In animal breeding, genetic variance for complex traits is often estimated using linear mixed models that incorporate information from single nucleotide polymorphism (SNP) markers using a realized genomic relationship matrix. In such models, individual genetic markers are weighted equally and genomic variation is treated as a “black box.” This approach is useful for selecting animals with high genetic potential, but it does not generate or utilise knowledge of the biological mechanisms underlying trait variation. Here we propose a linear mixed-model approach that can evaluate the collective effects of sets of SNPs and thereby open the “black box.” The described genomic feature best linear unbiased prediction (GFBLUP) model has two components that are defined by genomic features.We analysed data on average daily gain, feed efficiency, and lean meat percentage from 3,085 Duroc boars, along with genotypes from a 60 K SNP chip. In addition information on known quantitative trait loci (QTL) from the animal QTL database was integrated in the GFBLUP as a genomic feature. Our results showed that the most significant QTL categories were indeed biologically meaningful. Additionally, for high heritability traits, prediction accuracy was improved by the incorporation of biological knowledge in prediction models. A simulation study using the real genotypes and simulated phenotypes demonstrated challenges regarding detection of causal variants in low to medium heritability traits.The GFBLUP model showed increased predictive ability when enough causal variants were included in the genomic feature to explain over 10 % of the genomic variance, and when dilution by non-causal markers was minimal. In the observed data set, predictive ability was increased by the inclusion of prior QTL information obtained outside the training data set, but only for the trait with highest heritability.The online version of this article (doi:10.1186/s12863-015-0322-9) contains supplementary material, which is available to authorized users. Standard genomic best linear unbiased prediction (GBLUP) models produce accurate predictions of genetic merit when applied in highly structured populations with many close relationships, as typically found in livestock species . GBLUP mHowever, genome-wide association studies suggest that many genetic variants with independent effects are located in the same genes, and that many of these genes are connected via biological pathways . Thus, eWe present a GFBLUP modelling approach in the present paper. We investigated whether its use could increase prediction accuracy using real and simulated phenotypes from a purebred Danish Duroc pig population comprising highly related individuals . The tesInformation on known QTL regions is available in several publicly available databases, such as Animal QTLdb . QTLs arSus scrofa) using genomic features defined by the QTL categories listed in the Pig QTLdb database , which were each replicated 50 times. Table Phenotypes were simulated using the following linear model: The present study was not subject to ethical approval since it was based on pre-existing data belonging to the Danish Agriculture and Food Council, Pig Research Centre, and did not require the application of additional experimental procedures. The simulated data is available upon request.The genotypic and phenotypic data on the Danish Duroc population used in this study is private property of the Danish pig breeders and the authors are not at liberty to disclose them in the public domain. However, the simulated data are available upon request.


Triticum aestivum L.) and 1,604 hybrids derived from them were evaluated for seven quality traits in up to six environments. The 135 parental lines were genotyped using a 90k single-nucleotide polymorphism array. Genome-wide association mapping initially suggested presence of several quantitative trait loci (QTLs), but cross-validation rather indicated the absence of major effect QTLs for all quality traits except of 1000-kernel weight. Genomic selection substantially outperformed marker-assisted selection in predicting hybrid performance. A resampling study revealed that increasing the effective population size in the estimation set of hybrids is relevant to boost the accuracy of prediction for an unrelated test population.Bread-making quality traits are central targets for wheat breeding. The objectives of our study were to (1) examine the presence of major effect QTLs for quality traits in a Central European elite wheat population, (2) explore the optimal strategy for predicting the hybrid performance for wheat quality traits, and (3) investigate the effects of marker density and the composition and size of the training population on the accuracy of prediction of hybrid performance. In total 135 inbred lines of Central European bread wheat ( Triticum aestivum L.) is one of the most important crops grown on 200 million hectares of farmland worldwide  × 100, where P1 and P2 were performance of two parental lines.The adjusted means of each genotype across environments were estimated with the following model:y was the vector of BLUEs across environments, μ was the vector of intercept term, gcam was the vector of GCA for male lines, gcaf was the vector of GCA for female lines, sca is the vector of special combining ability (SCA) of hybrids. XM, XF and XS were corresponding design matrices for gcam,gcaf and sca.The general combining ability (GCA) of parental lines was estimated with the following model:y was the vector of phenotypic performance, μ was the vector of intercept term, l was the vector of environment effects, t was the vector of trial effects, r was the vector of replication effects, b was the vector of block effects, p was the vector of genetic effects of parental lines, zpl was the vector of parent-by-environment interaction effects, h was the vector of genetic effects of hybrids, zhl was the vector of hybrid-by-environment interaction effects, and e was the vector of residuals. XL, XT, XR, XB, XP, XPL, XH, and XHL were corresponding design matrices. Except μ, all effects were treated as random.In addition, we estimated the genetic variance components of hybrids and parental lines as well as the variance of genotype × environment interactions by a one-step model:Significance of variance component estimates were tested by model comparison with likelihood ratio tests where the halved P values were used as an approximation . Using tDNA was extracted according to standard procedures from all parental genotypes and fingerprinting was performed with a 90k SNP array based on an Illumina Infinium assay . Hybrid Y stands for the adjusted entry means of the 1,739 genotypes within environments, β is a vector of environment effects, s is a vector of SNP effects, u is a vector of polygene background effects, and e is a vector of residual effects. X, S, and Z are incidence matrices relating Y to β, s, and u. β and s were treated as fixed effects and u as random effect. To check whether the population or family structure was adequately controlled by the model, a QQ-plot was drawn based on the observed P-values and expected P-values of all markers [Data from each environment were used in association mapping scans with