Identifications of these risk variants remain a very challenging problem. There is a need to develop more powerful statistical methods to leverage available information to improve upon traditional approaches that focus on a single GWAS dataset without incorporating additional data. In this paper, we propose a novel statistical approach, GPA , to increase statistical power to identify risk variants through joint analysis of multiple GWAS data sets and annotation information because: (1) accumulating evidence suggests that different complex diseases share common risk bases, i.e., pleiotropy; and (2) functionally annotated variants have been consistently demonstrated to be enriched among GWAS hits. GPA can integrate multiple GWAS datasets and functional annotations to seek association signals, and it can also perform hypothesis testing to test the presence of pleiotropy and enrichment of functional annotation. Statistical inference of the model parameters and SNP ranking is achieved through an EM algorithm that can handle genome-wide markers efficiently. When we applied GPA to jointly analyze five psychiatric disorders with annotation information, not only did GPA identify many weak signals missed by the traditional single phenotype analysis, but it also revealed relationships in the genetic architecture of these disorders. Using our hypothesis testing framework, statistically significant pleiotropic effects were detected among these psychiatric disorders, and the markers annotated in the central nervous system genes and eQTLs from the Genotype-Tissue Expression (GTEx) database were significantly enriched. We also applied GPA to a bladder cancer GWAS data set with the ENCODE DNase-seq data from 125 cell lines. GPA was able to detect cell lines that are biologically more relevant to bladder cancer. The R implementation of GPA is currently available at  p-values as input, making it especially useful when only summary statistics, instead of the full genotype and phenotype data, are available. We applied GPA to analyze GWAS datasets of five psychiatric disorders and bladder cancer, where the central nervous system genes, eQTLs from the Genotype-Tissue Expression (GTEx), and the ENCODE DNase-seq data from 125 cell lines were used as functional annotation. The analysis results suggest that GPA is an effective method for integrative data analysis in the post-GWAS era.In the past 10 years, many genome wide association studies (GWAS) have been conducted to identify the genetic bases of complex human traits. As of January, 2014, more than 12,000 single-nucleotide polymorphisms (SNPs) have been reported to be significantly associated with at least one complex trait/disease. On one hand, about 85% of identified risk variants are located in non-coding regions, which motivates a systematic understanding of the function of non-coding variants in regulatory elements in the human genome. On the other hand, complex diseases are often affected by many genetic variants with small or moderate effects. To address these issues, we propose a statistical approach, GPA, to integrating information from multiple GWAS datasets and functional annotation. Notably, our approach only requires marker-wise  Despite of these successes, these significantly associated SNPs can only explain a small portion of genetic contributions to complex traits/diseases Hundreds of genome-wide association studies (GWAS) have been conducted to study the genetic bases of complex human traits. As of January, 2014, more than 12,000 single-nucleotide polymorphisms (SNPs) have been reported to be significantly associated with at least one complex trait http://www.genome.gov/gwastudies/) showed that 16.9% of the reported genes and 4.6% of the reported SNPs are associated with multiple traits p-value The last few years have seen concrete demonstrations of “pleiotropy”, i.e. the sharing of genetic factors, between human complex traits. For example, a systematic analysis of the NHGRI catalog of published GWAS , Schork et al. The increasing evidence of pleiotropy between complex traits and the increasing functional annotation data call for novel statistical methods to effectively analyze multiple GWAS data sets and functional annotation data simultaneously. Statistical methods to investigate pleiotropy have been actively researched , to prioritize GWAS results based on pleiotropy and annotation information. GPA also provides statistically rigorous and biologically interpretable inference tools for this purpose. The method can easily be used for other purposes as well, as we will discuss below. This article is organized as follows. First, we investigate the properties of GPA using extensive simulation studies and illustrate the versatility and utility of GPA with the analysis of real data. Specifically, we apply GPA to the five psychiatric disorder GWAS data from the Psychiatric Genomics Consortium with central nervous system gene expression data and show that GPA can accurately identify pleiotropy structure among these diseases. We further apply GPA to the bladder cancer GWAS data with the ENCODE DNase-seq data from 125 cell lines and show that GPA can detect cell lines that are biologically more relevant to bladder cancer. Lastly, we discuss many issues related to GPA. The details of our GPA model and its statistical inference procedures are provided in the p-values for non-risk SNPs can be simulated easily from a uniform distribution p-values via different approaches. The most favorable simulation for our GPA model is to simulate them from the Beta distribution. To examine the robustness of our GPA model, we adopted an alternative simulation scheme under the framework of the linear mixed model and liability threshold model that has gained increasing interest recently  as a measure of risk SNP prioritization accuracy. The left panel of We first evaluated SNP prioritization performance of GPA. Specifically, after the two data sets were simulated, we obtained the p-values of the risk SNPs obtained from the generative model in the simulation study may differ from the Beta distribution assumed in GPA. If the p-values of the risk SNPs are indeed generated from the Beta distribution, our GPA model can give fairly accurate estimates of Regarding parameter estimation, we found that GPA provided a satisfactory estimate of As a comparison, we also used the “conditional FDR” approach proposed by Andreassen et al. p-values obtained from any source. Therefore we implemented the GSEA method to test the enrichment of the Next, we evaluated the type I error and power of GPA for hypothesis testing on the significance of annotation enrichment for risk SNPs. Gene Set Enrichment Analysis (GSEA) We further evaluated the type I error rate and power of GPA for the test of pleiotropy in our simulations. The simulation parameters were the same as those in the previous simulations. Power was evaluated at Lastly, we performed additional simulations with moderate heritability  p-value is essentially zero), MDD and SCZ  are provided in the last column of p-value should be interpreted with caution: as shown in p-values listed in We further applied GPA to study all pairs of disorders using the CNS gene set as the annotation data. The estimated ANK3 gene. By using annotation data, the CACNA1C gene, which encodes an alpha-1 subunit of a voltage-dependent calcium channel, was identified by GPA. After incorporating pleiotropy information between SCZ and BPD, additional functionally relevant genes, such as PBRM1, C6orf136, DPCR1, SYNE1, were identified by GPA. For instance, SYNE1 encodes the synaptic nuclear envelope protein 1, and codes the protein Syne-1 that is found in many tissues and is especially critical in the brain. The Syne-1 protein is active (expressed) in Purkinje cells, which are located in the cerebellum and are involved in signaling between neurons. Mutations in the SYNE1 gene have been found to cause autosomal recessive cerebellar ataxia type 1 (ARCA1) and SYNE1 has recently been implicated as a susceptibility gene for BPD in a large collaborative GWAS study We also compared the results given by four different analysis approaches: single-GWAS analysis with or without annotation, and two-GWAS joint analysis with or without annotation data. The Manhattan plots are shown in http://www.ncbi.nlm.nih.gov/gtex/GTEX2/gtex.cgi) and took the intersection of these eQTL with the markers of the psychiatric disorders, resulting in 23,505 SNPs annotated as eQTL. To obtain our TFBS annotation, we used the key word “TFBS” to query the ANNOVAR database, resulting in 19,029 SNPs annotated as TFBS (More details can be found at http://www.openbioinformatics.org/annovar/annovar_faq.html#tfbs). We performed joint analysis of BPD and SCZ with these three annotations . The estimated parameters in the GPA model and their standard errors are shown in We also applied GPA with multiple annotation datasets to improve its performance. Beside the CNS gene set, we considered eQTL annotation from GTEx p-values of real data and the p-values simulated from the fitted GPA model to examine the goodness of fit. The results are given in Figures S88–S97 in Besides the evaluation of the statistical power of GPA on real data, we examined whether the Beta distribution of the GPA model fit the real data. We compared the Regarding computational time, the GPA algorithm takes less than 20 minutes to analyze two traits with one annotation data file. The speed of convergence depends on the strength of the GWAS signals. For example, it took about 7 mins and 3 mins to analyze ADHD and SCZ, repectively, as SCZ has stronger GWAS signals than ADHD. For joint analysis of BPD and SCZ, it took about 20 mins. All timings were carried out on a desktop with 3.0 GHz CPU and 16G memory.DNase I hypersensitive sites (DHSs) are regions where DNA degradation by enzymes like DNase I occur more frequently than elsewhere. As a result, DHSs can mark active transcription regions across genome and these patterns are known to be tissue or cell specific. The ENCODE project analyzed the DHSs in 125 human cell lines with the intention of cataloging human regulatory DNA p-value http://genome.ucsc.edu/cgi-bin/hgFileUi?db=hg19&g=wgEncodeAwgDnaseUniform). Note that the DHSs for these 125 cell lines were identified with a uniform analysis workflow by the ENCODE Consortium; this facilitates fair and unbiased comparison among cell lines as annotation for our GPA model.We downloaded genotype data for bladder cancer from dbGaP (NCI Cancer Genetic Markers of Susceptibility (CGEMS) project; accession number phs000346.v1.p1). We used samples genotyped from both Illumina 1 M chip and 610K chip for our analysis. For quality control, we removed SNPs with missing rates We applied GPA to analyze the bladder cancer GWAS p-value of the GPA annotation enrichment test is linearly related to We also compared GPA with the LMM-based approach Many GWAS have been conducted in the past 10 years that have led to the discoveries of thousands of genomic regions associated with many traits, and many more discoveries are expected from ongoing GWAS. As GWAS data accumulate, there is an urgent need to perform a systematic analysis of available GWAS datasets for a comprehensive understanding of the genetic architecture of complex traits, and provide new insights for functional roles of the implicated variants. To achieve this goal, there is a great interest in developing computational and statistical approaches to exploring genomic data in the post-GWAS era.In the following, we briefly discuss the relationship between GPA and other related methods, such as LMM, conditional FDR and GSEA. LMM is an effective method for exploring genetic architecture of complex traits and it has been implemented in a popular software package, GCTA LMM explores the genetic architecture underlying complex traits/diseases by estimating the gross phenotypic variance that can be explained by whole genome or a certain subset of SNPs. In contrast, GPA provides more “fine-grained” analysis by giving estimates of the local false discovery rate of each SNP, the proportion of SNPs that are associated with the phenotype  as its input. Typically, the genotype data may not be accessible as easily as the summary statistics. For example, when researchers want to implement integrative analysis for their own GWAS data at hand with related GWAS studies, it is much easier for them to obtain the summary statistics than the whole data sets of related GWAS studies. In this sense, GPA may greatly simplify the procedure of integrative analysis.Application of LMM requires the availability of