HLA locus for medical conditions, the bone mineral density locus WNT16 for physical measures, and the skin tanning locus MC1R and smoking behaviour locus CHRNA3 for lifestyle. Tissue-specificity investigation reveals several tissues associated with total genetic contributions, including the brain tissues for mental health. Such associations are driven by tissue-specific gene expressions, which share genetic basis with the total genetic contributions. TGCA can provide a genome-wide atlas for the overall genetic contributions in each particular domain of human complex traits.Quantifying the overall magnitude of every single locus’ genetic effect on the widely measured human phenome is of great challenge. We introduce a unified modelling technique that can consistently provide a total genetic contribution assessment (TGCA) of a gene or genetic variant without thresholding genetic association signals. Genome-wide TGCA in five UK Biobank phenotype domains highlights loci such as the  Quantifying the effects of individual loci on the human phenome is a challenging task. Here, the authors introduce a modelling technique, TGCA, that assesses total genetic contribution per locus and apply this to UK Biobank phenotype domains, revealing top loci and links to tissue-specific gene expression. During the past decade, a large amount of genome-wide association studies (GWAS) of various phenotypes have shown that complex traits are highly polygenic, influenced by many genetic variants with small effects3. When many phenotypes are considered, distinguishing tiny genetic effects from noise becomes particularly challenging. Not only the spread of genetic effects, i.e. pleiotropy, is of concern, but also the magnitude of genetic effects requires consideration. Which variant, or gene, or part of the genome, contributes the most genetic effects to the measured human phenome? The question is yet to be well defined and scientifically answered.Understanding the magnitude of ubiquitous genetic effects across the genome is of fundamental importance for scrutinising the complexity of genetic architecture. The concept of pleiotropy, coined 110 years ago by the German geneticist Ludwig Plate4. For instance, in GWAS setting, a loose threshold (e.g. P < 0.05) may lead to too many false positives, while a stringent threshold (e.g. P < 5 × 10−8) may produce too many false negatives5. Without a significance threshold, summing up the association statistics across all phenotypes also suffer from the issue of too many negatives, so that noise dominates signals. Thus, it is strongly needed to develop a threshold-free method, to penalise the unassociated phenotypes and quantify the total contribution of a gene or genetic variant6. Correlations across a wide range of phenotypes also need to be accounted for4.Quantifying the overall effect of a gene or genetic variant on the human phenome is not trivial. Although this seems to be as simple as adding up each variant’s genetic effect on each phenotype, there are some major difficulties. The key issue is that it is hard to distinguish associated phenotypes from noise. Simply applying a statistical significance threshold to association summary statistics cannot solve the problemIn this work, we develop a statistic for total genetic contribution assessment (TGCA) of a genetic variant, addressing the above difficulties. The TGCA statistic quantifies how much genetic effect in total a SNP contributes to a group of phenotypes. We achieve this by modeling GWAS summary statistics across a wide range of phenotypes in UK Biobank (UKBB). We integrate TGCA with tissue-specific gene-expression information to highlight the tissues most relevant and irrelevant to human complex traits. We also provide functional insights into the discoveries by integrating TGCA with functional genomic annotations. TGCA results can be considered as an atlas of general genetic architecture for complex trait variation.4, for every single genetic variant across multiple phenotypes (see Methods), yielding a vector of adjusted Z-scores per variant that are uncorrelated with each other. Denote the adjusted Z-scores of SNP i across k phenotypes as zi = . In the TGCA model, for j ∈ {1, . . . , k}, zij is drawn from a mixture Gaussian distribution ofπ− + π0 + π+ = 1. The μ parameters are the means of the genetic effects, and the σ2 parameters measure the dispersion of the genetic effects. We estimate all these parameters for each genetic variant in the genome by maximising the full likelihood via an EM algorithm  component serves as a penalisation term for phenotypes with null associations without introducing any significance threshold for GWAS summary statistics. Θ quantifies how much genetic effect in total a SNP contributes to the group of traits, the π parameters assess the proportion of these traits the SNP affects, and the μ parameters represent the average effect the SNP has on each trait.In order to quantify the total genetic effect per variant, we define a TGCA statistic Θ = ∣π and μ parameters are derived from the Hessian of the likelihood function at its maximum, so that the standard error of estimated Θ can be obtained via the Delta method  + π+N; a mixture with three non-null Gaussian π− = 2π+ = 2π++; and a mixture with two non-null t-distributed heavy-tailed components π−[t(1) + μ−] + π0N + π+[t(1) + μ+], where t(1) denotes a t-distribution with 1 degree of freedom, and π− = π+. In order to cover a wide range of values in the parameter space, the true parameters were drawn randomly from given distributions (Methods). We evaluated whether Θ and the other parameters can be consistently estimated with different true values setup . For each of the above Gaussian mixture true models, we estimated the model parameters and compared the estimates to the true values p-value distribution under the null, although slightly inflated, was close to uniform. For the same Θ value, the more the null effect traits were, the higher the power to