correction for population stratification with a kinship matrix . The kin markers .R2) was estimated using analysis of variance (ANOVA) with QTLs reordered according to the P-values and the proportion of phenotypic variance explained by all the QTLs (R2adj), and effects of detected QTLs were estimated using a standard multiple regression approach [pG) by single QTL and all the QTLs was determined as proportion of explained phenotypic variance standardized by broad-sense heritability (h2), i.e. pG = R2adj/h2.The Bonferroni-Holm procedure  was applapproach . The proBased on the adjusted entry means across environments for the 1,739 genotypes included in our study, we applied ridge regression best linear unbiased prediction (RR-BLUP) , weighteY stands for the adjusted entry means of the 1,739 genotypes across locations, while ln is a vector of ones and n is the number of genotypes, μ refers to the overall mean across all environments, a is the additive marker effect, and d is the dominance marker effect. ZA and ZD are design matrices for the additive and dominance effects of the markers as specified according to the F∞ metric of Falconer and Mackay [e is the residual. We assumed that additive and dominance marker effects have normal distributions μ, a, and d, which are denoted as where d Mackay , and e iequation :[μ^a^d^Im refers to an identity matrix with dimension of m, where m is the number of markers. The shrinkage parameters λA and λD were defined as the ratios between the modified variance of residuals  . σe2, σGFor a solely additive model, the equation is simplified to:af, df denote the additive and dominance effects of the functional markers, and FA and FD are the design matrices.The model used in W-BLUP is similar to the RR-BLUP model, but we added an additional effect for functional markers, which were defined as the three most significant markers based on association mapping in the training population:πg (g denotes either a or d) of the used markers is considered to contribute to the genetic variance. Based on this assumption, the model for Bayes-Cπ is:Whereas in RR-BLUP it is assumed that all markers contribute to the genetic variance, in Bayes-Cπ only a fraction 1–g has a prior distribution:The additional parameter δπg, resulting in a β-distribution for the full-conditional posterior [In Bayes-Cπ, a uniform  prior was assumed for osterior . For BayThe prediction accuracy of genotypic values from marker-assisted as well as genomic selection was checked by cross-validation. Due to the factorial mating design of the plant material used in our study, relatedness between estimation and test set was expected to influence prediction accuracy. To account for this effect, we followed the suggestion of Schrag et al.  and sampFor marker-assisted selection, genome-wide association mapping was performed on the sampled estimation set of each cross-validation run. The Bonferroni-Holm procedure  was applWe applied two further cross-validation strategies to unravel the potential impact of estimation set size and composition on the accuracy of prediction. To validate the impact of the number of parents included, we randomly sampled four different groups of hybrids derived from an increasing number  of female parents and a constant number of 15 male parents to mimic different population sizes. For each size, estimation sets then contained two thirds  of the selected female parents, 10 of the selected male parents, and 100 hybrids derived from them, and the remaining hybrids were split into three test sets according to the relatedness levels . To examIn addition, we randomly sampled k (k from 1 to 173) markers from every 173 markers of the whole marker array in order to follow the accuracy of prediction of genomic selection (RR-BLUP) in dependence on increasing marker density with marker numbers ranging from 100 to 17,300, with intervals of 100. For all outlined cross-validation strategies, 100 runs were performed and the mean of outcomes was calculated.For all seven wheat quality traits examined, we observed a broad variation of phenotypic values across environments . PhenotyThe quantile-quantile plot revealed absence of an excess of QTL , indicatFor all quality traits except starch content and test weight, the detected markers with significant (P < 0.05 applying Bonferroni-Holm correction) additive effects were distributed over different chromosomes . None ofr2) was detected among these markers  and male parents (10) constant . In contMarker-assisted selection is beneficial compared to phenotypic selection in particular for (1) traits that are controlled by major effect QTLs , 63 and For 1000-kernel weight, a robust putative QTL explaining 18% of genotypic variation was detected on chromosome 3B. The chromosomal region corresponds to a previously reported QTL for 1000-kernel weight . Accordiper se performance with an average increase of 30%. Our results for genomic selection in hybrid prediction . The tiFor the T0 and T1 scenarios, MP- and GCA-based prediction is not applicable, while genomic selection is a potential strategy to predict hybrid performance. Longin et al.  suggestePrevious simulation studies have shown that equal shrinkage of marker effects as applied in RR-BLUP can result in too strict shrinkage for QTL exhibiting large effects , 73. BayMeuwissen  reportedFor all seven quality traits scrutinized, association mapping detected QTLs, but cross-validation revealed a large overestimation of prediction accuracies of marker-assisted selection. Genomic selection generally showed improved prediction accuracies compared to marker-assisted selection and is the method of choice especially when predicting the performance of hybrids of T0 and T1 population. Prediction accuracies can be maximized when enlarging rather the number of parents in the training population than increasing the number of hybrid combinations per parent.S1 FigEstimation sets comprised random selections of 80 out of 120 female (F) and 10 out of 15 male (M) parental inbred lines as well as 610 hybrids derived from them. Test sets included only hybrids not assigned to the respective estimation set that had either both parents (T2), one parent (T1) or no parent (T0) in common with the hybrids.(EPS)Click here for additional data file.S2 Fig(EPS)Click here for additional data file.S3 FigArrows indicate means of values.(EPS)Click here for additional data file.S4 FigP < 0.05, P < 0.01 and P < 0.001 levels of probability for phenotypic performance of different traits being significantly correlated.The upper right triangular section shows correlations among quality trait values; the lower left triangular sections plot maps for each pair of quality trait values; while the diagonal shows the histogram and density lines of quality trait values. *, **, and *** indicate (EPS)Click here for additional data file.S5 FigFour different biometrical approaches were performed: (1) without correcting for population structure, (2) with correcting for population structure with a heterotic effect, (3) with correcting for population structure with a kinship matrix, and (4) with correcting for population structure with a kinship matrix and a heterotic effect.(EPS)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.