genotype data, while GPA only needs the summary statistics ). In the presence of multiple highly correlated annotations, the current version of GPA may not perform well. Hence, when multiple sources of annotation data are available, the correlation among the annotation datasets should be evaluated before using GPA with them. In fact, in the analysis of psychiatric disorders, the correlation among the three annotation data  is nearly zero, and thus we can analyze them simultaneously. If they are highly correlated, we suggest incorporating them into GPA one at a time, as shown in our analysis of bladder cancer GWAS data with ENCODE annotation. We realize that simultaneous analysis of multiple correlated annotation data may be more powerful and will investigate this issue in our future work.The parameters in the GPA model should be interpreted with caution because parameter estimation is based on the model assumption as discussed above. For example, as we showed in simulation study, the estimated There are also some limitations of the current GPA model. Although extensions to three or more GWAS are straightforward in principle  from just one GWAS data set, and then extend our model to handle multiple GWAS data sets and annotation data. Suppose we have performed hypothesis testing of genome-wide SNPs and obtained their p-values: p-values are assumed to come from the mixture of null and non-null, with probability j-th SNP is null or non-null, where p-values from the null group are from the Uniform distribution on , denoted as p-values from the non-null group are from the Beta distribution with parameters  data – then j-th SNP is an eQTL, then d-th annotation, and d-th annotation. Therefore, d-th annotation. The statistical inference about enrichment of annotation data will be discussed in details in Section “Hypothesis testing of annotation enrichment and pleiotropy”.To incorporate information from functional annotation data, we extend the basic model as follows. Suppose we have collected information from p-values from two GWAS: p-values, where p-value of the j-th SNP in the k-th GWAS. Similarly, we introduce latent variables j-th SNP and the two phenotypes: j-th SNP is associated with neither of them, Now we extend the above model to handle multiple GWAS data sets. To keep the notation uncluttered, we present the model for the case of two GWAS data sets. Suppose we have j-th row of To incorporate annotation information into the multiple GWAS model (7), similarly, we model the relationship between Parameters in the GPA model can be estimated using the Expectation-Maximization (EM) algorithm After we estimate the parameters in the GPA model, SNPs can be prioritized based on their local false discovery rates j-th SNP belongs to the null group given its p-value, i.e., j-th SNP, if it is claimed to be associated with the first phenotype, the second one, and both, i.e., direct posterior probability approachTo present the local false discovery rate based on our GPA model, we begin with the simplest case: single GWAS without annotation data. In this case, there are only two groups: null and non-null. The false discovery rate is defined as the probability that the A indicates the Annotation enrichment test. Note that Given an annotation file, we may be interested in whether there is statistical evidence for enrichment of GWAS signals in this annotation file. We propose to use the likelihood ratio test (LRT) to assess the statistical significance. To keep the notation simple, we drop the index of annotation files. Specifically, the significance of enrichment of an annotation for single-GWAS data analysis can be assessed by the following test: For joint analysis of two GWAS with annotation data, test (13) becomes P indicates the Pleiotropy test. The test statistic Click here for additional data file.


Eucalyptus badjensisconcerning the genetic variation for growth traits and the potential of the speciesin supporting a breeding programme. The field trial was a provenance/progeny testestablished in Campina da Alegria, Santa Catarina, Brazil  in a soil classified as LatossolicAlumino-Ferric Brown Nitosol. The experiment comprised 60 open-pollinated progeniesfrom the provenances Glenbog and Badja StateForest, New South Wales, Australia. Ten replicates and plots with six plantsin row were used. At the age of 17 years, 279 trees were assessed for diameter of thebole at breast height (DBH), total tree height (H) and volume of wood with bark(Vol). After submitting the data to statistical genetic analysis, the overall meansfor DBH, H and Vol were 45.17 cm, 33.30 m and 2.84 m3, and the estimatesof additive coefficient of variation [3 for DBH, H and Vol, respectively.The aim of this study was to evaluate  Eucalypt plantations in the southern region of Brazil represent slightly over 11% of thetotal area cultivated with this genus in the country, nowadays estimated at 5.47 millionhectares  areE. badjensis is the ease of sprouting,according to several visual observations made in Brazil and published reports fromstudies carried out in South Africa  and Badja State Forest (P2), NewSouth Wales, Australia. The geographical and climatic features of both locations aresummarized in The provenance origins of We admitted the degree of relatedness of half-sibs for the plants that compose eachprogeny, mainly due to the fact that they are the result of open-pollination process.This allowed us to adjust the most appropriate mathematical model for estimating theintended genetic parameters and other calculations that supported the present study. Thefield trial was established on March 19, 1996, following a compact family block design,with 10 replicates and linear plots containing six plants each. The plant-to-plantdistance within rows was 2 m and the spacing between rows was 3 m. Two lines surroundingthe trial composed the border, with the same layout. The total area of the experimentwas 2.2 ha. At the time of assessment, the experiment had already been thinned twotimes, lowering the density of plants to approximately 165 individuals per hectare.The geographical coordinates of the site in which the field trial was done are: latitude26°52′05.1″ S, longitude 51°48′47.5″ W and altitude 1,020 m above sea level. Accordingto W. Köppen's system, the climate type in Campina da Alegria-SC is classified as warmtemperate (Cfb), with a great number of cold hours accumulated during the winter. Withrespect to precipitation, the mean annual reaches 2,030 mm (Climatic Station ofIrani-SC), well distributed along the seasons and with occasional dry periods. There isalways a positive difference between the monthly mean precipitation and the potentialevapotranspiration . The relH) inmeters and, by calculation, volume of wood with bark (Vol) in cubic meters. In order tocompute the effective volume of wood, a form factor of 0.50 was adopted. For thedetermination itself, the following expression was used:Each tree was assessed at the age of 17 years for the following traits: diameter of thebole at breast height (DBH) in centimeters, total tree height (DBH is diameter at breast height (cm), H istotal tree height (m), Fc a correction factor of units fromcm2 to m2 (104), and Ff the averageform factor (0.50).where The estimates of the components of variance and genetic parameters were obtained byusing the mixed linear models methodology (procedure REML/BLUP - Restricted MaximumLikelihood/Best Linear Unbiased Prediction). The data processing model n° 5 of thesoftware Selegen-REML/BLUP  wasusedThe referred model has the following mathematical structure :y is the data vector, r is the replicate effectvector (assumed as fixed) added to the overall mean, a is the vector ofthe individual additive genetic effect (assumed as random), p is theplot effect vector (assumed as random), s is the provenance effectvector (random) and e is the vector of experimental errors (random).The capital letters represent the incidence matrices for the cited effects.where Estimates were obtained for the following genetic parameters: heritability coefficientof additive effect , and the assessment of the statistical significance was madethrough the Likelihood Ratio Test (LRT).Finally, the Spearman's correlation coefficient combining DBH, H and Vol was used withthe purpose of investigating an eventual modification in the ranking of the selectedtrees according to their additive values. The formula is as follows:n represents the number of observations and di2 the square of the positioning differences in the classification betweenvariables.where E. badjensis exhibited a betterdiametric and volumetric growth in Brazil when compared with E. dunnii,E. viminalis and E. grandis, even considering thatit had not been submitted to any cycle of breeding so far. Only for tree heightperformance the species was positioned behind E. dunnii and E.grandis.Taking into account works carried out by the first author in the state of Santa Catarinain 2007 and 2008 (unpublished data), it was possible to make comparisons among thespecies under study and others planted in the same region with respect to theirperformances. A sample of the results is shown in E. badjensis came out as a very promisingspecies, representing an alternative to E. nitens in climaticallycritical areas. The authors also mentioned that a breeding programme of E.badjensis was established in the 1990s, in which the initial steps were theevaluation of provenances and progenies in a set of environmental conditions in order toevaluate the effects of genotype x site interaction. Comparing the results of teneucalypt species under study, E. badjensis was amongst the mosttolerant species to frost, cold, snow, drought, termites and some strains of the fungusPhytophthora, the infectious agent of root-rot disease in youngtrees. The species was declassified only for the level of tolerance to defoliationcaused by snout beetle larvae. However, considering the rapid crown recovery, thetrouble became less important. The authors also reported the rapid initial growth of thetrees for height and diameter.In the study carried out by E. badjensis was planted.3, respectively, which represents increases around 24%, 10% and 62%compared to the overall means of the trial . These numbers indicated the feasibility of improving thegrowth rate in a breeding programme, as can be noted when comparing the mean annualincrements (MAIs) of the selected trees  with those ones of the complete sample .A preliminary analysis of the growth data allowed getting a series of descriptivestatistics for both the complete sample of trees and the selected ones only, and themain results are shown in The performance of the 39 selected trees is shown in ns), DBH × Vol(0.93**) and, finally, H × Vol (0.41**). This means that DBH and Vol ranked the selectedtrees in a very similar way. In addition, DBH was the trait that promoted a betterindirect representation of the woody production of a tree, corroborating a number ofstudies carried out in Brazil with eucalypts, both in young trees and adults  was computed foreach pair of variables. The results and respective significance by t-test (considering30 degrees of freedom presently) were as follows: DBH × H , inthis case represented by 20 progenies. Even though these results were obtained at veryearly ages, the Badja S.F. provenance proved to be of great importanceto develop a breeding programme, both in South Africa and in Brazil.Interestingly, the same The estimates of genetic parameters are summarized in The results show the feasibility to reach considerable genetic gains, despite therelatively large confidence interval for assessed corroborE. badjensis in South Africa, genetic gains around 11 and 12% overthe experiment mean were reported for DBH at the age of 5.5 years when selecting thebest 15 progenies of the trial, which are comparable with the expected gain.The expected genetic gains [Based on the results of the present work, we conclude that the genetic variability ofthe species is appropriate for carrying out a breeding programme for increasing thegrowth rate in successive cycles of improvement, especially for the traits DBH and Vol.Additionally, for the three traits evaluated , the statisticaldifferences in performance between the two provenances were not significant but, at theprogeny level, there were significant differences for DBH and Vol. Finally, the level ofcorrespondence between the rankings of the selected trees when comparing the traits DBHand Vol was very high, indicating that the first could be used as an indirect trait forselection focused on the increase in the volumetric growth rate as a whole.


