All data science methods have specific assumptions that are made in order for their inferences to be valid. Some assumptions impact statistical significance testing and some influence the models themselves. For example, a fundamental assumption of linear regression is that the relationship between the independent and dependent variables is additive such that a unit increase in one leads to a unit increase in the other with some error that can be modeled using a normal distribution. The presence of a nonlinear relationship between the variables violates this assumption and can lead to inaccurate inferences. We demonstrate this here using a simple example from human genetics and then end with some thoughts about the role of biological data mining in revealing nonlinear relationships between variables.AA, AG, and GG, respectively, at a single point in the DNA sequence. In this example, the G allele increases the mean by one half unit for each inherited copy. Twice the trait correlation among sibling pairs is an estimate of heritability due to additive genetic effects and is referred to as narrow-sense heritability (NSH). Twice the correlation is used here because siblings only share, on average, half their genes. Cousins share, on average, 12.5% of their genes and thus NSH is estimated from the trait correlation multiplied by eight.One of the central questions of human genetics is the extent to which variation in a quantitative trait such as cholesterol levels or blood pressure is due to variations in the DNA sequence. Heritability is one measure that is used to assess the relative contributions of genetic and non-genetic  variation to trait variation. Heritability ranges from zero to one with a value of one indicating that all variation in the trait is attributable to genetic variation. In reality, we never see heritability this high because nearly all biological traits have one or more environmental components and are generally measured with some error. Heritability estimates that take into account all of the different types of genetic effects are referred to as broad-sense heritability (BSH). Additive genetic effects have historically received the most attention because they are useful for animal breeding and can be estimated from the correlation of the trait between pairs of relatives. An example of an additive genetic model would be a quantitative trait that has means of 10, 10.5, and 11 for genotypes A and G) have equal frequencies of 0.5 in the population and assume genotype frequencies of 0.25 (AA), 0.5 (AG), and 0.25 (GG) that are consistent with Hardy-Weinberg expectations. We first simulated a single DNA sequence variation in 5000 unrelated parents using these genotype frequencies. We then simulated two children by drawing from the two alleles from each parent with 0.5 probability. We then simulated phenotypes for each parent and each sibling from a normal distribution with means and variance as described above for the additive genetic model. Figure AA, AG, and GG as 0, 1, and 2 so we can estimate the additive genetic variance component. The ratio of the additive variance over the total trait variance is an estimate of NSH. Here, this is equal to 0.60 which is exactly the heritability estimated from the trait correlation in the sib pairs. We confirmed this by estimating NSH from simulated half-sibs and cousins. We showed that the NSH for this additive genetic model drops in half and then in half again as the genetic relatedness of the relative pairs drops in half  have equal frequencies of 0.5 and genotype frequencies of 0.25 (AA), 0.5 (AG), and 0.25 (GG). For the second genetic variant, we assume alleles (T and C) have equal frequencies of 0.5 and genotype frequencies of 0.25 (TT), 0.5 (TC), and 0.25 (CC). We further assume that these two genetic variants are on different chromosomes and thus unlinked, so the loci are not correlated . We used an XOR (exclusive OR logic function) model for the epistasis effect such that the trait mean is 10 if the genotype at genetic variant one is AG OR the genotype at genetic variant two is TC but NOT both. Otherwise the trait mean is 11. This creates a pattern among the genotypic means such that both genetic variants are needed along with a nonlinear model to fully account for the genetic component of the trait variance. We assumed here the same trait variance of 0.3 and simulated parents and relative pairs as described above. Figure Any difference between BSH and NSH is due to other types of genetic effects such as deviation in the trait means due to dominance of an allele within a locus or epistasis (gene-gene interaction) between loci. Epistasis impacts trait variation through non-additive interactions between two or more DNA sequence variations. What is the impact of epistasis on relative pair correlations and estimates of NSH? To address this question, we carried out a similar simulation using an epistasis model such that the trait means are dependent on genotype combinations from two different DNA sequence variations. For the first genetic variant, we assume alleles (It is interesting to note that many biological traits exhibit a linear relationship in relative pairs that increases linearly with increasing genetic relatedness. What does this tell us about the nature of the genetic effects underlying the trait variation? Do observed linear relationships mean that the genetic effects are only additive at the exclusion of non-additive effects such as those coming from epistasis? To answer this question we combined the above simulations such that the trait from the additive simulation was added to the trait from the epistasis simulation yielding a new trait. We conducted the same heritability analysis as described above. Figure The results of this last simulation illustrate that non-additive genetic effects can be hidden or buried in seemingly linear relationships, thus violating a fundamental assumption of parametric linear regression. This phenomenon has been previously observed . Narrow-


CCKAR) plays an important role in animal digestive process. We examined the interplay of these three parameters in a local Chinese chicken population.The feed conversion ratio (FCR) and residual feed intake (RFI) are common indexes in measuring feed efficiency for livestock. RFI is a feed intake adjusted for requirements for maintenance and production so these two traits are related. Similarly, FCR is related to feed intake and weight gain because it is their ratio. Cholecystokinin type A receptor (rg = − 0.710). Furthermore, we identified 51 single nucleotide polymorphisms (SNPs) in the CCKAR and 4 of these resulted in amino acid mutations. The C334A mutation was specifically associated with FI and the expected feed intake (EFI) (P <  0.01) and significantly associated with the average daily gain (ADG) (P <  0.05). G1290A was significantly associated with FI and EFI (P < 0.05).The feed intake (FI) and body weights (BW) of 1,841 individuals were monitored on a daily basis from 56 to 105 d of age. There was a strong correlation between RFI and average daily feed intake (ADFI) and a negative correlation between the FCR and daily gain  contains supplementary material, which is available to authorized users. Feed expenses account for approximately 70% of chicken production costs . One wayAs a selection index, the FCR is cannot be used to determine whether FI or BWG predominate and this reduces the group selection difference and affects the efficiency of selection . From a In order to make up for the defects of FCR calculations, the RFI has been used as a production performance evaluation index for layer chickens since the 1970s. RFI is a measure of the feed utilization efficiency index of livestock first proposed in 1963 . The feeCCKAR in the individual brains are inversely proportional to growth rate [CCKAR knockout mice have significantly higher FI levels than their wildtype counterparts [CCKAR influences the regulation of feed intake and growth of animals.The brain-gut axis encompasses the hypothalamus, vagus nerve, stomach and intestine and regulates eating behaviors –11. Cholwth rate . Furtherterparts . TherefoCCKAR is a potential candidate gene associated with energy improvement, so we also analyzed the associations between variation in the CCKAR and the phenotypes measured.Chinese local chickens have several excellent production traits such as high meat quality, strong adaptation and crude feed tolerance . HoweverA Chinese local chicken population, a Tianlu Black chicken pure-line N416, was used for measurement of growth and feed conversion rate traits in this study. Chickens were housed in a closed type henhouse to control the temperature and illumination during the brooding period (0–35 d of age). After 35 d of age, chickens were transferred to a half-open vertical ventilation hoop henhouse, and electronic chips were placed in the middle of shank. A total of 912 male individuals were kept in three fence-separated pens (every pen had 304 birds) on one side of the henhouse, and 929 female ones were kept in three fence-separated pens  on the other side of the same henhouse. Each pen had seventeen 9ZC-5 intelligent type breeding and feeding automatic measurement stations  and 40 nipple water bowls, the 9ZC-5 stations can recognize each chicken’s electronic chip and record the FI and BW of the chicken. The chickens were fed a diet containing 12.1 MJ/kg ME and 190 g CP/kg. Daily feed intake and body weights were recorded for each bird throughout the feeding trial from 56 to 115 d of age, and this working was performed as previously described , as someThe RFI calculation was based on a previously described model . The expμ is the intercept, a is the regression coefficient, DOT was the day of testing and e is the residual. A DOT value of 25 is put into Eq. 