identify Θ, as the model became more identifiable when the components in the mixture were more apart from each other.For the four simulated model and a null model with no genetic effect, we evaluated the operating characteristics of the p-values testing the null hypothesis of Θ = 0  or phenotype domains2. The HOPS Pm statistic sums up GWAS χ2 statistics, trying to assess a total genetic effect, however, without penalising the null associations, the performance is similar to pleiotropy quantification with thresholding  > 0.005. We obtained all the estimated parameters as well as the TGCA Θ’s with their standard errors , mental health (189 traits), physical measures (117 traits), lifestyle (172 traits), and diet 139 traits)  Scoring tissue-specific gene expressions to identify specifically expressed genes in each tissue; (2) Estimating and testing the GWAS-analysed trait’s heritability enrichment on SNPs annotated on tissue-specifically expressed genes.Integration of genome-wide summary association statistics and tissue- or cell-type-level gene-expression data was shown to be able to locate gene-expression-mediated genetic regulation of complex diseases, e.g. schizophrenia9, using stratified LD score regression (S-LDSC)11 to test the enrichment of total genetic contributions in different tissues. The expression tissue-specificity score of each gene was calculated as the proportion of expression across 48 GTEx tissues (v7). For each tissue, the top 10% tissue-specifically expressed genes were selected, and SNPs on these genes were annotated and passed onto S-LDSC for genome partitioning 13, which explain substantially enriched heritabilities for a wide range of complex traits11. With the assessment of total genetic contribution in different trait domains, we expected that the overall genetic contribution would also enrich at cis-expression quantitative trait loci (eQTL). Furthermore, if a particular tissue is associated with a certain domain of phenotypes via tissue-specific gene expressions, we hypothesised that such an association were driven by the cis-eQTL of the tissue-specifically expressed genes.The cis-eQTL scan summary statistics of the tissue-specifically expressed genes in each tissue. The tissue-specifically expressed genes were the same as in the above S-LDSC analysis. We represent each cis-eQTL with its lead variant, i.e. the SNP with the smallest p-value across the tested cis-SNPs by both the eQTL scan and our TGCA analysis. We examined the squared Z-score (χ2) distribution for cis-eQTL for specifically expressed genes in each tissue , and what the average effect the SNP has on each trait (the μ’s), and how much genetic effect in total a SNP contributes to the traits (Θ); (2) The Gaussian mixture is easier to handle computationally in an EM algorithm. Numerically, in the UKBB analysis, there were about 5% SNPs for which the mixture model fitting could not be stably achieved due to likelihood boundary properties. Some of such lost SNPs could harbour interesting loci, so mathematical and computational algorithms for mixture models might be developed further to increase parameter identifiability.We do not necessarily expect that the effects truly follow the described TGCA model. In fact, we do not know the true model. Nevertheless, there are two advantages of the three-Gaussian TGCA: (1) The parameters are straightforward to interpret, such as on what proportion of the traits the SNP affects  is reasonable, as the expected variance of the GWAS Z-scores is 1 under the null due to the constrain. We have shown via simulation that the simple model is generally applicable and identifiable in various scenarios.In order to balance the sample size difference across the traits, we standardised the GWAS Z-scores by the square root of the sample sizes as weights, with a constrain that the average weight across the traits equals to 1. Although modelling the null component variance differently for traits with different sample sizes would fit the data better, modeling the null component as p-values testing the total genetic contribution parameter against Θ = 0. First, the power for the inference of Θ and any other parameter in the mixture model increase with both the sample sizes of the GWASs and the number of phenotypes modelled .We downloaded the UK Biobank round 2 genome-wide association study (GWAS) summary statistics released by the Neale’s lab. The GWAS was conducted on 361,194 genomic British individuals  for 4203 phenotypes. The analysis corrected from baseline characteristics including sex, age, age15. For continuous and ordinal phenotypes, we filtered out the phenotypes for which there were less than 50,000 non-missing samples. For binary phenotypes, we filtered out those with less than 1000 cases. This resulted in 1511 phenotypes in total, including 1036 binary, 237 continuous, and 238 ordinal phenotypes  βij is tiny, for each SNP j, the correlation between two estimates In order to model independent test statistics from multiple GWAS, the correlation between the genetic effects of each pair of phenotypes, β1 = β2 = 0, i.e. no genetic effect, the Pearson’s correlation coefficient between the two estimated genetic effects vectors 16. Such an estimator has two major advantages: (1) it naturally incorporates the level of sample overlap between the two GWAS, which reduces to zero when the two GWAS are performed on independent samples; (2) it directly produces phenotypic correlations for binary phenotypes on corresponding continuous logistic scale, making the estimates mathematically more straightforward to handle. In practice, it is tricky to select SNPs with zero true genetic effects. The above estimation procedure is valid as long as the genetic variance captured by each selected SNP is small. Thus, instead of putting constraints on estimated SNP effects, we selected the 169,537 SNPs that have minor allele frequency (MAF) less than 5 × 10−4 and used the correlation matrix of their test statistics (Z-scores) as