Association mapping is a statistical approach combining phenotypic traits andgenetic diversity in natural populations with the goal of correlating thevariation present at phenotypic and allelic levels. It is essential toseparate the true effect of genetic variation from other confoundingfactors, such as adaptation to different uses and geographical locations.The rapid availability of large datasets makes it necessary to explorestatistical methods that can be computationally less intensive and moreflexible for data exploration.Brassica rapa accessions ofdifferent morphotypes and origins was explored to find genetic associationbetween markers and metabolites: tocopherols, carotenoids, chlorophylls andfolate. A widely used linear model with modifications to account forpopulation structure and kinship was followed for association mapping. Inaddition, a machine learning algorithm called Random Forest (RF) was used asa comparison. Comparison of results across methods resulted in the selectionof a set of significant markers as promising candidates for further work.This set of markers associated to the metabolites can potentially be appliedfor the selection of genotypes with elevated levels of thesemetabolites.A core collection of 168 The incorporation of the kinship correction into the association model didnot reduce the number of significantly associated markers. Howeverincorporation of the STRUCTURE correction (Q matrix) in the linearregression model greatly reduced the number of significantly associatedmarkers. Additionally, our results demonstrate that RF is an interestingcomplementary method with added value in association studies in plants,which is illustrated by the overlap in markers identified using RF and alinear mixed model with correction for kinship and population structure.Several markers that were selected in RF and in the models with correctionfor kinship, but not for population structure, were also identified as QTLsin two bi-parental DH populations. In plants association mapping has been developed as a tool to relate geneticdiversity, expressed as allelic polymorphisms, to the observed phenotypic variationin complex traits without the need to develop mapping populations. Results obtainedwith association mapping methods in various crops indicate that this technique canbe successful in the identification of markers linked to genes and/or genomicregions associated to a desirable trait However, one of the most important constraints in the use of association mapping incrop plants is unidentified population sub-structure, which arises as a result ofadaptation, genetic drift, domestication or selection As a consequence, when association mapping is used to identify genes responsible forquantitative variation in a group of accessions, there is enough evidence thatconfounding will be a significant problem, especially if the trait variesgeographically, as is the case for example of flowering time Several methods can be used to infer multiple levels of relatedness in a populationFurthermore, the power to detect epistasis in moderately sized populations in generalis low, while Random Forest can implicitly use interactions among regressorvariables to predict the phenotype and can help identify multi-locus epistaticinteractions Brassicarapa accessions, representing the wide variation in crop types and geographical origins. Brassicarapa has been cultivated for many centuries in different parts of theworld, increasing the variation within the species as a result of breeding.B.rapa is a diploid species which includes vegetable-,fodder-and oil crops. The leafy vegetables include both heading types (Chinesecabbage) and non-heading types , the turnips include vegetable andfodder turnips, and the oil crops include both annual and biannual crops. Most leafyvegetables, turnips and biannual oil types are self-incompatible and as aconsequence the genebank accessions of this type are heterogeneous and plants areheterozygous. A smaller group of Brassica rapa is formed by thesarsons (brown sarson (Dichotoma), toria(Dichotoma) and yellow sarson (trilocularis))characterized by very early flowering and self-compatibility of many accessions,which results in heterogeneous accessions with merely homozygous plants For this study we choose to work with a core collection of 168 B. rapa gene pool In a previous study the genotypic fingerprinting of a large collection of 160accessions showed that there is considerable genotypic variation within theB. rapa accessions associationanalysis with correction for population structure led to the identification of 27AFLP markers, related to the variation in leaf and seed metabolites as well asmorphological traits B. rapa accessions of different morphotypes andorigin. We explore the results obtained with association methods that correct forkinship and population structure which mainly aim to reduce the rate offalse-positive associations, and in addition we make use of Random Forest forcomparison to the commonly used association methods.Previously, in a collection of 160 Myb and SSR polymorphicbands).The genetic population structure of the core collection of 168 accessions wasinferred using 553 markers , yellow sarson (YS) and rapid cycling (RC) ; subpopulation 2included several types from Asian origin: pak choi (PC), winter oil, mizuna,mibuna, komasuna, turnip green, oil rape and Asian turnip (PC+T);subpopulation 3 included mainly accessions of Chinese cabbage (CC) andsubpopulation 4 included mostly vegetable turnip (VT), fodder turnip (FT) andbroccoletto accessions from European origin (VT+FT) .There was a high level of admixture between the different subpopulations. Of the168 accessions, 109 were assigned to a subpopulation with a membershipprobability of p>0.70. Fifty-nine accessions were assigned to more than onesubpopulation and had membership probabilities below 0.7 corresponding toseveral subpopulations .The PCO-MC is a method, which couples principal coordinate analysis to aclustering procedure for the inference of population structure from multi-locusgenotype data. The PCO and STRUCTURE output produced comparable results. Afterthe PCO analysis, in the second dimension one small distinct, statisticallysignificant subpopulation, corresponding to oil types of Indian origin, could bedistinguished. This subpopulation corresponds to subpopulation 1 as identified in STRUCTURE . In the Brassica napusIn B.rapa morphotypes, boxplots were constructed based on the totalcontent value per metabolite in each subpopulation as defined by STRUCTURE(b and lutein was significantly differentbetween few subpopulations and the content of tocopherols was just significantlydifferent between the Chinese cabbage (CC) subpopulation 3 compared to the othersubpopulations . As a result the number of significantly associatedmarkers to a specific metabolite after multiple test correction was stronglyinflated and ranged from 2 (for δ tocopherol) to 98 (for folate) permetabolite. The highest numbers of significant markers associated to a trait(>80) were found for β-carotene, neoxanthin, violaxanthin and folate;these metabolites also showed the greatest variation in content betweensubgroups.To account for the level of relatedness between individuals we included thekinship correction (K matrix) in model (3). However, with the inclusion ofthis correction the number of significantly associated markers remained high(2–94). The results of these two models are highly similar not only innumber but also in the identity of the significant markers for eachmetabolite.In addition to the K matrix we introduced the STRUCTURE Q matrix as acorrection. After accounting for population structure in model (2) thenumber of significant markers found per metabolite after a multiplecorrection step was dramatically reduced. Only for violaxanthin and folatefew markers were identified. This drop down was as strong for themetabolites with subpopulation variation (carotenoids and folate) as for thetocopherols, which showed significant variation only between the CCsubpopulation and the other subpopulations.When we combined the information from the Q matrix and the K matrix in thefull model (4), following the described approach After correcting for multiple testing in the KQ correction model, only tenmarkers remained significantly associated with metabolites: Alu_M476_0,pTAmCAC_148_3, Hae_M294_2, pGGmCAA_335_2 and pTAmCAT_312_3 forβ-carotene; Alu_263_6, pTAmCAC_101_7 and pTAmCAC_270_9, Br13 and Br46for violaxanthin and pGGmCAA_335_2 for folate.Myb, five AFLP and twomicrosatellite markers significantly associated to the metabolites(P<0.05). This network allowed us to connect the metabolites of similarpathways through markers (To summarize the results obtained from the full model (4), we constructed anetwork with a total of three  markers .The overlap of significant associated markers between all the pathways was very limited asexpected if we consider that biochemically different precursors areinvolved. We found only one marker (pGGmCAA_335_2) that was significantlyassociated to folate and β -carotene.The number of significantly associated markers per metabolite ranged fromeight for α-tocopherol to 39 for neoxanthin. Interestingly, whencompared to the simple model (1), the number of significant markers obtainedwith the RF approach was much lower for all the metabolites except forδ-tocopherol.Nonetheless, the overlap of significant markers between methods is large;many of the significant markers found with RF were also significant with thesimple model (1) and with the model with correction for kinship (3). Forexample, an overlap between 20% and 30% of significant markerswas observed for β-carotene, neoxanthin, violaxanthin, folate,α-tocopherol and β-tocopherol .In contrast, when the results obtained with Random Forest are compared to theresults obtained with the full model (4) six out of the ten markers fromthis model are included in the Random Forest output.In the case of the microsatellite markers the overlap between significantlyassociated markers in Random Forest and in model (1) was high and almostcomplete for both markers except for those identified for δ-, β- andα-tocopherol. Additionally, one out of two significant SSR markers frommodel (4) were found also significant in the Random Forest output.B. rapa. Results from both principal coordinate analysis (PCO)and STRUCTURE illustrate the highly admixed nature of the accessions within thiscollection. We decided to use membership probabilities obtained from STRUCTURE inthe association mapping model to correct for populations structure, as it is awidely used method. In addition correction for kinship was included in othermodels.An important consideration for the use of association mapping in crop plants is thepresence of population structure. If a group of diverse accessions is chosen forthis type of studies the risk exists that some of the accessions are more closelyrelated to each other than the average pair of individuals taken at random in apopulation In the four models we explored the impact from STRUCTURE (model 2), kinshipcoefficients (model 3) or both (model 4) in the association models.Correcting for the level of relatedness using the Q matrix from the STRUCTURE output,resulted in a significant reduction of the number of marker-trait associations asshown by comparing model (1) and both models (2) and (4). Although there was alwayssome overlap between the marker-trait associations identified by these models, newassociations arose with models (2) and (4).The inclusion of the kinship matrix in models (3) and (4) did not reduce the numberof significant marker-trait associations. This was most likely due to the fact thatkinship values were very low and the accessions of the core collection showedsimilar