, some information on a genotype’s or a related individual’s phenotypic performance in a particular environment is important for training prediction models and minimizing risks. In addition, assessment of the cost–benefits by integrating GS and HTP in a breeding program is critical for the effective implementation of these technologies. Nevertheless, this study has successfully evaluated GS- and HTP-based predictions in CIMMYT’s EYT nurseries, and we conclude that they can be integrated in increasing the size of populations screened and evaluating unphenotyped large nurseries within years.In conclusion, predicting GY in stressed environments across years is challenging due to its complexity, plasticity, and Fig. S1The high-throughput phenotyping platform comprising a hyperspectral camera  from the Alava Remote Sensing Spectral Solution  (right), mounted in a Piper PA-16 Clipper aircraft (left) (TIFF 6068 kb)Fig. S2Phenotypic variance for grain yield within the full-sib families of each elite yield trial (EYT) nursery evaluated in drought-stressed and late-sown heat-stressed environments (TIFF 13125 kb)Fig. S3Heatmaps of the pedigree and genomic relationship matrices for all the lines in the four elite yield trial (EYT) nurseries (TIFF 34450 kb)Supplementary material 4 (CSV 71011 kb)Supplementary material 5 (DOCX 16 kb)Below is the link to the electronic supplementary material.


GEBVs) in farm animals. In this study, we conducted genomic prediction for 20 economically important traits including growth, carcass and meat quality traits in Chinese Simmental beef cattle. Five approaches  were used to estimate the genomic breeding values. The predictive accuracies ranged from 0.159 (lean meat percentage estimated by BayesCπ) to 0.518 (striploin weight estimated by BayesR). Moreover, we found that the average predictive accuracies across 20 traits were 0.361, 0.361, 0.367, 0.367 and 0.378, and the averaged regression coefficients were 0.89, 0.86, 0.89, 0.94 and 0.95 for GBLUP, BayesA, BayesB, BayesCπ and BayesR respectively. The genomic prediction accuracies were mostly moderate and high for growth and carcass traits, whereas meat quality traits showed relatively low accuracies. We concluded that Bayesian regression approaches, especially for BayesR and BayesCπ, were slightly superior to GBLUP for most traits. Increasing with the sizes of reference population, these two approaches are feasible for future application of genomic selection in Chinese beef cattle.Genomic prediction has been widely utilized to estimate genomic breeding values ( Genomic prediction has been widely utilized to estimate genomic breeding values (GEBVs) for quantitative traits in breeding program of farm animals , which is particularly renowned for rapid growth rate and palatable meat quality  .Animals originated from five farms in Ulgai Grassland, Xilingole League, Inner Mongolia of China. All animals were born between 2008 and 2013 and were weaned at approximately six months of age. After weaning, animals were moved to Beijing Jinweifuren farm for fattening and raised under the same feeding conditions. Animal were measured for growth traits every six or 12 months until slaughter. Live weight was measured after 24 h of fasting. Slaughter age ranged from 18 to 24 months. After slaughter, carcass traits and meat quality traits were measured according to the Institutional Meat Purchase Specification for fresh beef guidelines and GB/T 27643‐2011. In this study, a total of 20 traits were measured and analyzed . SNPs satisfying these criteria were used to interrogate the linkage disequilibrium with syntenic SNPs located with a window of 100 neighboring markers, which resulted in only one SNP form each pair of highly correlated SNPs (r2 > 0.995) remaining in the SNP dataset. After these quality controls, the final data consisted of 1217 individuals and 459 268 filtered SNPs in the autosomes. Genotype data are available from the Dryad Digital Repository (https://doi.org/10.5061/dryad.4qc06).A total of 1302 Simmental beef cattle were genotyped with the Illumina BovineHD SNP array. Missing SNPs were imputed using asreml v3.0 software  (GBLUP) VanRaden  and (ii)In all cases, the statistical model used was the following:y is an N × 1 (N = number of observations) vector of phenotype in Equation X is an incidence matrix of the fixed effects, Z is the incidence matrix allocating records to