DCDC2 and KIAA0319, in RD, with recent studies suggesting they also influence LI, verbal language, and cognition. Here, we characterize the relationship of the DYX2 locus with RD, LI, and IQ. To accomplish this, we developed a marker panel densely covering the 1.4 Mb DYX2 locus and assessed association with reading, language, and IQ measures in subjects from the Avon Longitudinal Study of Parents and Children. We then replicated associations in three independent, disorder-selected cohorts. As expected, there were associations with known RD risk genes KIAA0319 and DCDC2. In addition, we implicated markers in or near other DYX2 genes, including TDP2, ACOT13, C6orf62, FAM65B, and CMAHP. However, the LD structure of the locus suggests that associations within TDP2, ACOT13, and C6orf62 are capturing a previously reported risk variant in KIAA0319. Our results further substantiate the candidacy of KIAA0319 and DCDC2 as major effector genes in DYX2, while proposing FAM65B and CMAHP as new DYX2 candidate genes. Association of DYX2 with multiple neurobehavioral traits suggests risk variants have functional consequences affecting multiple neurological processes. Future studies should dissect these functional, possibly interactive relationships of DYX2 candidate genes.Reading disability (RD) and language impairment (LI) are common neurodevelopmental disorders with moderately strong genetic components and lifelong implications. RD and LI are marked by unexpected difficulty acquiring and processing written and verbal language, respectively, despite adequate opportunity and instruction. RD and LI—and their associated deficits—are complex, multifactorial, and often comorbid. Genetic studies have repeatedly implicated the DYX2 locus, specifically the genes The online version of this article (doi:10.1007/s00439-014-1427-3) contains supplementary material, which is available to authorized users. Communication disorders and learning disabilities are common, and can have long-lasting, adverse effects on affected individuals’ academic performance, self-esteem, and socioeconomic outcomes. Specifically, reading disability (RD or dyslexia) and language impairment (LI) affect 5–17 and 5–8 % of schoolchildren, respectively , raising the question of whether the risk haplotype also tags risk variants in TDP2 , a gene adjacent to TDP2, was associated with asymmetry in functional activation of the superior temporal sulcus during reading tasks , which influences the neuromodulator γ-hydroxybutyrate and the metabolism of γ-amino-butyric acid (GABA). Recent investigations have associated other neurotransmitter factors, including DRD2, DRD4, and COMT, with verbal language and LI, suggesting that neural signaling influences linguistic and cognitive traits  marker panel designed to capture the known common variation of the entire DYX2 locus. We genotyped this DYX2 marker panel in the Avon Longitudinal Study of Parents and Children (ALSPAC) and performed association analysis using reading, language, and cognitive measures collected between the ages of 7 and 9 years. We then replicated our associations in three cohorts selected for either RD or LI. We hypothesized that we would confirm the associations of http://www.bristol.ac.uk/alspac) . DNA samples for genetic analysis were available for 10,259 subjects. Reading, language, and IQ were assessed at ages 7, 8, and 9 years using standardized measures. We excluded subjects with IQ <75 on the Wechsler Intelligence Scale for Children (WISC-III) full scale IQ to prevent confounding effects of intellectual disability . The ALSPAC is a population-based birth cohort based in Avon, United Kingdom. Subjects were recruited before birth—a total of 15,458 fetuses were recruited, of whom 14,701 were alive at 1 year of age. Recruitment, participants, and study methodologies are described in detail elsewhere , or that had an overall call rate <85 %, were not used for genetic analyses. In the discovery ALSPAC cohort, single marker SNP analyses of case–control status and quantitative traits were completed using SNP and variation suite (SVS) v7.6.4 . Linkage disequilibrium was assessed and haplotype blocks were constructed using the four-gamete rule option in HaploView v4.2. Haplotype-based association tests were performed with haplotypes that had frequencies ≥1 % using PLINK v1.07 , while the family-based Italian RD and Colorado RD cohorts were examined using PLINK v1.07  RD, (2) LI, and (3) IQ. For the sake of clarity, we present our association findings domain-by-domain, with an emphasis on replication as opposed to correction for multiple testing.KIAA0319 and TDP2  Severe RD and (2) Moderate RD Table . For SevP2 Table . There ws et al. . TDP2 maDCDC2 and Severe LI. The DCDC2 haplotype that associated with severe LI is discussed in Powers et al.  severe LI, (2) moderate NWR, and 3) moderate WOLD  among our marker panel to determine whether the associated SNPs were tagging the same variation in the locus. Our previous work showed that DCDC2 associations tagged READ1 alleles  DCDC2, (2) the 5′ half of KIAA0319, (3) FAM65B, and (4) CMAHP.In our analyses, we observed replicated associations in the following genes: KIAA0319 and DCDC2 with LI. Additionally, we identify FAM65B and CMAHP as candidate genes for linguistic traits. Markers within the DYX2 locus showed association with multiple aspects of communication, including RD, LI, and verbal IQ. However, there was a marked absence of DYX2 associations with full scale IQ and performance IQ, suggesting that the DYX2 locus influences language-related processes to a greater extent than general cognition.In this investigation, we characterized the relationship of the DYX2 locus with RD, LI, and IQ Fig. . Our resFOXP2, KIAA0319, CMIP, ZNF385D, CNTNAP2, and DCDC2 —multiple elements, possibly regulatory in nature, within DYX2, influence language processes. However, DYX2 has repeatedly shown strong linkage to RD, a pattern generally indicative of one or two variants of large effect, and not of multiple independent variants with more modest effect sizes.That multiple DYX2 genes showed association with the phenotypes in this study is interesting, and at first glance somewhat unexpected. One possibility is that one or two genes are not solely responsible for the consistent implication of this locus in reading, language, and cognitive phenotypes. KIAA0319, TDP2, ACOT13, and C6orf62. As shown in Fig. KIAA0319—one spans the 3′ half of the gene, while the other spans the 5′ region of KIAA0319 as well as ACOT13, TDP2, and part of C6orf62. Nearly all of the associations in this study localize to this 5′ LD block, which also contains the previously reported KIAA0319 RD risk haplotype —an intron of FAM65B and downstream of a pseudogene—may suggest additional regulatory regions that influence gene expression. Thus, any roles FAM65B and CMAHP play in RD and LI may be of small effect and modulatory in nature. Though much further work is needed, we postulate, based on these and previous results, that DCDC2 and KIAA0319 are the major effector genes responsible for DYX2’s influence on RD and LI risk and that alteration of gene expression levels or patterns is the mechanism by which this effect is exerted.Genes and regulatory elements within the DYX2 locus may contribute interactively to reading and language domains, as seen with the apparent non-additive relationship between putative regulatory variants in p values and a statistical threshold correcting for 195 genetic markers (threshold of 0.000256) to present the reader with the context of our findings in terms of multiple testing. Nonetheless, our three replication cohorts were not identical and had inherent differences to each other and relative to the discovery cohort that may have prevented replication. These differences included (1) the disorder each cohort was selected for (RD vs. LI vs. unselected), (2) severity of case definition and recruitment, and (3) country of recruitment , and language spoken . Iowa LI and Colorado RD had moderate case definitions, which may be more comparable to Moderate RD, Moderate NWR, and Moderate WOLD case definitions in ALSPAC. On the other hand, Italy RD used a more severe case cutoff of 2 standard deviations, which may be more comparable to severe RD and severe LI case definitions in ALSPAC. Regardless, our observation of multiple replicated associations throughout the DYX2 locus increases confidence in these results.In our study design, we emphasized replication of genetic associations in independent cohorts, as opposed to reliance on statistical corrections for multiple testing, for validation of associations in the ALSPAC discovery cohort. The replications of genetic association with our neurocognitive traits of interest, particularly in the varied cohorts in this investigation, provide strong evidence that the results of this study are not due to type I error. However, we also report uncorrected DCDC2, KIAA0319, FAM65B, and the pseudogene CMAHP. Our association results within the DCDC2 and KIAA0319  areas are in LD with two previously reported risk variants: the READ1 regulatory element in DCDC2 and the KIAA0319 risk haplotype in KIAA0319 and TDP2. These results point strongly, albeit circumstantially, to variation in gene expression as a mediator of DYX2’s effect on reading and language phenotypes. As these variants appear to demonstrate pleiotropy, the role of DYX2 in other neurobehavioral disorders, including attention deficit-hyperactivity disorder, autism spectrum disorders, and speech-sound disorder, awaits full characterization to determine the potentially wide range of effects the DYX2 locus has upon the brain and behavior.In summary, our analyses indicate four association signals for RD, LI, and Verbal IQ in the DYX2 locus: Supplementary material 1 (DOCX 15 kb)Below is the link to the electronic supplementary material.