0.75.where The MMBW and ADG of each bird were used as independent variables to establish the linear regression models,andb0 is the intercept, b1 and b2 are partial regression coefficients for MMBW and ADG, respectively, and e was the residual and the RFI is the e of these models. The experimental data were then divided into two groups by sex and two equations were developed using ADFI, MBW and an ADG estimate of the EFI.In these models, ADFI is the average of the daily feed intake of individuals during the period of the experiment, FCR is the net feed consumption of livestock unit weight gain. The FCR for each individual was estimated based on the ratio between unit weight gain and feed consumption.We constructed the multi-trait animal model:Y is the vector under observation, X and Z was incidence matrices, b is a vector of fixed effects (including two gender levels and 6 pen levels), a is the vector of the animal additive genetic effect and e is the vector of random residuals.to obtain estimates of the phenotypic and genetic (co)variance and heritability, and this model was based on the restricted maximum likehood method of the DMU statistical package , 20, 22.Relative selection efficiencies were used to compare the expected effects of selection on FCR and RFI on other growth traits. In order to estimate the correlated response to selection on feed efficiency, we referred to previous report  and consC∆G represents the FCR and RFI for indirect selection efficiencies on growth. ∆G represents direct selection efficiencies that are induced through selection of growth and other primary traits. rA1A2 represents genetic correlation coefficients between primary and secondary traits and h1 and h2 represents the heritability of primary and secondary traits, respectively.where CCKAR (NCBI Gene ID: 422801) were designed using Primer Premier 5.0 software (http://www.premierbiosoft.com). Primers were synthesized by Shanghai Jierui Biological Technology. Five pairs of primers were designed to perform mixed pool sequencing for an initial screen of SNPs in CCKAR . PCR primers for chicken 2, 0.3 μL dNTP and 1.5 μL 10× buffer. The PCR procedure was as follows: 94 °C for 3 min, followed by 36 cycles of 94 °C for 15 s, 55 °C for 30 s and 72 °C for 30 s with a final step of 72 °C for 10 min. The PCR products were purified by using ExoI  and FastA . Genotyping was performed using a commercial kit  using 2 μL of purified products as directed by the specification, the purified primers were showed in Additional file SNP genotyping was performed using the SNaPshot method . Based ohttp://analysis.bio-x.cn/myAnalysis.php). We excluded polymorphic sites that did not conform to the Hardy-Weinberg Equilibrium (HWE) for the analysis. D´ was a standardized Lewontin LD coefficient as the evaluation criterion for LD. │D´│ > 0.75 represented a strong LD between each pair of polymorphic sites. A full-precise-iteration algorithm was used for haplotype analysis. This was based on the equation:Linkage disequilibrium (LD) and haplotype analysis for this study population was performed using SHEsis software (N(11) represents the number of “11″ haplotype, N(12/11) represents the number of samples that carried “12″ haplotype on one chromosome and “11″ on another, N(XX) represents the number of samples carrying both “1/2″ genotypes at the two loci that was ambiguous for haplotype recognition.where The PROC-GLMR algorithm  was usedY is the observed value of growth traits, μ is the population mean value of growth traits, G is the effect of genotype on growth performance, F is the fixed effect of family, S is the gender effect (two levels), and e is the random error effect corresponding to the observed value. The evaluation of traits among individuals with different genotypes was performed using the paired comparison method of ANOVA using SPSS version 19.0 software.where At the beginning of the feeding trial, the average BWs of male and female individuals at 56 d of age were 802 ± 86 g and 671 ± 73 g respectively. The average BWs at 115 d of age were 1,915 ± 191 g for male and 1,632 ± 175 g for females  less than the higher RFI group . This meant that the FCR had a greater impact on ADG and selected for low FCR individuals. This would results in an ADG increase. The genetic and phenotypic correlation coefficients between RFI and ADFI were 0.334 and 0.501, and that two correlation coefficients between FCR and ADFI were rg = − 0.143 and rp = − 0.11, so the correlation coefficients of between FCR and ADFI were both much less than that between RFI and ADFI   as well as between SNP G219A-C448T and C334A-G1290A (D′ > 0.75 and r2 > 0.3)  and significantly associated with ADG (P < 0.05). The FI and EFI of individuals with the CC genotype were significantly lower than with the other two genotypes (P < 0.05). However, the ADG in this CC genotype group was significantly lower than in the AA group (P < 0.05). G1290A was significantly associated with FI and EFI (P < 0.05) in which the FI and EFI associated with the GG genotype were significantly lower than those associated with the AA genotype (P < 0.05)  Table .Table 6AThe classical breeding index FCR has been studied extensively in chickens . HoweverAs a new indicator of the efficiency of feed utilization, the RFI has been widely used in chicken , sheep  and beefP < 0.01) than the lower RFI group. This demonstrated that the FI in the lower RFI individuals were less than the higher RFI group and that their growth performance was also better. These low RFI individuals can achieve a greater feed efficiency.The reason may be that up-regulated genes were associated with energy metabolism, cell proliferation and fat metabolism [As the FCR, ADFI and BW8 of higher RFI group were extremely significant higher . The AA type was significantly higher than the GG type at FI at locus G1290A (P < 0.05). Furthermore, the FCR has a strong negative selectivity on ADG, and a slight negative selectivity towards ADFI. RFI has a strong positive selectivity for ADFI but a slight negative selectivity on ADG.The principle novelty of this research lies in the association between variation in CCKAR gene and four resulted in amino acid changes. However, only C334A and G1290A were significantly associated with the daily feed intake and daily gain.The heritability of FCR and RFI from chickens from 56 to 105 d of age were moderate. RFI was phenotypically independent of daily gain and medium metabolic weight but there were certain genetic correlations. The FCR had a higher relative selective efficiency than RFI on weights. 51 SNPs were found in the Additional file 1:Table S1. Primer sequences used in this study. (DOCX 18 kb)Additional file 2:Table S2. SNPs in the CCKAR gene of Tianlu Black Chickens. (DOCX 20 kb)Additional file 3:Table S3. SNP genotypes, allelic frequencies and HWE. (DOCX 18 kb)


Canis lupus familiaris is a powerful model for studies of the genetics of inherited disease due to its unique history of domestication. To gain insight into the genetic basis of reproductive traits across domestic dog breeds, we collected phenotypic data for four traits, cesarean section rate, litter size, stillbirth rate and gestation length, from primary literature and breeders' handbooks.The diversity of eutherian reproductive strategies has led to variation in many traits, such as number of offspring, age of reproductive maturity and gestation length. While reproductive trait variation has been extensively investigated and is well established in mammals, the genetic loci contributing to this variation remain largely unknown. The domestic dog, By matching our phenotypic data to genomic data from the Cornell Veterinary Biobank, we performed genome-wide association analyses for these four reproductive traits, using body mass and kinship among breeds as covariates.CACNA2D3 with gestation length, MSRB3 and MSANTD1 with litter size, SMOC2 with cesarean section rate and UFM1 with stillbirth rate. A few of these loci, such as CACNA2D3 and MSRB3, have been previously implicated in human reproductive pathologies, whereas others have been associated with domestication-related traits, including brachycephaly (SMOC2) and coat curl (KRT71).We identified 12 genome-wide significant associations between these traits and genetic loci, including variants near We hypothesize that the artificial selection that gave rise to dog breeds also influenced the observed variation in their reproductive traits. Overall, our work establishes the domestic dog as a system for studying the genetics of reproductive biology and disease.The genetic contributors to variation in mammalian reproductive traits remain largely unknown. We took advantage of the domestic dog, a powerful model system, to test for associations between genome-wide variants and four reproductive traits  that vary extensively across breeds. We identified associations at a dozen loci, including ones previously associated with domestication-related traits, suggesting that selection on dog breeds also influenced their reproductive traits. Cricetulus migratorius, to 21 months in the African bush elephant, Loxodonta africana . Th. ThSMOC2tic pigs . Finallylatelets . Other klatelets . Howevers breeds .To identify SNPs that are significantly associated with variation in litter size among breeds, we retrieved litter size data from 10 810 litters of 224 breeds registered in the Norwegian Kennel Club . For theRCL1, uncorrected P = 2.6 × 10−8, Perm P = 0.001), Myb/SANT SNA Binding Domain Containing 1  versus unripe human uterine cervix, implying that MSRB3 functions to ripen the cervix before the onset of labor [MSRB3 is associated with ear erectness [HMGA2 gene that has been previously associated with body mass in several different organisms . Thfficking . MSANTD1in goats , 85.To examine whether there are