The goals of quantitative genetics differ according to its field of application. In plant breeding, the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments. Keeping quantitative genetics current requires keeping old concepts that remain useful, letting go of what has become archaic, and introducing new concepts and methods that support contemporary breeding. The core concept of continuous variation being due to multiple Mendelian loci remains unchanged. Because the entirety of germplasm available in a breeding program is not in Hardy–Weinberg equilibrium, classical concepts that assume random mating, such as the average effect of an allele and additive variance, need to be retired in plant breeding. Doing so is feasible because with molecular markers, mixed-model approaches that require minimal genetic assumptions can be used for best linear unbiased estimation (BLUE) and prediction. Plant breeding would benefit from borrowing approaches found useful in other disciplines. Examples include reliability as a new measure of the influence of genetic versus nongenetic effects, and operations research and simulation approaches for designing breeding programs. The genetic entities in such simulations should not be generic but should be represented by the pedigrees, marker data, and phenotypic data for the actual germplasm in a breeding program. Over the years, quantitative genetics in plant breeding has become increasingly empirical and computational and less grounded in theory. This trend will continue as the amount and types of data available in a breeding program increase. The marriage between quantitative genetics and plant breeding, albeit nonexclusive, has reaped benefits for both during the last 100 years. Estimates of genetic variances and heritability in many plant species have increased our understanding of the inheritance and variation of important traits related to yield, quality, and adaptation Gardner . QuantitOpinion article is to provide a framework for reflection, discussion, and constructive debate of reasons and ways to reinvent quantitative genetics within the context of current plant breeding. The ideas proposed herein apply mainly to this context and they might not apply to other fields, such as human genetics and animal improvement, where quantitative genetics has also played an important role.That being said, developments in both plant breeding and quantitative genetics in the last several decades should cause us to pause and ponder how quantitative genetics can best be applied in contemporary plant breeding. The purpose of this Plant breeders may sometimes think that quantitative genetics was developed for the purpose of enhancing plant and animal improvement. After all, most economically important traits in crops and livestock species are quantitative rather than qualitative. However, quantitative genetics was developed not to provide a basis for artificial selection in different species, but to model how variation for continuous traits arises from unknown genes. Quantitative genetics originated more than a century ago in the aftermath of a heated dispute between two groups of eminent English scientists: the biometricians led by Karl Pearson and W.F.R. Weldon, and the Mendelists led by William Bateson Provine .The field of biometry began with Francis Galton’s work on how human characteristics, particularly height, were passed from parent to offspring Galton , 1889. GThese findings by the biometricians disagreed with Mendel’s findings, which were rediscovered independently in 1900 by Hugo DeVries, Carl Correns, and Erich von Tschermak. Mendel’s results indicated a particulate nature of inheritance that led to distinct classes, rather than a continuum of observations for a given trait. The absence of distinct phenotypic classes then suggested to the Mendelists that continuous traits are not heritable. DeVries went to the extent of considering the continuous versus discontinuous nature of variation as a criterion for a trait’s transmissibility Mather .The correlation between relatives on the supposition of Mendelian inheritance” that sought to reconcile the conflicting views of the biometricians and Mendelists. In so doing, this seminal article established the foundations of quantitative genetics as we know it today. The “on the supposition“ phrase in the title indicated the conjecture that quantitative traits are controlled by genes that behave in a Mendelian fashion, and the crux of Fisher’s supposition was that continuous variation is the result of the cumulative effects of many such genes. Fisher showed that such a model for quantitative variation could lead to the well-established correlations between relatives found by the biometricians. Fisher initially made two key assumptions to make the model tractable: the individuals mated at random, and each biallelic locus behaved independently of others. These two simplifying assumptions enabled genotype frequencies to be expressed in terms of allele frequencies and vice versa according to Hardy–Weinberg equilibrium, and allowed the cumulative effects across loci to be described in terms of the effect at an individual locus. At several junctures in his article, Fisher investigated the effects of multiple alleles, linkage, assortative mating, and epistasis.In 1918, R.A. Fisher wrote a paper entitled “VA). On the other hand, the non-transmissible portion of effects included dominance deviations as well as any environmental effects; to Fisher, dominance deviations were “a residue which acts in much the same way as an arbitrary error introduced into the measurements.” The variance due to dominance deviations has since become known as dominance variance (VD). Fisher recognized the existence of effects due to interactions of alleles at different loci and treated such effects as higher-order extensions in a linear model: “We may use the term Epistacy to describe such deviation, which although potentially more complicated, has similar statistical effects to dominance.”A key feature of Fisher’s derivations was the partitioning of effects into a transmissible and a non-transmissible portion. The transmissible or “additive” portion was due to the effects of individual alleles passed on by a parent to its offspring. These transmissible effects of alleles have since become known as the average effect of an allele Fisher . The varVA/(VA + VD). Because Fisher treated VD as a residual value that was not any different from random error, we can modify this parent–offspring regression as being equal to ½VA/VP = ½h2, where VP is the phenotypic variance and h2 = VA/VP is the narrow-sense heritability. Returning to our height example, suppose the difference between the height of a father and the population mean is denoted by S. If the height of the father and mother is uncorrelated , the expected deviation (from the population mean) of the height of the offspring is then equal to ½h2S.Fisher revisited Galton’s concept of parent–offspring regression and derived this regression as being equal to ½R = h2S, where R is the response to selection and S is the selection differential  yield , rice (Oryza sativa L.), soybean (Glycine max (L.) Merrill), and tomato (Solanum lycopersicum) have preferred the expediency of a nonrecurrent line and hybrid development system with biparental crosses instead of longer-term recurrent selection with broadbase populations. Because the variance among recombinant inbreds in a biparental cross is constant at 2 VA, there is little or no difference in the gains from line development via different methods  as long as reliable phenotyping of lines is done at some point during the line development process.The reality, however, is that sufficient answers to the first two questions are obtained without any detailed quantitative-genetic analysis whatsoever. For example, a large set of germplasm can be phenotyped to identify candidates with the best mean performance. Information on germplasm origins or, since the 1990s, data on molecular markers can be used to assess germplasm diversity. Hybrid cultivars are feasible if a hybrid outperforms its parents by a substantial amount, and if hybrid seeds can be produced in a cost-effective manner, with estimates of Manihot esculenta). This singular emphasis on finding lines, hybrids, or clones with the best genotypic value is a much more focused objective than the above three questions from 50 years ago  and perennial ryegrass (Lolium perenne L.) but, as mentioned above, not in row crops such as maize and wheat. The F2 of a biparental cross between homozygous maize or wheat parents has the same 1:2:1 genotype ratio attained via random mating. Each F2 population can therefore be treated as a random-mating population, and VA, VD, and h2 can be estimated, but such estimates apply only within the given F2 population.The two main assumptions invoked by Fisher —random mIn most situations, the entirety of germplasm within a breeding program does not comprise a random-mating population. Maize-breeding germplasm in the United States, for example, includes lines derived from key progenitors, such as A632, B37, B73, Iodent, LH82, Maiz Amargo, Minnesota 13, Mo17, and Oh43 Troyer . Maize bThe assumption of linkage equilibrium or independence among segregating loci is particularly problematic (Cockerham http://techservicespro.com/).Two technological developments have enabled new approaches in both quantitative genetics and plant breeding. First, cheap and abundant molecular markers in different plant species have allowed new types of analysis that were not possible prior to the 1980s. Breeders and geneticists were limited to the use of only up to a few dozen isozyme markers in the 1970s, but the number of available markers increased with the development of restriction fragment length polymorphism (RFLP) markers in the 1980s ij is the genotype × environment interaction effect associated with genotype i and environment j; and ɛij is the within-environment error. This classical linear model remains unchanged. However, there may be multiple ways to model the gi, ej, and (ge)ij components. For example, (ge)ij can itself be modeled as a multiplicative effect obtained as the product of an interaction score due to genotype i and an interaction score due to environment j  head blight resistance in wheat  × Parent 1)BC1. Whereas the F2 population can be assumed to behave as a random-mating population because the expected genotype ratio of 1:2:1 at segregating loci is the same as that with random mating, the same assumption cannot be made for the BC1 population because the expected genotype ratio is 1:1 at segregating loci, with one of the homozygotes not being recovered. At this point, the breeder is simply interested in identifying the best recombinant inbreds, regardless of whether an inbred was derived from the F2 or the BC1. The breeder has no need to make inferences regarding the mean or VA or h2 in the F2 or BC1, and it is therefore moot that one population is in Hardy–Weinberg equilibrium and the other is not.To illustrate, suppose recombinant inbreds are developed by selfing from a (Parent 1 × Parent 2)F2 genotype frequencies are those expected with random mating. Both the Edinburgh and Birmingham schools therefore apply to F2 populations encountered in plant breeding.The preceding example also brings to light the historical divergence between two schools of thought in quantitative genetics: the Edinburgh/Alan Robertson/Falconer  school tci2/(n − 1), where ci is the fixed effect of the ith candidate and n is the number of candidates.Not needing a reference population also circumvents the issue of whether the candidates are random members of a base population or are a fixed set of lines, clones, or hybrids that are not random members of any population. Suppose the candidates are a set of wheat cultivars and pre-commercial lines