CACNA1S), renin catalysis (REN), blood groups (ABO), apolipoprotein (APOA5), and cardiovascular diseases (RASGRP1). Simulation studies showed that our homozygosity association tests controlled type 1 error well and had a promising power. This study provides a useful analysis tool for studying HD and allows us to gain a deeper understanding of HD in the human genome.Homozygosity disequilibrium (HD), a nonrandom sizable run of homozygosity in the genome, may be related to the evolution of populations and may also confer susceptibility to disease. No studies have investigated HD using whole genome sequencing (WGS) analysis. In this study, we used an enhanced version of Loss-Of-Heterozygosity Analysis Suite (LOHAS) software to investigate HD through analysis of real and simulated WGS data sets provided by Genetic Analysis Workshop 18. Using a local polynomial model, we derived whole-genome profiles of homozygosity intensities for 959 individuals and characterized the patterns of HD. Generalized estimating equation analysis for 855 related samples was performed to examine the association between patterns of HD and 3 phenotypes of interest, namely diastolic blood pressure, systolic blood pressure, and hypertension status, with covariate adjustments for age and gender. We found that 4.48% of individuals in this study carried sizable runs of homozygosity (ROHs). Distributions of the length of ROHs were derived and revealed a familial aggregation of HD. Genome-wide homozygosity association analysis identified 5 and 3 ROHs associated with diastolic blood pressure and hypertension, respectively. These regions contain genes associated with calcium channels ( Homozygosity disequilibrium (HD) describes a phenomenon in which a nonrandom pattern is observed for a sizable run of homozygosity (ROH) in the human genome, where ROH indicates a contiguous set of homozygous genotypes in an intact genomic region or allows to be interrupted by a small proportion of heterozygous genotypes arising from genotyping errors, missing genotypes, or mutations . HD can GAW18 provided a combined imputation data set derived from deep sequencing data for the whole genomes of 464 individuals and genome-wide association genotype data for 495 individuals. All 959 individuals were from 20 large independent pedigrees enrolled in the T2D-GENES (Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples) Project 2. Full information about blood pressures (DBP and SBP) and covariates (age and gender) was also available for 855 of these individuals. In this study, an individual was considered hypertensive if he or she had ever taken antihypertensive medication or his or her DBP was greater than 90 mm Hg or SBP was greater than 140 mm Hg at the most recent examination. The genome of each individual was sequenced by Complete Genomics with an average depth of coverage of 60x. Multiple quality control procedures were carried out to filter out single-nucleotide variants (SNVs) with poor performance in allele balance, strand bias, fraction of bases with low quality, and Mendelian errors by GAW18. The WGS data set of 464 individuals contained 24 million of SNVs that passed quality filters, and more than 51% of them were rare variants (RVs). The combined data set of 959 individuals contained 8,348,663 single-nucleotide polymorphisms (SNPs) and 5,573,886 RVs for odd-numbered autosomes. In addition, GAW18 provided 200 simulation data sets of quantitative trait Q1. Q1 was generated from a normal distribution and was independent of genetic variants in this study.For this study, we developed an enhanced version of the Loss-Of-Heterozygosity Analysis Suite (LOHAS) software . LOHAS wA and a, respectively. SNVs were classified as SNPs if their minor allele frequency (MAF) was higher than 0.05 or as RVs if lower than 0.05, where MAF was calculated across the whole population. For the SNP analysis, the coding system was the same as that used in the original LOHAS software. Homozygotes (aa and AA) were coded as 1 and heterozygotes (Aa) as 0. For the RV analysis, rare homozygotes (aa) and heterozygotes (Aa) were coded as 1 and 0, respectively. Because common homozygotes (AA) of RVs are less informative and therefore could dilute the assessment of other informative homozygotes when defining ROH, they were analyzed separately. Homozygosity intensity of a window anchored at a common homozygote of a RV was estimated by inputting the physical position of the anchor into the fitted local polynomial model, which was built based on genotypes except for common homozygotes of RVs. We also expanded LOHAS software by adding model-based methods for studying a dichotomous or quantitative trait with or without an adjustment for covariates. A new analysis module of generalized estimating equation (GEE) was included for analysis of related individuals, and a new analysis module of linear regression model was included for analysis of unrelated individuals.We extended LOHAS to handle large numbers of SNPs and RVs in the WGS data by introducing the following adapted coding system of homozygote-heterozygote status. Major and minor alleles at a SNV were denoted To estimate whole-genome homozygosity intensities of all 959 individuals, a window size, 5% of SNVs on a chromosome, was considered. Each window contained 11,968 to 65,465 SNVs. The GEE was used to analyze 855 related samples with WGS data, blood pressures, hypertension status, and covariates. Homozygosity intensities were modeled as a continuous response to correlate with DBP values, SBP values, and hypertension status, with concomitant adjustment for age and gender.We also evaluated type 1 error and test power of the homozygosity association tests using simulation data. Type 1 error was analyzed by examining the association between homozygosity intensities and Q1 (with covariate adjustments for age and gender) using the GEE analysis. We calculated the proportion of times that the null hypothesis was rejected over 200 simulations at each window and then calculated the average type 1 error over all windows. Test power was analyzed by choosing 3 regions on chromosome 21 containing 200 SNVs for each with varying proportions of RVs. The 3 regions contained 51.5%, 66.5%, and 80.0% RVs representing the 10th, 50th, and 90th percentiles of proportions of RVs on chromosome 21, respectively. The 3 regions were designated as Q1-associated ROHs by a logistic regression model as follows:p is the probability that all genotypes in the region were replaced by homozygotes and b0 and b1 are the regression coefficients. The test power was calculated as the proportion of times that the null hypothesis was rejected over 200 simulations at a Q1-associated ROH.where Our analyses were performed without knowledge of the underlying simulation model. Whole-genome profiles of homozygosity intensities for 959 individuals were derived from the GAW18 data set. Approximately 4.48% of individuals (43/959) carried sizable ROHs with homozygosity intensities greater than 0.9 and run lengths greater than 5 Mb. The minimum, 25th, 50th, and 75th percentiles and maximum of ROH lengths were 5.07, 5.66, 7.40, 13.61, and 44.60 Mb, respectively. The minimum, 25th, 50th, and 75th percentiles and maximum of total lengths of ROHs carried by an individual were 5.07, 5.64, 7.54, 14.81, and 105.85 Mb, respectively. Figure p-value = 0.0396), from 31.9 to 38.1 Mb on chromosome 9 , from 41.4 to 48.5 Mb  and from 97.7 to 103.3 Mb  on chromosome 11, and from 108.0 to 112.1 Mb on chromosome 13 . Hypertension-associated ROHs were located in the regions ranged from 132.7 to 137.9 Mb on chromosome 9 , from 109.5 to 116.1 Mb on chromosome 11 , and from 33.7 to 37.5 Mb on chromosome 15 . No SBP-associated ROHs were found.We carried out whole-genome homozygosity tests to identify DBP-, SBP-, or hypertension-associated ROHs. GEE analysis of 855 related individuals identified several DBP- or hypertension-associated ROHs after controlling for false discovery rate Figure . DBP-assb0 = −20 and b1 = 0.5 in our simulation model. For the GEE analysis of 855 related individuals, the power for the 3 Q1-associated ROHs containing 51.5%, 66.5%, and 80.0% RVs was 1.00, 1.00, and 1.00, respectively. The power was reduced to 0.910, 0.975, and 0.945 when b0 = −20 was changed to b0 = −10.We evaluated type 1 error of the homozygosity association tests by analyzing 200 simulation data sets of quantitative trait Q1. For a GEE association analysis of the 855 related individuals, the mean of type 1 errors was 0.03. We also evaluated the test power of our homozygosity association tests by analyzing the 200 simulation data sets with 3 Q1-associated ROHs created under the parameters that http://www.stat.sinica.edu.tw/hsinchou/genetics/loh/LOHAS.htm.This study has made several contributions to WGS data analysis of HD in the human genome. First, we adapted LOHAS software to enable more complete analysis of WGS data for HD. Two new homozygosity association analysis modules, a regression-based analysis for unrelated individuals and a GEE-based analysis for related individuals, have been incorporated into LOHAS. Software, examples, and user guide are now available free of charge at Second, we characterized the patterns of HD by analyzing a large WGS data set of 959 individuals from 20 pedigrees. The distribution of lengths for sizable ROHs and a distribution of total run length for one individual were obtained. The larger individual total run lengths of an individual may suggest autozygosity owing to inbreeding, consanguineous marriage, or a recent common ancestor. This approach may also be useful in identifying specific types of chromosomal aberrations such as uniparental disomy, hemizygous deletion, and loss of heterozygosity in cancer studies. In addition, we found that patterns of HD differ among individuals. We also observed familial aggregation, suggesting a genetic component of HD. A sensitivity analysis, which considered 3 thresholds of MAF for defining RVs , showed that the results were robust to a small change in the threshold of MAF for defining RVs. These findings suggest potential applications of these methods in genetic studies.CACNA1S) and play a role in renin catalysis (REN), both of which are important for the regulation of blood pressure. IGFBPL1 on 9p13.1 encodes IGF binding protein. Within the hypertension-associated ROHs, ABO on 9q34.2 is associated with the ABO blood group system. APOA1, APOA4, APOA5, and APOC3 on 11q23-q24 encode apolipoproteins and have been associated with cardiovascular diseases. RASGRP1 on 15q14 encodes a protein that functions as a Ras activator as well as a switch that is regulated by calcium and diacylglycerol, and guanosine triphosphate-guanosine diphosphate exchange. However, these results are still preliminary, and the findings should be further investigated in future studies.Third, our GEE-based homozygosity association tests identified 5 DBP-associated ROHs and 3 hypertension-associated ROHs. Genes in these ROHs include some that are associated with calcium channels, renin catalysis, insulin-like growth factor (IGF), blood groups, apolipoprotein, cardiovascular diseases, and rat sarcoma. Specifically, within the DBP-associated ROHs, two genes on chromosome 1q32 encode proteins that inactivate calcium channels in skeletal muscle cells  using a linear regression analysis. However, probably owing to the relatively small number of samples, none of the ROHs in this analysis was found to be associated with DBP, SBP, or hypertension after controlling for false discovery rate.In summary, the enhanced LOHAS developed in this study represents a useful tool for studying HD under different ascertainment schemes , phenotypes of interest (dichotomous disease status and quantitative traits), and experimental platforms (SNP microarrays and next-generation sequencing experiments). Performance of the improved LOHAS homozygosity association tests was evaluated by simulation studies, and the results suggest that the methods are reliable with a high test power and well-controlled type 1 error. Additional simulation studies and real data analyses will further elucidate the limitations of our methods and helps us further understand HD in the human genome.The authors declare that they have no competing interests.HCY conceived of the study, developed statistical methods, and prepared the manuscript. HWL developed analysis software and analyzed the data with HCY. Both authors read and approved the final manuscript.