SNPs that are significantly associated with variation in stillbirth rate among breeds, we retrieved data for stillbirth rates for 57 of the 162 dog breeds . The datUFM1, uncorrected P = 2.01 × 10−7, Perm P = 0.049) and near a novel gene . The UFM1 SNP has been previously associated with coat color variation in the domestic dog [To test if any SNPs are significantly associated with the observed variation in stillbirth rate across domestic dog breeds, we conducted an across-breed GWAS analysis using 149 834 SNPs and stillbirth rate data from 56 dog breeds . We idenstic dog , but notTo examine whether there is variation in gestation length among breeds, we identified individual gestation length averages by breed predominantly in breeder handbooks. Utilizing breeders’ handbooks, we were able to identify gestation length means for a total of 23 of the 162 dog breeds that we had genotypic data for . Among tSLC9A8, uncorrected P = 3.7 × 10−11, Perm P = 0.001), calcium channel, voltage-dependent, alpha-2/delta Subunit 3 .To identify SNPs significantly associated with the observed variation in gestation length across domestic dog breeds, we conducted an across-breed GWAS analysis using 149 834 SNPs and gestation length data from 23 dog breeds . Our anaSLC9A8, an integral transmembrane protein that exchanges extracellular Na+ for intracellular H+. SLC9A8 serves multiple functions [CACNA2D3. This gene is involved in regulating the influx of Ca2+ ions entering the cell upon membrane polarization [CACNA2D3 is differentially methylated in the amnion between normal and pre-eclamptic pregnancies [CACNA2D3 is one of four genes recently described as influencing cranial morphology in human populations [CACNA2D3 is downregulated by Colony Stimulating Factor 2 (CSF2) in the trophectoderm of pregnant cattle, which increases the ability of the preimplantation embryo to advance to the blastocyst stage [CACNA2D3 is under diversifying selection associated with environmental adaptations to altitude [PCGF5, a gene previously shown to be necessary for neural differentiation in embryonic growth cell in humans [The first SNP resides in intron 78 of unctions  and is eunctions . Knockouunctions . The secrization , a critirization . In prevgnancies  and in bgnancies , 93. Addulations . In othest stage . In the altitude . Finallyn humans .Mammals exhibit a great deal of variation in their reproductive traits, yet remarkably little is known about the genetic basis of these traits. To begin to address this, we used GWAS analyses to examine the genetic basis of four reproductive traits  across up to 97 domestic dog breeds. We identified several significant genetic associations for each trait , Table 3SMOC2, a gene previously associated with brachycephaly in dogs [SMOC2 variant identified directly influences parturition and birth timing in dogs  versus unripe human uterine cervix and may be involved in the onset of labor [SMOC2 is also known to be expressed in human reproductive tissues . Similarly, the cesarean section phenotype is largely determined by the owner and the veterinarian. In this way, it is an elective phenotype measurement but is informed by the breed-specific likelihood of a healthy delivery. However, cesarean section rates for some breeds are extremely high (e.g. 92.3% in Boston terrier), which seems to indicate that cesarean section procedures are necessary to preserve the health of both the mother and the pups. Therefore, we assume that these rates reflect veterinarians’ information and knowledge of potential breed-specific birthing risks.Previous analyses of traits, such as body mass, in the domestic dog have found that much of the variation can be explained by a few large-effect loci , 102. Wheoz015_Supplementary_DataClick here for additional data file.


BMP2 (bone morphogenetic protein 2), which we recently discovered in a related study. Variant effect prediction revealed that 15 high impact variants for the traits back fat thickness, meat fat ratio and carcass length were among the statistically significantly associated variants.In order to gain insight into the genetic architecture of economically important traits in pigs and to derive suitable genetic markers to improve these traits in breeding programs, many studies have been conducted to map quantitative trait loci. Shortcomings of these studies were low mapping resolution, large confidence intervals for quantitative trait loci-positions and large linkage disequilibrium blocks. Here, we overcome these shortcomings by pooling four large F2 designs to produce smaller linkage disequilibrium blocks and by resequencing the founder generation at high coverage and the F1 generation at low coverage for subsequent imputation of the F2 generation to whole genome sequencing marker density. This lead to the discovery of more than 32 million variants, 8 million of which have not been previously reported. The pooling of the four F2 designs enabled us to perform a joint genome-wide association study, which lead to the identification of numerous significantly associated variant clusters on chromosomes 1, 2, 4, 7, 17 and 18 for the growth and carcass traits average daily gain, back fat thickness, meat fat ratio, and carcass length. We could not only confirm previously reported, but also discovered new quantitative trait loci. As a result, several new candidate genes are discussed, among them  Mapping experiments in livestock generally serve two purposes: The first is to understand the genetic architecture of quantitative traits, and to derive and prove new hypotheses of trait expression. The second is the identification of genetic markers that may be useful for livestock breeding. There have been many quantitative trait loci (QTL) mapping experiments carried out over the last decades (see review article by ). These With the aim to overcome the aforementioned limits in mapping resolution and to fully exploit the potential of the resource populations, we pooled four well-characterized F2 designs , three oet al.  and for the effect of RYR1 gene  was done on an Illumina HiScan SQ using TruSeq SBS v3 Kits. For the library construction, the DNA samples were fragmented on a Covaris S220 ultrasonicator. Parameters were adjusted to yield 350 bp inserts. Fragment length was measured with High Sensitivity DNA Chips on an Agilent Bioanalyzer. Sequencing adapters and indexes were ligated using Illumina’s TruSeq DNA PCR-Free Library Prep Kits. Quantification of libraries was done by qPCR using KAPA Library Quant Kits. Flow cells were prepared using an Illumina cBot and TruSeq PE v3 Cluster kits. Raw sequencing data were demultiplexed and converted into FASTQ files using Illumina’s CASAVA software.Sus scrofa 11.1 (GCA_000003025.6 provided by Swine Genome Sequencing Consortium on NCBI). Base quality score recalibration was performed with dbSNP build 150 as the knownSites dataset. Truth datasets used for Variant Quality Score Recalibration (VQSR) were as follows. SNPs: Illumina Infinium PorcineSNP60 v2 BeadChip and Affymetrix Axiom PorcineHD. INDELs: High confidence fraction  of the PigVar database. Training dataset for SNP VQSR was also a high confidence fraction of the PigVar database  . A truth sensitivity of 99.0 was chosen for SNPs and INDELs. The known dataset for SNP and INDEL VQSR was dbSNP build 150. Since SNPs were filtered with two truth datasets a Ti/Tv free recalibration according to the GATK best practice guidelines was applied to the data. Low coverage sequencing reads of F1 animals were processed according to the GATK best practice guidelines with the following deviations. SNP Calling was performed using GATK HaplotypeCaller v. 3.8 in joint mode with the settings minPruning 1 and minDanglingBranchLength 1 as well as BCFtools mpileup v 1.9  for each variant on QTL harboring chromosomes was calculated with an in house R script.To make use of the most recent phasing algorithms Beagle 5.0 was used for all phasing operations . Haplotyi.e., 0.05/number of independent tests). Manhattan plots were created with R, where variants with p-values > 0.001 were excluded due to software limitations. Clusters incorporating potential genomic regions of interest were defined using the Manhattan Harvester (MH) tool  and human peak identification data. For this study, the variants with a p-value below 1.0x10−7 (option -inlimit) were included and further the clusters with a GQS > 3.5 (1 is min and 5 is max) were taken into account. Conditional association analyses were performed by including single highly associated variants as fixed effects in a LOCO analysis.Single-trait association analyses were performed with GCTA v. 1.92.4 beta 3 on the F2 population only   was used for a systematic and integrative analysis. The gene list from the VEP output was the input for DAVID  and Sus scrofa genes were considered as the background. Gene Ontology (GO) terms  from the functional annotation chart report which were significantly overrepresented with an EASE Score  below 0.05 and with a gene count higher or equal to 5 were retained.To predict variant effects the Ensembl Variant Effect Predictor (VEP) release 94 was utilized, which is part of the Ensembl advanced programming interface (API) (2) for each variant on QTL harboring chromosomes where calculation was possible. Supplementary Table 2 containts the complete list of clusters identified in the GWAS with additional supporting information for cluster assignment. GRMs from F2 60k genotypes (File_S1.zip) were created by a “leave one chromsome out” approach using the program “Genome-wide Complex Trait Analysis (GCTA) version 1.91.4 beta3”. GWAS was conducted with imputed sequence level F2 genotypes (Supplementary File_S2.zip) for each chromosome using the GRM where the respective chromosome was left out Phenotype files are located in Supplementary