Stenocarpella maydi; however, little information about genetic resistance to this pathogen is available in maize, mainly related to candidate genes in genome. In order to exploit this genome information we used 23.154 Dart-seq markers in 238 lines and apply genome-wide selection to select resistance genotypes. We divide the lines into clusters to identify groups related to resistance to Stenocarpella maydi and use Bayesian stochastic search variable approach and rr-BLUP methods to comparate their selection results.The identification of lines resistant to ear diseases is of great importance in maize breeding because such diseases directly interfere with kernel quality and yield. Among these diseases, ear rot disease is widely relevant due to significant decrease in grain yield. Ear rot may be caused by the fungus Through a principal component analysis (PCA) and hierarchical clustering, it was observed that the three main genetic groups  were clustered in a consistent manner, and information on the resistance sources could be obtained according to the line of origin where populations derived from genetic subgroup Suwan presenting higher levels of resistance. The ridge regression best linear unbiased prediction (rr-BLUP) and Bayesian stochastic search variable (BSSV) models presented equivalent abilities regarding predictive processes.Stenocarpella maydis. This claim is based on the acceptable level of predictive accuracy obtained by Genome-wide Selection (GWS) using different models. Furthermore, the lines related to background Suwan present a higher level of resistance than lines related to other groups.Our work showed that is possible to select maize lines presenting a high resistance to The online version of this article (doi:10.1186/s12863-016-0392-3) contains supplementary material, which is available to authorized users. Stenocarpella maydis, which is a fungus responsible for rot in ears and kernels and causes a disease known as ear rot.Throughout its evolution, maize has undergone an intensive domestication process and concurrently it has presented particular susceptibility to certain pathogenic microorganisms that directly influence kernel production and quality, such as S. maydis with corn seeds may also substantially compromise germination and seedling vigor [In addition, to losses in yield, the nutritional and economic values of the kernels may be depreciated because of mycotoxins known as diplodiatoxins, which may compromise the final feed quality and could be toxic to birds and cattle . The assng vigor .S. maydis in farming areas because of its necrotrophic nature. Moreover, ear rot occurs in both tropical and temperate regions; thus, it is a disease of global importance [The harmful economic impact of this disease increases every year and is driven by increases in the use of irrigated areas as well as by the use of no-tillage systems. These factors contribute to the propagation and survival of portance , 36.S. maydis inoculum, such as crop rotation, sowing healthy seeds, planting at the recommended density, and using resistant cultivars [Certain agronomic practices have been suggested to reduce ultivars . Accordiultivars , crop roultivars . Among tultivars .S. maydis.Despite the clear advantage of plant breeding to obtain resistant genotypes, there is a considerable lack of resistant cultivars. Therefore, breeding programs from public and private institutions must work intensively to obtain cultivars resistant to S. maydis, such as in the percentage of rotten ears and cobs and tilting of ears in the plant [Plant breeding used to target resistance to ear rot is usually performed using traditional phenotypic analysis methods, with data obtained in studies conducted in environments with high disease pressure. Evaluations of this disease are performed via secondary traits that may be used effectively in the selection of plants resistant to he plant . In prache plant .In addition to phenotypic selection, the identification of quantitative trait loci (QTLs) and the application of marker-assisted selection (MAS) practices  are alsoAn efficient alternative to mitigating certain limitations of MAS was suggested by Meuwissen et al. . The proThe statistical models to be adopted in Genomic Selection (GS) greatly depend on the genetic architecture to be studied. In general, infinitesimal models, such as genomic and ridge regression best linear unbiased prediction , have a good predictive power and can adequately describe the genetic architecture in infinitesimal models . The infS. maydis, the objectives of this work are: (i) evaluate the usefulness of GS in the selection of genotypes resistant to S. maydis; (ii) compare the rrBLUP and Bayesian stochastic search variable (BSSV) selection methods in terms of the selection (iv) genetically characterize the germplasm bank of the Federal University of Lavras for resistance to ear rot.Because of the scarcity of information available on the genetic mechanisms of resistance to ear rot and lack of studies to identify genomic regions involved in resistance to The genomic relationships among the lines obtained by 23,154 Dart-seq markers were submitted to spectral decomposition. In total, it was observed 6 % of missing data point and it were imputed using the EM approach by A.mat function in rr-BLUP library deleting markers presenting more than 90 % of missing data. The inbred lines were clustered into distinct genetic groups through a Principal Component Analysis (PCA) analysis based on the relationship data. This approach was effective in the clustering of our genetic background even explained just 15.24 % of the genomic additive matrix  trait; thus, when the BSSV approach was used, the ρ mixing parameter values of the BSSV model were 0.37 and 0.32, respectively. This result suggests the presence of sufficient sample information for the identification of genes with probabilities different from zero. Therefore, cross-validation analyses were performed for PRK and ERIS only using the rrBLUP and BSSV methods.For the percentage of rotten kernels (PRK) and Ear Rot Incidence Score (ERIS) traits, the As shown in Table n-k) and the observed breeding value from full data (n) i.e., r2 = 0.878 and r2 = 0.874 for rr-BLUP and SSVS respectively. That is approximately 10.84 % (rrBLUP) and 10.96 % (BSSV) higher compared with the ERIS trait. On the other hand, when we used the predictive ability as a measure of accuracy based on