with diverse genetic backgrounds. In this situation, the variance component for lines (if the lines were random) is substituted by ∑Bos taurus) is of utmost importance because a top bull is prized not for its own milk yield (which is zero), but it is prized for the superior milk yield of its female progeny. In contrast, the genotypic value of a wheat line or a cassava clone is of utmost importance because producers would grow the wheat or cassava cultivar itself, rather than the cultivar’s progeny. The ability to genetically replicate plants but not animals therefore plays a key role in this distinction. The foregoing does not imply that breeders are uninterested in the performance of the progeny of an individual: on the contrary, selection of good parents is a key to success in plant breeding. What the foregoing implies is that individuals used as future parents are first and foremost selected on the basis of their superior genotypic value as individuals.Classical quantitative genetics as founded by Fisher  focused The concept of breeding value is shown to have no useful meaning when mating is not random.” The assumption of random mating, as discussed earlier, is typically violated in plant breeding.Second, breeding value is defined only when the mate is chosen at random and, as Falconer  indicateVA be meaningful because VA is the variance among breeding values. The VD and epistatic variance (VI) would likewise not be meaningful because these variances are derived from the same framework as VA. Therefore, quantitative genetics reinvented for plant breeding would retire the concepts of VA, VD, and VI. On the other hand, plant breeding students will still need to learn about VA, VD, and VI so that they can understand classical literature and communicate with quantitative geneticists who work with non-plant species, for which these concepts remain important.If we accept that the classical concept of breeding value is not meaningful to plant breeders, neither would VA, VD, and VI? The logical alternative is to simply calculate the variance component due to the candidates. In other words, breeders can calculate VF2 among F2 plants; VF3 among F3 lines; VRI among recombinant inbreds; VClones among clones; VHS among half-sib families; VFS among full-sib families; and VSX among single crosses. Single crosses are typically made between parents from two heterotic groups that complement each other, and VSX can be partitioned into VGCA1 for the general combining ability (GCA) of parents from the first heterotic group, VGCA2 for the GCA of parents from the second heterotic group, and VSCA for specific combining ability effects. It will be important to not use the symbol VG for any of these variance components because VG is traditionally defined as the sum of VA + VD + VI. Avoiding the VG notation will therefore reduce confusion.What then should be used as a substitute for VF2 or VClones or VSX has the advantage of being a direct expression of the variation due to genetic effects among the candidates undergoing selection. As previously mentioned, for example, the variance component for recombinant inbreds is VRI = 2 VA. The VRI therefore quantifies the amount of genetic variation expressed among the candidates, whereas VA by itself does not. Fisher’s /VP, has traditionally provided such measure. Calling H as a form of “heritability” is oxymoronic because dominance and nonadditive types of epistatic effects captured in H are nonheritable from a parent to its offspring.Retiring the concepts of h2 and H have actually been recognized as being muddled in plants as far back as the 1960s VA because only a quarter of the VA is expressed among half-sib families. Hanson (becomes lost in a maze of confusion” and he raised the need (but was reluctant) to consider an alternative to h2 and H.The concepts of s Hanson . The def. Hanson  concludeVSubjects/(VSubjects + Ve), where VSubjects is the variance component due to subjects and Ve is the error variance. In plant breeding, reliability can be defined as the variance component due to the candidates divided by VP.The concept of “reliability” can be borrowed as an alternative measure of the influence of nature versus nurture on phenotypic measurements Bernardo . Reliabii2, is then strictly tied to the selection unit used. If selection is among recombinant inbreds, reliability is i2RI = VRI/VP(RI), where VP(RI) is the phenotypic variance among recombinant inbreds. If selection is among clones, reliability is i2Clones = VClones/VP(Clones). The VP should be calculated on an entry-mean basis. Suppose that cassava clones are evaluated in e environments with r replications in each environment. The VP(Clones) is calculated as VClones + (1/e)(VClones × Environments) + (1/re)Vɛ, where Vɛ is the within-environment error variance.Reliability, which we denote by Repeatability has been used as a measure of consistency among repeated measurements Falconer . While ri2 indicates consistent measurements, information on what constitutes a statistically significant difference would also be helpful for the purposes of selection. For example, breeders might be aware that h2 is about 0.40 for Fusarium head blight resistance, but they might be surprised to find that this level of h2 could correspond to a line having 0% infection in one test and 7% in a different test. As a standard practice, it would be helpful to report estimates of both i2 and the least significant difference, e.g., “Among recombinant inbreds, estimates of reliability and the least significant difference  were 0.50 (0.72 Mg ha–1) for yield, 0.70 (0.85%) for protein percentage, and 0.40 (8.5%) for Fusarium head blight incidence.” Relaxed significance levels (P = 0.10 or 0.20) are recommended, given the relative impacts of a Type I error versus a Type II error in cultivar evaluation  are input into a manufacturing system  to have products (cultivars) that are marketed and distributed after rigorous testing and quality control  Bernardo . IndividR for individual crosses via the breeder’s equation, genetic gains for a breeding program as a whole can be simulated vis-à-vis the costs and time required. Simulation packages such as QU-GENE  of fixed effects and BLUP of random effects  used in GBLUP, which is equivalent to (1 − h2)/h2 in BLUP, can be estimated by a grid search followed by cross-validation to find the λ value that maximizes the predictive ability of the model  become available to inform breeding decisions.The latter paragraph should be modified today because mixed-model analysis now uses SNP marker data in GBLUP rather than pedigree-based coefficients of coancestry via traditional BLUP. The shrinkage factor (


Vitamin D deficiency is a candidate risk factor for a range of adverse health outcomes. In a genome-wide association study of 25 hydroxyvitamin D (25OHD) concentration in 417,580 Europeans we identify 143 independent loci in 112 1-Mb regions, providing insights into the physiology of vitamin D and implicating genes involved in lipid and lipoprotein metabolism, dermal tissue properties, and the sulphonation and glucuronidation of 25OHD. Mendelian randomization models find no robust evidence that 25OHD concentration has causal effects on candidate phenotypes , but many phenotypes have (direct or indirect) causal effects on 25OHD concentration, clarifying the epidemiological relationship between 25OHD status and the health outcomes examined in this study. Vitamin D is a precursor of the steroid hormone 1,25-dihydroxyvitamin D3, and its deficiency is associated with many adverse health outcomes. Here, Revez et al. perform a genome-wide association study for circulating 25-hydroxyvitamin D in 417,580 individuals and test for potential causal relationships with other traits using Mendelian randomization. Vitamin D, the sunshine hormone, is the precursor of a seco-steroid transcription regulator that operates via a nuclear receptor, and like other steroid hormones, exerts transcriptional control over many regions of the genome across many different tissues. In environments with access to adequate sunshine, ultraviolet radiation on the skin converts a precursor of cholesterol to vitamin D3. This is then further converted to 25-hydroxyvitamin D3 , and then to the active hormone 1,25-dihydroxyvitamin D3  in a variety of tissues. Some foods and vitamin D supplements also contribute to vitamin D levels. Definitions of vitamin D deficiency  are predominantly based on bone health2—according to these definitions, vitamin D deficiency is common in many countries, regardless of latitude and economic status3.In recent decades, there has been considerable interest in the links between vitamin D concentration and general health. While classically linked to bone disorders, there is growing evidence to suggest that suboptimal vitamin D status may be a risk factor for a much wider range of adverse health outcomes1. With respect to the genetic architecture of 25OHD, twin and family studies have reported a wide range of heritability estimates (from 0%4 to 90%5). A recent multivariate twin study demonstrated that approximately half of the total additive genetic variation in 25OHD may reflect genetic variation in skin colour and sun exposure behaviour6. Genome-wide association studies (GWAS) have identified common single-nucleotide polymorphisms (SNPs) located in biologically plausible genes7. The largest GWAS to date  reported six significant loci, which include GC (the vitamin D-binding protein gene), the DHCR7/NADSYN1 region (DHCR7 is involved in a conversion of a 25OHD precursor molecule to cholesterol) and CYP2R1 and CYP24A1 genes (which encode enzymes involved in 25OHD metabolism8). In total, common SNPs explain 7.5% (standard error (s.e.) 1.9%) of the variance of 25OHD8.Environmental factors such as season of testing and latitude contribute substantially to the serum concentration of 25OHD 9 and conduct a suite of post-GWAS analyses to aid interpretation of the results . Because we have an interest in the association between 25OHD and psychiatric disorders11, we use Mendelian randomisation methods to investigate the bidirectional association between 25OHD and psychiatric disorders, as well as with a wider range of traits and diseases. In addition, we present a GWAS to identify loci associated with variance in 25OHD  analysis) which can identify putative genotype environment interactions without prior identification of the environmental effect12. We identify 143 independent loci in 112 1-Mb regions associated with 25OHD concentration, and our findings implicate genes involved in lipid metabolism, dermal tissue properties and conjugation of 25OHD. We find no robust evidence that 25OHD concentration has causal effects on candidate phenotypes. However, we show that many phenotypes have (direct or indirect) causal effects on 25OHD concentration.Here, we conduct a GWAS of 25OHD based on the large UK Biobank (UKB) samplelts Fig. . We pres−1 . The distribution of 25OHD concentration, in keeping with expectation, is right skewed  > 0.2 to at least one other person in the set , from whom we estimate the heritability of 25OHD to be 0.32 (s.e. = 0.01) with little evidence for inflation from shared family environment  when estimated only from individuals measured for 25OHD in summer months (June to October) compared with those measured in winter months (December to April)  , not significantly different from 1. The proportion of SNPs estimated to have an effect on the trait (polygenicity parameter) using the SBayesS method13 was 0.8% or 9000 SNPs of the ~1.1 million HapMap3 panel14 common SNPs . Estimation of −1 per BMI unit (−0.036 RINT(25OHD) standard deviation (SD) units per BMI unit, linear regression P < 2.2 × 10–16) and a phenotypic correlation of −0.17 2, we chose the more conservative threshold of 25 nmol L−1. We conducted analyses bisecting 25OHD into a