levels of relatedness. The results from STRUCTURE and the identical levelsof relatedness as observed in K seem to contradict. Similarities based on theJaccard measure were also tested in model (3), with the same results as obtainedwith the similarities obtained from SPAGeDi.We tested thereafter both corrections in phenotypic models identical to models (2)and (3) but without the marker effect, and compared the resulting residual variancewith the “empty” model: trait  =  error. We foundthat whereas Q explained the phenotypic variation by as much as 60% for sometraits, the K matrix did not seem to explain any part of the phenotypic variation,for all traits. This seems to support earlier evidence that K alone in some casesmay not correct for population structure In the present study we considered the use of Random Forests (RF) as a complementarymethod to our association study. The performance of this method in associationanalysis has been recently tested in Arabidopsis In our study we evaluated the RF results in comparison to the results obtained withthe already validated and widely used model (4) and the simple model (1). Onestriking result of the RF analysis is the small number of associated markers thatare found for all the metabolites in comparison to model (1). Random Forests israther robust to outliers, as opposed to linear models, making it an attractivealternative to the traditional linear models. We decided to evaluate the overlap ofRF and the simple model (1), which does not include any correction, and the fullmodel, which includes the Q and K matrix correction (4). Seven out of elevenmarker-trait associations found significant after multiple test correction withmodel (4) were also found significant with RF, while also many Random Forest markerswere identified with models 1 and 3 (K correction).B. rapa genome synteny (datanot shown). This is a confirmation of the effect of the marker-trait association andmakes these markers important candidate genes for further study.Several markers that are associated with the metabolites studied, were alsoidentified in QTL studies for the same metabolites in DH populations derived fromcrosses between two accessions (yellow sarson (YS 143) x pakchoi (PC 175) and theirreciprocal cross , or map For eight of the eleven metabolites analyzed, Random Forest selected at least onemarker that mapped in the QTL interval for the respective metabolites in thebiparental QTL studies. For several metabolites except the tocopherols, thesemarkers were also identified in model 1 (no correction) and 3 (kinship correction)but not in models 2 and 4 (with Q correction).In these same two doubled haploid populations QTL for lutein and chlorophyll-a and -boverlap in the region where the marker pTAmCAC_148_3 is located and identified assignificant for β-carotene by all models. In this genomic region of linkagegroup A03 the genes ε-cyclase, β-carotene hydroxylase and carotenoidisomerase are predicted based on synteny with Arabidopsis B. rapa collections or breeding populations to identifygenotypes with elevated levels of important metabolites that are considered ashealthy compounds. While further validation of these markers for marker assistedselection in B. rapa is needed, at least the eight myb and AFLPmarkers and two microsatellites markers found significant with model (4), aftermultiple testing correction In this study we have identified several markers that can be applied to screenAt present we are in the process of expanding the core collection so that associationmapping within the four subpopulations becomes feasible and to increase the power ofthe statistical analysis. In an attempt to separate true from spurious associationsand/or false negatives in future association studies using the present corecollection we will follow a similar approach, which takes into account the level ofrelatedness between individuals (K and Q) and the use of Random Forest.Brassica rapa core collection included a total of 168accessions of diverse morphotype and origin , neepgreens, turnip rape, brocoletto (turnip tops) and turnip types are mainlyself-incompatible and as a consequence the accessions are heterogeneous andheterozygous. The annual yellow sarson oil seed accessions are self-compatible,which results in homozygous plants. The modern cultivars and breeding lines fromseed companies are homogeneous hybrids and inbred lines. 137 accessions wereobtained from the Dutch Crop Genetic Resources Center (CGN) in Wageningen, theChinese Academy of Agricultural Sciences (CAAS)-Institute for Vegetable andFlowers (IVF) and the CAAS Oil Crop Research Institute (OCRI) genebanks and theOsborn Lab, while six different breeding companies providedFrom each frozen powder, 0.15 g was weighed and 1.8 ml of Na-acetate buffercontaining 1% ascorbic acid and 20 µM DTT, pH 4.7, was added.After sonication for 5 min and heating at 100°C for 10 min, total folatecontent of samples was quantified using a Lactobacillus casei–basedmicrobiological assay, after enzymatic deconjugation for 4 h at 37°C pH4.8, with human plasma as a source of γ-glutamyl hydrolase activityExtraction and analyses of carotenoids, tocopherols and chlorophylls wereperformed as described in Bino et al. Pst Iand Mse I and ligated to adaptors. Pre amplifications wereperformed in 20 µl volume of 1x PCR buffer, 0.2 mM dNTPs, 30 ng of adaptorprimer, 0.4 Taq polymerase and 5 µl of a 10x diluted restriction ligationmix, using 24 cycles of 94°C for 30 s, 56°C for 30 s and 72°C for 60s. Pre-amplifications products were used as template for selective amplificationwith three primer combinations .The AFLP procedure was performed as described by de Vos et al.Myb family targeted profiling, total genomic DNA wasdigested using the following enzymes per reaction: Hae III, Rsa I, Alu I and MseI and ligated to an adaptor. Pre amplifications with one primer directed to acommon myb motif  and one adaptor primer were performed in25 µl of 1X PCR buffer (with 15 Mm MgCl2), 0.2 mM dNTPs, 0.8 pMol Genespecific primer, 0.8 pMol Adapter primer, U Hotstar Taq polymerase (Qiagen) and5 µl of a 10X diluted restriction ligation mix. Amplification productswere used as template for selective amplification.For the Myb profiling images were analyzed using QuantarPro™ software. This marker dataset (359 polymorphic bands) was scored aspresent (1) or absent (0) and treated as dominant markers. A map position couldbe assigned for 69 markers from this dataset; these markers were distributedover different positions in the linkage groups of a doubled haploid population.AFLP and B.rapa and distribution over all the linkage groups (A01–A10)For microsatellite (SSR) screening, 28 primers were selected for amplification inthe accessions of the core collection. From the primers 10 were genomic and 18were new Est based SSRs ). The primerswere selected because of their map position in different maps of Myb, SSR) were used to identify the differentsubgroups and admixture within the accessions of the core collection through amodel of Bayesian clustering for inferring population structure. For the SSRsonly the most frequent SSR allele was taken into account to avoid overrepresentation of the SSR loci.Marker data , by varying the assumednumber of subpopulations between one and ten, with a total of 300,000 iterationsfor Markov Chain Monte Carlo repetitions and 100,000 burns in.A total of 539 markers was included in the analysis, and ploidy was set to one.The number of subpopulations was determined using the software STRUCTURE 2.2 (Box plots were chosen as a tool to explore the variation of metaboliteconcentrations according to different STRUCTURE subpopulations. One-way ANOVAwas performed for each metabolite to find the mean differences among the fourSTRUCTURE subpopulations. Least significant differences (LSD) were calculated tocompare the differences of means of metabolite content between the foursubpopulations obtained with STRUCTURE. Boxplots, ANOVA and LSD calculationswere performed using R statistical software.www.maizegenetics.net). A total of 243 markers with an allelicfrequency higher than 10% was included in the association analysis. SinceAFLP and Myb markers gave dominant marker scores and TASSELworks with co-dominant data, within TASSEL we set the ploidy to one to work withdominant scores as we had done with STRUCTURE. In the case of the 28microsatellites all alleles were included within TASSEL in a different run ascodominant markers.Association analysis was performed in several steps of increasing complexity;with and without correction for population structure In the first step a “naïve” model was used to associate eachmarker to the trait, G = σ2K; VG isthe variance-covariance matrix of the random genotype effects, K is the matrixof kinship coefficients and σ2 is the additive geneticvariance.In the second step the vector of cluster memberships Q obtained from Structurewas added as a fixed term to the previous modelMyb and SSRs data to estimate both K and Q. The percentageof variation was also implemented in TASSEL and extracted from the output forfurther analysis and comparison.In the fourth and final step we correct for kinship as well as populationstructure using a linear mixed model that combines the information contained inthe two previous models. It is also known as the Q+K method The p-values resulting from all the models for association analysis werecorrected for multiple testing using a resampling method as implemented in the Rpackage “multtest” Myb, and 28 SSR marker set) associated to thetocopherol, carotenoids, flavonoids and folate metabolites. This method uses abagging approach by bootstrapping samples Random Forest (RF) regression This procedure is fast and can handle high-dimensional data (predictor variables>> number of samples). Each tree is fully grown (unpruned) to obtainlow-bias, high variance (before averaging) and low correlation among trees.Finally, RF averages are calculated over all the trees and result in low biasand low variance of predictions of the trait based on the markers used in theRandom Forest The parameter “mtry”, which indicates the number of random variablesconsidered at each splitting node, was optimized by choosing the“mtry” with the highest percentage of explained variation amongseparate RF analyses done on “mtry” values 3, 6, 12, 24, 48 and 96successively on the same data set. The variance explained in RF is defined as1-(Mean square error (MSE) / Variance of response), where MSE is the sum ofsquared residuals on the OOB samples divided by the OOB sample size In general RF yields only the relative importance of markers that explain thevariation present in metabolites, but does not give a significance thresholdlevel to select a subset of associated markers. Therefore, a permutation methodwas used to calculate the significance of each marker association in this studyRF regressions of metabolites on markers were conducted using the “RandomForest” package of the R-software A network is an extended graph, which contains additional information on thevertices and edges of the graph Table S1Membership probabilities and group assignment of all accessions used inthis study based on STRUCTURE.(XLSX)Click here for additional data file.Table S2LSD result of metabolite variation based on STRUCTUREsubgroups(XLSX)Click here for additional data file.Table S3Overview of associations between markers and metabolites for allmetabolites investigated in this study across methods with p-valuesafter multiple testing correction. For mapped markers genetic mappositions are listed. For RF only significant markers are indicated. In thelast column QTL identified in DH populations from crosses between YS 143 andPC 175 and their reciprocal cross (map presented in (XLSX)Click here for additional data file.