File_S2.zip for the traits ADG, BFT, MFR, and CRCL were used in the GWAS. Crosses were used as covariates in the GWAS and provided as a gcta compatible covar file in Supplemental File_S4.zip. SNP locations can be found in the bim files of the genotype data (Supplementary File_S1.zip and Supplementary File_S2.zip). Population structure information is provided in form of a Beagle 4.0 compatible pedigree file (Supplementary File_S3.zip). Raw sequencing data are accessible via the NCBI Sequence Read Archive (SRA) under BioProject ID PRJNA553106. File_S5 contains the 60k chip genotype data in variant call file (VCF) format. Genomic positions have been lifted to genome assembly Sus scrofa 11.1 (GCA_000003025.6) and annotated with dbSNP build 150. gcta compatible covar files for the conditional association analyses with top variants are provided in File_S6. Supplemental material available at FigShare: https://doi.org/10.25387/g3.8287847.Sequencing data, which were used to conduct this study will be made publicly available upon publication of the article in the NCBI Sequence Read Archive (SRA). Supplementary Tables have been uploaded to GSA. Supplementary Table 1 contains the coefficients of determination  sequencing reads per sample were aligned to the reference genome in the F0 generation with an average mapping efficiency of 99.37%. In the F1 generation an average of 26,562,876  reads were mapped to the reference assembly with an average mapping efficiency of 99.33%.With respect to the number of SNPs detected in the founder population, 22,671,759 were previously reported and 3,950,955 were novel. Furthermore, 1,482,139 of the INDELs were previously reported and 4,335,345 were novel. Per chromosome, average distances among the variants are summarized in To detect local inaccuracies in the imputed data, we imputed chip data from each founder with the remaining 23 founders as a reference panel. The data does not provide information about the imputation accuracy of the experiment since pedigree information could not be used. The coefficient of determination for each variant located on a chromosome harboring relevant QTL was determined where feasible. The average coefficients of determination for each chromosome analyzed are summarized in i.e., 4 for ADG, 33 for BFT, 22 for MFR and 61 for CRCL) and they were located on the following Sus Scrofa chromosomes (SSC): 1, 2, 4, 5, 7, 17, and 18. The complete cluster list with additional supporting information for cluster assignment can be found in Supplementary Table 2. From each of the defined clusters, the top 5 variants were retained. The genes incorporating or lying nearby these highly significant associations are presented in e.g., SSC17 for CRCL and SSC18 for MFR. To evaluate all possible relations among the variants exceeding the significance threshold for each trait, a Venn diagram was used  was between BFT and CRCL and the second highest was between BFT and MFR . To get an estimate of systemic bias, quantile-quantile plots were generated for all p-values from each GWAS . As a measure of association between observed and expected p-values, lambda values were calculated for all four traits: λADG = 1.282319, λBFT = 1.333425, λCRCL = 1.422044, and λMFR = 1.35587.From the genome-wide association study conducted in the pooled F2 population, the following number of variants exceeded the genome-wide significance threshold: 448, 17,105, 6635, and 27,641 for ADG, BFT, MFR, and CRCL, respectively. Manhattan plots of the GWAS for the four phenotypic traits are shown in was used . The higTCN1 for the trait MFR. For the BFT, the most severe consequences were located in the genes C6orf89, PI16, DST, and PRIM2, while for the CRCL disruptive impact variants were found in NEU1, four novel genes, ABCD4, DST, PRIM2, and LPCAT4. Notably, the same two splice donor variants affect the common genes for BFT and CRCL: DST and PRIM2. Sorting Intolerant From Tolerant (SIFT) scores were determined for all significant missense variants and are summarized in Supplementary Table 3 . The gene set for the CRCL trait was associated with two BP terms (GO:0001666 response to hypoxia and GO:0008283 cell proliferation) and two CC terms .GO functional enrichment analysis revealed eleven significantly overrepresented GO terms including molecular functions (MF), biological processes (BP), and cellular components (CC). A list containing the GO terms and the associated list of genes is presented in IGF2, which has been extensively described to influence muscle development  clusters incorporating strong evidence for trait-associated chromosomal regions were defined, ii) the effect of the significant variants was predicted, and iii) a gene set analysis was employed to identify sets of genes jointly associated with the traits of interest.To fully exploit the potential of the four resource populations, the crosses were pooled and further used for conducting GWAS. The increased sample size together with the increased marker density ensures a high resolution that might allow the pinpointing of more specific causative genes and mutations. Further experiments, e.g., fat percentage in the carcass and fat-cuts percentage) were considered in order to allow an adequate comparison given that the trait has few records in the database and the trait definition can be country dependent. Most of the clusters overlapped or were in the vicinity of the previously reported QTL. This was expected as the database has been recently updated and also includes our previous results . It is assumed that many of these large QTL regions might in fact not be due to a single mutation, thus representing haplotype effects caused by several causative variants  of the HMGCLL1 gene, which was shown by Comuzzie et al. to be associated with childhood obesity in the Hispanic population and to influence creatinine levels. Another QTL on SSC2 contains 112 intron variants in SHANK2 . SHANK2 was also shown to be associated with childhood obesity in the same study and to have an influence on estradiol blood concentrations (−13) affecting LYN, which encodes for the LYN proto-oncogene, which was also identified by Comuzzie et al. and correlated with the amount of fat mass in obese children (−12) lie in an intergenic region 13,463 – 14,460 bp downstream of RPS20, a gene which in interplay with GNL1 is critical for cell growth , which is a regulator of IGF2 expression  is an intron variant in gene C6orf106. C6orf106 is a target of the human miRNA has-miR-192, which has been identified to have regulatory functions in type 2 diabetes mellitus . RIPOR2 expression and protein levels are upregulated during muscle cell differentiation in human fetal muscle cells . Overexpression of KIFC1 promotes cell proliferation in non-small cell lung cancer , which induces cartilage and bone formation (−15) were found in the cluster on SSC4.A QTL for BFT with a very prominent peak was detected on SSC7. The SNP with the lowest p-value . Of 72 variants 6 were located in KRTAP5-5-like introns and 66 in the vicinity of the gene. KRTAP5-5 was shown to control cytoskeletal function and cancer cell vascular invasion , which is a transcription factor that regulates proliferation of epithelial cells  and CTTN . CTTN’s protein product Cortactin binds to and is indirectly phosphorylated by obesity factor PTP1B , which has been associated with obesity traits in humans  and in SNTG1 , which has been associated with type 2 diabetes , a gene which has been linked to improved piglet birth weight , which in a whole exome sequencing study was found to be associated with type 2 diabetes in a Mayan population  were found in the intron and coding region (silent mutation) of FAM83B (or C6orf143) respectively. A total of 62 significant variants in FAM83B were discovered comprising of 60 intron variants, 1 silent mutation, and 1 missense mutation. Cipriano et al. demonstrated that overexpression or mutation of FAM83B leads to EGFR hyperactivation by direct interaction and consequent hyperactivation of the EGFR downstream effector phospholipase D1, which was previously associated with BMI in humans , which have been assigned to the RSL24D1 gene. RSL24D1 has been identified as a potential target in familial hypercholesterolemia (−38), a bone formation inducing factor  and CRCL . Knockout of DST leads to intrinsic muscle weakness and instability of skeletal muscle cytoarchitecture in mice . A deficiency of the NEU1 gene product Neuraminidase 1 leads to vertebral deformities in humans  and one splice donor variant in NUTM1 , both oncogenes (PLAC1 has been found to be highly expressed in various types of tumors (Various high impact variants were discovered by variant effect prediction. A splice donor variant (rs80834233) in Drosophila melanogaster (Functional validation studies based on appointed candidate genes and genetic variants will be considered in follow-up studies. Besides understanding the underlying molecular mechanisms of ADG, BFT, MFR and CRCL, the results of GWAS can render a substantial increase in the reliability of genomic predictions in breeding programs. This concept was demonstrated in several studies in cattle (Putting the results of previous simulation studies to test, we conducted GWAS in four pooled F2 designs, which have been imputed to sequence level based on high coverage founder and low coverage F1 sequencing. We found that by pooling the designs the sequence level marker density can be exploited efficiently. QTL for four well-characterized traits were identified in agreement with previous mapping studies and candidate genes and pathways were unraveled, that should be subject to further studies. Thus, the approach applied herein is a feasible strategy to efficiently utilize extremely well phenotyped experimental designs that have been established in the past.