binary trait , but the results were consistent (given the expected reduced power) with our reported results treating 25OHD as a quantitative trait . To identify independently associated loci, we applied the GCTA–COJO method18 to the GWAS summary statistics using LD between SNPs estimated from a UKB subset (“Methods”), and identified 143 independent loci (including one on chromosome X)  14 were non-synonymous variants that alter protein coding , and (b) 9 were annotated to include small insertion/deletions. A summary of the results is provided in Fig. A total of 8,806,780 SNPs with MAF > 0.01 were tested in the GWAS analysis. Of these, 18,864 were genome-wide significant   identified 15,154 GWS variants, 150 GCTA–COJO independent SNPs , UKBR (N = 1632) and SUNLIGHT  consortium replication samples, respectively (Supplementary Data P = 6.7 × 10−6), 97  and 89  had the same sign of association test statistic as in the UKB discovery sample . The pairwise correlations between allele effect size estimates in the different cohorts were all highly significant, ranging from 0.44 between QIMR and UKBR and 0.91 between UKB and SUNLIGHT. Polygenic score prediction into the QIMR sample using SNP effects estimated in the UKB and the standard P-value thresholding method explained a maximum of 7.5% of the variance in RINT  . When the polygenic scores were derived from SNP weights from COJO or SBayesR applied to the GWAS summary statistics22, the prediction variance was higher 10.5% and 9.6%, respectively , while scores using the COJO SNP weights explained 3.6% of the variance (P = 1.6 × 10−14) and those using SBayesR SNP weights explain 5.5% of the variance  at the nominal significance level of 0.05 (Supplementary Data P (PLDSC) < 2.4 × 10−4). In partitioned SNP-based heritability analysis using SNP annotation to 53 functional categories25, 11 passed multiple testing significance threshold . These results are discussed in detail in Supplementary Note To identify 25OHD SNP associations with statistical evidence consistent with a causal/pleiotropic association via gene expression, we used summary-data-based Mendelian randomisation (SMR)28 genetic correlation estimated from 25OHD and BMI GWAS summary statistics was −0.17 (s.e. = 0.03) , with no support for a causal effect of vitamin D on BMI   and b25OHD.BMI = −0.15 . Hence, despite the clear evidence for a causal relationship between high BMI and low 25OHD, the biological relationship between these traits is more complex.First, we investigated the relationship between 25OHD and BMI. The LDSCrg) between 25OHD and 746 traits with GWAS summary statistics available in LD Hub30, and we used LDSC to estimate rg between 25OHD and 18 traits (including six psychiatric disorders) with GWAS summary statistics that are more recent than those included in LD Hub. Although many of the traits are highly correlated, we use a Bonferroni correction for 764 tests as the threshold for discussion of rg. The LDSC regression intercepts were close to zero, suggesting no sample overlap  with intelligence. There was also a significant negative rg with hours spent using a computer (PH0:rg=0 = 5.1 × 10−15). These findings may be mediated by an association between higher intelligence and behaviour associated with less exposure to bright sunshine . Of note, behaviours associated with outdoor activity  were positively associated with 25OHD, while phenotypes related to chronic disability were negatively associated with 25OHD.Next, we estimated genetic correlations . Such associations can reflect genotype-by-environment interaction in the absence of measurement, or indeed knowledge, of the interacting environmental risk factor12. Using data from 318,851 unrelated individuals of European ancestry, we tested 6,098,063 variants with MAF > 0.05, and identified 4008 GWS vQTLs, of which 25 were independent , and several were in genes with previously described links to vitamin D-related pathways . Of the 25 independent vQTLs, 23 were also QTLs  while the two non-QTL loci were still associated at PGWAS < 10−5 , which are involved in vitamin D metabolism32. Variants in POR have previously been associated with coffee intake33. The other exclusive vQTL (rs1030431) is 12,126 bp upstream from UBXN2B; the SNP is significantly associated with gall bladder diseases and lipid metabolism traits in the UKB34.We conducted a genome-wide vQTL analysis, as implemented in OSCAP < 5 × 10−8) interaction with season, and 1120 (99%) were also GWS in the vQTL analysis. From the 1127 GWS interactions, five were independent  and were located in regions that have well-known vitamin D-related genes in chromosomes 11  and 14   interactions with season of blood draw, we performed a GxE analysis with season (winter vs. summer). Of 6,098,063 variants tested (MAF > 0.05), 1127 had a GWS . rs1352846 (MAF = 0.29 (G)) is in the GC locus20, which encodes a protein synthesised in the liver that binds to, and transports vitamin D and its metabolites. rs116970203 is a low-frequency variant (MAF = 0.03 (A)) located in intron 11 of the PDE3B gene. It is also a perfect proxy for rs117913124 (LD r2 = 1), a low-frequency synonymous coding variant in CYP2R1, which was previously reported to associate with 25OHD19. Another CYP2R1 synonymous variant was also identified ). CYP2R1 encodes a crucial hepatic enzyme involved in the hydroxylation of vitamin D to 25OHD. Given the complexity of the association pattern observed in chromosome 11, we confirmed the independence of the COJO identified variants using individual-level data  and common SNP (rs12794714 or rs10741657) were largely independent.We have identified 143 loci associated with 25OHD concentration. Recognising that only six associated loci had been reported to date, these discoveries provide important insights into previously unknown or poorly understood vitamin D-related pathways, and substantially increase our knowledge of the genetic correlates of 25OHD compared with previous studies35 . In addition, several inter-genic loci had closest upstream or downstream genes of interest to lipid and lipoprotein pathways . Variants in these genes influence overall lipid concentrations, including the concentration of 7-dehydrocholesterol in the skin. We identified a locus (chr11:rs12803256) in an uncharacterised RNA gene (FLJ42102) 11,057 base pairs upstream from DHCR7. This region has been identified in previous GWAS studies, and DHCR7 is a strong candidate gene because of its known role in the conversion of 7-dehydrocholesterol in the skin to pre-vitamin D3. We note that the broad region on Chr11 containing DHCR7 and NADSYN1 included several loci of interest according to both GCTA–COJO and SMR analyses—this complex area warrants additional research.Our findings provide convergent evidence that genes related to lipid- and lipoprotein-related pathways influence 25OHD concentration. In particular, we confirm a unidirectional relationship between SNP instruments that influence higher BMI and lower 25OHD concentration, but not the reciprocal relationship. This relationship exists against a background of a highly intercorrelated pattern of relationships between genes that influence both 25OHD and a wide range of lipid-related metabolic phenotypes. There were variants within genes with well-described functions related to lipid and lipoprotein-related pathways1, our findings provide evidence that SNPs associated with genes that influence dermal development 36 and integrity 38 are also associated with 25OHD status. It has been suggested that variants in the FLG gene may have evolved in order to optimise 25OHD production at high latitude40. HAL (histidine ammonia-lyase) codes for an enzyme that deaminates L-histidine to trans-uronic acid. The top SNP in this region (rs10859995) is within an intron of this gene. The gene is expressed in the skin, and is upregulated during keratinocyte differentiation41. It has been demonstrated that trans-urocanic acid in the stratum corneum can absorb UVB42 and can reduce the production 25OHD43. The MAGMA gene-set analysis23 also showed that variants associated the uronic acid pathways were significantly overrepresented in our findings HSD17B1, HSD3B1), a family of short-chain dehydrogenases/reductases, which are involved in steroidogenesis and steroid metabolism. CYP2R1 is a key regulator of 25OHD status, via hepatic conversion of vitamin D to 25OHD—two loci were found within this gene. Other members of this large family of enzymes associated with 25OHD concentrations include CYP7A1, CYP26A1 and CYP24A1.Our study expands the range of enzymes implicated in the synthesis and breakdown of vitamin D-related molecules. These include genes from the hydroxysteroid 17-beta dehydrogenase family 49. A proportion of the total 25OHD may exist in the sulphated form, which could act as circulating reservoir for later de-sulfation in peripheral tissues. In addition, conjugated versions of 25OHD with glucuronide45 and sulfate46 have both been detected in bile, which suggests enterohepatic mechanisms may provide another reservoir that buffers total 25OHD reserves. The findings also have implications for how to assay total 25OHD reserves. Current extraction and assay techniques used to quantitate 25OHD are not optimised for sulphonated or glucuronidated species of 25OHD, thus total 25OHD status may not accurately reflect the contribution of these conjugated species. In addition, these mechanisms would contribute to the functional half-life of 25OHD, and thus influence vitamin D status during periods of reduced exposure to bright sunshine . Finally, variants in a range of previously unreported enzymatic pathways were also associated with 25OHD concentration .We identified many variants within genes related to the modification of lipophilic molecules . Associated regions on chromosomes 2 and 4 include enzymes in the UDP-glucuronosyltransferase family, which are critical in the glucuronidation pathways. The involvement of these genes in the degradation and potential conjugate recycling of 25OHD has recently been describedThe large sample size afforded by the UKB sample provides a thorough description of the genetic architecture of 25OHD. The SNP-based heritability (which captures the contribution to variation between people associated with common DNA variants) estimated in the UKB was 0.13 (95% CI: 0.12–0.14), which means that all genotyped/imputed variants with MAF > 0.01 explain about 41% of the heritability estimated from close relatives  may help with this prioritisation (Supplementary Data Pdifferent = 1.5 × 10−3), and this reflected an increase in genetic variance rather than a decrease in residual variance  for low 25OHD. Genetic correlations were significant between 25OHD concentration and a range of phenotypes  is a large population cohort with phenotype, genotype and clinical information on more than 502,000 individuals (age range from 40 to 69 years old). Participants were registered with the National Health Service, and lived ~25 miles from one of the 22 recruitment centres across the UK56 and UK10K57 reference panels by the UKB group58. We extracted variants with minor allele count (MAC) > 5 and imputation score >0.3 for all individuals, and converted genotype probabilities to hard-call genotypes using PLINK2 59. Then, we excluded variants with genotype missingness >0.05, Hardy–Weinberg equilibrium test P > 1 × 10−5, and minor allele frequency (MAF) < 0.01. In total, 8,806,780 variants ), including 260,713 SNPs in the X chromosome, were available for analysis.Genotype data were quality-controlled and imputed to the Haplotype Reference Consortium (HRC)60), using Hap Map 3 (HM3) SNPs with MAF > 0.01 in both data sets. European ancestry was assigned based on >0.9 posterior probability of belonging to the 1KGP European reference cluster.Individuals of European ancestry were identified by projecting the UKB