the estimate of the phenotypic correlation between the 1511 traits, which is also an estimate of the correlation matrix of the GWAS test statistics for each single variant in the genome. The use of such low-MAF variants provides more efficient estimates of the phenotypic correlations than the other state-of-the-art methods7. We removed the phenotypes that have an estimated correlation larger than 0.9 with another trait. This resulted in an estimated phenotypic test statistic correlation matrix R for 1376 traits , i.e. R is the correlation matrix of the columns of Z. We have c is a constant. As R is symmetric and semi-positive definite, ∃ Z* = ZR−1/2 so that Z* are uncorrelated, which is similar to the decorrelation procedure in the HOPS method4. We obtained R−1/2 via eigen-decomposition of the estimated R matrix. We approximated the R−1/2 matrix by its first M eigenvectors, yielding Z* = ZR−1/2 with M columns, where M is determined with a cut-off on the eigenvalues so that the eigenvectors capture 90% of the information in R. For each SNP, we conduct modeling of the distribution of the Z* values.Denote the Z-score matrix of the Among the 1,376 QCed phenotypes, 122 traits were classified into the medical conditions domain, 189 traits were classified as mental health traits, 117 traits as physical measures, 172 traits as lifestyle traits, and 139 traits were classified as diet-related according to the UK Biobank phenotype catalogue  + π+N; Three non-null Gaussian mixture distribution π− = 2π+ = 2π++; Two non-null t-distributed heavy-tailed components π−[t(1) + μ−] + π0N + π+[t(1) + μ+], where t(1) denotes a t-distribution with 1 degree of freedom, and π− = π+. μ− was randomly drawn from −∣N∣, μ+ and μ++ were drawn from ∣N∣, and the σ2’s were randomly come from χ2(1). Five different true values of π0, 0.1, 0.3, 0.5, 0.7, and 0.9 were examined. In each scenario, the estimates of all model parameters including Θ were estimated and compared to the true values. The simulation was repeated for 999 times.We generated 200 independent Z-scores for a single genetic variant that came from four scenarios of true models: Two non-null Gaussian mixture distribution k0 = π0k, k+ = π+k, k− = π−k, and the + and − subscripts indicate that the Z-scores were generated from positive and negative components of the mixture, respectively. The true value of Θ was calculated as z’s are the elements of Z− and Z+ vectors, respectively. The true values are comparable across different true models. The true Θ measures the weighted average non-null genetic effect.For each true model, the true value of Θ was determined by knowing the generated Z-scores from their pre-assigned components in the mixture distribution. Denoting a set of independent Z-scores as For the three true models above with Gaussian components, the real phenotypic correlation matrix between 1376 UKBB phenotypes were used to generate 1376 correlated Z-scores for a single genetic variant. We adjusted the phenotypic correlations as described above prior to the TGCA analysis. The simulation was repeated for 999 times.k0 = π0k, k+ = π+k, k− = π−k, and the + and − subscripts indicate that the Z-scores were generated from positive and negative components of the mixture, respectively. The true value of Θ was calculated as z*’s are the elements of R+ and R− are the correlation matrices for Z− and Z+ vectors, respectively.Similar to the case with independent Z-scores, for each true model, denoting a set of generated correlated Z-scores as Z* matrix across 2,787,891 QCed SNPs. Standard errors of the parameters were obtained through the Hessian matrix of the likelihood function. The SNPs whose model fitting did not converge in 9999 iterations were filtered out. The SNPs that could not obtain standard errors due to numerically ill-conditioned likelihood surface, i.e. the maximum likelihood estimates could not be properly identified near the boundaries, were filtered out. For each SNP, the standard error of We applied the mixture model to the above UK Biobank a method . We evenWe downloaded the mean gene-expression data summarised from RNA sequencing by the GTEx project. The GTEx v7 data covers gene expressions of 19,791 genes in 48 human tissues. Gene-expression values were normalised to numbers of transcripts per million reads (TPM) so that they are comparable across tissues. In order to measure the expression specificity of each gene in each tissue, the specificity was defined by dividing the expression of each gene in each tissue by the total expression of that gene in all tissues, leading to specificity ranging from 0 to 1 for each gene.17 to test whether the 10% most specifically expressed genes in each tissue were enriched for First, we used stratified LD score regression (S-LDSC)4, we used a SNP-based regression with LD-corrected ℓj is the LD score of the j-th SNP, pre-calculated by the ldsc software; Aj takes a value of zero or one, as an indicator for whether the SNP is annotated to be within a tissue-specifically expressed gene; γ is the parameter of interest. The more the tissue-specifically expressed genes can explain the variation in γ would be. As LD exists across the analysed SNPs, directly applying the regression to all the SNPs would underestimate j, j + 100, j + 200, ⋯ , j = 1, 2, ⋯ , 100, so that the LD correlations were pruned. These resulted in 100 Second, similar to the strategy used by the HOPS methodcis-eQTL scan summary statistics of the top 100 tissue-specifically expressed genes in each tissue. We represent each cis-eQTL with its lead variant, i.e. the SNP with the smallest p-value across the tested cis-SNPs by both the eQTL scan and our TGCA analysis. We examined the squared Z-score (χ2) distribution for cis-eQTL for the 100 specifically expressed genes in each tissue, where the Z-score is χ2(1) distribution under the null.From the GTEx v7 data resource, we extracted the Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1-20Reporting Summary