Lumbar disc degeneration (LDD) is age-related break-down in the fibrocartilaginous joints between lumbar vertebrae. It is a major cause of low back pain and is conventionally assessed by magnetic resonance imaging (MRI). Like most other complex traits, LDD is likely polygenic and influenced by both genetic and environmental factors. However, genome-wide association studies (GWASs) of LDD have uncovered few susceptibility loci due to the limited sample size. Previous epidemiology studies of LDD also reported multiple heritable risk factors, including height, body mass index (BMI), bone mineral density (BMD), lipid levels, etc. Genetics can help elucidate causality between traits and suggest loci with pleiotropic effects. One such approach is polygenic score (PGS) which summarizes the effect of multiple variants by the summation of alleles weighted by estimated effects from GWAS. To investigate genetic overlaps of LDD and related heritable risk factors, we calculated the PGS of height, BMI, BMD and lipid levels in a Chinese population-based cohort with spine MRI examination and a Japanese case-control cohort of lumbar disc herniation (LDH) requiring surgery. Because most large-scale GWASs were done in European populations, PGS of corresponding traits were created using weights from European GWASs. We calibrated their prediction performance in independent Chinese samples, then tested associations with MRI-derived LDD scores and LDH affection status. The PGS of height, BMI, BMD and lipid levels were strongly associated with respective phenotypes in Chinese, but phenotype variances explained were lower than in Europeans which would reduce the power to detect genetic overlaps. Despite of this, the PGS of BMI and lumbar spine BMD were significantly associated with LDD scores; and the PGS of height was associated with the increased the liability of LDH. Furthermore, linkage disequilibrium score regression suggested that, osteoarthritis, another degenerative disorder that shares common features with LDD, also showed genetic correlations with height, BMI and BMD. The findings suggest a common key contribution of biomechanical stress to the pathogenesis of LDD and will direct the future search for pleiotropic genes. Human intervertebral discs (IVDs) are fibrocartilaginous structures that lie between adjacent vertebrae. These IVDs hold the vertebrae together, facilitate some vertebral motion, and act as shock absorbers to accommodate biomechanical loads Oxland, . IVD is Twin studies have demonstrated a strong genetic contribution to LDD   whose p-values are below some threshold in the GWAS of discovery sample. It can then be used as a predictor of target phenotypes in the testing sample using regression analysis. PGS has been widely used to predict disease risk  population-based cohort . A subset of the cohort (N = 815) also had their blood metabolite profiles measured by quantitative serum nuclear magnetic resonance (NMR) platform . Sample recruitment and MRI procedures have been described in detail previously  procedures have been described in our previous study  was a prospective cohort study of over 9,000 Southern Chinese residents in Hong Kong  was a collection of unrelated, UK-based individuals of European ancestry with knee and/or hip OA from the arcOGEN Consortium . Individual PGS profiles were calculated by summing up the dosage of trait-increasing alleles from imputed genotypes weighted by the reported effect sizes. This strategy has the advantage of including secondary signals within the same locus and increased accuracy of effect size estimates from a larger independent replication sample (for LS- and FN-BMD).p-value informed clumping algorithm [linkage disequilibrium (LD) r2 < 0.1 across 500 kb] that selected SNPs most associated with the base phenotype in a locus to generate sets of independent SNPs. PGS was created using clumped SNPs whose p-value in the base GWAS were below pre-specified threshold. We varied p-value thresholds  to select the one that maximized the variance explained (R2) for the base phenotype in the validation sample.As a second strategy, we performed genome-wide PGS analysis using PRsice . The derivation and validation of this approximation formula is given in Appendix where R2 on the observed scale. Finally, the observed R2 was converted to the liability scale using the transformation formula by Lee et al.  were included in polygenic analysis. The basic demographic and phenotype summary are shown in Table P < 1.0E-10 for height, P = 1.6E-07 for BMI), after adjusting for age, sex and principle components. It is 2~3-fold lower than previous reports in independent European samples, which were 16% for height , also lower than previous reported ~5% in Europeans . Theoretical model fitting under a range of plausible parameters  and disc degeneration score  after adjusting for sex, age and lumbar injury. The results are consistent with obesity as a major risk factor for LDD development and progression  after further adjusting for height but disappeared after adjusting for BMI or body weight  and remained significant (P < 0.05) after further adjusting for height, BMI or weight (Table We then applied PGS to test genetic overlaps between anthropometric traits and LDD Table . In the ht Table . The PGSht Table . The samht Table . The lacht Table .P < 0.01) and explained 0.35% of disease liability. The association cannot be explained by body weight, because the BMI PGS is better associated with weight but does not show association with LDH (P > 0.5). The result provides a genetic basis to the previous epidemiological observation that being tall is a risk factor for hospitalization due to LDH  whose lipid levels were measured by the high-throughput NMR approach. All PGS were significantly associated with the corresponding lipid levels. Except for LDL-C, the PGS of known lipid loci showed the best prediction performance  was directly genotyped in the HKDD cohort and reliably imputed in the Japanese case-control cohort. The allele A was coupled to the LDH risk allele and significantly increased both disc displacement and disc degeneration scores , which is expected given the strong evidence for a causal role of BMI  and LS-BMD (P = 0.012) but not for FN-BMD (P > 0.1).Finally, LDD has been suggested to share common features with OA which is also known as degenerative joint disease . Taken together, the results suggest that like LDD, OA also shares genetic overlaps with height, BMI and BMD.The genetic correlation between osteoarthritis and LS-BMD was less significant though its effect was stronger than between osteoarthritis and height, which was possibly due to smaller sample size of the BMD GWAS. Since the genetic architecture of BMD was dominated by fewer number of causal SNPs with larger effect sizes Table , it is aIn this study, we adopted a trans-ethnic PGS strategy to evaluate the genetic overlaps between different traits where GWAS of base phenotypes were done in Europeans and validation and testing samples were East Asians. Although most GWAS findings were generally replicated in populations different from the initial discovery, heterogeneity commonly existed in the estimated effect sizes , they are expected to have more similar effect sizes to the Chinese sample. To evaluate the tradeoff between sample size and effects heterogeneity, we projected expected prediction performance (R2) of height and BMI using a theoretical model with parameters of genetic architecture compatible with the observed PGS results . Despite smaller sample sizes, using East Asian GWAS as the discovery sample is expected have comparable maximum R2 as European GWAS to predict height in the Chinese population (Figure R2 (Figure R2 for height is capped at 8% but roughly doubles for BMI. Notably, when using East Asian GWAS as the discovery sample, the best prediction performance can only be achieved at p-value thresholds >0.01. However, whole-genome summary statistics of East Asian GWASs were not publicly available for us before the start of this study. Also consistent with the theoretical predictions, incorporating East Asian GWAS top hits to the PGS of GWAS hits only marginally increased R2 in predicting height and BMI, and their associations with the LDD scores remained insignificant (Table The use of European GWAS in the current study is mainly due to large sample sizes and publicly available summary statistics. GWAS meta-analyses of height and BMI were also conducted in East Asians (Wen et al., n Figure . For BMI2 Figure . Furthernt Table .Given genetic architecture and sample sizes, the power of PGS in detecting genetic overlaps is mainly determined by the performance PGS in predicting the corresponding base phenotype. Therefore, the theoretical results suggest that the use of European GWAS as discovery sample in PGS analysis can still be a favorable approach in