sample to the first two principal components (PCs) of the 1000 Genome Project (1KGP3 and 25OHD2). Participants with 25OHD concentrations below or above the validated range for the assay (10–375 nmol L−1) were excluded. The average within-laboratory coefficient of variation (CV) (and standard deviation) ranged from 5.04 (4.73) to 6.14 (2.21)61.Vitamin D 25OHD levels were measured in blood samples collected at two instances: the initial assessment visit, conducted between 2006 and 2010, and a repeat assessment visit, conducted between 2012 and 2013. The Diasorin Liason®, a chemiluminescent immunoassay (CLIA) was used for the quantitative determination of 25OHD. The assay measures total 25OHD concentration  had vitamin D 25OHD levels (data field 30890) measured, mostly from the initial assessment visit . Our analyses were limited to the 417,580 individuals of European ancestry with 25OHD concentrations available, of whom 318,851 are unrelated (gcta --rel-cut-off 0.05).62. fastGWA is a tool implemented in GCTA63 for mixed linear model (MLM)-based GWAS. It uses a sparse genomic relationship matrix (GRM) to account for genetic structure within the cohort, making it a resource-efficient method for the analysis of large data sets like the UK Biobank62. The sparse GRM was generated for UKB individuals of European ancestry using HapMap3 SNPs.Figure We applied a rank-based inverse-normal transformation (RINT) to the phenotype (vitamin D 25OHD levels) and fit age at time of assessment, sex, assessment month, assessment centre, supplement-intake information, genotyping batch and the first 40 ancestry PCs as covariates in the model (see Supplementary Methods for more details).18 of the GWAS results, accounting for the correlation structure between SNPs within a 10-Mb window (COJO default parameter) and using a random subset of 20,000 unrelated Europeans from the UKB as linkage disequilibrium (LD) reference. For comparison, we used PLINK1.9 (--clump)64 to identify regional lead SNPs for genome-wide significant index variants (--clump-p1 5e-8) and variants were clumped with this lead SNP if they were located less than 10 Mb (--clump-kb 10000) away from, and with r2 > 0.01 (--clump-r2 0.01) with the index variant. To identify previously unreported associations, we a conducted a COJO analysis that conditioned (gcta --cojo-cond) on the six loci previously reported as genome-wide significant 65.To identify independent associations, we a conducted a conditional and joint  analysis8, used BMI as a covariate, hence we also generated UKB results including BMI in the model and used those for meta-analysis. In addition, the UKB GWAS results used for meta-analysis differed from the reported GWAS results in that 25OHD levels were natural-log transformed, and supplement intake was not included as a covariate. Before meta-analysis, we imputed the SUNLIGHT summary statistics  with ImpG66. After data management, we used a sample size-based approach67 to perform the meta-analysis (Supplementary Methods) on 6,912,294 SNPs that were shared between the data sets.The largest GWAS for 25OHD to date, from the SUNLIGHT consortium10. For this reason, previous GWAS of 25OHD have included BMI as covariate in their analyses8. However, given that BMI is a highly heritable trait, covariate adjustment can induce collider bias15 and affect downstream analyses. To better understand the relationship between 25OHD and BMI, we estimated the phenotypic and genetic correlation between them and used generalised summary-data-based Mendelian randomisation (GSMR)16 to test for statistical evidence for putative causal effects between the two traits. We confirmed through simulation that the MR regression statistic is not biased by sample overlap  > 0.2 to at least one other person in the set . Among these, there was a set including all pairs with 0.4 < r < 0.6 (1st degree), and a set including all pairs with 0.2 < r < 0.3 (2nd degree). We used these sets to estimate heritability of RINT(25OHD) levels (gcta --reml). To estimate SNP-based heritability, we drew a random subset , selected so that no pair of individuals had r > 0.05. We used a model that fits a single random genetic effect with a single genomic relationship matrix (GRM) constructed from all SNPs68, and also a GREML-LDMS model69 that fits ten random genetic effects and hence ten GRM (gcta --reml --mgrm). The ten GRM were constructed from SNPs annotated to five MAF  bins each divided into two by median LD score of the SNPs within the bin. The LD score of a SNP is a measure of the common genetic variation tagged by a SNP. The sum of the estimates for each MAF-LD bin is an estimate of the total SNP-based heritability. Under a neutral model, each of the five MAF bins is expected to explain 20% of the variance. Analyses were conducted with and without BMI as a covariate, and genetic correlation between 25OHD and BMI was estimated in a bivariate GREML analysis (gcta --reml-bivar). In addition, we estimated the genetic correlation and the genetic variance explained by 25OHD levels assessed in summer and winter , using bivariate GREML. Heritability and SNP-based heritability estimated as part of the GWAS analysis using fastGWA are also reported. Finally, we estimated SNP-based heritability by LD score regression28 (software default settings for European ancestry samples), SBayesR13 and SBayesS13 from GWAS summary statistics. From SBayesS, we also estimate the polygenicity (π) and selection (S) parameters.Our UKB sample included a set of 58,738 individuals who were related with coefficient of relationship (N = 1632 unrelated)6 for replication analyses. Samples were collected between May 1992 and January 2014, mostly from South–East Queensland (latitude 27° S). At this latitude, there is sufficient UVR to allow for vitamin D synthesis throughout the year70. Legal guardians gave written, informed consent prior to inclusion and testing. Studies were approved by the Human Research Ethics Committee of the QIMR Berghofer Medical Research Institute. Additional details of this study are provided elsewhere . Genotypes were imputed to phase 3 version 5 of the 1000 Genomes Build37 (hg19)21. The phenotype analysed was RINT(25OHD) pre-regressed on sex, age, month of collection, ten ancestry PCs and imputation batch. Association analysis was conducted in PLINK for the genome-wide significant COJO SNPs from the UKB analysis. We tested for the same sign of effect size between the UKB and the QIMR results. Next, using the sample, we conducted polygenic score analyses. Using only SNPs present in the Brisbane cohort, we selected independently associated SNPs from the UKB cohort in order to conduct standard P-value thresholding PRS analysis, choosing a range of P-value thresholds  and calculating polygenic scores for each individual in the QIMR cohort. We also calculated polygenic scores from SNP weights estimated by COJO72, SBayesR22 and SBayesS13. The Bayesian methods better account for the complex relationship between strength of association of, and correlation between, SNP effect sizes. For each set of polygenic scores, we estimated the proportion of variance explained by the scores in linear regression. We repeated these analyses in a sample of 1632 individuals selected from the UKB, whose PC1 value was just outside our cut-off for white European .We used the QIMR Brisbane-based twin and family sample 75.We conducted a number of analyses to annotate the 25OHD GWAS results. First, we used the FUMA online pipeline26. SMR integrates GWAS and eQTL  results with the aim of identifying pleiotropic or causal associations between a trait of interest and gene expression. We used eQTLs derived by the eQTLGen consortium from gene expression in whole blood27, using the a large sample for blood eQTLs , identifying 15,504 genome-wide significant eQTLs. In general, SNPs controlling variation in one tissue are found to control variation in other tissues76, hence using a large eQTL dataset is the most powerful approach. Moreover, blood is a relevant tissue for vitamin D-related gene transcription77. Other relevant tissues are the liver, skin and, given our hypotheses about the relationship between 25OHD and psychiatric disorders, the brain. To capture tissue-specific eQTLs in these tissues, we used GTEX eQTL data sets, despite the fact that these data sets are much smaller than the eQTLGen sample . In addition, we used eQTLs identified in pre-frontal cortex (N = 1866) from the PsychENCODE project78, and foetal brain samples (N = 120) from O’Brien et al.79. SMR significant results were declared at PSMR < 0.05/M per tissue, where M is the number SMR tests performed  have robust support for the direct causal or pleiotropic relationships of the trait-associated SNPs influencing gene expression.To help prioritise putative causal genes with expression underlying 25OHD levels, we used the summary-data-based Mendelian randomisation method (SMR)80, including psychiatric and brain-related disorders81 including intelligence31. To characterise the relationship between vitamin D and psychiatric traits, we conducted two sets of analyses. First, we used bivariate LD score regression28 to estimate the genetic correlation between vitamin D and psychiatric traits using the GWAS summary statistics generated with the UKB dataset and GWAS summary statistics that are available for attention deficit/hyperactivity disorder (ADHD)82, Alzheimer’s disease (AD)83, major depression (MD)84, schizophrenia (SCZ)85, bipolar disorder (BIP)86 and autism spectrum disorder (ASD)87. In addition, we obtained genetic correlation estimates between vitamin D and 746 traits available through the LD Hub database30. Second, we conducted generalised summary Mendelian randomisation (GSMR) analyses16 to assess if there was any statistical evidence that observed correlations could be explained by a causal relationship for seventeen traits .Published epidemiological studies have provided an extensive set of hypotheses about causal relationships between vitamin D and a range of phenotypes12, an approach to detect presence of genotype-by-environment interaction in the absence of measurement or knowledge of the interacting environmental risk factor, to identify SNPs associated with variance in 25OHD. Specifically, we used the Levene’s median test implemented in OSCA88. Following the guidelines of Wang et al.12, we (1) adjusted 25OHD levels for selected covariates (see below), (2) removed outliers more than 5 SD from the mean and (3) standardised the residuals to have mean 0 and variance 1. Each step was performed within one of eight groups defined based on sex  and supplement intake . This approach removed both the mean effect of covariates and the mean and variance differences between gender and supplement- intake groups, while retaining other distributional properties of the measure. Covariates included in the phenotype pre-regression were age at assessment, assessment month, assessment centre, genotyping batch and the first 40 PCs. To avoid spurious associations due to coincidence of low-frequency variants with phenotype outliers12, this analysis was restricted to SNPs with MAF > 0.05. To identify near-independent vQTLs, we clumped the vQTL GWAS results with PLINK1.9 (--clump) as above, using a 5 Mb window as recommended12.25OHD concentration is known to be affected by season of measurement, but other environmental factors may also impact 25OHD measures. We conducted a genome-wide vQTL analysis59 (--gxe) to include an interaction term with season of blood draw. For this analysis, the phenotype (25OHD levels) was processed as described for the vQTL analysis.To assess if significant vQTL associations reflected a GxE with season of testing, we conducted season-stratified GWAS and compared the results with the vQTL GWAS results. Specifically, we stratified the UKB cohort into two groups after visual inspection of the mean 25OHD concentrations per month (Supplementary Fig. Further information on research design is available in the Supplementary InformationDescription of Additional Supplementary FilesSupplementary Dataset 1Supplementary Dataset 2Supplementary Dataset 3Supplementary Dataset 4Supplementary Dataset 5Supplementary Dataset 6Supplementary Dataset 7Supplementary Dataset 8Supplementary Dataset 9Supplementary Dataset 10Supplementary Dataset 11Supplementary Dataset 12Supplementary Dataset 13Supplementary Dataset 14Reporting Summary