phenotypic values, it was not so high, ranging from 0.241 to 0.569 (Table 2 = 0.648 for PKH and 0.265 for ERIS). In general, the rr-BLUP and BSSV were equivalent in the prediction of the Genomic Breeding Values GBVs for both traits.The PRK trait provides a higher predictive power when we use the predicted breeding values obtained from the training population  was identified as the largest source of resistance to this pathogen. In the class of susceptible lines, the methods produced conflicting results regarding the genetic group with the highest proportion of these genotypes. The predominantly susceptible group identified by the BSSV analysis was SSS (25 %), whereas the predominant group identified by rrBLUP was IODENT (29.17 %).Following the genomic analysis and calculation of GBVs via rrBLUP and BSSV, 10 % of the most resistant and susceptible inbred lines were classified based on predicted values. The highest proportion of lines resistant to ds Table . For theDisease evaluation and line selection in tropical environments constitutes a great challenge for breeders. In addition to the difficulty of obtaining reliable methods, interactions between genotypes and environments further hamper the selection of superior genotypes. In this work, a high Genotype –By- Environment (G x E) interaction was observed in the analysis of phenotyping data from ERIS, PRK and NESR. In the preliminary data analysis obtained with these methods, genetic variances of 67,843, 0.04709 and 18.2104 were observed, whereas the genetic variances of the G x E component were 12,921, 0.4766 and 7.1249 respectively. This strong interaction may have been caused by differences in climate between the two environments. The climate in Lavras is classified as highland tropical, whereas the climate of Uberlândia is classified as tropical with a dry season. The incidence of this pathogen is generally restricted to higher altitudes and humidity environments, which include the region of Lavras. Thus, we believe that this difference in climates may be the factor that triggered the high G x E interaction observed between those two environments.S. maydis because it shows higher heritability and is highly correlated with direct measures of disease incidence, such as ERIS and NESR. Moreover, unlike ERIS, the PRK method is not a subjective method. The quantitative nature of PRK resulted in improved predictions and identification of regions of resistance to S. maydis. It is worth noting that these three measures correlated positively among themselves and negatively with weight of ears without husk. For example, the correlation between NESR quantified by the weight of ears without husk −0.84 [Regarding the method of evaluating pathogen incidence, our results indicated that evaluating resistance to ear rot is problematic. In general, the ERIS and NESR measures presented low heritability compared with PKR, although these three measures were highly correlated in the lines, with the NESR and PRK traits showing a correlation of 0.92. Thus, we suggest that the PRK trait may be used as a parameter in the evaluation of resistance to sk −0.84 , which sAs shown in our study, selecting the model that best describes the genetic architecture may be decisive when adopting a breeding strategy, such as when a breeder only wants to select the most resistant lines or perform MAS. Thus, the results of cross-validating and identifying candidate genes may aid the breeder during decision making.In the cross-validation process using the BSSV and rrBLUP methods, differences were not observed between both procedures for GBV prediction and only a slight difference for phenotypic value predictions Tables  and 2. TIn regular studies involving GWS and cross-validation methods, the supervised learning process is applied to evaluate the model performance based on its prediction ability for missing data. It is very usual to use the correlation between predicted GBV and phenotype values where the residual is assumed as a nuisance amount. In this scenario, the maximal correlation is limited by the trait heritability. On the other hand, if the residuals are removed from the phenotypic values, the GBV might be assumed as “true” values, where the squared correlation threshold is equal to 1. It is because the covariance among missing genotypes is equal to their variance see . In thisr2). Wray et al. [Another important point about the cross-validation is related to the necessity of performing repeated k-fold to evaluate the reliability of the prediction measure  analysis obtained by the line markers matrix showed a pyramidal cluster of heterotic groups in our breeding program. The separation of tropical groups, SSS and NSSS was evident with both clustering methods.A as a source of information for the spectral decomposition because these authors used the markers’ Euclidean distance matrix. [The PCA-based cluster analysis strategies of maize inbred lines were performed in a similar way by Romay et al. , who cha matrix.  argue thIn the clustering pattern obtained by Romay et al. , strong S. maydis, such as dominance and epistasis effects, was not explored in depth in this work. Nonetheless, our results are a starting point for improving the introduction of resistance alleles in susceptible lines and for performing directed crosses.Because of the adequate group characterization, most of the resistance sources  are clustered in the tropical material as expected. Also, the lines belonging to the SSS and IODENT group of temperate origin were the most susceptible. This result, although expected, clarifies the importance of good germplasm characterization for a better understanding of resistance sources. The technique associated with GWAS and the identification of candidate genes regions provides breeders with a powerful tool in the selection process. We must note that the inheritance of resistance to S. maydis. The rrBLUP and BSSV methods present the same efficiency in the prediction of resistant lines. In addition, the use of a PCA along with additive relationship information was efficient at defining genetic groups. Thus, it was possible to identify groups resistant to S. maydis in tropical accessions, particularly in lines distributed within the Suwan genetic group.Our results showed that the PRK trait may be used as an evaluation method in the genomic selection and for resistance to Four hundred and forty-seven lines were genotyped with 23,154 DArTSeq™ obtained by Diversity Arrays Technology Pty. Ltd Yarralumia ACT, Australia. This technology is based on a complexity reduction method in order to obtain genome sequences copies and further sequencing based on next-generation sequencing using HiSeq2000  More details about the method can be obtained in Raman et al. .A.mat function and mean method in the rrBLUP package [A) proposed by Vitezica et al. [Missing data were imputed using the  package  of R sofa et al.  given byq is the frequency of the unfavorable allele; WA is the deviation matrix of the markers centered in p ; and 2∑pq is the sum of the variances of the loci.in which p is the frequency of the favorable allele; A, and the first two principal components were subsequently plotted. Thus, instead to carry out the SVD from original genomic marker matrix we used the spectral decomposition of Vitezica et al. [Genetic clustering of the inbred lines was performed by spectral decomposition of the relationship matrix a et al.  positivehclust function of the hclust package in R software [Wald method was also conducted using a Euclidean distance matrix of the elements of the matrix A as an object.A hierarchical cluster analysis through the software  calculatThe incidence of ear rot was evaluated in 238 lines of the 447 genotyped lines, together with four resistant controls from the germplasm bank of the Federal University of Lavras . Only elite lines were phenotyped while the others 209 were not since these lines were recently introduced in our breeding program and present a small number of evaluations. Therefore, the genome data for these lines were inserted in this study in order to present the pattern of our breeding program. The 238 lines were evaluated in crop year 2012/2013 in two environments in the municipalities of Lavras  and Uberlândia  in the state of Minas Gerais, Brazil.S. maydis. The experimental plots consisted of a 3-m row with 0.7-m spacing.The population was evaluated in an augmented incomplete block design interspersed with common controls. The block consisted of 10 treatments (8 regular treatments and 2 common) and 3 replicates. The common treats are resistance and susceptive lines for S. maydis isolates were obtained and replicated at the Seed Phytopathology Laboratory of the UFLA using the methodology by Clements et al. [s et al.  with sev6 conidia*mL−1 on the day of the inoculation. Pathogen inoculation was performed 15 days after 100 % of the field plants had emitted the style-stigma using a pipette for the inoculation of 1 mL of isolate suspension into each corn ear.The isolates were cultured in complete medium for 30 days. After this period, the conidial suspension was adjusted using a Neubauer counting chamber to 10The incidence of ear rot was evaluated based on three methods: (i) ear rot incidence score (ERIS); (ii) number of ears with symptoms of rot (NESR); and (iii) percentage of rotten kernels (PRK). A diagrammatic rating scale proposed by Reid et al.  was usedx environments interaction (G X E) and residuals. The mixed model adopted was as follows:Data analyses were performed in two stages. In the first phase, a mixed model was used for observation corrections according to the following effects: replicates, environments, genotypes y is the n × 1 vector of observations; X is a n × p fixed effects incidence matrix ; T is a n × q genetic effects incidence matrix; Ω is a random block effects incidence matrix within replicates; W is a line x environment interaction effects incidence matrix; and β, g, b, δ are vectors of the effects related to X, T, Ω and W, respectively and e represents the residual effects. The distribution of effects g, b, δ and e are assumed to be N, N, N and N, respectively. The estimates of the best linear unbiased predictor (e-BLUPs) and variance components were obtained using residual maximum likelihood (REML) function maximization [where mization .The mixed model utilized in this study was calculated as follows:n × 1; j is a unit vector corresponding to the mean; u is the sample mean; Z is the marker’s genotype incidence matrix; and a and e are vectors of the additive genetic for each marker and residual effects, respectively.where V is given as follows:The matrix of phenotypic variances G = Aσa2 is an additive genetic variance matrix and Iσe2 is the residual variance diagonal matrix and where The GWAS analysis was performed with mixed.solve in the rrBLUP package  of R sofAmong the Bayesian models proposed in the literature, the BSSV model was used in this study because of its ability to select large-effect markers in models with multiple markers. Adjustments to the original model proposed by Yi et al.  were proi obtained by model 1, μ is the sample intercept, zij is the genotype of marker j of individual i, aj is the effect of the marker j and ei is the error of observation i following distribution N.where The acceptance of a marker effect depends on a combination of priori assumptions conditioned to a set of latent or indicator variables. Therefore, we can assume that the a priori additive effects of the markers are as follows:σa2j and δ represent high and low magnitude variance in the genetic marker effects, respectively. In this study, it was assumed a priori thatwhere δ = 10− 6 The prior hyperparameters v and s2 are related to Bayes A method described in [δ = 10− 6 corresponds to individual marker heritability at 1 % of phenotypic variance i,e δ = σy2 × 0.01/m.and ribed in . The δ =ρ was modeled in advance by a Beta distribution ρ|a, b ~ Beta instead of 0.5 as originally described by Yi et al. [Δj was assumed for residual variance σe2.Another modification in the original BSSV method was the assumption that hyperparameter i et al. . The a pμ of the full posterior conditional distribution:Sample 2.aj of the full posterior conditional distribution:Sample The numerical integration of the posterior conditionals distribution was performed using the Markov chain Monte Carlo algorithm via Gibbs sampling , which ivai = ηiσa2i + (1 − ηi)δ, with η : {1, 0} and p(η) ~ Bernoulli(ρ)3.Sample 4.η of a Bernoulli distribution:Sample 5.