Sustainability in livestock farming requires monitoring of autochthonous breeds which are well adapted to the local environment. The morphometric measurements seem to be the first approach which can provide useful information on the suitability of animal genetic resources for selection. In this work, thirteen morphometric variables were used for the phenotypic characterization of 130 adult autochthones cattle randomly selected from 30 local farms in Guelma. There were cases from four commonly accepted and traditional ecotypes: Guelmois, Cheurfa, Sétifien and Fawn. The results showed several and significant positive correlations between the different variables. Correlations were analyzed using Varimax orthogonal rotation PCA and three factors were extracted, which explain more than 75% of the total variation in the four ecotypes. Stepwise discriminant analysis showed that 6 of the 13 variables had discriminatory power to define the phenotypic profile of the ecotypes. Canonical discriminant analysis indicated that the Sétifien ecotype is separate from the other three ecotypes. Mahalanobis distances were significant between the different ecotypes except for the distance between the Guelmois and Fawn ecotypes. The cross-validation procedure assigned 91.42% of the Sétifien animals to their genetic group, while the percentages of animals assigned to the Cheurfa, Guelmois and Fawn ecotypes were 80.00%, 65.71% and 53.33% respectively. The multivariate approach has proven to be effective in differentiating the four ecotypes, with clear morphological differences from the Sétifien ecotype that may benefit from a genetic improvement program for more sustainable genetic resources preservation. In order to deal with the effects of globalization, urbanization, mechanization, increase in world population, global warming and climate change, it is urgently needed to transform our agriculture and livestock farming systems to more sustainable agriculture by taking into account the environmental considerations  , 2. MoreAlgeria is rich in a wide variety of indigenous cattle breeds, which are appreciated for their adaptive traits such as tolerance to heat stress and diseases resistance –8. Thesei) the “Guelmoise” ecotype, whose coat is dark gray, commonly; ii) the Cheurfa ecotype, characterized by a light gray, almost whitish coat; iii) the “Setifiénne” characterized by a uniform blackish coat; iv) the “Fawn” (Chélifien” or “Tlemcenien”), the color of the coat of which varies between brown and beige. However, this diversity has been exposed to poorly planned crossbreeding, mainly with artificial insemination based on imported semen, which has reduced drastically the number of local breeds , 10, 11.To preserve this genetic diversity, and after the adoption of the Global Plan of Action for Animal Genetic Resources , conservMorphometric measurements are used to assess the characteristics of different animal breeds, and can provide useful information on the suitability of animals for selection –19. In tMultivariate discriminant analyses of morphological traits have been reported, in several previous morphometric studies, to be effective for a precise and objective discrimination of different population of cattle –28, goatThis study aims to evaluate the morphological differences among the Algerian brown Atlas cattle subpopulations, and to determine the major variables/traits for the provision of maximum separation among the four local ecotypes. These morphological characters have significant role in the programs of improvement and sustainable conservation of indigenous breeds.www.rias.gr/bovisol) whose protocol has been approved by the Bioethics Committee on Animal Research of 8 Mai 1945 Guelma University, Algeria. The study involved taking body measurements from cattle with the consent and in the presence of the cattle herder. There is no specific legislation for body measurements and hence no approval was necessary.This study was carried out as part of the Bovisol project  and the IBM SPSS Statistics for Windows, Version 20 .Collected data were processed and analyzed using XLSTAT Version 2016.02, Addinsoft, Paris, France  were calculated for morphometric variables. Data were analyzed with the Weighted least squares general linear model (WLS-GLM) which uses the least squares method, which included ecotype group, sex  and age group as fixed effects.The statistical model used took the form:ijk: is the value of the different morphometric descriptors .Yi shows the fixed effect of the different ecotypes with .EcotypeSex (i) j is the fixed effect of male and female sex .The fixed effect of animals’ age (j) K with .Animals were reared on farms with almost the same farming and grazing practices. Consequently, the effects of husbandry and localities were confounded with the ecotype and were not included in the model.Interactions between effects were analyzed and significant effects were reported. For each body measurement and age, comparisons of the least squares means were carried out using the Bonferonni test after examining the effect of significance on the observed variables.Pearson correlation coefficients were estimated for different body measurements. The Cronbach’s alpha coefficient (α) was calculated to assess the homogeneity and internal consistency of a set of variables for a given group.In order to reduce dimensionality of our data set, principal component analysis (PCA) was performed. According to Everitt et al. , PCA is The coefficients being chosen so that y1, y2. . . .., yp take into account decreasing proportions of the total variance of the original variables, x1, x2,. . . ., xp. In order to test the validity of the factor analysis of the data set, the Kaiser-Meyer-Olkin (KMO) sampling adequacy criterion was calculated. The low values of KMO indicate that the correlations between any variable and the other variables are unique, and are not related to the remaining variables outside of every single correlation. Pundir et al.  