Region-based genome-wide scans are usually performed by use of a priori chosen analysis regions. Such an approach will likely miss the region comprising the strongest signal and, thus, may result in increased type II error rates and decreased power. Here, we propose a genomic exhaustive scan approach that analyzes all possible subsequences and does not rely on a prior definition of the analysis regions. As a prime instance, we present a computationally ultraefficient implementation using the rare-variant collapsing test for phenotypic association, the genomic exhaustive collapsing scan (GECS). Our implementation allows for the identification of regions comprising the strongest signals in large, genome-wide rare-variant association studies while controlling the family-wise error rate via permutation. Application of GECS to two genomic data sets revealed several novel significantly associated regions for age-related macular degeneration and for schizophrenia. Our approach also offers a high potential to improve genome-wide scans for selection, methylation, and other analyses. Bij, characterized by start positions i and end positions j (“binning”), sometimes defined by setting scanning parameter values (“sliding window”) , 21HLA-Bp value of 3.48 × 10−10, p′ value of 2.76 × 10−11, and OR of 1.18 . This bin overlaps with the protein-coding HLA-B, which plays a very important role in the immune system . This bin was found to be significantly associated with AAMD with p value 1.71 × 10−10, p′ value of 2.08 × 10−13, and OR = 1.27   was found to be significantly associated with AMD with p value of 3.78 × 10−80, p′ value of 1.23 × 10−70, and OR = 0.53   of 12 rare variants (MAF ≤ 0.05) was found to be significant with a tem Fig. . Interesith AAMD . Also, b38] Fig. . An exam 1.12, 1.. This bit of AMD . Another57] Fig. . Our fink of AMD . For mor−08 (Tables ADPGK), 17 , and 22 (CERC1)  comprising 20 rare variants (MAF ≤ 0.05), p′ value of 3.89 × 10−11, and OR = 1.37 . This gene was not previously reported to be related to schizophrenia. The relatively small sizes of the detected significant bins in the WES data of schizophrenia indicate that the availability of large whole-genome sequencing studies will enable a considerable power gain for our method  Table . These gene Fig. . Althougod Table .Table 2SWhile genome-wide scans with heuristically predetermined analysis regions are an established approach, they are limited in their scope, resolution, and power by requiring a prior choice of the analysis regions. In the context of selection analysis, Akey fittingly compared the scan with a hatchet and called for more refined scalpel-like approaches . We arguN = 1000, was found to be stricter (α = 2.95 × 10−8) than the commonly used threshold of α = 5.0 × 10−8. This result is consistent with previously published results [−8, which is anticonservative for large-scale association studies.GECS is scalable to large association studies of imputed and sequenced variant data, as demonstrated by our simulation of the null model. The efficiency of our implementation allowed us to estimate significance thresholds for RV analysis in whole-genome sequenced data for association studies comprising up to 20,000 individuals. As a by-product, the analysis offered another opportunity to study significance thresholds (FWER control at 5%) for single-marker analysis (SMA), which, even for small sample sizes of  results , 29 and α allow us to assess the absolute power of the region-based exhaustive scan in future whole-genome deeply sequenced data sets. In contrast to previous studies [The estimates of  studies , the pow studies .We applied GECS to real-world data sets, namely of AAMD (imputed microarray data) and of schizophrenia (WES), and performed very stringent quality control of both sets to avoid possible type I errors. Application of GECS to AAMD confirmed a multitude of previously reported rare associated SNPs, for which SMA was underpowered to pick up many signals due to the low MAFs. We confirmed that exhaustively scanning for association through all possible combinations of contiguous rare variants from different MAF thresholds alleviates the limitations posed by previous fixed-bin strategies. The in-depth follow-up analysis showed high enrichment of genes covered by identified bins in pathways with key roles in the development and function of immune system. Our approach was also successfully applied to the schizophrenia data set, however, judging by the limited spatial extent of the resulting bins, the approach might be underpowered due to limited coverage of the genome in WES studies and will probably improve with availability of WGS data.GECS is a powerful approach for detecting phenotypic association of genomic regions harboring rare variants and for refining our understanding of their contribution to predisposition for complex diseases. We conclude that our approach is well-suited for whole-genome and whole-exome association analyses. However, GECS utilizes the simple allele counting function of COLL to achieve perfect, essentially base-pair-level spatial resolution. As COLL is only able do dichotomize individuals by the carrier status, the test is not able to distinguish between carriers of one or more minor alleles. We alleviated the limitations of COLL by performing follow-up analysis of candidate regions with locally exhaustive scans using SKAT. Enabling the exhaustive scan with more sophisticated tests that take more sources of information into account, like allele counts and covariates, might reveal further associated candidate regions. The challenge of extending the exhaustive scan approach to more complex association tests is purely computational in nature. Our algorithm does not generalize to other published association tests in a straightforward manner, so that new solutions will be required to generalize the exhaustive association scan beyond the collapsing method.p values.Application of exhaustive scans is not limited to association testing and could be useful in further applications, in particular for studying methylation and evolutionary selection. In fact, our preliminary results show that the exhaustive scan is feasible for the study of selection when used with SFS-based tests such as Tajima’s D (data not shown). This is due to the fact that the computational complexity of SFS-based tests is independent from the number of individuals in the study, since only allele count data is required. As a consequence, the quadratic space of all contingent regions can be computed by brute force, even for very large data sets. Moreover, modern, efficient coalescent simulators such as msprime  and fastIn summary, we developed a method that allows for an exhaustive scan of all possible contiguous genomic regions with the collapsing test and eliminates the choice of candidate bins. Instead, the space of all possible bins is tested. This eliminates binning as a source of type II error and is expected to improve power. Furthermore, the speed-up by several orders of magnitude allows for computation of nonconservative genome-wide significance thresholds by permutation, leading to improved power when compared with conservative correction methods such as Bonferroni’s. We show that GECS indeed improves statistical power in both simulated and empirical data sets.TheExhaustiveGenomicScan_Supplementary_Revision2External_data


P-value < 0.05 to achieve good power in rare disease association detection.Due to the affordability of whole-genome sequencing, the genetic association design can now address rare diseases. However, some common statistical association methods only consider homozygosity mapping and need several criteria, such as sliding windows of a given size and statistical significance threshold setting, such as p-values into continuous scores based on the maximal segmental score (MSS) , converts re (MSS)  for detere (MSS) .p < 0.05. For our observed data, the bone morphogenetic protein 1 (BMP1) gene on chromosome 8, the Violaxanthin de-epoxidase-related chloroplast (VDR) gene on chromosome 12 associated with OI, and the tetratricopeptide repeat domain 7A (TTC7A) gene on chromosome 2 associated with MIA have previously been identified as harboring the relevant pathogenic mutations.Our simulation results show that eMSS had higher power as the number of non-causal haplotype blocks decreased. The type I error for eMSS under different scenarios was well controlled, When compared to HDR-del, our eMSS is powerful in analyzing even small numbers of recessive cases, and the results show that the method can further reduce numbers of candidate variants to a very small set of susceptibility pathogenic variants underlying OI and MIA. When we conduct whole-genome sequence analysis, eMSS used 3/5 the computation time of HDR-del. Without additional parameters needing to be set in the segment detection, the computational burden for eMSS is lower compared with that in other region-specific approaches. In thousands of patients with rare diseases, whole-genome sequencing has been used to identify new causes of disease, which can help us increase our understanding of biological processes and improve clinical care. Because DNA sequencing is affordable, the genetic association design can now address diseases affecting fewer than 1,000 people. However, the statistical association methods that have been used so far to detect disease-related loci need several criteria to achieve good power in association detection, especially when the number of individuals with a rare disease is small. Compared to common diseases in the general population, rare diseases are low-prevalence health conditions that affect only a few individuals. Rare diseases include rare cancers, genetic diseases, and degenerative diseases. Among them, 80% of rare diseases are influenced by genetic effects . In situA single-marker association test may be inefficient when each genetic marker contributes only a small amount of association to a disease trait/phenotype. More powerful methods are region-specific tests, which take into account information on the heterogeneous genetic backgrounds of adjacent markers due to differences in allele frequencies and marker characteristics . Scan stFor set limits on window size, Autosomal recessive (AR) disorders usually occur in only one generation, so genetic linkage analysis is unlikely to be powerful. In previous AR studies, Here, we develop a novel region-specific method for the whole sequence called eMSS; it expands our previous continuous version of the MSS method  and is uIn short, the proposed eMSS converts any sequence of marker-wise testing results into a visualized MSS plot in which most susceptibility regions of markers can easily be identified. It comprises the following steps:(1)p-values on testing the difference between case and control groups.To calculate marker-wise (2)p-values into appropriate scores.To transform (3)To convert the sequence of scores into an MSS plot and identify the region with maximal segmental score (MSS region).