cross-trait analysis in the East Asian population. But we caution that the trans-ethnic PGS strategy may not be suitable for other populations like African. Nevertheless, whenever possible ancestry-matched GWAS of base phenotype with large sample sizes should be used to improve the power. Since summary data from large scale GWAS in non-European populations have started to become available recently (e.g., Akiyama et al., In this study, we analyzed three LDD phenotypes, including two semi-quantitative scores derived from MRI assessment and one clinically defined symptom. The PGS of height, BMI and BMD were associated with at least one LDD phenotype. It highlights the complexity in operationally defining LDD, as the current diagnostic approach only captures certain aspects of the degenerative process. Therefore, comparison between different studies should clarify how phenotypes are defined. And it will be fruitful to jointly evaluate multiple MRI features in future genetic studies. However, although MRI is the current gold standard that gives best resolution in defining LDD, it is too expensive to be carried out in large samples.An alternative strategy is to use the a “proxy phenotype” such as patient-based LDH in which large number of cases can be identified based on electronic medical records. Use of proxy phenotype has been demonstrated to improve the power in GWAS (e.g., Okbay et al., The observed genetic overlaps can be explained by either causality or genetic pleiotropy or both. Interestingly, BMI, BMD and height also showed suggestive evidence of positive genetic correlation with OA. It is possible that they can be explained by some common mechanisms. Although formal assessment of causality could utilize the Mendelian randomization paradigm in larger sample sizes, PGS can be used to nominate candidate phenotypes (Evans et al., Alternatively, the observed genetic correlations are also consistent with the genetic pleiotropy and shared pathways among skeletal phenotypes. In supporting this notion, several individual OA associated SNPs were associated with height or BMD (Reynard and Loughlin, In summary, the current study is the first attempt to evaluate genetic overlap between LDD and related traits using GWAS data. Our trans-ethnic polygenic analysis supports the genetic correlations of height, BMI and BMD with LDD, and sheds new light on understanding the pathological mechanism of degenerative skeletal disorders.https://goo.gl/6gpt9g.The genome-wide association summary statistics of the HKDD cohort is available at This study was carried out in accordance with the recommendations of the ethical principles and guidelines for the protection of human participants of research, Human Research Ethics Committee, The University of Hong Kong. The protocol was approved by the Human Research Ethics Committee, The University of Hong Kong. All subjects gave written informed consent in accordance with the Declaration of Helsinki.XZ and PCS conceived the study and coordinated the research. KS-EC obtained the funding. XZ developed the methods and performed analysis. JK and KM-CC evaluated MRI images of the HKDD cohort. TK, Y-QS, KC, YK, and SI contributed the Japanese LDH GWAS summary data. C-LC contributed the HKOS GWAS summary data. Y-HH contributed the GEFOS consortium GWAS summary data. DS contributed the NMR data. YL and DC applied for the arcOGEN consortium GWAS summary data. XZ drafted the manuscript with inputs from PCS, KS-EC. DS, TS-HM, C-LC, and JK reviewed and revised manuscript. PCS and KS-EC participated discussion.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.


Widely used genomic prediction models may not properly account for heterogeneous (co)variance structure across the genome. Models such as BayesA and BayesB assume locus-specific variance, which are highly influenced by the prior for (co)variance of single nucleotide polymorphism (SNP) effect, regardless of the size of data. Models such as BayesC or GBLUP assume a common (co)variance for a proportion (BayesC) or all (GBLUP) of the SNP effects. In this study, we propose a multi-trait Bayesian whole genome regression method (BayesN0), which is based on grouping a number of predefined SNPs to account for heterogeneous (co)variance structure across the genome. This model was also implemented in single-step Bayesian regression (ssBayesN0). For practical implementation, we considered multi-trait single-step SNPBLUP models, using (co)variance estimates from BayesN0 or ssBayesN0. Genotype data were simulated using haplotypes on first five chromosomes of 2200 Danish Holstein cattle, and phenotypes were simulated for two traits with heritabilities 0.1 or 0.4, assuming 200 quantitative trait loci (QTL). We compared prediction accuracy from different prediction models and different region sizes . In general, highest accuracies were obtained when 100 adjacent SNPs were grouped together. The ssBayesN0 improved accuracies over BayesN0, and using (co)variance estimates from ssBayesN0 generally yielded higher accuracies than using (co)variance estimates from BayesN0, for the 100 SNPs region size. Our results suggest that it could be a good strategy to estimate (co)variance components from ssBayesN0, and then to use those estimates in genomic prediction using multi-trait single-step SNPBLUP, in routine genomic evaluations. G) computed from genetic markers , is equivalent to BayesA or GBLUP when a fixed region size is set at one SNP or the whole genome, respectively. We hypothesize that, at any other region size, but these two extreme sizes of genome regions, higher prediction accuracies can be obtained using BayesN0. Although it ignores the fact that a proportion of the genome regions, and therefore a proportion of the SNPs, may not have any influence on the trait of interest, prediction accuracy may increase compared to BayesA by benefiting from the increase in the accuracy in estimation of SNP variances, and compared to BLUP-based models by allowing SNPs in different regions to have different variances. Partitioning of the covariate matrix of marker genotypes, M, or in other words, assigning priors to genome regions rather than individual SNPs, was shown to influence the accuracy of genomic predictions   to introduce a multi-trait whole genome regression model that allows heterogeneous (co)variances, (ii) to compare accuracies from single- and multi-trait genomic prediction, and (iii) to investigate the use of region-specific estimates of (co)variances in genomic predictions using ssSNPBLUP.The genotype data were simulated for five generations (Gen1−Gen5) based on real haplotypes of 2200 Holsteins (Gen0), as described in Karaman et al. . At eachPhenotypic values of the two traits were simulated to have heritabilities of 0.1 and 0.4, which represents low (L) and high (H) heritability traits, respectively. Total number of quantitative trait loci (QTL) was set at 200, which were randomly selected from the SNP set, ensuring that the average minor allele frequency (MAF) of QTL is 0.15 , and a correlation of 0.9. The 78% of those QTL were assigned to a correlation between effects on two traits of 0.9, and 22% of −0.9 randomly. The correlation group of −0.9 was achieved by switching the sign of QTL effect for one of the traits at random. The QTL effects, which were assumed to have a correlation of 0.9, were assigned a negative or positive sign at random for both traits. In the second scenario, scenario N5, effects of all pleiotropic QTL were simulated from a bivariate normal distribution with a correlation of 0.5. Although fluctuated across the replicates, all scenarios lead to genetic correlations of about 0.45 at Gen0. The QTL SNPs were excluded from the final data set of SNP for the analysis. Random residual effects were sampled from Two scenarios, G9 and N5, were considered in terms of the distribution of QTL effects and correlations for the effect of pleiotropic QTL. In the scenario G9, the effects of the pleiotropic QTL were achieved by simulating two correlated gamma variables Dvorkin  with marFinal data (see Table A novel multi-trait Bayesian whole genome regression model (BayesN0), single-step SNPBLUP and single-step Bayesian regression models introduced by Fernando et al.  were comyL and yH are the vectors of phenotypes, 1 are vectors of ones, μL and μH are general means, ML and MH are the matrices of genotypes for k markers, αL and αH are the vectors of marker effects, and eL and eH are the vectors of random residual effects, for traits “L” and “H”, respectively. In our simulations, animals had records for both traits or none of them. Therefore, ML = MH, and these matrices will be denoted as M hereinafter, to simplify the demonstration. Residuals, e | R0 ~ N, where I is an identity matrix.A multi-trait mixed model including only general means as fixed effects and marker effects as random effects can be