ρj of a Beta distribution using the following conditional:Sample 6.Sample residual variance:where 7.Repeat the steps described until convergence is attained.where RSS is the residual sum of squares.Wald test. The statistics of this test W(λ) under the null hypothesis follow an asymptotic distribution χ2 with one degree of freedom. The test values may be obtained withThe significance of the marker effects was determined with the χtab2 = 3.84), considering an error rate of 5 %. The data set and the R program are available in Additional file where entclass1pt{minima χtab2 = .84, cons(n-k) until all groups were used as the validation population. Predictions of the breeding values of lines (ŷp) containing the validation population were based onThe 5-Fold cross-validation method was used to assess the accuracy of the models. The set of 242 observations was randomly subdivided into five training populations, with four groups each containing 48 observations and one group containing 50 observations. One group was sequentially eliminated in the analysis process to be used as the validation population, and the remaining four groups were used as training populations Zk is the marker matrix of the individuals belonging to the k-th validation population and a is the vector of the marker effects estimated for individuals from the training population.where r2) between the predicted breeding values from validation set Za. In addition, the (r2) between e, the expected maximal squared Pearson correlation is Za based on full data (n) and the predicted BLUPs n-k data the G12 is the covariance between missing and observed genotypes, G1 is the covariance among the missing genotypes and G2 the covariance between the observed genotypes. In this last case, the threshold is equal 1 given that G122 = G1G2. Therefore, the rmax2 based on observed and predicted GBVs are re-scaled to a maximal threshold equal to 1.The efficiency of prediction was measured by the determination coefficient (Using the predicted breeding values we ranked the 10 % of the most resistance lines in order to select the best germplasm. These predicted breeding values include all markers used in this analysis; presenting, therefore, minor and larger associative markers.BSSV, Bayesian stochastic search variable; EM, expectation-maximization; ERIS, ear rot incidence score; G x E, Genotype –By- Environment; GBLUP, genomic best linear unbiased prediction; GBV, genomic breeding value; GS, genomic selection; GWAS, genome-wide association studies; GWS, genome-wide selection; IBS, identity-by-state; MAS, marker-assisted selection; MCMC, Markov Chain Monte Carlo; NESR, number of ears with symptoms of rot; NSSS, non-stiff stalk synthetic; PCA, principal component analysis; PRK, percentage of rotten kernels; QTLs, quantitative trait loci; REML, residual maximum likelihood; rr-BLUP, the ridge regression best linear unbiased prediction; SNPs, single nucleotide polymorphisms; SSS, stiff stalk synthetic


High-throughput sequencing technology allows researchers to test associations between phenotypes and all the variants identified throughout the genome, and is especially useful for analyzing rare variants. However, the statistical power to identify phenotype-associated rare variants is very low with typical genome-wide association studies because of their low allele frequencies among unrelated individuals. In contrast, a family-based design may have more power because rare variants are more likely to be enriched in families than among unrelated individuals. Regardless, an analysis of family-based association studies needs to account appropriately for relatedness between family members. We analyzed the observed quantitative trait systolic blood pressure as well as the simulated Q1 data in the Genetic Analysis Workshop 18 data set using 4 tests: (a) a single-variant test, (b) a collapsing test, (c) a single-variant test where familial relatedness was accounted for, and (d) a collapsing test where familial relatedness was accounted for. We then compared the results of the 4 methods and observed that adjusting for familial relatedness could appropriately control the false-positive rate while maintaining reasonable power to detect several strongly associated variants/genes. Current platforms for genome-wide association studies are limited to scanning common variants. Although rare variants may contribute a significant proportion of heritability, the statistical power to detect rare variants is low because of their low allele frequencies. Recent advances in high-throughput sequencing technologies have provided us great opportunities to delve deeper into the genetic components of complex traits by identifying millions of rare variants in the human genome  and alloIn an effort to increase the power to detect rare-variant associations, many methods have been proposed to aggregate the effects of multiple rare variants within a specific functional unit, for example, a gene . Among tThe Genetic Analysis Workshop 18 (GAW18) data consists of genotyping and sequencing data for 959 individuals from 20 extended families. Among them, 849 individuals had at least 1 blood pressure measurement. For the real data, we used the first nonmissing measurement of systolic blood pressure (SBP) as the target quantitative trait. For the 200 replicates of the simulated phenotype, we also used the first measurement of SBP as the target quantitative trait. Finally, to evaluate the false-positive rate, we used the simulated Q1 data as the null phenotype.The common variants in the genotyping data were used to estimate the genetic similarity matrix. As for the sequencing data, we selected only the nonsynonymous mutations for the association test in recognition of the fact that variants causing amino acid alterations tend to have large effects on the phenotype.Y represents the phenotype (quantitative trait), C represents the collection of the covariates (age and gender), X includes the genotypes of the variants to be tested, and Z is the design matrix for the whole-genome polygenic random effects α. Finally, γ and β are fixed effects and e is the random residual. When the random effects are integrated out, the model is marginalized as α and e, respectively. As for K, one could use twice the theoretical kinship matrix to represent the familial relationships. However, to account for potential cryptic relatedness between individuals across different families, we used a genetic similarity matrix that was estimated from the genotyping data as follows: ith individual at the mth marker, mth marker, and p is the total number of markers in the genotyping data.We used the following linear mixed model to adjust for familial relatedness: We investigated 4 methods of association analysis: (a) a single-variant