(4)For subsequences in the above MSS region, repeat step 3 to search for the second MSS region, etc.There are many ways for testing marker-specific differences between case and control groups, and for our interest in rare diseases with extremely small numbers of cases, we use the following pairing scheme developed by G = 0 (REF/REF), 1 (REF/ALT or ALT/REF), or 2 (ALT/ALT). m controls, as illustrated in m case–control pairs, and the control–control group comprises m(m − 1)/2 control–control pairs. For a prespecified region width, they calculate a Hamming distance ratio (HDR) of the markers within it and obtain the t statistics on the difference of HDR between case–control and control–control groups. They show that the method is efficient to identify disease-related markers for rare diseases /2 for case–control or control–control pairs, respectively. The dissimilarity between the two individuals in a pair is then measured by the absolute difference, | G1 − G2|. For example, for a genotype pair of  = , the dissimilarity is |1 − 2| = 1.For illustration, we simplify the HDR method by considering only the smallest width of region that contains only one marker. Let t statistic to test the following hypothesis:If a variant is disease causing, the mean dissimilarity in case–control pairs is expected to be greater than that in control–control pairs, i.e., we use a one-sided, two-sample againstThe motivation for our approach is that we expect a larger “distance” between individual cases and individual controls for DNA fragments containing pathogenic variants than for random DNA fragments.Y1, …, Yn, which represent the dissimilarity of n markers between the DNA sequences of two individuals. As the simplest example, Yi = 1 if, at marker i, both sequences carry the same genotype; otherwise, Yi = −1. Note that a necessary condition for MSS to work is E[Yi] < 0, i.e., Yi should more likely be negative than positive in the sequence.To take into account the markers flanking each SNP, we develop a scoring system based on our previous continuous version of the MSS method. MSS was proposed by Yi by a continuous score, which is a monotone function of Pi , where Pi is obtained from a two-sample t-test on testing the difference between the case–control and control–control groups at marker i in the sequence.In our application, we replace the discrete p-values and make the MSS plot more visually friendly, we employ the Fisher transformation, −2ln(Pi), which transforms a uniformly distributed p-value into a chi-square distribution with 2 degrees of freedom. Furthermore, to allow for the MSS condition, E[Yi] < 0, we use the left-censored Pi truncated by its 10th percentile (denoted as Pc) to avoid infinity from extremely small Pi, i.e.,To smooth the wiggly plot based on original and define the score asYi = −2 ln (Pi) − Pf, i = 1,…, n markers,Pf is set to be f > 1 to assure a negative mean of Yi (E[Yi] < 0). The choice of f is analogous to the rotation parameters in factor analyses, in which some f can make the display of the MSS plot easier to identify susceptibility regions of markers. In our applications, we found that f = 1.2–1.5 has the best visualization. We illustrate it by simple examples after the description of the MSS procedure.where The MSS procedure includes the following steps:(1)Calculating the partial sum of the sequence of marker scoresY1, …, Yn] are aggregated in a sequential manner to form a sequence of partial sum scores , where U0 = 0 is the initial partial sum score, and m = 1, 2, …, n. Um is the partial sum up to the mth marker in the sequence. The partial sum scores Um as a function of the single marker scores Yi are increasing or decreasing with i because Yi can be negative.The single marker scores , ladder points are defined as J0 = 0, Jv = minj {j : j ≥ Jv + 1 + 1, Uj − UJv + 1 < 0}, v = 1, 2, …, nl, where nl = the number of ladder points Identifying the maximal segmental scoreSv, is computed as the difference between the largest partial sum of a subsequence and the initial partial sum of the subsequence. The equation used to obtain the segmental score is as follows:For each subsequence, the segmental score, Sv is a non-negative value defined as the difference between the largest partial sum and the initial partial sum value within the subsequence defined by two adjacent ladder points. In the example , 0, 0, 0, 0, 0, (U18 − U8), 0. A zero score denotes no increase between two adjacent ladder points. The larger the score, the more likely the target SNP is in the segment. The maximum segmental score for the whole sequence is recognized as eMSS = max . In the example shown in U18 − U8). The statistical significance of eMSS is assessed by permutation as shown below.where  example , the Sv (4)Permutation testp-value of the eMSS is estimated by permutation. In order to derive the null distribution of eMSS while preserving the genotype data structure, we generate m replicates by randomly shuffling the case–control status of all individuals and then carrying out the above described steps each time. The observed eMSS is then compared to the null distribution to derive the empirical p-value, which is defined as the proportion of permuted eMSS at least as large as the observed eMSS. A significance level of 0.05 was used here.To test the null hypothesis of no disease genes, the (5)f for better visualization of MSS plotsVarying f is small, say f = 1, the region with MSS tends to be too useless, i.e., the region is nearly half the whole sequence and is not helpful for identifying the small number of target markers. f. In f = 1, the region is nearly half the whole sequence, which is not helpful for identifying the small number of target markers. On the other hand, if f is large, say f = 1.25, then the Yis are mostly negative, and the MSS plot tends to be steeply decreasing either without any positive segmental score or non-significant MSS  in this region. The segmental score is the maximum height in this region, and the region with highest MSS is considered to be the most likely to contain the disease-related markers than other regions. The ideal situation is that the MSS region occurs with as few markers as possible so that the disease-related genes can easily be identified. If cant MSS . An ideaIn our simulation study, we used the simulation software SNaP  to gener(1)Number of haplotype blocks: (2)Haplotype frequency: (3)Allele frequency (AF): The allele frequency of a causal variant at AF = 0.01 and AF = 0.001.(4)Number of cases and controls: one case versus 32 controls, one case versus 50 controls, and three cases versus 32 controls.First, the simulation results showed that eMSS had higher power and lower type I error in low-density haplotype blocks  than in high-density  haplotype blocks  gene (BMP1) gene  gene  was founP1) gene  was obseP1) gene . BecauseP1) gene . All affP1) gene , 2016. IP = 0.015). In refinement analysis  on chromosome 8 for OI associated analysis using the ALSPAC data set.Results obtained by our eMSS analysis show that we were able to identify the OI disease variants to be in the top three of sequence segments ranked on chromosome 8  and MIA P = 0.002). In the eMSS refinement, the sequence segment extended over 143 kb on chromosome 2  (MCFD2) and tetratricopeptide repeat domain 7A (TTC7A). Using the ALSPAC data set, that segment ranks first on chromosome 2 of the MIA correlation analysis.For MIA analysis, there were 3,484 SNPs on chromosome 2 for the intersection of two sets ALSPAC and three MIA cases . In the data set of three MIA cases and 32 ALSPAC controls, the length of the most significant sequence segment detected by the eMSS method was 29,759 kb  . This seP = 0.002 in all three MIA cases considered together) was also detected by patients F1 , F4 , and F6 , separately. In the eMSS refinement for the patient F1, the sequence segment ranged over 4 kb on chromosome 2   were also considered separately in our study. The most significant sequence segment detected by the eMSS method in all three MIA cases considered together, the sequence segment  . Thus, p= 0.030) , S5.BMP1 gene on chromosome 8 associated with recessive OI and (2) in the TTC7A gene on chromosome 2 associated with recessive MIA (Mutations had been identified (1) in the sive MIA . Thus, wp = 0.0303) and F6  patients. When considering ROHs of length between ±1.5 Mb of the lengths of the pathogenic regions, out of 4–345 candidate variants, HDR-del successfully narrowed down pathogenic variants to be ranked 2 (for F6) through 26 (for OI)  . When co(for OI) .Except that eMSS flags shorter causal chromosomal regions, eMSS succeeded in detecting a pathogenic region for OI and MIA . However, we have fine-tuned the parameter settings, such as window size, but HDR-del only succeeded in detecting OI and F6.VDR mutation responsible for OI.We also applied eMSS to other real data from Chinute, Pakistan . Blood sP = 0.015, P = 0.015, P = 0.015, P = 0.015, VDR gene on chromosome 12 associated with recessive OI  separately versus 32 control individuals from the ALSPAC  data setssive OI . Furtherp = 0.0303, p = 0.0303, We also applied the HDR-del  approachAlthough eMSS and HDR-del both successfully detected the causal chromosomal regions of III-5 and III-15, the precision of the two methods to determine the causal regions was not similar. In the eMSS refinement, the candidate causal region flagged in the eMSS can keep shrinking this region.p-values into continuous scores and does not need to set segment sizes. The eMSS has several advantages over existing HDR-based and MSS-based methods (Our eMSS method converts  methods : (1) OurWe drive the selection of ladder points by matching amino acid sequences based on similarity scores (such as BLAST) . In our Pi in Yi from a two-sample t-test to a simple t-test for a difference in case and control means. For a single case individual, by subtracting case value from each control, the case–control group has a mean equal to the difference between the control mean and the case. However, for the control–control group, since the subtractor and subtrahend are in random order, the mean of this group is not necessarily zero; therefore, the HDR t statistic does not wind down to a one-sample t-test. Actually our simulation had shown that the one-sample t-test has much lower power due to the small sample size. From our simulation result, in the L block and E haplotype frequency pattern, we found that eMSS with the Pi obtained from a one-sample t-test had much lower power (55.1%) compared to 96.2% from a two-sample t-test. Similarly, in the worst scenario , eMSS with the Pi obtained from a one-sample t-test showed a 59.8% decrease in power down to 5.5%. Moreover, eMSS with the Pi obtained from a one-sample t-test gave a slightly higher type I error. Especially at H block and nE haplotype frequency pattern, eMSS with the Pi obtained from a one-sample t-test had 11.5% type I error compared to 3.0% with the Pi obtained from a two-sample t-test , and more rarely, collagen, type I, alpha 1 (COL1A1) point mutation or small deletion and short stature. VDR anomalies in the development of the diseases occurring with hereditary osteoporosis. The pathogenic region in BMP1 and VDR can be detected successfully in our OI analysis. Our eMSS can analyze rare disease one-case studies and is very useful for detecting pathogenic regions related to specific disease subtypes.Osteogenesis imperfecta is a genetic disease characterized by low bone mass, increased bone fragility, and recurrent fractures . Autosom in 2012  as the dFor MIA, our data set involved three case individuals . We compared the results from consideration of three MIA case individuals together and the consideration of three MIA case individuals separately; we found the latter consideration in the refinement could efficiently narrow down the segment size –S5. TherPf settings to detect associated segments across 22 chromosomes in a sequence, pathogenic variation information might be diluted. Hence, we suggest that researchers use our eMSS method separately by chromosomes.In our Québec authentic data analysis, we combined 22 chromosomes in sequence data to detect