MBMDR-3.0.3, a software that is able to identify genetic interactions, for a variety of SNP-SNP based epistasis models effectively. On the other hand, that implementation turned out to be less suitable for genome-wide interaction analysis studies, due to the prohibitive computational burden.The purpose of the MaxT algorithm is to provide a significance test algorithm that controls the family-wise error rate (FWER) during simultaneous hypothesis testing. However, the requirements in terms of computing time and memory of this procedure are proportional to the number of investigated hypotheses. The memory issue has been solved in 2013 by Van Lishout’s implementation of MaxT, which makes the memory usage independent from the size of the dataset. This algorithm is implemented in MBMDR-4.2.2, as part of the MB-MDR framework to screen for SNP-SNP, SNP-environment or SNP-SNP-environment interactions at a genome-wide level. We show that, in the absence of interaction effects, test-statistics produced by the MB-MDR methodology follow a mixture distribution with a point mass at zero and a shifted gamma distribution for the top 10 % of the strictly positive values. We show that the gammaMAXT algorithm has a power comparable to MaxT and maintains FWER, but requires less computational resources and time. We analyze a dataset composed of 106 SNPs and 1000 individuals within one day on a 256-core computer cluster. The same analysis would take about 104 times longer with MBMDR-3.0.3.In this work we introduce gammaMAXT, a novel implementation of the maxT algorithm for multiple testing correction. The algorithm was implemented in software These results are promising for future GWAIs. However, the proposed gammaMAXT algorithm offers a general significance assessment and multiple testing approach, applicable to any context that requires performing hundreds of thousands of tests. It offers new perspectives for fast and efficient permutation-based significance assessment in large-scale (integrated) omics studies.The online version of this article (doi:10.1186/s13040-015-0069-x) contains supplementary material, which is available to authorized users. MBMDR-4.2.2 is a software dedicated to genome-wide association interaction studies (GWAIs), the purpose of which is to identify pairs of SNPs and/or environmental factors that might regulate the susceptibility to the disease under investigation. The difficulty is to find a good balance between four main issues, that we summarise in the following objectives: Minimize the amount of false discoveries.Achieve sufficient statistical power to detect relevant pairs.Reduce the computational burden implied by the high number of tests for interactions.Provide a versatile software package that accommodates different study designs and study features, including flexibility in trait measurement types and the possibility to adjust for important predictor variables and confounders.Personalized medicine proposes to customize healthcare using molecular analysis –5. HowevMDMDR-3.0.3 is a C++ software tool based on the MB-MDR methodology, achieving good results regarding objectives (1), (2) and (4)  rather than calculated exactly. A detailed explanation of how we perform such an improvement is provided in the next section.In Mi. We hypothesize that test values in , with i>0, follow a mixture distribution of a shifted gamma distribution , with i>0, we can define the probabilities δ(x) is a point probability mass at x=0, x>0 and 0 otherwise. The parameter π depends on the data at hand and can be estimated with the Maximum Likelihood Estimation (MLE) method . Due to the fact that our main goal consists in predicting a maximum, we are not particularly interested in fitting the distribution of Ti,n+1,…,Ti,m] is given by We have indicated before that MB-MDR offers a flexible framework to test for SNP-SNP interactions. The software in which the framework is implemented has a modular built-up that allows a flexible choice of association test, depending on the input data. For instance, for quantitative traits, t-tests or non-parametric equivalents can be carried out. For binary traits, chi-squared test of independence can be chosen. The association test that best reflects the data at hand is used in both stage 1 and stage 2 of the MB-MDR framework . After tribution  and a poribed in . We assi) method  from theγ is the lower incomplete gamma function, y0 is the location parameter, k is the shape parameter and θ the scale parameter. Some authors discourage the use of the gamma distribution for model fitting due to the difficulty of parameter estimation  is given by q independent and identically distributed (i.i.d.) values y1,y2,…,yq, then We assume that the shifted gamma distribution is a good fit to the tail of timation . Howeverπ, y0, k and θ are stable from one permutation to another. This assumption is a plausible one, given the results in Table We postulate that the parameters Mi is estimated from a sample of size S=106 of strictly positives values in  rather than calculated directly. The parameter π is estimated on the fly using a variable z, counting the amount of zeros encountered during the sampling process. The new step 3(c) is described in Table As mentioned in the introduction, the gammaMAXT algorithm only differs from Van Lishout’s implementation of maxT Table  with resk requires more elaboration. According to .A simulated dataset D4 on Crohn’s disease, for which the trait is expressed on a binary scale . A balanced number of cases and controls is sampled.A set S2 with the same properties as S1, except that the trait is expressed on a continuous scale.A set S3 of 200 datasets, each composed of 104 SNPs and 1000 individuals, constructed in the same way as S1.A set S4 with the same properties as S3, except that the trait is expressed on a continuous scale.A set To study the control of the FWER, we run p-value below 5 %. On each set, we note that the estimated rates are within the interval  and satisfies thus Bradley’s liberal criterion of robustness for the significance level α=5 % [α, if the empirical rate We report the observed false-positive rates in Table el α=5 % . This crp-value below 5 %. We observe that the original MaxT and the new gammaMAXT algorithm leads to very similar power. By predicting the Mi values instead of computing them explicitly, we can of course not win power, so that the power of the gammaMAXT algorithm is obviously equal or lower than the one of MaxT. However, we observe that the difference is small, the largest power reduction being of 1,7 %.To evaluate the power, we create nine sets of data with GAMETES. Each set consists in 1000 datasets, all composed of 1000 individuals (500 cases and 500 controls) and 200 SNPs (out of which exactly one pair is linked with the trait). The heritability varies across the datasets from 0.03 to 0.01. In this way, we provide a range of decreasing effect sizes showing the power reduction. Table MBMDR-4.2.2, as part of the MB-MDR framework to screen for SNP-SNP, SNP-environment or SNP-SNP-environment interactions at a genome-wide level. In this context, we analyzed a dataset composed of 106 SNPs and 1000 individuals within one day on a 256-core computer cluster. The same analysis would take about 104 times longer with Van Lishout’s implementation of maxT, which was already an improvement of the classic Westfall and Young implementation [In this work we introduced gammaMAXT, a novel implementation of the maxT algorithm for multiple testing correction. The algorithm was implemented in software entation . These rMBMDR-4.2.2 can be downloaded for free at http://www.statgen.ulg.ac.be.


We have studied the marginal impact of these regions on disease status in the past, but we extend the method to deal with environmental factors present in data collected over several exam periods. We consider the respective interactions between such traits as smoking status and age with the genetic information and hope to augment those genetic regions deemed influential marginally with those that contribute via an interactive effect. In particular, we focus only on rare variants and apply a procedure to combine signal among rare variants in a number of "fixed bins" along the chromosome. We extend the procedure in Agne  The possible influence of rare variants on disease susceptibility has garnered more attention in recent years,3. A rarHypertension as a disease has often been linked to environmental factors such as smoking status  and age Unfortunately, even those procedures that deal with rare variants -3 do notOne method of addressing "finding the useful information from the vast amounts of messy and noisy data available" builds on the method of partitions . Among tIt should be noted that the methods proposed were developed and implemented without prior knowledge of the true causal single-nucleotide polymorphisms (SNPs) or the model generation process. Even though, upon learning of the true model, the attempt to identify interactive effects in the simulated data is doomed to be fruitless, the analysis is carried out in order provide a unique and repeatable procedure that can be applied to a more general data set. This is especially useful to consider real data has that have proved be full of interactions ,7.Genetic Analysis Workshop 18 (GAW18) contains whole genome sequencing (WGS) data in a pedigree-based sample. Longitudinal phenotype data for hypertension and related traits includes sex, age, year of examination, systolic and diastolic blood pressure, use of antihypertensive medications, and smoking status at up to 4 time points. A total of 200 replicates of simulated longitudinal phenotype data are provided based on real genotypes, pedigree structures, and trait distributions. Analysis in this study is focused on chromosome 3, which after eliminating with those SNPs without reference sequence contains two files of 773,088 and 62,915 SNPs, with 849 subjects with information on both genotype and phenotype data. Among the unrelated individuals, 142 subjects can be definitely mapped to subject IDs. We use the first replicate of the simulated data for our analysis.et al [et al [In this study, we look only at chromosome 3. As in Agne et al , we impll [et al , the senet al [case subjects to be those with hypertension status = 1 and control subjects to be those with hypertension status = 0. In Agne et al [We examine each exam period separately, and similar to Agne et al , we consThis method can indeed be applied to the data at hand, but we will suggest that the updated interactive score, in the absence of interactive effects, will extract similar information.We only consider one-way interactions between a single environmental trait and genetic information. To incorporate a potential interaction between SNPs and longitudinal traits, we establish a simple dichotomy of subjects via these traits. We consider smoking status and age. For smoking status, we take advantage of the natural dichotomy of smokers and nonsmokers, labeling nonsmokers as "low" on smoking status and smokers as "high" on smoking status. For age, we pick the median age as a cutoff, establishing those younger than the median age within an exam period as "low" on age and those at least as old as the median age as "high" on age. The median was especially convenient because it ensured an equal number of subjects in both the "high" and the "low" partitions. In practice, it is very similar to a two-means clustering approach, which has been proven effective in the past . PartitiTo establish a potential interactive influence on disease status , we must combine the information between the "high" and "low" groups. To do so, we establish the following for each longitudinal trait (smoking status and age):Because we are only interested in rare variants, our measure calculates the proportion of rare variants that are considered case (diseased) out of the total (case or control) number of rare variants in a