written asM and vector α given in Eq.  are vectors of SNP effects for corresponding genomic regions. We assume that all SNPs j  in the same genomic region s  have the same (co)variance for the two traits:The columns of n in Eq.  can be dμ, were assigned a flat prior, and other parameters of the model were assigned a normal or an inverse Wishart (IW) prior for conjugacy:μ, αsj, Bs, and R0 can be obtained after some algebra:y*, y* is the vector of phenotypes corrected for all other effects, Likelihood of the model is given as:g et al. , to multn stands for the non-genotyped animals, and g stands for the genotyped animals. Note that in our simulations, animals had records for both traits or none of them. In a multi-trait single-step SNPBLUP (ssSNPBLUP) analysis, the phenotypes are modeled as , where I is an identity matrix. Vector of α is assumed to follow α | B ~ N with Bi are diagonal matrices consisting of SNP variances (BL and BH) or covariances (BLH = BHL). Vector of G0 is the additive genetic (co)variance matrix. The Ang, Agg and Ann are submatrices of the pedigree-based relationship matrix, A, corresponding to the relationships between non-genotyped and genotyped individuals, among the genotyped individuals, and among the non-genotyped individuals, respectively. The matrix of imputed genotypes, In the following expressions, A−nn is the part of the inverse of pedigree-based relationship matrix, A, corresponding to the non-genotyped individuals, and R = R0 ⊗ I.The mixed model equations corresponding to the model in Eq.  is as foμ*. Priors for α, e, Bs and R0 were the same as in BayesN0. A multivariate normal prior, G0 was assigned an inverse Wishart prior, G0 | vG, VG ~ IW. Full conditional distributions of μ*, αsj, Bs, G0, R0 can be obtained after some algebra:y*, SR are as defined before, Nn is the number of non-genotyped individuals, and The single-step SNPBLUP requires the estimation of (co)variance components, and then use of these in mixed model equations to estimate breeding values. In contrast, Bayesian approach can be used to obtain the vector of fixed and random effect estimates, o et al. . In prinvB = vR = vG = 5. It is worth noting that inverse Wishart distribution imply a scaled inverse chi-square distribution for each variance with specific parameters  were fitted with varying region sizes . The parameters of the priors for SNP, residual and genetic (co) variance matrices in the multi-trait models were Single-trait BayesN0 and ssBayesN0 models were special cases of their multi-trait counterparts, for which the multivariate normal priors for SNP effects, model residuals and imputation residuals were replaced with univariate normal priors Markov-chain Monte Carlo (MCMC) algorithm with Gibbs sampling method was used to obtain samples of each parameter from its full conditional posterior distribution. Chain length for the analyses using BayesN0 and ssBayesN0 consisted of 50,000 or 70,000 cycles, of which the first 30,000 or 50,000 cycles were discarded as burn-in, respectively. Convergence was tested by comparing results for the two chain lengths  on a random subset of the replicates and region sizes variances and SNP (co)variances were obtained as the mean values of the posterior samples from BayesN0 or ssBayesN0. The genetic (co)variances required in mixed model equations for The predicted breeding values of animals using multi-trait BayesN0 were obtained fromt-tests, for which accuracies were paired across each replicate for the same validation population. A Bonferroni correction was used to control the Type 1 error rate of 0.05, caused by multiple comparisons.Prediction accuracy was assessed as the correlation between true and predicted breeding values of validation individuals. The bias of prediction was assessed based on the slope of the regression of true breeding values on the estimated breeding values of validation individuals. Accuracy for single- and multi-trait models with different region sizes were compared for each trait, and each model separately. Prediction accuracy for all methods was compared for each trait and at each scenario of region size. All comparisons were performed separately for genotyped and non-genotyped individuals using a two-sided paired Prediction accuracies from single- and multi-trait BayesN0 models are given in Tables Prediction accuracies from single- and multi-trait analysis are given in Tables h2 = 0.1), and similar to or higher accuracies than their single-trait counterparts for trait H (h2 = 0.4) (Tables h2 = 0.1) was improved with multi-trait analysis, while accuracy for a high heritability (h2 = 0.8) trait remained unchanged. For a low heritability (h2 = 0.05) trait, which had incomplete data, Guo et al. (rg = 0.5) trait with high heritability (h2 = 0.3) was available. Cheng et al. (π) for gall volume (h2 = 0.12), when the correlated trait was presence (or absence) of rust (h2 = 0.21), in Loblolly Pine (Pinus taeda L.)  Tables . This wa) Tables . Hayashi) Tables  comparedo et al.  showed tg et al.  reportedBeside heritability, another factor influencing accuracy is the absolute difference between genetic and residual correlations , where γt is the vector of QTL effects, VM is the (co)variance matrix of SNP genotypes, and VMQ is the covariance matrix of SNP and QTL genotypes  is zero. Under some assumptions, (co)variance of the SNP effects are proportional to s . Because recombination rates vary over the genome, and SNPs are typically in imperfect LD with QTL, each Genomic prediction rests on the LD between QTL and SNPs  was able to account for the heterogeneous correlation structure across the genome to some extent, compared to multi-trait GBLUP (BayesN0 with whole genome as one region), which assumes a constant correlation across the genome Tables  and 4. ASimulation studies have shown that Bayesian whole genome regression models, which allow variances of SNP effects differing among loci or genome regions, perform better than GBLUP model  or identified via GWAS using the current data , are col et al. . Althougl et al. .de novo GWAS , or without running a In a simulation study for single-trait genomic prediction, Zeng et al.  showed tImplementation of our novel Bayesian multi-trait model (ssBayesN0) using the methodology of Fernando et al.  yielded For genotyped individuals, using multi-trait ssBayesN0 led to higher accuracies than using multi-trait BayesN0 Tables  and 4. AIn this study, the estimates of the (co)variances were obtained from BayesN0 or ssBayesN0. The former led to ssSNPB1 model for which the (co)variance components were obtained using only the information of genotyped individuals, while the latter led to ssSNPB2 model for which the (co)variance components were obtained using the information of genotyped and non-genotyped individuals. In practice, the (co)variance components can be estimated less frequently compared to routine genomic evaluations without harming the prediction accuracies  accounting for the part of breeding values, which cannot be modeled by imputed markers, are estimated variance structure in single-step genomic prediction could be to construct weighted −12 in 200 and 203 iterations (average of two traits) in single-trait analysis, and in 435 and 478 iterations in multi-trait analysis, respectively. It should be noted that these numbers apply only to the current data, and could vary with equivalent formulations of the models advantages of ssSNPBLUP, nor its convergency properties. Both ssGBLUP and ssSNPBLUP, though, are known to have some computational challenges  or the whole genome (GBLUP). Our results showed that assigning priors to genome regions defined as fixed number of SNPs, e.g., 100 SNPs, may improve accuracies over BayesA and GBLUP by accounting for heterogeneous (co)variance structure across the genome efficiently. The model was also implemented in single-step (ssBayesN0) Bayesian regression approach, which unifies pedigree, phenotypes and genotypes in a single analysis. Highest prediction accuracies were obtained when 100 adjacent SNPs were assumed to have a common (co)variance in ssBayesN0. For routine genomic evaluations, it could be a good strategy to estimate (co)variance components from ssBayesN0, and then to use those estimates in genomic prediction using multi-trait single-step SNPBLUP. Such a strategy has the potential to provide reliable estimates of breeding values for both genotyped and nongenotyped individuals.Supplementary tables