segments potentially containing pathogenic variants via our eMSS method, but the most important sequence segment ranging from 20,884,737 to 25,042,515 bp on chromosome 8 cannot be detected in our OI analysis. One of the possible reasons is that gene density varies greatly among the chromosomes . For exap-values) not limited to a particular test. On the other hand, an appeal of p-value–based methods is that raw data is often not required. The eMSS avoids predefined thresholds or window sizes in identification of tentative association regions. On the contrary, HDR-del is limited to a particular test and parameter settings to achieve better detecting performance for causal regions.eMSS is based on association statistics (or Homozygosity Mapper  providesWNT1) mutation is responsible for OI. However, there was only one SNP located in the WNT1 on chromosome 12 for the intersection of two sets ALSPAC and Pakistani in our authentic data set analysis. Hence, eMSS cannot find significant segments located in the WNT1 in our study. That is one of the limitations of using public data.In Pakistani previously published results, A limitation of our study is that eMSS requires control individuals in addition to a single or a few case individuals in our authentic data analyses. We used 32 control individuals as a compromise between cost and efficiency, which proved to be adequate for the given data. Applied to our case individuals and corresponding control individuals, the eMSS method narrowed down the length of the pathogenic sequence segment more than the previous region-specific method . AlthougProgram Availability: The software package containing the R source code and a detailed documentation are freely available for download at http://www.csjfann.ibms.sinica.edu.tw/eag/programlist/eMSS/eMSS.html. Availability of Data and Material: Source code developed for this project is available at http://www.csjfann.ibms.sinica.edu.tw/eag/programlist/eMSS/eMSS.html. Data to ALSPAC samples used in our manuscript have been deposited with the European Genome-phenome Archive (EGA), Wellcome Trust Genome Campus, Hinxton, Cambridge CB10 1SD, United Kingdom, with study accession number EGAD0000100740.A-RH, JO, I-BL, and CF contributed to the statistical analysis and writing of the manuscript. JS and CC contributed to the statistical analysis.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Both genetic and nongenetic factors can predispose individuals to cardiovascular risk. Finding ways to alter these predispositions is important for cardiovascular disease prevention.We used a novel whole‐genome approach to estimate the genetic and nongenetic effects on—and hence their predispositions to—cardiovascular risk and determined whether they vary with respect to lifestyle factors such as physical activity, smoking, alcohol consumption, and dietary intake. We performed analyses on the ARIC (Atherosclerosis Risk in Communities) Study (N=6896–7180) and validated findings using the UKBB . Lifestyle modulation was evident for many cardiovascular traits such as body mass index and resting heart rate. For example, alcohol consumption modulated both genetic and nongenetic effects on body mass index, whereas smoking modulated nongenetic effects on heart rate, pulse pressure, and white blood cell count. We also stratified individuals according to estimated genetic and nongenetic effects that are modulated by lifestyle factors and showed distinct phenotype–lifestyle relationships across the stratified groups. Finally, we showed that neglecting lifestyle modulations of cardiovascular traits would on average reduce single nucleotide polymorphism heritability estimates of these traits by a small yet significant amount, primarily owing to the overestimation of residual variance.Lifestyle changes are relevant to cardiovascular disease prevention. Individual differences in the genetic and nongenetic effects that are modulated by lifestyle factors, as shown by the stratified group analyses, implies a need for personalized lifestyle interventions. In addition, single nucleotide polymorphism–based heritability of cardiovascular traits without accounting for lifestyle modulations could be underestimated. A novel whole‐genome approach reveals that lifestyle factors can modulate genetic and nongenetic effects on cardiovascular traits.Lifestyle changes are relevant to cardiovascular disease prevention, but the associated cardiovascular health benefits are greater for some individuals than others, implying a need for personalized lifestyle interventions.ARIC Atherosclerosis Risk in CommunitiesG‐C genotype–covariateGREML genomic restricted maximum likelihoodMRNM multivariate reaction norm modelR‐C residual–covariateRNM reaction norm modelUKBB UK BiobankCardiovascular diseases (CVDs) are the world's number 1 cause of mortality, claiming an estimated total of 17.9 million lives globally in the year 2016 alone—that is 31% of the total deaths in a single year.Given the substantial genetic and nongenetic contributions to CVD risk, identifying ways that modify their effects can have important implications for CVD prevention. In fact, the idea of genotype–environment or genotype–covariate (G‐C) interaction is well established for traits such as body mass index (BMI).Understanding G‐C and R‐C interactions in the context of cardiovascular traits will not only translate into empowering public messages but also enable personalized lifestyle changes for CVD prevention according to individuals’ genetic and nongenetic information, as opposed to a one‐fits‐all approach that neglects individual differences. Aside from its practical implications, studying G‐C and R‐C interactions is also of theoretical value as it may offer some insight into missing heritability.To date, G‐C interaction estimates for cardiovascular traits are based on a limited number of genetic variantsSimulated data used in this article can be obtained from the authors upon request. Our access to the ARIC (Atherosclerosis Risk in Communities) Study data was under the code phs000090, and access to the UKBB (UK Biobank) data was approved by the UKBB research ethics committee under the reference number 14 575.dbgap-help@ncbi.nlm.nih.gov) and the UKBB (access@ukbiobank.ac.uk). The ARIC Study was chosen for our primary analyses because it covers a wider range of cardiovascular traits than the latter data set. The UKBB, which has a larger sample size than the ARIC Study, was chosen as the validation set. The sample sizes for our analyses depended on the availability of phenotype and genotype data, which varied between studies and cross traits. For the ARIC Study, the sample sizes were between 6896 and 7180. For the UKBB, the sample sizes were between 14 076 and 34 538.Our analyses were based on the following 2 data sets: the ARIC Study and the UKBB. Because of the sensitive nature of the data collected for this study, requests to access the data sets from qualified researchers may be sent to the database of Genotypes and Phenotypes . All ARIC Study and UKBB participants gave written informed consent.The ARIC Study is a prospective study on the cause of atherosclerosis, with data collected from up to 5 visits over 15 years from participants of 4 U.S. communities  who were aged between 45 and 64 years in 1987 to 1989.A total of 23 cardiovascular health‐related traits were selected. Coagulation factors were determined in the ARIC Central Hemostasis Laboratory using previously published procedures.A total of 22 lifestyle covariates were selected. Smoking was indexed by “cigarette years of smoking,” derived by multiplying the average number of cigarettes per day with the number of years smoked. Alcohol intake was indexed by usual ethanol intake from wine, beer, and hard liquor in grams per week. Dietary composition was assessed using a 66‐item food‐frequency questionnaire based on the Willett 61‐item questionnaire.The ARIC Study genotype data set contains 609 441 SNPs that are genotyped for 8291 participants. We first selected autosomes from white European participants then applied standard quality control procedures to the selected data set. This involved (1) excluding SNPs with a genotyping rate less than 95%, ones that failed the Hardy–Weinberg test at the 0.0001 level or had a frequency less than 0.01; (2) excluding individuals who were missing 5% of genotype data; and (3) removing related individuals by excluding 1 person at random using a Bernoulli distribution with a selection probability of 0.5, from each pair that had an estimated genomic relationshipThe UKBB contains health‐related data from ≈500 000 participants aged between 40 and 69 years who were recruited throughout the United Kingdom between 2006 and 2010.The second release of the UKBB genotyping data set was used. Before quality control, the dataset contains 92 693 895 imputed autosomal SNPs of which genotypes are available for 488 377 individuals. We selected the third phase of the International HapMap project (HapMap3) SNPs from individuals of white British ancestry only and applied the same quality control procedures as for the ARIC Study genotyping data set. Only HapMap3 SNPs were selected because they were shown to yield reliable and robust estimates of SNP‐based heritability and genetic correlation.To estimate the variances of G‐C and R‐C interaction effects, we used multivariate reaction norm models (MRNMs),Of note, the full model versus the null model comparison method on its own does not disentangle orthogonal G‐C or R‐C interaction effects. As documented in Data Before fitting MRNMs, all selected cardiovascular traits were adjusted for demographic and lifestyle variables using linear models that regressed phenotypes on demographic and lifestyle variables. The demographic variables included age, sex, education level, marital status, field center identification, and population structure, as measured using the first 15 principal components of the estimated genomic relationship matrix. All lifestyle variables described in the previous section were included for the adjustment. Depending on the cardiovascular trait, some additional adjustment factors were also included. For resting heart rate, blood pressure measures, electrocardiography variables, and coagulation factors, additional adjustment factors included hypertension, defined as systolic blood pressure ≥140 or diastolic blood pressure ≥90, and hypertension‐lowering medication use. For total cholesterol and triglycerides levels, additional adjustment factors were hypertension, hypertension‐lowering medication use, cholesterol‐lowering medication within 2 weeks, and medications that secondarily affect cholesterol. As the second trait in the multivariate reaction normal model . Specifically, nongenetic effects, in contrast to genetic effects, are referred to as effects of unknown factors that are not explicitly specified in our model and hence are partitioned as residual effects. On the other hand, lifestyle covariates are known factors and hence are explicitly specified in our model as modulators of genetic and nongenetic effects. The distinction is shown in Figure We also considered the consequence of neglecting G‐C and R‐C interactions on heritability estimates. Specifically, we estimated heritability of each trait using 2 models, one that includes no interaction term at all, that is, the null model (that uses genomic restricted maximum likelihood [GREML] for parameter estimation), and the other, referred to as the “interaction model,” that includes significant interaction terms that emerged from our primary analyses, and compared the estimates of the 2 models. To reduce computational burden, we used univariate RNMs as opposed to MRNMs. Details of univariate RNMs can be found in Data We had a total of 23 CVD traits, and for each trait we screened 22 available lifestyle covariates for G‐C and R‐C interactions. Of