Genome-wide pathway association studies provide novel insight into the biological mechanism underlying complex diseases. Current pathway association studies primarily focus on single important disease phenotype, which is sometimes insufficient to characterize the clinical manifestations of complex diseases. We present a multi-phenotypes pathway association study(MPPAS) approach using principle component analysis(PCA). In our approach, PCA is first applied to multiple correlated quantitative phenotypes for extracting a set of orthogonal phenotypic components. The extracted phenotypic components are then used for pathway association analysis instead of original quantitative phenotypes. Four statistics were proposed for PCA-based MPPAS in this study. Simulations using the real data from the HapMap project were conducted to evaluate the power and type I error rates of PCA-based MPPAS under various scenarios considering sample sizes, additive and interactive genetic effects. A real genome-wide association study data set of bone mineral density (BMD) at hip and spine were also analyzed by PCA-based MPPAS. Simulation studies illustrated the performance of PCA-based MPPAS for identifying the causal pathways underlying complex diseases. Genome-wide MPPAS of BMD detected associations between BMD and KENNY_CTNNB1_TARGETS_UP as well as LONGEVITYPATHWAY pathways in this study. We aim to provide a applicable MPPAS approach, which may help to gain deep understanding the potential biological mechanism of association results for complex diseases. Genome-wide association studies(GWAS) are successful for identifying common genetic variation underlying complex diseases in recent years Motivated by the gene set enrichment analyses of microarray data Current pathway association studies primarily focus on single important phenotype of complex diseases. A potential limitation of single phenotype pathway association studies is that single phenotype is sometimes insufficient to characterize complex diseases due to its complicated clinical manifestations. For example, obesity can be measured by body mass index, fat mass and proportions of fat mass in total body mass in practice. To address this issue, some researchers collected a set of disease-related phenotypes, and conducted pathway association tests of each phenotype ignoring the correlation among multiple disease phenotypes Recently, multivariable analyses approaches were applied to SNP association studies, which could simultaneously detect associations between SNPs and multiple disease phenotypes In this study, we present a flexible MPPAS approach using principle component analyses (PCA). In our approach, PCA is first applied to multiple correlated quantitative phenotypes for exacting a set of orthogonal phenotypic components. The extracted phenotypic components are then included into pathway association analyses instead of original disease phenotypes. Four statistics combining the association evidence of multiple genes within testing pathways, were proposed for assessing the overall association strength of the pathways with target traits. To illustrate the application of our method, extensive simulation studies using the real data from the HapMap project, were conducted to evaluate the power and type I error rates of PCA-based MPPAS under various scenarios, considering sample sizes, additive and interactive genetic effects. PCA-based MPPAS can be applied to GWAS data. A real GWAS data set of osteoporosis was analyzed by PCA-based MPPAS in this study.The power of PCA-based MPPAS using p = 4.62×10−5) and LONGEVITYPATHWAY (p = 3.59×10−5). Detailed description of KENNY_CTNNB1_TARGETS_UP and LONGEVITYPATHWAY pathways can be found at GSEA Molecular Signatures Database (http://www.broadinstitute.org).Pathway association studies are based on the fact that different causal genes of a complex disease are likely to be functionally related, for instance belonging to same biological pathways The PCA-based MPPAS have potentially two advantages over single phenotype pathway association studies. First, single phenotype is sometimes insufficient for characterizing complex diseases. In this situation, one strategy is to collect multiple disease phenotypes, and conduct single phenotype pathway association studies following by picking up the shared pathways with significant association signals among different studies. One issue of this approach is that the association finding of common causal pathways may be difficult to be replicated across various single phenotype pathway association studies, due to the difference of mechanism underlying different disease phenotypes. Second, multiple testing corrections are usually requested by this approach. Because of the stringent significant threshold after multiple testing corrections, the causal pathways with moderate but meaningful associations may be missed by single phenotype association studies. In contrast, MPPAS incorporate the genetic information of multiple correlated disease phenotypes into single test statistic. The causal pathways with moderate association signals in single phenotype pathway association studies, are likely to present strong association signals in MPPAS avoiding multiple testing corrections.PCA-based MPPAS can be applied to GWAS data. A real GWAS data of BMD was used to assess the performance of PCA-based MPPAS in this study. We observed significant associations with BMD for KENNY_CTNNB1_TARGETS_UP and LONGEVITYPATHWAY pathways. Previous studies may provide some hints for understanding the associations detected by this study. For instance, previous studies found that the GHR, GH1, ATK1, IGF1 and IGF1R genes of LONGEVITYPATHWAY (containing 14 genes) contributed to the variation of BMD A potential extension of our approach is that haplotype association studies may also be applied to PCA-based MPPAS instead of SNP association studies used by this study. It is known that haplotype association studies preserving the polymorphism and linkage disequilibrium information of multiple adjacent SNPs, was more powerful for detecting rare genetic variants than SNP association studies in some cases Population stratification is a problem in population–based SNP association studies. SNP association studies conducted in an admixed population with subpopulations having different allele frequency distribution, may result in spurious association results In summary, we present a flexible PCA-based MPPAS approach avoid multiple testing corrections. Simulations and real GWAS data analyses results illustrated the application of PCA-based MPPAS for identifying causal pathways underlying complex diseases. PCA-based MPPAS may help to overcome the limitations of single phenotype pathway association studies, and gain deep understanding the molecular mechanism of association results for complex diseases.All studies were approved by the Institutional Review Boards of Xi'an Jiaotong University. Informed-consent documents were read and signed by all study participants.n unrelated subjects and k quantitative phenotypes, which was determined by a biological pathway with m genotyped SNPs. Let k×1 phenotype vector, and m×1 genotype vector of subject i . In this study, we coded j = 1,…,m) to be 0, 1 or 2, representing the copy number of minor allele of subject i at the jth SNP. l = 1,…,k) can be formulated asth quantitative phenotypes. j for the lth quantitative phenotypes. u and SNP v for the lth quantitative phenotypes. i for the lth quantitative phenotype.Suppose a sample of k standardized quantitative phenotypes for n subjects. The matrix element lth quantitative phenotype, respectively.Because different phenotypes may be measured using different units in practice, we first standardize the original quantitative phenotypes. Let http://www.r-project.org/) is then applied to k extracted phenotypic components for n subjects. The matrix element lth phenotypic components. i.PCA denotes the largest statstic of gene j for the ith phenotypic component. Let ith phenotypic component. Based on the idea that a pathway with more genes associated with target traits, is more likely to be disease-causing pathway, we present four statistics to evaluate the overall association strength of a pathway with target traits. The first one takes a linear combination of statistics of all genes within the pathway, defined byith phenotypic component. The phenotypic information harboring by different components are different, and can be measured by the explained proportions of phenotypic variation in PCA. k quantitative phenotypes.The phenotypic components extracted by PCA are included into pathway association analysis instead of original quantitative phenotypes. Suppose a pathway with Because of combining the association evidence of all genes within the pathway, r and m denotes respectively the numbers of genes and SNPs within the pathway.Recently, SNP raio tests were proposed for pathway association studies For statistical tests, a permutation precedure was implemented to evaluate the significance levels of http://hapmap.ncbi.nlm.nih.gov/downloads/index.html.en). HAPGEN was then used to simulate genome-wide genotype data of Caucasian with default running parameters recommended by HAPGEN developers.HAPGEN program was used here for genotype simulations http://www.biocarta.com), KEGG(http://www.genome.jp/kegg/), Ambion GeneAssist Pathway Atlas(http://www5.appliedbiosystems.com/tools/pathway/), and GSEA Molecular Signatures Database(http://www.broadinstitute.org). The obtained pathway-gene annotation file was used to link pathway and gene information in following pathway simulation studies.333 pathways or gene ontology with sizes ranging from 20 to 40, were collected from four public pathway databases, including BioCarta were then randomly selected from different genes of the causal pathway as the causal loci of Q1. The same precedure was also conducted for Q2 and Q3, respectively. Let jth quantitative phenotype value of subject i, defined byjth quantitative phenotype. u for the jth quantitative phenotype. i at SNP u. u and SNP v for the jth quantitative phenotype. Without loss of generality, we assume that there was an interactive genetic effect between SNP1 and SNP3 for Q1 in this study. i for the jth quantitative phenotype, and follow a zero-mean normal distribution with variance Genetic epistatic model was applied here for quantitative phenotype simulations. Suppose a complex disease underlying by a biological pathway, was mesured by three correlated quantitaitve phenotypes, Qp values≤0.05) obtained from the pathways simulated with and without genetic effects in 1,000 replicates. All our data simulations and analyses were implemented with statistical package R The simulated genotype and phenotype data were simultaneously analyzed by PCA-based MPPAS using p values of p values≤5.19×10−5 after Bonferroni correction(0.05/963).PCA-based MPPAS using