given bin. To do so, the numerator is the number of rare variants that are affected by disease (case) in a given bin. The denominator is the total number of rare variants either affected or unaffected by disease (case or control) in a given bin. This statistic is then calculated for each (of the two) partitions of the subjects and summed to give the final interaction statistic.In this article, we define "rare" variants as either having only 1 (private) or 2 minor alleles in the sample. Although the previous marginal procedure used only private variants as rare, any cutoff can be used. A more inclusive cutoff means a larger sample size of so-called "rare" variants.et al [p-value for fixed bin i is defined as #{observed i,interact p< permuted i,interactp}/1000. This ensures that regions with an unusually high observed i pvalue will produce a low p-value, indicating significance.We use the standard procedure as established in Agne et al . AffecteOur method relies on treating each exam period as a separate data set. This ensures that no subject is counted more than once in any analysis. However, it will be interesting to examine any possible agreements, discrepancies, or trends regarding our results for the several exam periods, each of which can be considered a cross-sectional analysis and none of which overlap.We are also interested in subjects that show as influential cross-sectionally during a single exam period via both the gene-smoking and gene-age tests.We ran 1000 permutations investigating the interactive effect between rare variants and smoking status for the first, second, and third exam periods. We then ran 1000 permutations investigating the interactive effect between rare variants and age for each of those three time periods. The significance levels for each of 629 fixed-bin regions (of 100 SNPs each) is shown in Figure We observe 58 instances of influential regions in the 3 exam periods via the gene-smoking analysis and 61 via the gene-age analysis. Among those, we observe SNPs in 8 "answer" genes, as displayed in Table NMNAT3 were highlighted as influential in the both the gene-smoking and gene-age analyses for both exam periods 1 and 2.There were multiple overlapping regions for exam periods via the gene-smoking analysis 11 totals). There were also multiple overlapping regions for exam periods via the gene-age analysis . There were also several overlapping regions between the gene-smoking and gene-age analyses . Among these, 5 instances of SNPs in "answer" genes showing up as significant in more than 1 testing period and/or interaction scheme (gene-age or gene-smoking) were observed. These are shown in Table 1 totals.Ultimately, the goal of any such method would be to evaluate the power of a statistic in the context of its false-positive rate. However, because true interactions were not actually simulated in the data set, power analysis would not be appropriate. Although there is the potential for the method to pick up signal from marginal effects, the previous work  with fixAlthough analysis involving the influence of common variants is well established, methods tackling the issue of influential rare variants are still needed. The method outlined here will have little power to determine influential common variants, but as a result, its potential to pinpoint extremely rare variants of an influential nature will be very difficult to match by a common variant approach. Moreover, this method goes beyond simple marginal methods and has the potential to identify influential genetic regions that might only exhibit a strong association with disease when considering interaction with other dynamic traits such as smoking status and age.I score statistic as proposed in [The method does, of course, have limitations. For instance, if both effects that are positively and negatively (protective) associated with disease are present in a given bin, the effects may cancel. This is one disadvantage of this statistic over the similar posed in ,11, whicet al [Deeper interactions, such as those between smoking and age, might be examined. Furthermore, the extension to multiple replicates is easy by the ranking method of return frequency as outlined in Agne et al . We noteThe authors declare that they have no competing interests.SHL, MA, and CHH designed the study. MA, CHH, SHL, and TZ performed the study. MA, CHH, IH, HW contributed to analysis of the data. MA, CHH, and SHL drafted the manuscript. All authors read and approved the final manuscript.


A complete approach for genome-wide selection (GWS) involves reliable statistical genetics models and methods. Reports on this topic are common for additive genetic models but not for additive-dominance models. The objective of this paper was (i) to compare the performance of 10 additive-dominance predictive models (including current models and proposed modifications), fitted using Bayesian, Lasso and Ridge regression approaches; and (ii) to decompose genomic heritability and accuracy in terms of three quantitative genetic information sources, namely, linkage disequilibrium (LD), co-segregation (CS) and pedigree relationships or family structure (PR). The simulation study considered two broad sense heritability levels  and two genetic architectures for traits .G-REML/G-BLUP and a modified Bayesian/Lasso  method performed best in the prediction of genomic breeding as well as the total genotypic values of individuals in all four scenarios (two heritabilities x two genetic architectures). The BayesA*B*-type method showed a better ability to recover the dominance variance/additive variance ratio. Decomposition of genomic heritability and accuracy revealed the following descending importance order of information: LD, CS and PR not captured by markers, the last two being very close.Amongst the 10 models/methods evaluated, the G-BLUP, BAYESA*B*  and BAYESA*B*  methods presented the best results and were found to be adequate for accurately predicting genomic breeding and total genotypic values as well as for estimating additive and dominance in additive-dominance genomic models. The goal of genome-wide selection (GWS) is early phenotype prediction; it relies on simultaneously predicting the effects (on phenotype) of a large number of molecular markers. Thus, it represents a new paradigm in quantitative genetics , 2 and pThe simultaneous prediction of marker effects is now common in genome-wide association studies (GWAS) –10 also.Recent methodologies for GWS and GWAS have been evaluated with simulation studies , 12. SimHill et al. , BennewiDominance estimation is essential, especially for vegetative propagated species  and crosBayesian, Lasso and Ridge regression approaches have not yet been compared for additive-dominance models. –20 and  applied Given the scarcity of papers on dominance genomic models in the literature and for the purpose of increasing knowledge and enriching discussion of such an essential topic in this field, the objective of this paper is two-fold: (i) to evaluate 10 estimation methods  for fitting additive-dominance genomic models for GWS; and (ii) to decompose genomic heritability and accuracy in terms of the three quantitative genetic information compounds LD, CS and PR.1 and p2 are the allele frequencies in the parental populations (1 and 2). Notice also that the LD value depends on the allele frequencies in the parental populations. Thus, regardless of the distance between the SNPs and/or QTLs, if the allele frequencies are equal in the parental population, Δ = 0. The LD is maximized (|Δ| = 0.25) when θ = 0 and |p1 - p2| = 1. In this case, the LD value is positive with coupling and negative with repulsion  cr cr38] crDa = diag and Dd = diag, were obtained by the BLASSO method  using GS3 software.An additive-dominance Ridge Regression (RR-BLUP) method can also be implemented that considers the heterogeneity of variances between markers, called RR-HET. In our paper, the matrices with specific variances for each marker, Each type of population was simulated 10 times under the same parameter settings, which preserved the same features and provided samples that were effectively of the same conceptual population. Nine replicates were used as training populations, and one replicate was used as a validation population. The estimations based on each of the nine replicates were validated by obtaining estimates of the parameters accuracy and bias. Validation and reference individuals belonged to the same population but to different families.In each replicate, marker effects were estimated and used to estimate the genetic values of individuals in the tenth population. These estimated genetic values were correlated with the parametric genetic values of individuals of the tenth population, providing the accuracy values. The results from the nine analyses were averaged across replicates to obtain final accuracies and heritabilities for each scenario.Methods for computing parametric accuracies under the additive-dominance models were derived following the method of . The folAdditive accuracy: Dominance accuracy:Genotypic accuracy:QTL is the number of QTL, N is the number of individuals in the estimation dataset, and ha2, hd2 and hg2 are additive, dominance and total heritability, respectively.where na posteriori statistics. Hence, 10,000 MCMC samples were used to construct the posterior densities. The convergence of the Markov chains was checked with a [For Bayesian methods, we used 120,000 iterations for the MCMC algorithms of the different models, with the first 20,000 iterations discarded as burn in. After every set of 10 iterations (thin) were performed, a sample was retained to calculate d with a  diagnostThe three types of quantitative-genetic information can be defined as in :Linkage disequilibrium: refers to founder alleles from different loci in the same gamete, and the loci are in LD  and describe genetic relationships between founders.Co-segregation: refers to non-founder alleles  from different loci in the same gamete, and the loci are linked .Genetic relationships: statistical dependency between alleles from the same locus in different gametes. This kind of information is of three types: When associated with markers, it refers to parentage only on the marker loci and does not involving a linkage between markers and QTL; when associated with the pedigree of individuals in a model with both markers and pedigree, it refers to residual polygenic effects; when associated with the pedigree of individuals only, it refers to total polygenic effects.G-BLUP makes use of the following: (i) co-segregation of QTL and markers due to linkage; (ii) pedigree genetic relationships between markers not linked to QTL; and (iii) LD between markers and genes to capture relationships at QTL . The genThe genomic relationship matrix includes LD, co-segregation and pedigree genetic relationships between markers not linked to QTL . Habier et al.  derived The data sets analyzed were as follows: overall (raw or without any correction of the phenotypes); within-family deviations across families ; and within each family with posterior averaging . The accuracy of genomic selection in the analysis using the within-each-family with posterior averaging dataset is due to LD and co-segregation. In the analysis using the dataset from within-family deviations across families, the accuracy is due only to LD, while the accuracy of the analysis with the overall dataset is due to family IBD relationships, LD and co-segregation.In the evaluation of the methods, the following quantities were subjected to comparisons: heritability and dominance/additive variation ratio (the best are the closest to being parametric); accuracies ; and bias .The results concerning the trait controlled by small gene effects with a heritability of 0.30 are presented in Table The additive accuracies for alternative methods were 0.68, 0.63 and 0.53 for parametric GWS, GWS by the best methods and pedigree, respectively. The