the 506 pairs of cardiovascular traits and lifestyle covariates, 214 yielded significant results at the 0.05 level, where the full model had a better fit than the null; after Bonferroni correction, 68 pairs remained significant Figure . Given tOf the 34 significant pairs remaining after the rank‐based inverse normal transformation, 17 were covered by the UKBB, allowing replication of the analyses conducted in the ARIC Study. The majority of these signals, 14 of 17, were present in both data sets Figure  right. Tσα12^ and στ12^ for G‐C and R‐C interaction effects, respectively), the greater the genetic or residual heterogeneity across different values of the lifestyle covariate, meaning the greater individual differences in the phenotype‐lifestyle relationship; hence stronger interaction effects. Thus, variance estimates of the interaction effects can serve as measures of interaction effect size and hence are indicative of the relative importance of different lifestyle covariates to a given trait. For example, the variance estimate of G‐C interactions of HDL3 cholesterol level is larger for physical activity (abbreviated as pa2) than for alcohol consumption . Such collinearity is likely attributed to the same covariate being used for estimating G‐C and R‐C interactions. Similar observations were noted in each replicate of simulated data, yet both variance estimates of G‐C and R‐C interactions were unbiased , between the 40th and 60th percentiles (middle), and above the 80th percentile (top), respectively, and plotted their phenotypic estimates, that is, α^0+·α^1, given their standardized values on the relevant lifestyle covariate c  as an example. Figure 1 that we used for group stratification is an aggregate of G‐C interactions over common SNPs of the whole genome, hence a genome‐wide estimate of G‐C interaction. Therefore, individual differences in α^1 would reflect systematic genetic variation, which would be the most pronounced between the 2 extreme groups, that is, top and bottom. A further exploration on pairwise genomic relationships for individuals within and between the 2 extreme groups revealed that the average genomic relationship within each group is greater than the grand average relationship of the entire data set, but the average between‐group relationship is less than the grand average . However, this problem will no longer exist in a repeated‐measures design or if a nonidentity matrix is fitted for the variance–covariance structure of residual effects.Although a genuine R‐C interaction can be unbiasedly estimated as shown in the simulation see Data , the modt=2.35, df=17, P=0.015). Thus, our results support the idea that phenotypic plasticityWe showed previously that lifestyle modulation of genetic and nongenetic effects, in forms of G‐C and R‐C interactions, is ubiquitous and sizable for cardiovascular traits. To highlight the importance of incorporating lifestyle modulation when estimating trait heritability, we compared SNP heritability estimates from 2 univariate RNMs . However, the results from the ARIC Study and UKBB data sets are somewhat different. In particular, some GREML estimates of genetic variance tend to be underestimated for the ARIC Study data, which is not evident for the UKBB data. This is likely attributed to the smaller sample size of the ARIC Study data than the UKBB data, which inevitably results in larger sampling errors for the estimates from the ARIC Study. Nonetheless, our results indicate that G‐C and R‐C interactions are primarily hidden in residual variance estimates in the null model; when they are explicitly estimated in an interaction model, residual variance estimates can be substantially reduced, thereby yielding higher SNP heritability compared with when these components are neglected. This is in line with our previous observation that residual variance is overestimated when fitting a null model to simulated data with genuine G‐C or R‐C interaction.Given that heritability is a function of genetic and residual variance, we further investigated the reason behind larger RNM heritability estimates by comparing GREML and RNM estimates of genetic and residual variance from both the ARIC Study and UKBB data sets Figure . On averIn this study, we used a novel linear mixed model to detect and estimate components of genetic and nongenetic variance that change with respect to modifiable lifestyle covariates, termed as G‐C and R‐C interactions, in the context of cardiovascular health. Using simulations, we showed that for a sample size of ≈7500 observations, our method has sufficient statistical power to detect genuine G‐C and R‐C interactions while keeping the false positive rate controlled. Applying our method to real data, for each of 23 cardiovascular traits selected from the ARIC Study data set, we screened for G‐C and R‐C interactions using 22 available lifestyle covariates that covered smoking, alcohol intake, physical activity, and dietary composition. G‐C and R‐C interactions were found to be ubiquitous among cardiovascular health related traits, and for some traits, estimates were relatively large, accounting for up to 20% of the total phenotypic variance.Among the 14 signals replicated in the UKBB, physical activity was found to alter both genetic and nongenetic effects on heart rate and BMI; genetic effects on HDL cholesterol level and nongenetic effects on waist‐to‐hip ratio. Alcohol consumption altered both genetic and nongenetic effects on BMI, whereas smoking altered nongenetic effects on heart rate, pulse pressure, and white blood cell count. In addition, saturated fat intake modified genetic effects on BMI, and total daily energy intake modified nongenetic effects on waist‐to‐hip ratio. To explicitly illustrate G‐C and R‐C interactions, we stratified individuals according to the per‐individual estimate of G‐C and R‐C interactions and showed that genetic and residual effects could take on different directions across groups. Although we did not identify any literature in the context of cardiovascular traits that examined R‐C interaction, the evidence of G‐C interaction in our studies is consistent with the previous literature  and the Australian Research Council . The Atherosclerosis Risk in Communities Study has been funded in whole or in part with federal funds from the National Heart, Lung, and Blood Institute, National Institutes of Health, Department of Health and Human Services . The UK Biobank is funded by the UK Department of Health, the Medical Research Council, the Scottish Executive, and the Wellcome Trust Medical Research Charity.None.Data S1–S3Tables S1–S9Figures S1–S8Click here for additional data file.


Recently, there has been a growing interest in the genetic improvement of body measurement traits in farm animals. They are widely used as predictors of performance, longevity, and production traits, and it is worthwhile to investigate the prediction accuracies of genomic selection for these traits. In genomic prediction, the single-step genomic best linear unbiased prediction (ssGBLUP) method allows the inclusion of information from genotyped and non-genotyped relatives in the analysis. Hence, we aimed to compare the prediction accuracy obtained from a pedigree-based BLUP only on genotyped animals (PBLUP-G), a traditional pedigree-based BLUP (PBLUP), a genomic BLUP (GBLUP), and a single-step genomic BLUP (ssGBLUP) method for the following 10 body measurement traits at yearling age of Hanwoo cattle: body height (BH), body length (BL), chest depth (CD), chest girth (CG), chest width (CW), hip height (HH), hip width (HW), rump length (RL), rump width (RW), and thurl width (TW). The data set comprised 13,067 phenotypic records for body measurement traits and 1523 genotyped animals with 34,460 single-nucleotide polymorphisms. The accuracy for each trait and model was estimated only for genotyped animals using five-fold cross-validations.The accuracies ranged from 0.02 to 0.19, 0.22 to 0.42, 0.21 to 0.44, and from 0.36 to 0.55 as assessed using the PBLUP-G, PBLUP, GBLUP, and ssGBLUP methods, respectively. The average predictive accuracies across traits were 0.13 for PBLUP-G, 0.34 for PBLUP, 0.33 for GBLUP, and 0.45 for ssGBLUP methods. Our results demonstrated that averaged across all traits, ssGBLUP outperformed PBLUP and GBLUP by 33 and 43%, respectively, in terms of prediction accuracy. Moreover, the least root of mean square error was obtained by ssGBLUP method.Our findings suggest that considering the ssGBLUP model may be a promising way to ensure acceptable accuracy of predictions for body measurement traits, especially for improving the prediction accuracy of selection candidates in ongoing Hanwoo breeding programs.The online version contains supplementary material available at 10.1186/s12863-020-00928-1. Improving meat production in beef cattle is an important breeding goal throughout the world because it has a considerable effect on the profitability of the beef industry. Linear body measurement traits are important economic traits in beef cattle, as they provide useful information for understanding the growth and frame size of the animals. The relationship between the linear type traits and economically important traits, such as reproductive traits , 2, longA) and relationship matrix based on genomic information (G) are combined into a single matrix (H) , birth place [the county where the farms were located (111 levels)], and age at the recorded date as a covariate; u is the vector of additive genetic effects of the individuals; X is the incidence matrix of b; Z is the incidence matrix of u, and e is the vector of the residuals. It was assumed that u ~ N  and e ~ N , where A was a pedigree-based genetic relationship matrix and σa2 was the additive genetic variance, and σe2 is the residual variance.The variance components and heritabilities were estimated implementing AIREMLF90 software , using tadj) were obtained for each trait and animal as the residual effects (e) of the y = Xb + e model which Finally, the adjusted phenotypes , a traditional BLUP method with pedigree-based relationship matrix (PBLUP), a GBLUP method based on genomic relationship matrix, and a single-trait single-step GBLUP (ssGBLUP) method by combining the relationship matrix constructed from genotyped and non-genotyped individuals and pedigree information, were used to predict breeding values.yadj is the vector of the observations for the trait adjusted for fixed effects, 1 is the vector of ones; μ is overall mean; other notations are the same as in the model eq.  above with the following assumptions;u was the vector of additive genetic effects of only genotyped individuals and Z was the incidence matrix of u. It was assumed that u ~ N , where G was the genomic relationship matrix constructed using SNP information as described by VanRaden [VanRaden :i is the allelic frequency of ith marker and M is the matrix of centered genotypes.H that was a combination of A (numerator relationship matrix) and G (the genomic relationship matrix) matrices. The inverse of the H matrix was obtained as the following equation [In the ssGBLUP method, the statistical model was similar to that used for traditional evaluation; however, the non-genotyped and genotyped animals were simultaneously included in the hybrid relationship matrix of equation , 52 and equation :\documeA22 is the numerator relationship matrix for genotyped animals.Where In this study, the accuracy and unbiasedness of prediction were obtained using five-fold cross-validation sets for all traits. Genotyped individuals were assigned to five mutually exclusive groups for cross-validation. K-means clustering, according to pedigree relationship coefficients, was used to minimize the relatedness between training and validation sets . The fivAdditional file 1: Figure S1. Location of body measurement parts in Hanwoo cattle.