Traditional candidate gene approach has been widely used for the study of complex diseases including obesity. However, this approach is largely limited by its dependence on existing knowledge of presumed biology of the phenotype under investigation. Our combined strategy of comparative genomics and chromosomal heritability estimate analysis of obesity traits, subscapular skinfold thickness and back-fat thickness in Korean cohorts and pig (Sus scrofa), may overcome the limitations of candidate gene analysis and allow us to better understand genetic predisposition to human obesity.FTO, the fat mass and obesity associated gene, identified from significant SNPs by association studies of each trait. These common genes were related to blood pressure and arterial stiffness (P = 1.65E-05) and type 2 diabetes (P = 0.00578). Through the estimation of variance of genetic component (heritability) for each chromosome by SNPs, we observed a significant positive correlation (r = 0.479) between genetic contributions of human and pig to obesity traits. Furthermore, we noted that human chromosome 2 (syntenic to pig chromosomes 3 and 15) was most important in explaining the phenotypic variance for obesity.We found common genes including MRPL33, PARD3B, ERBB4, STK39, and ZNF385B.Obesity genetics still awaits further discovery. Navigating syntenic regions suggests obesity candidate genes on chromosome 2 that are previously known to be associated with obesity-related diseases:  Candidate gene approach has been proven to be an extremely powerful and effective method for studying the genetic architecture of complex traits. This approach is, however, criticized for non-replication of results when followed up in subsequent association studies. Traditional candidate gene approach is also greatly limited by its reliance on the priori knowledge about the physiological, biochemical or functional aspects of possible candidates, and unfortunately, the detailed molecular anatomy of most complex traits still remains veiled. Such limitation results in a fatal information bottleneck, and comparative genomics serves as an extended strategy to solve the problem of information bottleneck. This strategy makes the utility of cross-species approach to characterize the effect of putative candidate genes ,2.FTO with intermuscular fat deposition in Italian Duroc pigs, confirmed in a later study by themselves and by a recent study of Fan et al. [TCF7L2, one of type 2 diabetes genes, and BFT [To date, several comparative analysis studies of human and pig on obesity-related traits have confirmed the human obesity genes affecting fatness traits of pigs . This study allowed us to expand the QTL results observed in pig to human common forms of obesity, but it still is a hypothesis-driven genetic approach as it only considered known QTL region instead of the genome. In order to overcome the lack of thoroughness and inclusiveness that candidate gene approach is criticized for, we conducted the genome-wide comparative studies on common form of obesity traits.Nevertheless, published comparative studies still do not break the barrier of information bottleneck, because it starts with presumed biology of one species and applies it to another species. Thus, we previously conducted local genomic Our study is also an integrated analysis, as it adopts the concept of the population-based heritability estimates which can provide a valuable metric of available genetic risk information . GCTA  site as the source of the H. sapiens genomic sequence (version GRCh37.p5) and Sscrofa10.2 for Pig (Sus scrofa) genome.The pig genome was mapped onto the human genome, using a large-scale alignment tool, LAST . The chr-3), and low genotype call rate (<95%). This quality-control process left 45,013 autosomal SNPs. The SNP probes were mapped on Sus Scrofa genome 10.2 from NCBI FTP using BLAT [The genomic DNAs of pig were genotyped on the Illumina Porcine 60 K SNP Beadchip. We discarded the markers with low MAF (<0.01), significant deviation from Hardy-Weinberg equilibrium  with high missing gene call rate (>5%), low MAF (<0.01) and significant deviation from Hardy-Weinberg equilibrium (P < 10–6) were excluded, leaving a total of 326,262 markers to be examined in 8,842 individuals.0 + b1 × age + e, and then we standardized the residuals to z-scores, in each sex group separately. We used the age data (days) at the time of slaughter. After excluding samples that do not have age information, we examined in 697 samples.We analyzed inbred Berkshire population, and a total of 14 meat quality traits were measured. Traits include back-fat thickness, carcass weight, meat pH, meat color, muscle shear force, drip loss, heat loss, water holding capacity, and intramuscular fat content, etc. The back-fat thickness, which we used for this specific study, was measured between the 10th and 11th rib. The phenotype (back-fat thickness) was adjusted by the age effect using the linear model of y = bThe subscapular skinfold thickness (human) was also adjusted by age and standardized in each gender and area group . Subscapular skinfold thickness is a measurement for upper body fat distribution. It is measured just below the angle of the left scapula with the fold either in a vertical line or slightly inclined . The samWe used the GCTA tool  to calcuLinear regression analysis was performed in an additive model with the data adjusted by sex and age using PLINK-linear option . GWAS haWe mapped the pig genome onto the human genome using the alignment tool (LAST) and found the syntenic region; the pig chromosomes are rearranged in human chromosome scale. The synteny map represents 22 and 18 autosomal chromosomes of human and pig  on human chromosome 16; H3GA0017791 and INRA0021406  for pig on chromosome 6. This gene encodes for 2-oxoglutarate-dependent nucleic acid demethylase of which expression in the brain seems regulated by feeding and fasting, and it is associated with increased lipolytic activity in adipocytes [GNPDA2 was associated with both traits  explained the largest proportion of heritability for common obesity traits. Therefore, we hypothesized that chromosome 2 is crucial for remained complexities of genetic architecture of obesity. Based on this knowledge, we further investigated this chromosome to suggest candidate markers and genes that possibly control obesity.SUB: Subscapular skinfold thickness; BFT: Back-fat thickness.The authors declare that they have no competing interests.JK designed, analysed the data and wrote manuscript. TL performed the analysis. TK and KL collected the samples and genetic data. HK conceived and designed the analysis. All authors read, commented and approved the manuscript.Table S1. Comparative analysis studies of human and pig on obesity-related traits.Click here for fileTable S3. A Synteny table of the pig and human genomes. Table S4. Number of syntenic SNPs of pig and human by each chromosome. Table S5. Number of autosomal pig SNPs mapped onto Sscrofa 10.2 by each chromosome.Click here for fileTable S2. Summary of heritability estimates by each chromosome for SUB and BFT traits.Click here for fileTable S6. Major genes predisposing to common obesity identified from multiple previous works and our study.Click here for fileFigure S1. Graphical summary (Manhattan plot) of genome-wide association results of SUB (above) and BFT. RASAL2, known as obesity gene, was significantly associated in SUB trait of pig.Click here for file


Hyperpigmentation of the visceral peritoneum (HVP) has recently garnered much attention in the poultry industry because of the possible risk to the health of affected animals and the damage it causes to the appearance of commercial chicken carcasses. However, the heritable characters of HVP remain unclear. The objective of this study was to investigate the genetic parameters of HVP by genome-wide association study (GWAS) in chickens.g = 0.34), but had negative genetic correlations with immune traits, such as the antibody response to Newcastle disease virus (rg = −0.42). The GWAS for HVP using 39,833 single nucleotide polymorphisms indicated the genetic factors associated with HVP displayed an additive effect rather than a dominance effect. In addition, we determined that three genomic regions, involving the 50.5–54.0 Mb region of chicken  chromosome 1 (GGA1), the 58.5–60.5 Mb region of GGA1, and the 10.5–12.0 Mb region of GGA20, were strongly associated (P < 6.28 × 10-7) with HVP in chickens. Variants in these regions explained >50% of additive genetic variance for HVP. This study also confirmed that expression of BMP7, which codes for a bone morphogenetic protein and is located in one of the candidate regions, was significantly higher in the visceral peritoneum of Huiyang Beard chickens with HVP than in that of chickens without pigmentation (P < 0.05).HVP was found to be influenced by genetic factors, with a heritability score of 0.33. HVP had positive genetic correlations with growth and carcass traits, such as leg muscle weight (rBMP7 gene appears to be upregulated in HVP-affected chickens. Findings from this study should be used as a basis for further functional validation of candidate genes involved in HVP.HVP is a quantitative trait with moderate heritability. Genomic variants resulting in HVP were identified on GGA1 and GGA20, and expression of the  MC1R) gene causes extended dark feathers[Gallus gallus) chromosome 20 (GGA20) determines dermal hyperpigmentation[EDN3) locus[Pigmentation is widespread amongst both plants and animals, and plays important roles in photosynthesis (in plants), camouflage, sex selection, and protection from sunburn. However, abnormal pigmentation in humans and other animals, including hyperpigmentation  locus. In facthttp://www.genome.gov/GWAStudies). Livestock breeders have begun to implement GWAS to map economically important quantitative trait loci (QTLs)[The development of molecular tools and strategies has allowed the investigation of the genetic basis of HVP. Genome-wide association studies (GWAS) have become an important strategy for investigating the genetic basis of many human diseases, including diabetes, breast cancer, pancreatic cancer, and hypertension, amongst others (i (QTLs)-22. Signi (QTLs),24. TherIn this study, we estimated the genetic parameters of HVP to illustrate the inheritance of HVP, and carried out a GWAS analysis of HVP using the chicken 60K single nucleotide polymorphism (SNP) panel in a commercial chicken population with a rich diversity of HVP.2 = 0.33) through estimating genetic parameters, suggesting that HVP was significantly affected by genetic factors and was not a simple Mendelian trait. As shown in Table P < 0.05), such as body weight at day 91 (rg = 0.27), carcass weight (rg = 0.24), net weight (rg = 0.27), breast muscle weight (rg = 0.17), and leg muscle weight (rg = 0.34). Moderately negative genetic correlations were identified between HVP and immune traits, especially the antibody response to Newcastle disease virus (rg = −0.42). These results indicated that the immune capacity of chickens with HVP could be inferior to that of normal non-pigmented chickens, but the growth capacity of chickens with HVP might be greater.HVP was found to have a moderate heritability (hP < 6.28 × 10-7) associated with HVP on both GGA1 and GGA20 . Thirteen SNPs with additive effects were located in the 50.5–54.0 Mb region of GGA1. In addition to this GGA1 region, seven SNPs with functional effects reached genome-wide significance, including two SNPs in the 58.5–60.5 Mb region of GGA1, and five SNPs in the 10.5–12.0 Mb region of GGA20. The extent of linkage disequilibrium (LD) in both GGA1 and GGA20 was about 2 Mb  for HVP , located in the 50.5–54.0 Mb region of GGA1. Another SNP, located 13.3 Kb downstream of MAP3K7IP1, also had a genome-wide significant additive effect for HVP. Because HVP was associated with immune traits  locus. HIPK2 participates in cell development, growth, and apoptosis, such as in the Wnt pathway, and was associated with HVP and chicken growth (Table BMP7), which can effect melanocyte growth and melanoma cell metastasis, and therefore BMP7 was also chosen as one of the most important positional candidate genes for HVP. In addition, according to information from the Kyoto Encyclopedia of Genes and Genomes (KEGG), Gene Map Annotator and Pathway Profiler (GenMAPP), and Biocarta databases, MAP3K7IP1, HIPK2, and BMP7 can all regulate mitogen-activated protein kinase kinase kinase 7 (MAP3K7) expression . However, the mRNA expression of MAP3K7IP1 and HIPK2 was not significantly different between the visceral peritoneum tissue of normal Huiyang Beard chickens and those with HVP (P > 0.05).As shown in Figure Interestingly, chickens with HVP showed no reduction in body weight, and were actually associated with improved production efficiency. This finding deviated from our hypothesis that HVP was likely associated with disease phenotypes, which could decrease chicken growth. However, HVP-affected birds still had greater health risks because of the observed negative genetic correlations with immune traits Table . The birTYR) gene changes the expression of TYR to interrupt melanin biosynthesis[During our investigation of HVP in chickens, we did not observe this HVP phenomenon in fast-growing birds with white feathers, such as Ross 308 broilers; HVP appeared to be limited to colored chicken breeds, such as Huiyang Beard chickens (unpublished data). The lack of the HVP phenotype in Ross 308 broilers may result from interference of the white dominance or recessive locus with the pigmentation in the abdominal septa of areolar connective tissues. A white recessive locus with a retroviral insertion in the tyrosinase  associated with HVP , agouti signaling protein, SRY (sex determining region Y)-box 10 (SOX10), myosin VA , solute carrier family 45, and member 2[MAP3K7IP1, HIPK2, and BMP7 could influence some pigmentation pathways. For example, Liang et al. found that down-regulation of HIPK2 expression suppressed the expression of MITF, resulting in melanocyte differentiation suppression by increasing C-terminal binding protein 2 levels[BMP7 is upregulated in the development of melanoma[BMP7 was associated with HVP in Huiyang Beard chickens . These findings indicate that MAP3K7IP1, HIPK2, and BMP7 could be candidate genes for HVP, and might affect the development of HVP by regulating the expression of the MAP3K7 gene. Further studies are needed to validate this hypothesis.More interestingly, the BMP7 gene was identified as a likely candidate gene for HVP.HVP was found to be a quantitative trait with moderate heritability. Three independent QTLs for HVP were detected by GWAS on GGA1 and GGA20, and the This study was approved by the Animal Care Committee of the Institute of Animal Science, Guangdong Academy of Agricultural Sciences , with approval number GAAS-IAS-2009-73. Animals involved in this study were humanely sacrificed as necessary to ameliorate their suffering.1, and 511 F2 individuals) with an accurate pedigree. All birds were immunized with a commercial avian influenza-inactivated H9 strain vaccine at day 40, and a commercial Newcastle disease virus live LaSota strain vaccine at day 50. At day 91, 511 F2 individuals from six hatches were slaughtered. At this time point, vein blood was collected and a portion transferred into centrifuge tubes containing ethylenediaminetetraacetic acid disodium salt solution, and then stored at −80°C. The remainder was used to prepare serum for measuring antibody responses  to Newcastle disease virus and avian influenza virus by enzyme linked immunosorbent assay. At day 91, body weight, carcass weight, net weight, dress weight, breast muscle weight, leg muscle weight, and abdomen fat weight were measured, as was small intestine length. Heterophil count, representing H/L, was measured following the method of Vleck et al.[A total of 585 commercial chickens were used in this study, consisting of three generations  and stored at −80°C. Total RNA was isolated by grinding the tissues to powder under liquid nitrogen and extracting with RNA TRIzol reagent . The RNA was reverse transcribed into cDNA with an M-MLV RTase cDNA Synthesis Kit . Quantitative real-time polymerase chain reaction (qRT–PCR) analysis was performed to test the expression of MAP3K7IP1, HIPK2, BMP7, and MAP3K7 in the visceral peritoneum tissue of the birds. The primers used for qRT-PCR were designed using Primer Express 2.0 software  and their sequences are shown in Table β-actin, according to the quantitation procedures recommended by Roche Applied Science.The visceral peritoneum tissue from eight normal and eight HVP-positive, 21-day-old Huiyang Beard chickens (a Chinese native chicken breed from Guangdong province) was collected and transferred into RNAVariance and covariance components were estimated using the average information restricted maximum likelihood algorithm implemeny was the vector of observations of HVP, e.g. body weight at day 91 and hatch (six levels); a was the vector of animal additive genetic effects; e was the vector of random residuals; and X and Z were corresponding incidence matrices.where Statistical tests of SNP-phenotype association were implemented using the generalized least square version of the epiSNP computer package, which considered sib correlation within each family,62. The Y was the phenotypic value of HVP, μ was the common mean of HVP, S was the fixed gender effect, H was the fixed hatch effect, f was the random family effect, SNP was the single-locus SNP genotypic effect, and e was the random residual. Additive and dominance effects were tested using linear contrasts of the single-locus SNP genotypic effect[P value of the 5% Bonferroni genome-wide significance was 6.28 × 10-7 (0.05/39833/2), based on the total number of SNP markers and two SNP genotypic effects (additive and dominance effects) in GWAS. Manhattan plots were produced using SNPEVG version 2.1[where c effect. The thrsion 2.1 to demon2 values for the F2 population, was calculated for GGA1 and GGA20 using Haploview[http://www.genome.jp/kegg/), GenMAPP (http://genmapp.org/), and BioCarta (http://genmapp.org/) databases.To evaluate the extent of LD and identify potential regions of causal mutation for HVP, pairwise LD, measured by raploview. PathwayMAP3K7IP1, HIPK2, BMP7, and MAP3K7 in the visceral peritoneum tissue, between the normal birds and the birds with HVP, was determined using a t-test with SAS 8.0 software .Differential expression of The authors have no competing interests to declare.CL, HQ, XH, NL, and DS conceived and designed the experiments. CL, HQ, JW, YW, JM, CYL, and DS performed the experiments. CL and HQ analyzed the data. CL, JM, CY, and DS contributed the materials. CL, HQ, and DS wrote the paper. All authors read and approved the final manuscript.Gallus gallus) chromosomes. A. LD on Chromosome 1. B. LD on Chromosome 20.Pattern of linkage disequilibrium (LD) on chicken (Click here for fileInteraction of genes. Blue, green, and red figures indicate the number of pathways that the genes are involved in, based on KEGG, GenMAPP, and BioCarta, respectively. BMP7 interacts with MAP3K7 via the ALK pathway in cardiac myocytes according to the BioCarta database. HIPK2 interacts with MAP3K7 via an enzyme linked receptor protein signaling pathway and Wnt netPath 8 according to the GenMAPP database. MAP3K7IP1 interacts with MAP3K7 via the MAPK and Toll-like receptor signaling pathways according to the KEGG database, by the NF-κB signaling pathway, signal transduction through IL1R, the TGF-β signaling pathway, and the WNT signaling pathway according to the Biocarta database, and by receptor signaling protein activity, the MAPK signaling pathway, and TGF-β-receptor netPath 7 according to the GenMAPP database.Click here for fileBasic information on the 39,833 SNP markers on the chicken physical map.Click here for file


When testing association between rare variants and diseases, an efficient analytical approach involves considering a set of variants in a genomic region as the unit of analysis. One factor complicating this approach is that the vast majority of rare variants in practical applications are believed to represent background neutral variation. As a result, analyzing a single set with all variants may not represent a powerful approach. Here, we propose two alternative strategies. In the first, we analyze the subsets of rare variants exhaustively. In the second, we categorize variants selectively into two subsets: one in which variants are overrepresented in cases, and the other in which variants are overrepresented in controls. When the proportion of neutral variants is moderate to large we show, by simulations, that the both proposed strategies improve the statistical power over methods analyzing a single set with total variants. When applied to a real sequencing association study, the proposed methods consistently produce smaller p-values than their competitors. When applied to another real sequencing dataset to study the difference of rare allele distributions between ethnic populations, the proposed methods detect the overrepresentation of variants between the CHB (Chinese Han in Beijing) and YRI (Yoruba people of Ibadan) populations with small p-values. Additional analyses suggest that there is no difference between the CHB and CHD (Chinese Han in Denver) datasets, as expected. Finally, when applied to the CHB and JPT (Japanese people in Tokyo) populations, existing methods fail to detect any difference, while it is detected by the proposed methods in several regions. Genome-wide association studies (GWAS) have become popular tools for identifying genetic susceptibility variants for complex diseases. The success of this approach relies on the common disease-common variant (CDCV) hypothesis, which presumes that phenotypic variation of common diseases is explained by several common variants, each with a relatively small effect Despite the fruitful findings of recent GWAS When analyzing rare variants for association with phenotypes, ordinary variant by variant methods have insufficient statistical power due to allelic heterogeneity as well as the extreme rarity of individual variants In this study, aiming to improve statistical power of association tests in the presence of neutral rare variants, we propose two alternative strategies. We utilize simulations to investigate and compare the performance of tests with different strategies under a variety of conditions. Finally, we apply the proposed methods to two real sequencing datasets to demonstrate their utilities.cn affected individuals and un normal individuals, so that the total number of individuals is n = cn+un. Assume that a genomic region containing L rare variants (MAF<0.01) is to be examined for association with the disease, and genotype data ilg  are available at all variants for each individual. Here, the unit of analysis is the set of variants rather than individual variants. Given the set of L variants, a variety of grouping strategies exist. In the simplest way, a single set, termed TG, is formed by including all variants. This grouping strategy, referred to as total grouping, is widely adopted by existing methods. We here describe two alternative grouping strategies. In the first one (selective grouping), two sets are selectively formed: one in which each variant has a greater frequency in cases than in controls, and the other in which each variant has a greater frequency in controls. We term the two formed sets as CG and UG. In the second one (exhaustive grouping), a total number of R = 2L-1 subsets  are formed exhaustively. Below we outline two popular association tests and their implementations with various grouping strategies.Assume that there are i:Given a set of variants, the collapsing method Association is then examined on X is defined on the set TG. The Fisher exact test (FET) is used to test the association and a two-sided p-value is reported.In the total grouping strategy, X is defined and examined on the two sets CG and UG separately. To compare with the total grouping method fairly, we perform a two-sided test by examining whether rare variants distribute differently between cases and controls. In order to implement this test, the FET is applied to CG and UG separately, and two one-sided p-values, termed cp and up, are obtained. Note that the FET here is merely a device measuring the strength of evidence against the null hypothesis. A provisional index of significance, q, is calculated as the minimum of the two nominal p-values obtainedIn the selective grouping strategy, q is determined by Monte Carlo permutation testing k replicates. In each replicate, we permute the case/control status and perform the FET on the permuted sample, from which the provisional index for the replicate is obtained. A permutation p-value will be reported, which is defined as k0/k, where k0 is the number of replicates that have the indexes equal to or smaller than q.The significance of X is defined on each of the R formed subsets. The FET is applied to each subset separately, and the smallest