reported2 value (P <0.05). Linear combinations of body measurements were performed by canonical analysis, which used to perform multivariate analysis that calculated the Mahalanobis distance (D2) between the different cattle ecotypes.Stepwise discriminant analysis was carried out to identify the morphological traits having a discriminating power between the studied ecotypes. The importance of these morphological features was assessed according to their partial RThe phenotypic discrimination among breed populations was assessed with a cross-validation test. This required the removal of 1 individual from the first matrix, and then a discriminant analysis was performed with the remaining observations to classify the omitted individual. Performance was evaluated according to the percentage of correctly and incorrectly classified bovine. The morphological distinctness of each ecotype was defined using the percentage of correctly-classified individuals.A total of 130 animals which raise two different ecotypes (73%), or one ecotype (27%) were used. Differences between the different ecotypes for morphometric variables are presented in For the Sétifien ecotype, the average of the chest measurement is equal 175.88 cm which is the largest in comparison with the other ecotypes. These results indicate good conformation and harmonious development of the internal organs. The body measurements observed in Sétifien and Cheurfa cattle are related to the geographic location where they are generally found in the plain while the Guelmois and Fawn ecotypes are often found in mountainous areas. This observation was confirmed by the dactyl-thoracic index which evolves in the opposite direction to the animal walking ability.The coefficients of variation for the different measures showed a generally low variability (i.e. 70% of the variables studied recorded a coefficient of variation which does not exceed 10% which indicates that the cattle from each ecotype have similar size). These coefficients vary from 3.98% (PL) to 23.15% (HOL) for the Guelmois ecotype, from 3.05% (CG) to 15.10% (HOL) for the Cheurfa ecotype, from 3.38% (PL) to 19.82% (HOL) for the Sétifien ecotype and from 3.25% (PL) to 19.46% (HOL) for the fawn ecotype.The length of the horns (HOL) represents the most heterogeneous biometric parameter in the ecotypes studied, which is in concordance with results reported by Boujenane , who shoP <0.05) for parameters with economic importance such as CG, HW, HC, PW and PL. These parameters are very sought in genetic improvement programs. However, no significant effect was recorded for parameters which are not important in selection programs, such as HOL, EL, CC and DTI  was not correlated with BL, HW, MC, HC, and PW, indicating the independence of these variables with EL. This independence was more observed in the Sétifien ecotype. Also, other correlations but not significant were recorded between the length of the horns (HOL) and the other measured variables except for the Muzzle Circumference (MC) which was negatively correlated with the length of the horns (HOL) for the Cheurfa and Fawn ecotypes.The correlations found in this study are stronger than those obtained in other studies across the world , 20, 24.The results obtained allow us to note an internal consistency of (0.816), (0.816), (0.875) and (0.864) for the Guelmois, Cheurfa, Sétifien and Fawn ecotypes respectively, which indicates better internal coherence, especially of the Sétifien sample. Homogeneity is satisfactory when the value of the coefficient is at least equal to 0.80 .The estimate of sampling adequacy using Kaiser-Meyer-Olkin (KMO) gives an overall mean for all the variables equal to (0.622), (0.621), (0.677) and (0.680) respectively for Guelmois, Cheurfa, Sétifien and Fawn cattle.P <0.0001) which allows a reduction in the dimension of all thirteen morphometric variables.The overall significance of the correlations tested with Bartlett’s test of Sphericity for the biometric traits was significant  represents 75.79% of the total variance. For Cheurfa cattle, factors 1, 2 and 3 represent respectively 47.56%, 15.78% and 11.92%, and 75.27% of the total variance. Also, for the Sétifien and Cheurfa cattle, the first 3 factorial axes explained a cumulative amount of information of 77.48 and 76.47%, respectively .Tolenkhomba et al.  extracteFor the other ecotypes, the coefficients show that the highest relative contributions to factors 1, 2 and 3 were HW, PL and MC for the Cheurfa ecotype, CG, DTI and EL, for the Sétifien ecotype and BL, PL, and HOL for the Fawn ecotype. The variables most closely associated with factor 1, regardless of the ecotype studied, were CG, BL, and HW. These variables tend to describe the general size of the animal, while the factors 2 and 3 indicate the shape of the animal, which is in concordance with the literature data , 46.Also, the commonality of the variables, which represents the proportion of the variance of each of the 13 variables shared by the factor axes selected, vary from 0.619 (HC) to 0.882 (EL), from 0.449 (HC) to 0.918 (BL), from 0.630 (HOL) to 0.933 (CC) and from 0.519 (HW) to 0.918 (MC) for the Guelmois, Cheurfa, Sétifien and Fawn ecotype respectively .The lower commonality of certain traits, such as the circumference of hock (HC) and the length of head (HL) in the Guelmois ecotype, the circumference of hock (HC) and the length of the horns (HOL) in the Cheurfa ecotype, the width of muzzle (MW) and the length of the horns (HOL) in the Sétifien ecotype, the height at the withers (HW), the width of muzzle (MW) and the length of the horns (HOL) in the Fawn ecotype indicate that these traits are less effective, to explain the total variation in body conformation compared to the other traits. Similar results have been reported by Tolenkhomba et al. . The thr2 varied from 0.261 to 0.095. Then, the other traits  were removed from the final model. These traits were the PL, followed by MC, CG, HL, PW and HW in decreasing order