Genome-wide association studies often collect multiple phenotypes for complex diseases. Multivariate joint analyses have higher power to detect genetic variants compared with the marginal analysis of each phenotype and are also able to identify loci with pleiotropic effects. We extend the unified score-based association test to incorporate family structure, apply different approaches to analyze multiple traits in GAW20 real samples, and compare the results. Through simulation studies, we confirm that the Type I error rate of the pedigree-based unified score association test is appropriately controlled. In marginalanalysis of triglyceride levels, we found 1 subgenome-wide significant variant on chromosome 6. Joint analyses identified several suggestive genome-wide significant signals, with the pedigree-based unified score association test yielding the greatest number of significant results. The increasing availability of high-density genomic data with thousands of samples enables the identification of single-nucleotide polymorphisms (SNPs) contributing to complex traits on a genome-wide scale. Research studies often collect data on multiple related phenotypes to better understand disease structure; however, genome-wide association studies (GWAS) commonly analyze each trait independently. For example, body mass index (BMI) and waist-to-hip ratio (WHR) are both proxy traits for obesity and commonly collected in an obesity-related study. The standard approach usually analyzes each phenotype separately and reports the corresponding findings of each analysis, ignoring the dependency among traits. Approaches considering joint analyses have been proposed to tackle multiple phenotypes. Yang and Wang  and Ott We aimed to study the performance of various approaches for jointly analyzing multiple phenotypes. We first reviewed existing methods. We then expanded USAT to related samples as a pedigree-based USAT (pUSAT). We found that the Type I error rate of pUSATwas well preserved through simulations. Finally, we analyzed GAW20real data using multiple phenotype methods and compared the results.K correlated phenotypes Y1,…, YK in N individuals. Let Yk be the N × 1 vector of kth phenotype and Y be the N × K matrix for all individuals. The test of interest is the association of a single variant with the K phenotypes. Suppose Gi is the genotype score  for a SNP of interest i, and G is the N × 1 vector of genotypes for all individuals. Moreover, define C =  as the N × q matrix of a set of q-adjusted covariates for all samples.Assume α refers to the overall mean of kth phenotype, βk is the regression coefficient representing the linear fixed genetic effect on the kth phenotype, and γk is a q × 1 vector of fixed covariate effects on the kth phenotype. Qk and ϵk are random effect and error, respectively, assumed to follow normal distributions I is an N × N identity matrix and Φ is an N × N matrix of pairwise measures of genetic relatedness.To handle multiple phenotypes, the most intuitive and simplest approach is to implement marginal LMM to test each SNP against 1 phenotype at a time. For the kth marginal model, the null hypothesis is that the given SNP is not associated with the kth phenotype (Hk0 : βk = 0). The estimation of parameters can be obtained through the maximum likelihood estimator (MLE) or the restricted MLE (RMLE) [The linear mixed model (LMM) is frequently used to account for the sample relatedness or the cryptic relatedness due to population structure. For a given SNP, the standard LMM is:E (RMLE) , and testk is the association statistic for the kth phenotype with a given marker from a marginal model, for example, from eq. , where Φ is the row covariance matrix for relatedness, Vg is the K × K column covariance matrix for the genetic variance component; ϵ is an N × K matrix of errors with ϵ~MVNN × K, where IN × N is the row covariance matrix, and Ve is the K × K column covariance matrix of the environmental variance component. The null hypothesis of interest is that the SNP effect sizes for all phenotypes are zero: H0 : β1 = … = βK = 0. These parameters can be estimated through either MLE or RMLE [MANOVA considers the trait correlation directly in the test statistics and corresponding distributions . For fam or RMLE . The mvLTw be the weighted statistic Tw = wTM + (1 − w)TS, where w is a weight from 0 to 1, TM is the MANOVA test statistic, and Ts is the SSU test statistic combining the marginal results. TM and TS are the statistics from the analyses assuming the independence among samples. Under the null, Tw is approximately a linear combination of chi-squared distributions and the p value pw of Tw can be calculated using Liu et al. [w can be considered from a grid of {w1 = 0, w2 = 0.1, …, w11 = 1}.The true genetic sizes and the direction of associations are usually unknown a priori and therefore one would not know which approach is the best for the study. Ray et al.  proposedu et al. . The optTw, pUSAT = wTmvLMM + (1 − w)Ts, LMM, where TmvLMM is the mvLMM test statistic, and Ts, LMM is the SSU test statistic combining the marginal LMM results. In this way, the relatedness among study participants is taken into consideration in the test statistic. Then, the optimal pUSAT test statistic is defined as:pw, pUSAT is the p value of Tw, pUSAT. An approximated p value for TpUSAT using numerical integration is [Here, we expand their method to related samples. Specifically, we define the proposed pUSAT as ation is :tpUSAT is the observed value, qmin(wb) is the (1- tpUSAT)th percentile of the distribution of wb, TS, LMM, TmvLMM. The details of this calculation can be found in Ray et al. [y et al. . The pUSp value<10e-6), which results in a total of 587,358 variants. Individuals with more than 5% missing genotypes were also excluded from analysis.GAW20 provides the dense genome-wide SNPs from the 821 pedigree-based individuals with triglyceride (TG) and high-density lipoprotein cholesterol (HDL-C) levels measured. We used the log-transformed average of pretreatment values at visits 1 and 2 of TG and HDL-Clevels and investigated the pleiotropic variants involved in blood lipids. The GAW20 data has been genotyped using the Affymetrix Genome-wide Human SNP Array 6.0. SNPs were excluded with a call rate < 95%, minor allele frequency < 5%, and failure of the Hardy-Weinberg equilibrium test (Vg = h2B(ρ), Ve = (1 − h2)E and h2 is the heritability varying from 0 to 1. For the genetic covariance matrix B(ρ) and the environmental covariance matrix E, we used acompound symmetry (CS) correlation structure with B(ρ)ij = Eij = ρ, where a single parameter ρ can control the model and define the correlation among the phenotypes. We used the kinship matrix Φ ofGAW20 data and considered h2 as 0.5%. The different correlation ρ ‘s  were assessed in the simulation. We evaluated the Type I error rate using 1000 null phenotype data setssimulated from eq.  in the data set, is − 0.45. The empirical genetic relatedness matrix was calculated before conducting analyses. Besides SSU, mvLMM, USAT, and pUSAT, the univariate analyses were also performed and shown. All statistical models were adjusted for age, sex, indicators of field center, and smoking status, and implemented in GEMMA  . Table 2p value = 1 × 10− 7). We observed no genome-wide significant SNPs for either phenotype; however, we did identify1 subgenome-wide significant locus on chromosome 6  as associated with TG levels. LRFN2is related to TGs in the suggestive genome-wide significance level (p < 5 × 10− 6) [LRFN2 is reported to be associated with working memory deficits [p value of 1.69 × 10− 13 from USAT is suspicious as no other approach  reports even nominal significance signal. In addition, USAT analysis ignored the dependency among the individuals, which could potentially lead to the inflated signals. In addition, we did not identify any signals that reached GWAsignificance by another multivariate approach , as shown in Fig. p value as representative within ± 500 kb (Table p values by integrating information from SSU and mvLMM. Closer investigation shows that some SNPs are outstandingly noticeable for pUSAT, but not for SSUormvLMM, especially on chromosomes 2,3,4, and 6.Figure p values for most SNPs.The explosion in datacollection and the increasing evidence that some loci affect multiple traits require more complex statistical models for analyses to better understand the properties of association. Here, we reviewed several different methods for multiple phenotypes in GWAS, and expanded the USAT approach to related samples as pUSAT. The proposed method can provide insight into the underlying associations, and help the researchers to identify pleiotropic loci especially when prior information is unavailable. The simulation studies demonstrate that the Type I error rate of pUSAT is conservative under different correlations. We also applied various methods to the GAW20 data with TG and HDL-C as the phenotypes. One suspicious locus was identified as GWA-significant by the regular USAT, which assumes independent individuals, whereas other multivariate analyses missed this locus. Several suggestiveGWA loci were detected by the joint multivariate analyses; however, pUSAT highlights the importance of joint analysis for multiple phenotypes and yields smaller