two-sided p-value over the R tests is taken as the statistic.In the exhaustive grouping strategy, G as an example, if one of its subsets Gr-, formed by removing a variant r from G, renders a smaller p-value than that attained with G, then none of subsets of G containing the variant r are likely to yield a smaller p-value than attained with Gr-, and consequently do not need to test. This observation is driven by the fact that all variants in a set act additively. We thus propose a simple and efficient algorithm to reduce the number of tests. The algorithm is outlined below:Identifying the subset of variants that renders the smallest p-value by testing subsets exhaustively, however, is computationally demanding. When the number of variants involved is large, e.g., several dozens to hundreds, the exhaustive grouping strategy may become computationally prohibitive. We note that some subsets do not need to test. Taking a particular set G, which is specified by the rare variants it contains, and is initialized to include all variants. Set a global variable P for the minimal p-value, which is initialized to be equal to the p-value rendered by the initialized set G.Set a candidate global set of variants G, remove it from G to form a subset G−1. Collapsing test is then examined on G−1 and a two-sided p-value is obtained. For m rare variants in G, there will be m subsets each consisting of m-1 rare variants. Of the m calculated p-values, the minimal one and the corresponding subset are denoted as P' and minG, respectively.For each variant in G = minG, and set P =  P' if P'<P.Set G contains no variant.Repeat steps 2) and 3) until the set P will be the p-value sought. Here, we adopt a step-wise approach and exclude one variant in each repetition. In this way, the number of subsets that need to be tested is reduced from 2L-1 to L(L+1)/2 and the computation cost is reduced accordingly. By running 100 simulated datasets each with 10 or 20 variants, we observed that the algorithm found the correct minimal p-values in all cases. Nonetheless, there is no guarantee for the accuracy, so we will call this test the approximately optimal collapsing (AOC).The value k times, and for each replicate the approximately smallest p-value is calculated by the algorithm. A permutation p-value is estimated and reported.The significance of the test is again evaluated by Monte Carlo permutation testing. Specifically, the case/control status is permuted GWWS performs a one-sided test of whether there is an excess of rare variants in a particular population, i.e., cases. In the total grouping strategy, the GWWS method l, calculate a weight For each variant i, calculate a genetic score ilI is the number of mutant allele at the lth variant.For each individual All individuals are ranked according to genetic scores calculated in 2).S, is taken as the statistic.The sum of rank of case individuals, termed k replicates, case/control status is permuted and the statistic is calculated. A normality approximation is used to estimate p-value. Denote the mean and standard deviation of S over the k replicates as The significance of the test is again evaluated by permutation testing. Specifically, in each of sz approximately follows a standard normal distribution under the null hypothesis of no association, from which a two-sided p-value will be evaluated and reported.The statistic CG and UG separately, and two normality approximated p-values, p1 and p2, are obtained. The final p-value sp is taken as the minimal of the two p-values adjusted by the Bonferroni correctionIn the selective grouping strategy, GWWS is applied to R subsets, a series of permutations are required to evaluate the significance. We thus do not implement the exhaustive grouping strategy for GWWS.The exhaustive grouping strategy is applied to GWWS as well in principle. However, the computation will be expensive since for each of the There also exist several extensive methods that test association between rare variants and diseases N1, the bottleneck population size bN, the duration of time T after the bottleneck (measured by generation), and the population growth rate In order to investigate and compare the performance of various methods, we conducted a series of simulation studies. We focused on the European population and simulated sequence data by the use of a four-parameter demographic model Using the inferred demographic model, we simulated full range frequencies of sequence data to mimic a sequencing association study. Specifically, we simulated sequence data for a gene with 1,000 nucleotides. The number of generated variants may vary, but is approximately proportional to gene length.Both common and rare variants may contribute to complex diseases. However, the usual way for an association study is to analyze these two kinds of variants separately. As the intention of this study is to analyze rare variants, we thus use rare variants (MAF<1%) only to generate phenotype and to test association. Though we focused on a case/control study design, we simulated a pool of quantitatively phenotyped individuals, from which we selected individuals with extreme phenotypes as case/control subjects. This extreme sampling study design is widely adopted in practical applications On simulating phenotype, a specified proportion of variants were randomly selected as causative, while the remainder were assumed to be neutral. Unless otherwise specified, we set the proportion to be equal to 30%. To take into account the uncertainty of phenotypic model under which multiple rare variants jointly influence phenotype, we simulated the phenotype under three phenotypic models.iModel 1: Causative alleles affected the phenotype equally and in a cumulative way. Specifically, we defined a genetic score for each individual cL was the number of causative variants. Since homozygous mutant genotypes are much rarer for rare variants, we assumed an additive mode of inheritance and encoded where Model 2: The presence of one or more causative variants caused the same shift of phenotypic mean. Specifically, the genetic score was defined as an indicatorThis model corresponds to the assumption adopted by the collapsing method Model 3: Rarer variants were assumed to render larger per-allele effects. Correspondingly, the genetic score was defined as a weighted sumlp was the allele frequency in the population. This model corresponded to the assumption adopted by GWWS where In Under each model, the phenotype was generated by the ordinary regression equationμ was the grand mean; ie was assumed to follow a normal distribution with mean zero. The coefficient β was determined by the locus heritability h2, which was defined as the proportion of phenotypic variation explained by x,where h2 to zero, whereas power was evaluated by setting it to a specific value. Unless otherwise specified, the value of h2 was set to 0.5% to simulate a modest genetic effect. Both type I error rate and power were estimated on 1,000 replicates, at the significance levels of 0.05 and 1.0E-3, respectively. For each replicate, 10,000 permutations will be performed when needed. Both type I error rate and power were defined as the proportion of replicates in which the p-value was equal to or smaller than the significance threshold.We evaluated the performance of various tests described in this manuscript: collapsing, GWWS, approximately optimal collapsing (AOC), selective collapsing (SCollapsing), and selective GWWS (SGWWS). Statistical properties, including type I error rate and power, of these tests were investigated by simulation studies. Type I error rate was evaluated by setting the locus heritability While all other tests have correct type I error rates that are close to the target level, SGWWS has a type I error rate lower than the target level . This coIn We then evaluated the power of various tests under different gene heritabilities. All tests have improved power with increasing heritability . Among tFixing the proportion of causative variants and gene heritability, we then estimated the effect of gene length on power estimate. As shown in The computation time was determined by running a dataset containing 500/500 individuals and a gene with 1,000 nucleotides on a desktop computer with an Intel 2.40 GHz Core 2 Duo CPU E4600. All tests but AOC complete the computation within seconds for 10,000 permutations; AOC takes approximately one hour with 1,000 permutations. This is because the time complexity for AOC is quadratic to the number of variants while it is linear for other tests.NPC1L1 with low density lipoprotein cholesterol (LDL-C) level, the authors sequenced the gene in an initial sample with two groups each comprising 128 individuals with lowest and highest ratios of campesterol to lathosterol (Ca∶L ratio) from the Dallas Heart Study . A total number of 16 rare non-synonymous variants were discovered, 13 of which are exclusive in cases and 3 exclusive in controls.As a first application, we re-analyzed the sequence data produced by Cohen et al. To validate their findings, the authors sequenced the same gene in a second sample comprising the same numbers of individuals again from the DHS with the next lowest and highest Ca∶L ratios (Sample 2). A total number of 12 rare non-synonymous variants were discovered, 10 of which are exclusive in cases and 2 exclusive in controls.In addition to analyzing the two samples separately, we combined them and analyzed the total rare variants together (Combined).As shown in th 2008) were downloaded from the project ftp site (ftp://ftp.hgsc.bcm.tmc.edu/pub/data/HapMap3-ENCODE/ENCODE3//ENCODE3v1/). Variants that failed to be called in all individuals were excluded. Within each region, we examined the difference of rare allelic distributions between CHB and each of the other three populations. This is equivalent to an association study by labeling individuals from one population as cases and that from the other population as controls As a second application, we analyzed the sequence datasets produced by the ENCODE3 project We first tested the overrepresentation of rare variants between the CHB and YRI populations. The results from the proposed tests clearly show that rare allelic distribution between the two populations is significantly different . Among tWe then analyzed the CHB and JPT populations, as listed in Finally, we analyzed the CHB and CHD datasets. As individuals in these two datasets are from the same population, it is expected that no difference exists between these two datasets. As expected, none region except ENr213 shows any significant difference by any test . SCollapIn this study, in order to improve statistical power of testing disease-associated rare variants, we proposed two alternative grouping strategies to the strategy of grouping total variants. When the proportion of neutral variants is moderate to large we show, by simulations, that both the proposed grouping strategies improve power. The applications to two real sequencing studies demonstrate the utilities of the proposed methods.Currently, GWAS is the most widely used approach for identifying genes that are associated with complex diseases. In a typical GWAS, causative variants are usually not observable; instead, their effects are detected through nearby SNP markers, with the power depending on the strength of linkage disequilibrium (LD) between them. Thus, the pattern of LD underpins the validity and success of this indirect association approach. In sequencing studies, on the other hand, the observed genetic variants are usually hypothesized to be directly functional and are of primary interest. Furthermore, the level of LD between rare and nearby variants is usually extremely low The strategy of grouping rare variants has proven to be a powerful approach for analyzing rare variants. If potential causative variants account for the vast majority of variants, the utility of grouping total variants should be adequate, but this is unlikely to be the majority of cases in practical