of discriminating power  CAN1 and CAN2 representing respectively 53.55 and 45.46% of the total variation, these axes indicate a great reduction in the sampling space, with little loss (1%) to explain the total change. The third canonical axis (CAN3) was not taken into account because its values were very low .P <0.0001).Several studies show a reduction in the sampling space with a very small loss of the total variation by conserving the first two canonical vectors , 27, 48.The values of the first and second canonical axis enabled us to see that certain variables are correlated with the first canonical axis. Indeed, BL, HW, MC and PL are positively correlated . This fiEvaluations of cattle within each ecotype and their interrelations with other ecotypes have been shown in the projection of the four ecotypes in the plane defined by the first and the second canonical axes . This prP <0.001) except for the one between the Fawn and Guelmois ecotypes  in Fawn ecotype, followed by Guelmois, Cheurfa, and Sétifien ecotypes with 34.3%, 20% and 18% respectively . Indeed,ST mean value of (0.039) and high heterozygosity value (0.84). Indeed, the total genetic variation is dominated by differences among individuals (97.10%) while 2.90% among populations.The allocation results are in perfect agreement with results obtained from the molecular characterization of four Algerian cattle breeds  using 22 microsatellite markers . The autCurrently, several autochthones bovine ecotypes are of mixed origin, which makes it difficult to determine the phenotype of the original breed . Most inIn summary, the principal component analysis provided a mean of reducing the number of morphometric traits to be recorded into groups of variables that can be used to explain body conformation for animal selection program. Therefore, it is necessary to exploit specific traits of each ecotype to establish programs for sustainable genetic improvement. The characters HW, CG, MC, BL, PL and HL were the most discriminating variables to separate the four ecotypes . The study showed that the Sétifien ecotype was larger than the other ecotypes for the majority of morphometric traits. The approach used in this study could be very interesting in the assessment, management and conservation of different autochthones bovine populations, where the primary goal is to obtain local genetic resources with a pure phenotype for future selection, which is beneficial for breeding strategies improvement. Further studies, especially in molecular genetic analysis is necessary for the validation of current results.S1 Table(DOC)Click here for additional data file.S2 Table(DOC)Click here for additional data file.S3 Table(DOC)Click here for additional data file.


As a pivotal research tool, genome-wide association study has successfully identified numerous genetic variants underlying distinct diseases. However, these identified genetic variants only explain a small proportion of the phenotypic variation for certain diseases, suggesting that there are still more genetic signals to be detected. One of the reasons may be that one-phenotype one-variant association study is not so efficient in detecting variants of weak effects. Nowadays, it is increasingly worth noting that joint analysis of multiple phenotypes may boost the statistical power to detect pathogenic variants with weak genetic effects on complex diseases, providing more clues for their underlying biology mechanisms. So a Weighted Combination of multiple phenotypes following Hierarchical Clustering method (WCHC) is proposed for simultaneously analyzing multiple phenotypes in association studies. A series of simulations are conducted, and the results show that WCHC is either the most powerful method or comparable with the most powerful competitor in most of the simulation scenarios. Additionally, we evaluated the performance of WCHC in its application to the obesity-related phenotypes from Atherosclerosis Risk in Communities, and several associated variants are reported. Traditionally, Genome-Wide Association Studies studies (GWASs) aim to identify genetic variants associated with certain phenotypes for explaining complex diseases . In GWASp-values of univariate association analysis by means of different strategies. Recently, some approaches of univariate analysis have been proposed for exploring the association between multiple phenotypes and a genetic variant  and concurrently adjusting the correlations among various phenotypes  is proposed. Using extensive simulation scenarios, we compare the performance of WCHC with that of six existing methods: O’Brien’s method   to clusts method , MultiPhs method , MANOVA s method , SHet .(1) In each of the B permutations, we random shuffle the genotypes and then get the statistics (2) Calculate k = 1,2,…,K.b = 0,1,2,…,B;and then p-value of TWCHC is given by:(3) Then, the M phenotypes into K disjoint clusters C1,C2,…,CK, where ψ = {C1,C2,…,CK} with Ck⋂Cl = ∅(k≠l). Specifically, applying the bottom-up hierarchical clustering approach, we begin with each phenotype as a singleton cluster and then subsequently merge pairs of clusters with the largest similarity until all clusters have been merged into a single cluster that contains all phenotypes. The largest similarity in each iteration is referred as the height of the merged cluster in the dendrogram. A stopping criterion determines the number of clusters, which is similar to an established principle (hb is the largest similarity between two clusters in iteration b (b ≥ 1) or the height of iteration b. We define:The hierarchical clustering based on our previous work  is as forinciple . SupposeK clusters C1,C2,…,CK. On the calculation of correlation coefficient, the Pearson correlation coefficient, multiple correlation coefficient, and canonical correlation coefficient are respectively employed according to the number of phenotypes in the merged two clusters.Then, the number of clusters identified at the iteration