GEBVs, g is the vector of GEBVs and e is a vector of residuals. It is assumed that g follows a normal distribution N. Given b and g, y is conditionally independent and distributed as: ∼NFor GBLUP, y, X, b and e were defined as before, but g represented an M × 1 vector of SNP marker effects; Z is an N × M matrix of SNPs, coded with values 0, 1 or 2 for genotypes 11, 12 and 22 respectively; and Zij denotes marker j of individuals i.The Bayesian model used the same equation as in (1), where gj depends on the variance σj2 and the prior probability π. In BayesA, all SNPs have effects, i.e. σj2∼x-2, and π is equal to 0. σj2 denotes that SNP j has its own variance, with the parameters of v and Sa2. In BayesB, the two‐component mixture, with one component being t and the other component being a spike at 0, are provided as:j = 1, …… , PThe prior for π represents the proportion of SNPs with no genetic effects on the trait of interest. Sa2 is derived using following equation, Sa2=(v-2)∗E(σj2)v, where v is 4.2, as reported by Meuwissen et al. , and σg2 follows a scaled inverse χ2 prior with parameters v and Sa2. As a result, the SNP effects with probability (1 − π) follows a mixture of multivariate Student's t‐distributions t. The π parameter is treated as unknown with a uniform  prior distribution.Here, n et al. . In Bayeet al. et al. pi  in which the pi is drawn from a Dirichlet distribution  with pseudo‐counts of 1 for each component of the mixture. Thus, the prior assumes that the four components of the mixture are equally probable but with minimal prior knowledge of these probabilities.BayesR is an extension of BayesCπ, where SNP effects are assumed to be sampled from a mixture of normal distributions . To remove the influence of heritability on the predictive ability, Pearson's correlation between GEBV and corrected phenotype was divided by the square root of heritability , where y^ was the corrected phenotype. This value is approximate to the correlation between the true breeding value and GEBVs  was calculate to measure the degree of inflation or deflation of genomic prediction. Estimates of by^,GEBV close to 1 are indicative of predictions that are similar to that of corrected phenotype on scale.The slope of the regression of y^ and GEBV in the validation population was used to measure the overall fit of model, and the computation equation was MSE=1N∑(GEBV-y^), where N is the number of individuals. A large estimated value of predictive accuracy is indicative of reliable prediction, and a low MSE value means a better overall fit.The mean squared error of prediction (MSE) between Heritability estimates for 20 traits ranged from 0.04 to 0.62. We found that 10 traits showed relatively high heritabilities: FS (0.4), LW (0.43), RMW (0.43), ADG (0.47), BI (0.47), ICO (0.51), ER (0.52), OU (0.6), HS (0.61) and KN (0.62). Eight traits showed moderate heritabilities— BFI (0.21), ST (0.24), SR (0.26), CR (0.27), DP (0.31), CW (0.38), LMP (0.39) and TD (0.39)—whereas three traits had low heritabilities—pH (0.04), BFT (0.1) and SF (0.15). The standard errors for all heritability estimates were less than 0.04  ranged from 0.059 (for LMP estimated by BayesCπ) to 0.376  was observed across 20 traits using GBLUP compared with Bayesian methods Fig. . Among BAfter removing the influence of heritability from predictive ability, we found obvious difference in predictive accuracies ranging from 0.159 (LMP) to 0.518 (ST). The average predictive accuracies across traits were 0.361 for GBLUP, 0.361 for BayesA, 0.367 for BayesB, 0.367 for BayesCπ and 0.378 for BayesR respectively  and a large training population (n = T) give higher accuracies, which can be expected from the theory that Th2 is a critical parameter , we conducted genomic prediction for economically important traits including growth, carcass  and meat quality traits in Chinese Simmental cattle. Bayesian regression approaches, especially BayesR and BayesCπ, were superior to GBLUP for most traits. Thus, it may be feasible to apply these approaches for genomic prediction of these economically important traits in Chinese Simmental beef cattle. Further improvements are required to enlarge population size and reduce inflation of predictions. In addition, our findings provide valuable insights for further implementation of genomic selection in the commercial beef industry.The authors have no conflict of interest to declare.