expected additive accuracy estimate of the parametric GWS obtained using a deterministic formula is 0.68 in this case. BayesA*B* methods and the G-BLUP method fitted using GVC-REML software were the best and gave accuracies of 0.63, which is close to the parametric case. These results reinforce the value of GWS, which performed better than the pedigree phenotypic selection Table .Figure In general, compared to the parametric values, the methods for additive-dominance models slightly underestimate the narrow sense heritability. The G-BLUP fitted via GVC software slightly overestimated the dominance heritability. The best methods were able to sufficiently capture the dominance heritability but were not completely able to capture the additive heritability, perhaps due to a limited number of markers and/or imperfect LD. Dominance heritability was overestimated by G-BLUP and BLASSO and perfectly estimated by BayesA*-B*.Results concerning the trait controlled by a mixed  inheritance model with a heritability of 0.30 are presented in Table 2 = 0.5 were higher than for h2 = 0.3  of genetic variation explained by markers exclusively in LD was high, approximately 90 %. In such a case, genetic variation is mainly due to LD rather than co-segregation and residual polygenic effects; thus, the results are corroborated.From the genomic heritability (0.26), it can be seen that the main source of information is LD (0.16), followed by co-segregation (0.06) and family IBD relationships not linked to QTL (0.04). In the simulation, the proportion (rFrom the pedigree heritability (0.20), it can be seen that the main source of information is individual IBD relationships (0.14), which was a fraction (0.875 = 0.14/0.16) of the IBS-LD captured by markers, followed by co-segregation (0.06). These partitions are in accordance with results reported by . Not allrgĝr using the raw dataset) was 0.69. It can also be given as a function of accuracy due to pedigree (rgĝped) and the accuracy of unrelated individuals (rgĝu) by the following: rgĝr = rgĝped + (1 ‐ rgĝped)rgĝu = 0.45 + (1 − 0.45) 0.52 = 0.73, which is close to 0.69. It can be observed that the use of related individuals increases the accuracy.The additive accuracy of related individuals  degrees of freedom for the marker variance associated with the shrinkage parameter. Using 6 or 8° of freedom produced only small differences, the BayesA*B*  being slightly better. G-BLUP was as good as these BayesA*B* methods. Figure In general, the Bayesian Ridge Regression (BRR) method provided good results. This finding is in accordance with , who repσmai2 are df + 1 (where df is the prior degrees of freedom). Thus, it is only one degree of freedom higher than the prior degrees of freedom, independent of the number of observations (N) or markers (n) in the model [In BayesA and BayesB, the degrees of freedom of the fully conditional posterior distribution of he model . Howeverhe model .The accuracies were very close across the methods for all effects . This result is in accordance with the results in the literature , 45, whiThe IBLASSO  method, criticized by  in termsFor the estimation methods, 7 evaluation criteria were used. The accuracy did not differ much, even with contrasting methods, corroborating the majority of the reports in the literature , 38, 45.Across the 7 criteria, the additive-dominance BayesA*-B*-type or t-BLASSO methods  and G-BLUP performed best in over 5 criteria.With increasing degrees of freedom in the chi-square distribution for variance components, the DE distribution for marker effects goes to a normal distribution, with the t distribution between them. Because the Student t-distribution approximates the normal distribution when the degree of freedom v increases, G-BLUP can be considered a limiting case of BayesA. The fitting of the BLASSO with new double exponential and t distributions has been considered recently . They prFang et al.  reportedIn our paper, the additive-dominance BayesA*-B*-type methods that used t-distributed priors were the best for recovering the dominance variance/additive variance ratio Tables , 3 and 4The BRR method was the best in this criterion in one situation Table . The abiThe most probable true symmetrical distributions of genetic effects (genetic architecture) are normal (Gaussian), t (Studentian) and double exponential (Laplacean). Thus, it is imperative to test these three distributions by assuming them as priors in the methods of analyses. This approach will reveal which assumed prior distribution is more adequate and/or robust. Lehermeier et al.  reportedWang et al.  presenteAs advocated by , after tAmongst the 10 models/methods evaluated, the G-BLUP, BAYESA*B*  and BAYESA*B*  methods exhibited the best results and were found to be adequate for accurately predicting genomic breeding and total genotypic values, as well as for estimating additive and dominance in additive-dominance genomic models.


Solanum lycopersicum), as an example. Reliable phenotype prediction models for the simulation were constructed from actual genotype and phenotype data. Our simulation predicted that selection for both yield and flavour would eventually result in morphological changes that would increase the total plant biomass and decrease the light extinction coefficient, an essential requirement for these improvements. This simulation-based genome-assisted approach to breeding will help to optimise plant breeding, not only in the tomato but also in other important agricultural crops.Efficient plant breeding methods must be developed in order to increase yields and feed a growing world population, as well as to meet the demands of consumers with diverse preferences who require high-quality foods. We propose a strategy that integrates breeding simulations and phenotype prediction models using genomic information. The validity of this strategy was evaluated by the simultaneous genetic improvement of the yield and flavour of the tomato ( Genetic improvement of plant species, generally known as breeding, has played an important role in the development of human societiesIt is widely accepted that genomic information will be used to develop efficient breeding systems6111213et al.Unlike MAS and MARS, GS does not focus on the association between phenotypic variation and the genotype of any specified markers. In GS, selection candidates are chosen on the basis of predicted genetic potential  calculated by whole-genome prediction (WGP) models. The WGP model is designed to predict GEBVs by using genome-wide DNA markers as explanatory variables. GS was first proposed by Meuwissen Although GS has significantly contributed to animal breeding, it is difficult to apply a strategy that is efficient in animal breeding directly to plant breeding, due to the differences in breeding situations. Most of the literature related to GS in plants focuses on evaluating prediction modelsSolanum lycopersicum) as an example. Our simulation indicated that it is necessary to perform cycles of crossing and selection to simultaneously improve yield and flavour, confirming that, as suggested in previous studies, this is a difficult breeding objective181920In order to apply GS to a plant breeding programme in which changes in multiple traits are important, we propose a strategy that integrates a computer simulation of the breeding process and an evaluation of the simulated breeding population by using WGP models. In this study, for the proof of concept of this simulation-based method, we used simultaneous improvement of yield and flavour in tomato  marker sets have been developed, and their usefulness has been verified in diversity panels that include a wide range of varieties and wild relatives222324et al.The tomato genome has large pericentromeric regionsK = 2 according to the value of ∆Kr = 0.82). Thus, a population structure analysis revealed the relationship between the change in genome composition and the history of tomato breeding.As a highly structured population is not suitable for genetic analysis using WGPA genome-wide association study (GWAS) that detects the association between polymorphic patterns of DNA markers and phenotype values is now a common strategy to detect QTLs that are available for MAS or MARSfw9.1, originally identified as a QTL between cultivated and wild tomato Even if WGP is highly accurate, its use in breeding is hindered by the problem of whether it is possible to develop populations or lines that possess high GEBV through realistic crossing and selection. To address this issue, it is helpful to predict GEBVs for future crosses46n = 96. The number of progenies from each cross in the first generation was 24 (96/4 crosses), whereas the number was 12 (96/8 crosses) in the subsequent generations  in the simulated population . In the Interestingly, in the simulated population, several morphological changes were predicted that were necessary to improve both total fruit weight and soluble solids content. An increase in height to the first truss without an increase in the number of days to flowering indicates an increase in total plant biomass . PreviouOne of the main objectives in the present study was to assess the potential of genome-assisted breeding in plant species. We used commercial elite varieties as plant materials, unlike previous studies that used diversity panels to represent the genetic diversity of tomato5152fw2.2lcn2.15152fw9.1 . To promote fruiting, Tomato-tone  was diluted 100-fold and sprayed on each truss when the second to fifth flowers were at the flowering stage. The plants were deflorated to limit the maximum number of flowers per truss to six and were pinched above the fourth truss. A total of 20 traits were phenotyped (h2) was calculated from the estimates of genetic (σ2G) and residual (σ2E) variances derived from the expected mean squares of the analysis of variance to express the genetic effects of traits:Tomato seeds were sown on a granular soil , and 20 days later, seedlings were transplanted onto rockwool slabs. A mixture of Otsuka-A nutrient solution and Otsuka-5 nutrient solution  was provided to the plants. The electrical conductivity level was adjusted to 0.80, 1.20, 1.60, 2.00, and 2.40 dS·menotyped . The pheenotyped . Thus, w2G and σ2E was performed by using the R function ‘aov’.The calculation of σn = 4) of the variety and that the minor allele frequency was greater than 5%  with 1–10. Each test included five independent calculations. Optimal K was estimated based on the ∆K that is the rate of change in the log probability of data between successive K valuesK was calculated by using STRUCTURE HARVESTER version 0.6.94KFullSearch algorithm was used for the estimation. The PCA was conducted by using the R function ‘prcomp’.The population structure of the 96 varieties was estimated using hierarchical clustering, Bayesian clustering, and PCA. For hierarchical clustering and PCA, SNP genotypes were scored as 0, 2, and 1 for the two homozygotes  and the heterozygote (e.g. GA), respectively. The hierarchical clustering was conducted based on the Ward method with Euclidean distance by using the R function ‘hclust’. Bayesian clustering was conducted by using the program STRUCTER version 2.3rrBLUP version 4.3 for MLM, RR, and RKHS, and randomForest version 4.6–7 for RF. For BL, EBL, wBSR, and Bayes C, we used C language programs developed by Onogi et al.fw9.1Lycopersicum Invertase 5Details for the regression methods used in the present study are described in et al.et al.n = 96. Namely, the number of progenies from each cross in the first generation was 24 (96/4 crosses), whereas the number was 12 (96/8 crosses) in the subsequent generations .The tomato genome in this simulation study was represented by the linkage map from Shirasawa erations . Via simHow to cite this article: Yamamoto, E. et al. A simulation-based breeding design that uses whole-genome prediction in tomato. Sci. Rep.6, 19454; doi: 10.1038/srep19454 (2016).