https://github.com/YQHuFD/WCHC.The source code for WCHC method can be found in 1n be the all ones vector of length n and 0n be the all zeroes vector of length n, where n is a positive integer. We first list the following existing methods for power comparison with the proposed WCHC.For convenience, let OB (O’Brien’s method)  : Using aMultiPhen (Joint model of Multiple Phenotypes) (notypes) : ModelinMANOVA   × M)/2 freely estimated elements in covariances and variances. Standard MANOVA tests the null hypothesis that the M regression coefficients are all zeroes, which is asymptotically equal to the F-test.ariance) : In the SHet (Test for Heterogeneous genetic effects)  : The tesTATES (Trait-based Association Test that uses Extended Simes procedure)  sorted p-value in ascending order; Me and Me(j) denote the effective number of independent p-values among all M phenotypes and m specific phenotypes, respectively. The effective numbers can be obtained from the correlation matrix of p-values.ocedure) : TATES cWCmulP (Weighted Combination of multiple Phenotypes)  : WCmulP Assume that the population is in Hardy–Weinberg equilibrium (HWE), and the genotypes of the genetic variants follow the binomial distribution with parameter 2 and the minor allele frequency (MAF). We set MAF = 0.3 in this simulation study for all scenarios. The multiple phenotypes are generated via the following factor model :y = T is the M phenotypes; x is the genotype; λ = T is the vector of effect sizes of the variant on the M phenotypes; f is the vector of factors; f = T∼MVN,Σ = (1−ρ)I + ρA; I is the identity matrix; A is a matrix with elements of 1; R is the number of factors; and ρ is the correlation between factors; γ is an M × R matrix; c is a constant; ε = T is a vector of random errors; and ε1,…,εM are mutually independent and follow the standard normal distributions. Consider the following six models with varied numbers of factors.where R = 1, λ=β1M, and γ=1M.Model 1: There is only one factor, and the genotype has an influence on all phenotypes with the same effect size. Namely, R = 2, bdiag, which represents the block diagonal matrix of 1M/2 and 1M/2.Model 2: There are two factors and a genotype has an effect on one factor with the same effect. That is, R = 2, bdiag, where [1:M/2] represents the vector of components 1,2,…,M/2.Model 3: There are two factors, and a genotype has an effect on the second factor with different sizes. That is, R = 4, bdiag.Model 4: There are four factors, and a genotype has an impact on the last factor with the same size. That is, R = 4, bdiag.Model 5: There are four factors, and a genotype has an effect on the last factor with different sizes. Namely, R = 4, bdiag.Model 6: There are four factors, and a genotype has an impact on the last two factors with different effect directions. That is, c2 and the between-factor correlation is ρc2. For estimating type I error rates and powers, we fix N = 1,000 unrelated subjects, the number of phenotypes M = 16, 32. By means of setting β = 0, we generate all phenotypes that is independent of genotypes to evaluate the type I error rates of all methods, including OB, MultiPhen, MANOVA, SHet, TATES, WCmulP, and WCHC. The corresponding Q–Q plot of type I error rates is shown in c2 = 0.5 and between-factor correlation ρc2 = 0.1) but also change the values of within-factor correlation c2 = 0.3, 0.5, 0.7, and 0.9 (while between-factor correlation ρc2 = 0.1).For these six models, the within-factor correlation is j-th phenotype is given by M phenotypes is given by M, and MAF, we can calculate h2 for the different models.The calculation of heritability is as follows: the heritability of genotypes to the p-values of WCHC, WCmulP, and SHet are evaluated by 2,000 permutations; and the p-values of MANOVA, MultiPhen, TATES, and OB are evaluated by their asymptotic distributions. The type I error rates of the seven methods are estimated using 2,000 replicated samples. For 2,000 replicated samples, the 95% confidence intervals (CIs) for type I error rates of nominal levels 0.01 and 0.05 are about  and , respectively. The evaluated type I error rates of WCHC and other six methods are presented in M = 16) and M = 32). It is observed from these two tables that most of the type I error rates of WCHC are within 95% CIs, which shows the validity of the developed WCHC. Meanwhile, the type I error rates of WCmulP, SHet, MANOVA, MultiPhen, TATES, and OB are not obviously deviated from the nominal levels. See more information in Q–Q plots  As expected, in each model, the powers of all seven methods increase as the genetic effect β increases see , 2. (2) nd 6 see , 2. (4) Overall, from all the power simulation results, we could draw that our proposed WCHC has advantages over other methods in most scenarios, and especially in some scenes, the ascendancy is obvious. In other scenarios, WCHC is comparable with the most powerful test.phs000090.v4.p1).We applied our proposed method WCHC to the real data analysis from ARIC study , average skinfold thickness of the triceps brachii, mean subscapular skinfold thickness, waist, hip girth, waist-to-hip ratio, calf girth, and wrist breadth and three covariates including age, gender, and race. The specific description of these variables is listed in –7, not the traditional genome-wide significance threshold of 5 × 10–8. There are totally 11 SNPs that are significant for at least one method  samples, respectively. Instead of restricting analysis to the SNPs in r2 ≥ 0.8) via Qtlizer website. We restricted the eQTL association criteria with False Discovery rate (FDR) < 0.05. The results of eQTLs in Qtlizer, eQTLGen, and PsychENCODE are displayed in 6 to reveal that most of the proteins (nodes) encoded by the genes have certain interactions (edges), which suggests the proteins related the expression of genes might interact with each other for controlling a variety of biological phenomena including endocrine development, cellular response to hydrogen, and metabolic processes.In order