applications. A recent large-scale X chromosome sequencing study suggests that a large quantity of mis-sense substitutions in candidate genes exist indistinguishably in both of the case and control populations Both of our proposed grouping methods are intuitively straightforward. In the first strategy of exhaustive grouping, by testing all subsets, we aim to identify the subset with the clearest signal. This strategy has been previously adopted in the literature of haplotype based association cG and uG are formed. While the cG part may represent potentially causative variants, uG part is believed to represent background variation. However, including uG part into analysis could provide a two-sided test of whether variants are associated with the phenotype rather than a one-sided test of whether variants enrich in a particular population, i.e., cases. This broader hypothesis makes it comparable to compare between tests with various grouping strategies. The uG part could also be informative in the presence of beneficial mutations, i.e., those mutations which reduce the risk to the disease.In the selective grouping, two sets L rare variants, the time complexity for methods with exhaustive grouping is O(2L), while that for methods without exhaustive groupings is only O(1). The computation time for exhaustive grouping increases exponentially with the number of variants, and is prohibitive for analyzing several dozens to hundreds of variants. To circumvent this computation issue, we have developed a step-wise algorithm to search for the minimal p-value over the set, the time complexity of which is O(2L). Alternatively, the proposed selective grouping method is computationally effective, without additional increase in time complexity compared to total grouping. In practical applications where huge numbers of rare variants may be involved, e.g., exome studies, the selective grouping method is thus recommended, and exhaustive grouping should be regarded as a tool to verify significant results.For a set of Our simulations show that statistical power of testing association decreases as gene elongates, though the proportion of causative variants is fixed. To understand this phenomenon, gene heritability must be taken into consideration, which was always fixed at 0.5% as gene length varied in our simulations. Longer gene introduces more noise, which tends to reduce power. Though meanwhile it introduces a greater number of causative variants as well, the phenotypic effect of these causative variants, that is, gene heritability, remains unchanged. In other words, the per-variant effect gets smaller with longer gene. Consequently, though signal-to-noise ratio is fixed, the power would still tend to decrease as gene elongates. This trend of power with gene length (or number of variants) was also observed in previous studies The problem of population stratification by admixture of different ethnic populations is a serious concern for association studies In this study, we used a MAF cutoff 0.01 for a rare variant, but other cutoffs could be used as well. In our simulation studies we show that our proposed strategies could improve power when the proportion of causative variants is low to modest, while the power improvement is little or even negative when the proportion is large. Thus, the proper test for a particular study should be chosen according to the knowledge on the distribution of potential causative variants. In most practical applications where there is no knowledge on the potential causative variants, cross-validation of the results from various tests is warranted.Statistical methods derived not from classical statistical theories, like the ones proposed in this manuscript, may be biased. The biasness could be evaluated by simulation studies, which showed that on one hand, the power rate of the proposed tests was equal to the significance level under the null hypothesis. On the other hand, the power rate was an increasing function of locus effect and/or proportion of causative variants so that it would excess the significance level under the alternative hypothesis. These two aspects of power function under the null and alternative hypothesis together indicated that the proposed tests were unbiased.Despite the methods proposed in this manuscript, analyzing associations between rare variants and complex diseases remains quite challenging. When neutral variants comprise a large proportion of the total variants, the selective grouping is still low-powered, and more specialized approaches are expected to emerge. In the study of Tarpey et al. Appendix S1The appendix that describes the process of demographic model.(0.09 MB DOC)Click here for additional data file.Figure S1Fitness of simulated variants to experimental variants. Legend: Sequence data of European population from the ENCODE3 project were used to estimate demographic model. Data of 119 individuals (238 haplotypes) on 7 genomic regions were available. After filtering out variants with missing genotypes, a total of 83 gene-coding variants and 953 non-coding  variants were used for analysis, corresponding to 5.3 kb and 66.7 kb sequence sites respectively. A: the fitness of simulated allele frequencies to experimental data on neutral variants; B: the fitness of simulated allele frequencies to experimental data on gene-coding variants.(0.27 MB TIF)Click here for additional data file.Table S1Phenotypic models versus encoding schemes(0.07 MB DOC)Click here for additional data file.


Among many approaches, BLUP methods and Bayesian methods are most commonly used for estimating genomic breeding values. Here, we applied two BLUP methods, TABLUP and GBLUP, and three Bayesian methods, BayesA, BayesB and BayesCπ, to the common dataset provided by the 15For the 1000 progenies without phenotypic values, the correlations between GEBVs by different methods ranged from 0.812 (GBLUP and BayesCπ) to 0.997 (TABLUP and BayesB). The accuracies of GEBVs  and GEBVs) were from 0.774 (GBLUP) to 0.938 (BayesCπ) and the biases of GEBVs (measure as regressions of TBVs on GEBVs) were from 1.033 (TABLUP) to 1.648 (GBLUP). The three Bayesian methods and TABLUP had similar accuracy and bias.BayesA, BayesB, BayesCπ and TABLUP performed similarly and satisfactorily and remarkably outperformed GBLUP for genomic breeding value estimation in this dataset. TABLUP is a promising method for genomic breeding value estimation because of its easy computation of reliabilities of GEBVs and its easy extension to real life conditions such as multiple traits and consideration of individuals without genotypes. All individuals were genotyped for the 9990 SNPs without missing or genotyping error. Of the 15 progenies of each dam, 10 were phenotyped for a continuous trait. The 2000 progenies with phenotypic records and the other 1000 individuals  without phenotypic records were treated as reference and validation population, respectively.The variance components and the traditional BLUP EBVs were estimated using phenotypes and pedigree and the software DMUv6  based ony is the vector of phenotypes of individuals in the reference population, μ is the overall mean, a is the vector of additive genetic effects of the phenotyped individuals and their parents, Z is the incidence matrix of a, and e is the vector of residual errors. The variance-covariance matrices of a and e are where The reliabilities of the traditional EBVs were obtained from DMU directly and calculated as the square of the correlation between EBVs and the true unknown breeding values.BayesA, BayesB and BayesCπ were used to estimate SNP effects in the reference population based on the following model:g is the vector of random SNP effects, X is the matrix of genotype indicators .where g and e for the three Bayesian methods as those in [The differences between the three Bayesian methods lay in the assumptions for the prior distribution of SNP effects. BayesA assumes that all SNPs have an effect, but each has a different variance. BayesB and BayesCπ assume that each SNP has either an effect of zero or non-zero with probabilities π and 1-π, respectively, and for those having non-zero effects it is assumed that each SNP has a different variance in BayesB and a common variance in BayesCπ. In addition, in BayesB π is treated as a known parameter, while in BayesCπ it is treated as an unknown parameter with a uniform  prior distribution. In this study, we set π = 0.99 for BayesB, and adopted the same prior distributions of those in .The Markov chain was run for 50,000 cycles of Gibbs sampling , and the first 5000 cycles were discarded as burn-in. All the samples of SNP effects after burn-in were averaged to obtain the SNP effect estimate.The genomic estimated breeding values (GEBVs) of all genotyped individuals were obtained using five methods: BayesA, BayesB, BayesCπ, GBLUP and TABLUP.For BayesA, BayesB and BayesCπ, the GEBV of a genotyped individual was calculated as the sum of all marker effects according to its marker genotypes .For GBLUP and TABLUP, the GEBVs were estimated based on the following model:u is the vector of genomic breeding values of all genotyped individuals with the variance-covariance matrix equal to where G matrix  was constructed by using genotypes of all markers [TA matrix (trait-specific marker-derived relationship matrix), was constructed by using genotypes of all markers with each marker being weighted with its estimated effect obtained from BayesB following the rules proposed by Zhang et al. [The  markers . The TA g et al. .The accuracies of GEBVs were calculated as the correlation between GEBVs and the simulated true breeding values.The estimated additive genetic variance and residual variance were 24.82 and 58.65, respectively. Therefore, the estimated heritability was 0.30. These estimates were used for the subsequent estimation of SNP effects and GEBVs.Figure For the 20 sires, the reliability of traditional EBVs was 0.95. Table Table The availability of true breeding values (TBVs) of the 1000 progenies without phenotypic values allowed a more efficient assessment for methods. Table G matrix is replaced with TA matrix. In construction of the TA matrix, not only the marker genotypes, but also the marker effects are taken into account. The advantage of the TA matrix over the G matrix is that it not only accounts for the Mendelian sampling term, but also puts greater weight on loci explaining more of genetic variance for the trait of interest. This makes TABLUP more accurate than GBLUP. On the other hand, although TABLUP and the Bayesian methods gave similar accuracies, TABLUP has two important features that Bayesian methods lack. The first is that the reliability of an individual's GEBV can be calculated by TABLUP through the method outlined for GBLUP by VanRaden [TABLUP is an improvement of GBLUP in the way that the VanRaden  and StraVanRaden . The secVanRaden .BayesA, BayesB, BayesCπ and TABLUP performed similarly and satisfactorily and remarkably outperformed GBLUP for genomic breeding value estimation in this dataset. TABLUP is a promising method for genomic breeding value estimation because of its easy computation of reliabilities of GEBVs and its easy extension to real life conditions such as multiple traits and consideration of individuals without genotypes.QTL: quantitative trait locus; MAS: marker assisted selection; GS: genomic selection; BLUP: best linear unbiased prediction; GBLUP: BLUP with a realized relationship matrix; TABLUP: BLUP with a trait specific relationship matrix; EBV(s): estimated breeding value(s); GEBV(s): genomic estimated breeding value(s); TBV(s): true breeding value(s); SNP: single nucleotide polymorphism.The authors declare that they have no competing interests.CLW, PPM and ZZ contributed the data analyses and the manuscript. XDD and JFL contributed the modification of manuscript. WXF and ZQW carried out the data analyses. QZ coordinated the analyses and revised the manuscript. All authors have read and contributed to the final text of the manuscript.