The traditional quantitative genetics model was used as the unifying approach to derive six existing and new definitions of genomic additive and dominance relationships. The theoretical differences of these definitions were in the assumptions of equal SNP effects , equal SNP variances , and expected or sample SNP additive and dominance variances. The six definitions of genomic additive and dominance relationships on average were consistent with the pedigree relationships, but had individual genomic specificity and large variations not observed from pedigree relationships. These large variations may allow finding least related genomes even within the same family for minimizing genomic relatedness among breeding individuals. The six definitions of genomic relationships generally had similar numerical results in genomic best linear unbiased predictions of additive effects (GBLUP) and similar genomic REML (GREML) estimates of additive heritability. Predicted SNP dominance effects and GREML estimates of dominance heritability were similar within definitions assuming equal SNP effects or within definitions assuming equal SNP variance, but had differences between these two groups of definitions. We proposed a new measure of genomic inbreeding coefficient based on parental genomic co-ancestry coefficient and genomic additive correlation as a genomic approach for predicting offspring inbreeding level. This genomic inbreeding coefficient had the highest correlation with pedigree inbreeding coefficient among the four methods evaluated for calculating genomic inbreeding coefficient in a Holstein sample and a swine sample. Genomic relationship among individuals is a measure of genomic relatedness or similarity among individuals and allows genomic prediction and variance component estimation to use theoretical results and computational strategies of best linear unbiased prediction (BLUP). Genomic relationship is calculated using genome-wide single nucleotide polymorphism (SNP) markers without referencing to pedigree information. Therefore, genomic relationship is particularly appealing for wildlife and animal populations where pedigree information is unavailable or incomplete.G matrix for using BLUP to predict total marker effects was the approach of Nejati-Javaremi et al.G matrix as twice the average marker IBS probability (IBS  =  identity by state). VanRaden derived the first genomic additive relationship formula based on the standardization of the 2-1-0 (or 0-1-2) coding of SNP genotypes et al. proposed the quantitative genetics model that partitions a genotypic value into breeding value and dominance deviation for genomic prediction and variance component estimation of additive and dominance effects et al.et al. proposed genomic dominance relationships using the approach of standardization of the 0-1-0 dominance coding et al.The first attempt to use marker information to construct the et al.et al.et al. Inbreeding is a major issue in animal breeding and wildlife conservation because inbreeding may result in inbreeding depression associated with reduced survival and fertility In this study, we show that quantitative genetics theory can be the unifying theory for deriving existing and new genomic additive and dominance relationships and for studying the theoretical differences among various definitions of genomic relationships. We propose a method for calculating genomic inbreeding coefficient using a combination of genomic correlation from the quantitative genetics model, classical definition of inbreeding coefficient, and the theoretical expectation of genomic additive relationships. We also explore numerical differences among various genomic relationships and inbreeding coefficients using a Holstein sample and a swine sample.Under the assumption of Hardy-Weinberg equilibrium (HWE), the traditional quantitative genetics model partitions a genotypic value into the summation of a common mean, breeding value and dominance deviation Based on the genomic breeding value and dominance deviation defined in Using pedigree relationships, the covariances between breeding values and between dominance deviations of two individuals Z  =  N × q incidence matrix allocating phenotypic observations to each individual  =  identity matrix for one observation per individual (N  =  q), α  =  m ×1 column vector of gene substitution (additive) effects of SNP markers, α, δ  =  m ×1 column vector of dominance effects of SNP markers, δ, b  =  c ×1 vector of fixed effects, and X  =  N × c model matrix of b. Assumptions for the first and second moments are: Im  =  m × m identity matrix, and IN  =  N × N identity matrix. The W matrices of The mixed model to implement the quantitative genetics model of The average of the additive or dominance SNP coding in um (HWE) , Part A,Wα in Wδ in Wα in Wδ in The general formulations of genomic additive and dominance relationships are obtained by equating the genomic covariances of (19)where   =Ag  =  genomic additive relationship matrix and Dg  =  genomic dominance relationship matrix.Various existing and new definitions can be derived from Assuming equal SNP additive and dominance effects, (23)where  orAssuming equal SNP effects for all SNP markers and using the sample variances of Assuming equal additive and dominance variances rather than equal additive and dominance effects across SNP markers and using the expected variances of Using sample variances of Definitions I-II and IV-V of genomic relationships can be represented by two sets of formulations in matrix notations. For Definitions I and II assuming equal SNP effects, Genomic relationships between two individuals of Definitions I-II and IV-V as off-diagonal elements of the relationship matrices are not mathematically comparable for genomic relatedness because those off-diagonal elements are not exactly correlations. Genomic correlations (Definitions III and VI) among different individuals are mathematically comparable and provide a reference to evaluate other genomic relationship definitions.The general formulations of genomic additive and dominance correlations are:(31)where  anhttp://animalgene.umn.edu.(33)where   = I or II  or 25–26 IV or V  or 29–30We formulate genomic inbreeding coefficients using parental genomic relationships based on the following results: 1) The inbreeding coefficient of an individual is the coancestry coefficient between the parents, 2) The average values of genomic additive and dominance relationships were consistent with theoretical expectations of pedigree relationships in the Holstein sample  and the For the Holstein sample, the average genomic additive relationships were below but close to those of ‘2×(coancestry coefficient)’ calculated from the pedigree data. The genomic additive relationships of Definitions I-VI were 0.459–0.469 for parent-offspring, 0.489–0.515 for full-sibs, and 0.205–0.212 for half-sibs, compared to ‘2×(coancestry coefficient)’ average value of 0.574 for parent offspring, 0.575 for full-sibs, and 0.341 for half-sibs .For the swine sample, the average genomic additive relationships were almost the same as those of ‘2×(coancestry coefficient)’ calculated from the pedigree data. The genomic additive relationships of Definitions I-VI were 0.513–0.534 for parent offspring, 0.526–0.543 for full-sibs and 0.289–0.299 for half-sibs, compared to ‘2×(coancestry coefficient)’ average value of 0.528 for parent offspring, 0.530 for full-sibs, and 0.294 for half-sibs .Genomic additive relationships from the swine sample were clearly more consistent with the pedigree relationships than those from the Holstein sample. This difference likely was due to two factors. First, most Holstein cattle with SNP genotypes were distributed in the last 3–5 generations of the pedigree that approximately comprised of ten generations For genomic dominance relationships, only full-sibs are expected to have dominance relationship value of 0.25 assuming no inbreeding. Parent-offspring and half-sibs are expected to have no dominance relationship. The observed genomic dominance relationships were consistent with these theoretical expectations. The average genomic dominance relationships of Definitions I-VI were 0.283–0.306 in the Holstein sample and were 0.257–0.272 in the swine sample for full-sibs, and were nearly zero for parent-offspring and half-sibs in both samples. The higher mean values of genomic dominance relationships of full-sibs in the Holstein sample were due to the three outliers that were nearly ‘1’ among the 48 data points . With thGenomic and pedigree relationships had a major difference: genomic relationships had individual genomic specificity and large variations not observed in pedigree relationships. For the Holstein sample, the range of genomic additive relationships was −0.039 to 0.584 for parent-offspring, compared to pedigree relationships of 0.500–0.653; −0.042 to 1.036 for full-sibs , compared to pedigree relationships of 0.531–0.605; and −0.120 to 0.444 for half-sibs, compared to pedigree relationships of 0.250–0.508 . For theet al.We compared four methods for calculating genomic inbreeding coefficients: i) Using the individual's diagonal element of genomic additive relationship based on the SNP model matrix for genomic prediction:  methods . The ave1–0.131) . While hγ-VI (Method iv) had the smallest variations. For the group of individuals marked by ‘A’, all three genomic methods had high inbreeding coefficients whereas the pedigree method had ‘0’ inbreeding coefficients. These large differences between the genomic and pedigree estimates could have been due to pedigree errors or missing pedigree information. If either problem were true, this would be an example showing the usefulness of genomic inbreeding in the absence of pedigree information or in the presence of pedigree errors. For the group of individuals marked ‘B’, all three genomic methods had lower inbreeding coefficients than the pedigree estimates that were among the highest inbreeding coefficients in this sample. The correlation of inbreeding coefficients was 0.70–0.75 between Method iv) and Method i), and was 0.82 between Method iv) and Method ii), indicating that Method iv) maintained most of the genomic specificity of Methods i) and ii) while having the highest correlation with pedigree inbreeding coefficients , ii) and iv) with the pedigree method showed that Method iv) had similar patterns of the deviations as Method i) and ii) from the pedigree estimates of inbreeding coefficients and maintained most of the individual genomic specificity of a realized inbreeding coefficient. ficients . Method The high correlation between genomic inbreeding coefficients from Method iv) and pedigree inbreeding coefficients likely was due to two reasons. First, genomic correlations had smaller variations than genomic relationships, SD  = 0.043–0.044 for Definitions III and VI of genomic additive correlations, and SD  = 0.087–0.108 for Definitions I, II IV and V of genomic additive relationships . Second,et al.et al., the correlation between the genomic inbreeding coefficients using ROH and the pedigree inbreeding coefficients were higher than that of Yang et al.et al.We were unable to make direct comparison between Method iv) and the approach of runs of homozygosity (ROH) for calculating genomic inbreeding coefficients Definitions I-VI essentially had the same GBLUP of breeding values and dominance deviations that mostly had correlations of 0.99 among GBLUP from different definitions . For GREinitions . The difThe traditional quantitative genetics model was shown to be a unifying model to derive genomic additive and dominance relationships and genomic inbreeding coefficients. Genomic additive and dominance relationships between individuals on average agreed well with the pedigree relationship, but genomic relationships were realized genetic relationships with individual genomic specificity and had large variations not observed from pedigree relationships. Genomic relationships assuming equal SNP variances had larger variations than assuming equal SNP effects. Genomic inbreeding coefficients calculated from parental genomic correlations had high correlations with pedigree inbreeding coefficients and could be an effective genomic tool for predicting offspring inbreeding levels in breeding plans.S1 FigurePedigree of the swine sample with 3534 individuals.(PDF)Click here for additional data file.S2 FigureDiagonal elements of genomic additive and dominance relationships and pedigree additive relationships of the swine sample with 3534 individuals. Definition IVb of diagonal elements of additive relationships was that of Yang et al. (PNG)Click here for additional data file.S1 TableCorrelations between genomic additive and dominance relationships under Definitions I-IV and pedigree additive relationship measured by ‘2×(coancestry coefficient)’.(PDF)Click here for additional data file.S2 TableCorrelations of breeding values, dominance deviations and total genetic values under different genomic relationship definitions.(PDF)Click here for additional data file.S1 TextProofs and animal data.(PDF)Click here for additional data file.