to further study the biology function of the genetic variants, we performed enrichment analysis on genes associated with these 11 SNPs in Overall, our results showed that WCHC and other six methods could identify significant genetic variants for obesity phenotypes in real data analysis from ARIC. More importantly, functional annotations of genetic variants and enrichment analysis support that the variants are closely related to biological functions and metabolic pathways of obesity.In this article, we proposed WCHC to perform multivariate analysis of multiple phenotypes in association studies due to the following reasons. (1) Multiple correlated phenotypes are usually measured in complex disease for genetic association studies. Compared to univariate analysis, multivariate analysis considers multidimensional structure information. It indicates certain variance–covariance is included in multiple phenotypes. (2) Association analysis of multiple phenotypes separately cannot present genetic interactions between phenotypes. More and more evidence reveals that joint analysis of multiple related phenotypes, which considers the interactions between phenotypes comprehensively, can boost the power of detecting genetic variants associated with complex diseases. No matter whether the effects of genetic variants on phenotypes are consistent or not, WCHC provides a relatively simple way to incorporate the correlations between phenotypes into analysis. (3) Actually, we are not sure which phenotype or linear combination of phenotypes is more likely to elucidate the genetic structure of complex diseases. WCHC adopts clustering approach and linear combination of multiple phenotypes to account for the complex genetic information, which not only takes the similarity between phenotypes into consideration but also considers the heterogeneity, so it is helpful to explore the genetic mechanism of diseases.Our results manifested that WCHC has correct type I error rates and is either the most powerful test or comparable with the most powerful tests among the seven methods we adopted. None of the other methods observes consistently good performances under the simulation scenarios. OB is the most powerful test when the genetic effects are homogeneous, while it loses power dramatically when genetic effects are heterogeneous, especially if there exists opposite directions of genetic effects. In most simulation scenarios, SHet, MANOVA, MultiPhen, and TATES have similar powers, and they are less powerful than WCHC, and WCHC is more powerful when the genetic variant influences a part of phenotypes. However, WCmulP is less powerful in this scenario. Furthermore, in real data analysis, WCHC and MANOVA identified the largest number of significant SNPs (six SNPs). Therefore, the real data analysis results demonstrate that WCHC has excellent performance in detecting SNPs associated with complex disease with multiple related phenotypes such as obesity. As for the methods giving such different results when applied to the real ARIC data, we think that the parametric information of real data is unknown for us. Therefore, we may try various methods to analyze the real data for getting reliable results as much as possible. In our opinion, no method can guarantee 100% accuracy. We can only be cautious to say that the significant loci are more likely to be true signals, but further verification is still needed.In the context of association studies, population stratification (PS) refers to allele frequency difference between populations uncorrelated to the outcome of interest, but due to systematic ancestry differences. PS may cause confounding effects seriously if not adjusted properly . MethodsIn real data analysis, as the number of phenotypes elevates, the chance of missing at least one subject increases exponentially, especially in epidemiological and clinical research . We remop-value needs to be calculated by permutation procedure, which is time-consuming as compared with approaches whose test statistics have asymptotic distributions. To conduct GWAS, a small number of permutations  can be used to select genetic variants that reveal evidence of association, and then a large number of permutations are employed to estimate the selected significant genetic variants. We adopted this strategy to analyze the real dataset. Consequently, it seems to be efficient, and the bioinformatics analysis of significant variants supports our results. In conclusion, in the field of genotype–phenotype association studies, WCHC is an effective method for association analysis of multiple phenotypes, which considers both the correlations and differences among the multiple phenotypes. WCHC provides a convenient approach of association analysis for researchers to discover potential genes causing complex diseases, which does not need to assume the genetic model, and there is no limit to the number of phenotypes. Because the genetic structure of phenotypes is usually unknown, WCHC provides a convenient statistical method for the application of massive multi-phenotypic data in the future.One weakness of WCHC is that the test statistic does not have an asymptotic distribution and its https://github.com/YQHuFD/WCHC.Publicly available datasets were analyzed in this study. This data can be found here: phs000090.v4.p1. The source code for WCHC method can be found in The studies involving human participants were reviewed and approved by the ARIC. The patients/participants provided their written informed consent to participate in this study.LF and Y-QH: study concept and design and drafting of the manuscript. LF, Y-QH, and YW: acquisition of data. LF: methodology and interpretation of data. LF, YW, TL, and Y-QH: critical revision of the manuscript for important intellectual content. All authors have read and approved the final version of manuscript. We thank all reviewers and editors for their valuable suggestions on revision.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.