association test without adjusting for familial relatedness (UNI), that is, the component re GEMMA . The thire GEMMA  that ignre GEMMA . Specifip value of the variants in a gene to obtain the gene-level p value. To assess the false-positive rate, we also calculated the p values using Q1 as the phenotype. The power and the false-positive rate were calculated based on the 200 replicates. Table LEPR) whereas the collapsing method is more powerful for genes containing multiple variants with comparable effect sizes.For the simulated data, we analyzed the genes that explain the highest percentages of SBP variance (the percentages of SBP variance explained by each gene in the simulation were provided by the GAW18 organizers) using the 4 methods described above. Genes without nonsynonymous mutations were excluded. For the first two single-variant methods, we performed a Bonferroni correction on the smallest p value smaller than 0.05 (PBonferroni = 0.038). It is a coding variant for gene PDZD3. To our knowledge, the literature has suggested no role for this gene in blood pressure. For SKAT-ADJ, there is no gene with a Bonferroni-corrected p value smaller than 1.Consistent with our observation in the simulated data, the Q-Q plot Figure  shows thIn this study, we investigated the utility of linear mixed models in adjusting for familial structure. We also attempted to combine a linear mixed model method with a kernel score test--a state-of-the-art collapsing methodology that tests for association between a group of variants and a phenotype.We found that linear mixed models are able to satisfactorily adjust for familial relatedness in the sense that false-positive rates are well controlled at the nominal significance level. Not surprisingly, in terms of the statistical power, the performance of the single-variant method and the collapsing method depends on the distribution of the variants' effect sizes within the gene. The single-variant method is more powerful for genes with one dominating causal variant, whereas the collapsing method is more powerful for genes with multiple causal variants of similar effect sizes.The authors declare that they have no competing interests.CL and HZ designed the overall study; CY, CL, MC, XC, and LH conducted statistical analyses; and CL and HZ drafted the manuscript. All authors read and approved the final manuscript.


Background: Failure to account for the etiological diversity that typically occurs in psychiatric cohorts may increase the potential for confounding as a proportion of genetic variance will be specific to exposures that have varying distributions in cases. This study investigated whether minimizing the potential for such confounding strengthened the evidence for a genetic candidate currently unsupported at the genome-wide level.Methods: Two hundred and ninety-one first-episode psychosis cases from South London, UK and 218 unaffected controls were evaluated for a functional polymorphism at the rs1360780 locus in FKBP5. The relationship between FKBP5 and psychosis was modeled using logistic regression. Cannabis use (Cannabis Experiences Questionnaire) and parental separation (Childhood Experience of Care and Abuse Questionnaire) were included as confounders in the analysis.Results: Association at rs1360780 was not detected until the effects of the two environmental factors had been adjusted for in the model . A statistical interaction between rs1360780 and parental separation was confirmed by stratified tests . The genetic main effect was directionally consistent with findings in other (stress-related) clinical phenotypes. Moreover, the variation in effect magnitude was explained by the level of power associated with different cannabis constructs used in the model (r = 0.95).Conclusion: Our results suggest that the extent to which genetic variants in FKBP5 can influence susceptibility to psychosis may depend on other etiological factors. This finding requires further validation in large independent cohorts. Potentially this work could have translational implications; the ability to discriminate between genetic etiologies based on a case-by-case understanding of previous environmental exposures would confer an important clinical advantage that would benefit the delivery of personalizable treatment strategies. The broad etiological basis of psychosis adds to the expectation that the genetic pathways to the disorder will be similarly diverse. But evidence in support of this theory has been hard to come by in psychosis research. One reason for this is that exposures which may have contributed to the clinical state are rarely documented in genetic research. Gene–environment interaction (GxE) is the archetypal strategy for exploring interplay between genes and environment , 2 but iIn its present format, genome-wide association (GWA) is biased toward the discovery of associations that are robust to these concerns. In theory at least, one way the range of GWA variants for psychosis could be extended beyond this constraint is by incorporating the environmental structure of the cohort into GWA analyses, as was recently attempted in depression . We emplFKBP5 (FK506 binding protein 5) as a genetic risk factor for psychosis. FKBP5 performs a vital physiological function at the gene–environment interface, as it regulates the activity of the hypothalamic–pituitary–adrenal axis (HPA) system. This regulatory function is known to be perturbed by genetic and epigenetic events in some stress-related conditions  aged 18–65 years and presenting with their first-episode of psychosis to psychiatric inpatient wards in Lambeth, Southwark, and Croydon , between December 2005 and April 2011 were invited to take part in the study. All patients that met ICD-10 (n = 218) were drawn from the same geographical areas as cases. All controls were asked to complete a Psychosis Screening Questionnaire (PSQ) (Patients (t ICD-10  criteriare (PSQ)  in orderThe study cohort used is drawn from the Genetics And Psychosis (GAP) study, which was granted ethical approval by the South London and Maudsley and Institute of Psychiatry Local Research Ethics Committee (Ethics reference number: 05/Q0706/158). All cases and controls gave informed written consent after reading a detailed information sheet.n for the “frequency of use” measure was 234 in the subset of GAP with available data on adversity in childhood, whereas for the “life-time use” measure data on 455 was available