Using a multi-breed reference population might be a way of increasing the accuracy of genomic breeding values in small breeds. Models involving mixed-breed data do not take into account the fact that marker effects may differ among breeds. This study was aimed at investigating the impact on accuracy of increasing the number of genotyped candidates in the training set by using a multi-breed reference population, in contrast to single-breed genomic evaluations.g): uncorrelated (1), rg = 0; estimated rg (2); high, rg = 0.95 (3). Accuracy and bias of predictions obtained in the validation population with the multi-breed training set were assessed by the coefficient of determination (R2) and by the regression coefficient of daughter yield deviations of validation bulls on their predicted genomic breeding values, respectively.Three traits  were analyzed by genomic mixed linear models and Bayesian methodology. Three breeds of French dairy cattle were used: Holstein, Montbéliarde and Normande with 2976, 950 and 970 bulls in the training population, respectively and 964, 222 and 248 bulls in the validation population, respectively. All animals were genotyped with the Illumina Bovine SNP50 array. Accuracy of genomic breeding values was evaluated under three scenarios for the correlation of genomic breeding values between breeds (rg ranged from −0.01 for fertility between Montbéliarde and Normande to 0.79 for milk yield between Montbéliarde and Holstein. Differences in R2 between the three scenarios were notable only for fat content in the Montbéliarde breed: from 0.27 in scenario (1) to 0.33 in scenarios (2) and (3). Accuracies for fertility were lower than for other traits.The genetic variation captured by the markers for each trait was similar to that estimated for routine pedigree-based genetic evaluation. Posterior means for rUsing a multi-breed reference population resulted in small or no increases in accuracy. Only the breed with a small data set and large genetic correlation with the breed with a large data set showed increased accuracy for the traits with moderate (milk) to high (fat content) heritability. No benefit was observed for fertility, a lowly heritable trait. Increasing the accuracy of the prediction of breeding values has become a major objective in genomic selection (GS). The success of GS depends on many factors ,2, some It has been observed that accuracy increases with increasing size of the training data ,4. For tThree traits , which have different genetic backgrounds were analyzed in three major French dairy cattle breeds: Montbéliarde (M), Normande (N) and Holstein (H).u) as a sum of marker effects (g) so that u=Zg and ordered by breed (breeds 1 and 2 for illustration):Varona et al.  suggesteMarker effects were assumed to have a multivariate distribution: I is an identity matrix of order equal to the number of SNP markers and B is a 2 x 2 breed covariance matrix for SNP effects.Where GBLUP) that use a “genomic” relationship matrix, usually termed G, rather than a pedigree-based relationship matrix. Matrix G is an estimator of the “true” proportions of genes that are identical by descent between individuals . . ubreediTable -6) and Mendelian inconsistencies (the genotype of the father was deleted if more than 20% of his progeny showed contradiction). Editing was within-breed. Genotypes of the three breeds were merged, including only SNP which segregated  in each breed. In the final data set, only those loci fulfilling all requirements in all breeds were considered. Finally, 43 852 SNP were used. Pseudo-phenotypes for each bull were daughter yield deviations (DYD), as in VanRaden and Wiggans [All bulls were genotyped with the 50k SNP using the Illumina Bovine array. The SNP were filtered by extreme Hardy-Weinberg disequilibrium  was considered a different trait for each breed. To avoid confusion, these will be referred to as traits  and as scales .In the first analysis, we estimated genetic variances and correlations between breeds and the heritability of each trait and each breed using a combined data set including the three breeds. For computational reasons (see later), instead of the multiple-trait model (MTM), an almost equivalent Random Regression Model (RRM) was used, similar to that used by . The geny is a vector of 2*DYD; X is a matrix that allocates each DYD to a breed and b a vector of average breed effects; Wi are design matrices allocating DYD to GBV  for the M, N and H scales consecutively. For example, the equation corresponding to bull t of breed H, will have a value of 1 in the  position of WH and 0 in WM and WN, since no bull has daughters in several breeds. Vector ε is a vector of uncorrelated random normal pseudo-errors . Homogeneous pseudo-error variances were assumed across breeds. The co(variance) structure for GBV, ui,i=M,N,H, for one trait was:Where, G0 is the matrix of (co) variances of GBV in each of the three scales, M,N,H, for a given trait, named as genetic (co)variances henceforth; G is the genomic relationship matrix relating animals of the same and different breeds. The correlation of GBV in different scales for a given trait is denoted by rg, and it will be named as genetic correlation between breeds henceforth.Where, G was created as in VanRaden [Matrix VanRaden :Z is a centered incidence matrix of genotype covariates (0/1/2); 2 ∑ pi qi is a scaling parameter in which pi and qi are the allelic frequencies for SNP i (i = 1: 43852), which were computed across breeds; I is an identity matrix (included in order to make G invertible). Matrix I could have been replaced by A, following VanRaden et al. [I.Where n et al. , but thiG using facilities in the Blupf90 series of programs [G (which is a 6330 x 6330 dense matrix) for the MTM would take nine times as much space.To implement this model, the regular relationship matrix was replaced by programs ,22. Variprograms . MoreoveThe Gibbs sampler was run for a total of 20 000 iterations. The first 4000 iterations were discarded as burn-in. Convergence was checked visually and by the Geweke diagnostic of the Markov chain . PosteriIn a second set of analyses, BLUP with a multi-breed genomic relationship matrix (GBLUP) was applied to estimate the GBV of all genotyped bulls using the following MTM:yi is a vector of 2*DYD for breed i = {M,N,H}. In this model, each record is allocated to its breed-specific effects and breeding values.Where u was as for the RRM and estimated (co)variances obtained with the RRM were used in the MTM to estimate the corresponding GEBV. However, in the MTM, different residual variances for each breed were used:The covariance structure of σɛ,i2 = , where the σ* indicates values from routine genetic evaluations for these breeds .Because 2*DYD is pre-corrected data, its pseudo-residual variance is not the same as the actual residual variance. Thus, we used In both models (RRM or MTM), EDC were used as weighting factors and the GEBV were computed using BLUP90iod2 modified by Aguilar et al. .g, were assumed to compare the accuracy of GEBV. In scenario 1, rg was set to zero to simulate a situation where breeds were uncorrelated, which is equivalent to performing single-breed evaluations. In scenario 2, the estimated value for rg was used and in scenario 3, rg was set to 0.95, which is equivalent to the assumption that the population is close to homogenous (rg = 1) [For each model (MTM and RRM), three scenarios for the genetic correlation between breeds, r(rg = 1) ,9.2) and the estimated linear regression coefficients, δ0 (intercept) and δ1 (linear term) of the linear regression of 2*DYD on GEBV, weighted by the corresponding equivalent number of daughters (EDC), respectively.Accuracy and bias of the GEBV were assessed in the validation datasets, separately for each breed, by the coefficient of determination . Estimated accuracies in the validation populations were slightly greater under the nonzero rg scenarios (2 and 3), as compared to accuracies, estimated in a single-breed scenario (rg = 0), for both models for milk production and fat content. The most important increase of accuracy was observed for fat content for breed M (from 0.27 with the single-breed scenario to 0.33 in the nonzero rg scenarios). Female fertility was the only trait for which accuracy was not improved in any population or model when the genetic correlation between breeds was allowed to be different from zero. This result may be because of the low heritability and the smaller estimates of genetic correlations between breeds for this trait, which may indicate that fertility is biologically different between breeds.Estimated accuracies calculated as RAccuracies of GEBV were largest for the H breed for milk production  and fat content  traits because of the larger number of genotyped animals in this breed  was also used to test the impact of increasing the size of the reference population using multi-breed data. The expected value of δ1 is 1, and this is desired to avoid inflation (or under-inflation) of GEBV’s of young bulls. Table δ1 , whereas accuracies estimated by R2 for this breed were largest. Thus, the results show some degree of trade-off between R2 and δ1 used to evaluate the GEBV predictions. It is important to note that the H breed presented the best quality of predictions in terms of δ1 for all traits and breeds.The coefficient of regression of 2*DYD on GEBV  from using a multi-breed reference population was observed only for fat content in the M breed. The M breed showed the largest estimated genetic correlations with the H breed . This indicates that the SNP effects are more similar between the M and H breeds than with breed N. This might be because of the introgression of Red Holstein animals in the M breed in the 1970’s (e.g. ). Theref% from usFor female fertility, accuracies of GEBV in the validation populations were the same using multiple-breed or a single-breed reference population (scenarios 2 and 3 versus scenario 1), showing low sensitivity to the value of the genetic correlation. The small estimated correlations between breeds for fertility (−0.01 to 0.39) could explain the low gain in accuracies for fertility when GEBV were estimated by a multi-breed reference population. This might indicate that the LD between markers and QTL does not persist between breeds and/or that the effects of these QTL differ between breeds. In addition to no effect on accuracy, the regression coefficient of 2*DYD on GEBV was greater than one for fertility in the M breed, which indicates a severe underestimation of GEBV.De Roos et al.  and  genetic correlations between breeds were needed in this study to achieve slightly higher precisions. Therefore, for traits with moderately high heritabilities, and using existing genomic relationships between breeds, the genetic correlation between breeds might be an indicator of the expected increase in accuracy of GEBV from the use of a multi-breed reference population. In fact, the genetic correlation provides an indication about the concordance of the effect of the QTL on the trait between breeds  and about the concordance of LD between markers and QTL between breeds.A model fitting data on a trait in multiple breeds as correlated pseudo-traits has been presented. The trait that showed the lowest genetic correlation between breeds was female fertility. The use of a multi-breed reference population only increased the accuracy of GEBV for traits and populations that showed the largest correlations between breeds and in the breed with the smallest data set. Accuracies of GEBV for fertility were lower than for other traits and values of the regression of the DYD on the GEBV showed severe underestimation of GEBV for fertility in breed M.The authors declare that they have no competing interests.SK analyzed the data, AL conceived the approach and analyzed the data. SK, MJC, CD, AL interpreted the results and drafted the paper. All authors read and approved the final manuscript.