in the same subset.A simple yes/no question about life-time cannabis use was included in the original GAP questionnaire in 2005. A more detailed history of illicit drug use for each subject was introduced when the modified version of the Cannabis Experiences Questionnaire was implemented in 2006 . Three pChildhood adversity was assessed using the Childhood Experience of Care and Abuse Questionnaire (CECA.Q) . This isGenetic ancestry was derived from a panel of 57 ancestry informative genetic markers. These were genotyped using iPLEX technology developed for the MassArray platform . Further information on the makeup of the marker panel is available on request. Ancestry scores were derived using the program Structure  to implen = 126). Concordance between the two sources was 100%.DNA material from buccal swabs and blood samples was obtained from a total of 509 subjects (291 cases and 218 controls). DNA was extracted using a standard phenol–chloroform extraction procedure. A Taqman SNP assay  was used to report the presence of either one or both alleles (C and T) at the rs1360780 locus. Genotypic concordance was checked for a subset of cases for which cheek swab and blood DNA was available . All other analyses were conducted using STATA, release 12 . Genotypic coding for the genetic analysis reflected either additivity (CC vs. CT vs. TT) or dominance (CC vs. CT + TT). Chi-square tests were used to identify variables confounded with either diagnostic status or genotype. Logistic regression analyses incorporated these variables into a model that included age, gender, and genetic ancestry. A single measure of childhood trauma was selected for use in these analyses on the basis of statistical power, whereas three cannabis measures  were used in the analysis for comparison purposes. In this study G × E interaction is defined as a departure from multiplicativity, unless otherwise stated. Consideration of E × E effects was prompted by three previous studies in this area –7. TheseT allele) were compared with HAPMAP reference populations . Genotypes were in the expected proportions, given allelic frequency . Therefore, no evidence of bias in the derivation of genotypic data could be detected.A total of 509 out of 524 possible genotypes were obtained. This corresponds to an overall call rate of 97%. Allele frequencies , but the median age at assessment did not differ between the two groups . The comparison groups used in this study were diverse in terms of the self-reported ethnic labels used . For this reason, genetic ancestry scores are used henceforth to index quantitative ancestry. There was a high degree of correspondence between self-reported ethnicity and mean ancestry scores . The main effects of genetic and non-genetic risk factors on psychotic disorder are presented in Table The proportion of male psychosis cases was significantly greater compared to controls .Of the three measures of adversity shown in Table adj = 1.31, p = 0.19). However, daily cannabis use was significantly higher among cases than controls (54.2 vs. 18.1%) compared to all other intake regimes combined . There was also increased use of THC-enriched “skunk-like” varieties of cannabis among cases . No main effect between FKBP5 and psychotic disorder was observed in either crude or adjusted models.Although a higher proportion of cases admitted to having used cannabis during their life-time Table , this tr2X = 1.6, p = 0.8; cannabis type: 2X = 2.8, p = 0.1). In summary, the associations between parental separation, cannabis use, and psychotic disorder in this sample are consistent with our previously published data . Further group-specific analyses suggest that the association is exclusive to cases  and not controls ; this implies G × E between FKBP5 and parental separation, as opposed to gene–environment correlation.Table p ≥ 0.49; n ≥ 420). Based on this result interactions between environmental variables (E × E) were excluded from consideration in the full logistic model applied in the next section.The need to account for interaction between life-time cannabis use and childhood adversity in this sample –7 was asFKBP5 and parental separation  genotype class. This was enough to prompt a recode of genotype data in order to allow re-estimation of the same parameters under the dominance genetic model (models 4–6). This had the added advantage of addressing the statistical constraint imposed by the low representation of the TT genotype class (n = 67) . The direction of this effect accords with previous studies in which the T allele mediates increased risk . The interaction effect peaks in model 5, and is directionally consistent across models 1–6. The T allele confers protection from risk in this interaction. Overall, the inclusion of both main and interaction terms in the model significantly benefits model-fit performance .A trend effect found under the additive genetic model Table , model 2p < 0.05 level (data not shown). This suggests that the significant interaction terms in Table The interaction was reinterpreted using the additive scale . The intFKBP5 is obscured by etiological heterogeneity within the sample. We sought further clarification of the result from a stratified analysis. The importance of parental separation to the genetic model can be confirmed by the data shown in Table Table r = −0.78) as it does on the power of the cannabis construct used (r = 0.95) . This is also illustrated in Figure Table S4 in Supplementary Materials presents the power of the three cannabis constructs used in these analyses. Genetic power to detect the genetic main effects shown in Table FKBP5’s relevance to psychosis. This uncertainty includes a lack of GWA support and the mixed performance of the target locus in one recent study (p = 0.02). The genetic main effect found is directionally consistent with that of the same locus in other (stress-related) clinical phenotypes (r = 0.95). The statistical interaction between rs1360780 and parental separation was confirmed in a stratified analysis .This study attempted to investigate whether the etiological heterogeneity typically found in large clinical cohorts is a root cause of the uncertainty regarding nt study . Our appenotypes –10. MoreFKBP5 potentially demonstrates that greater variety and subtlety of signal detection could be achieved  if our awareness of non-genetic risk factors is harnessed in the discovery process. Failure to accomplish this may come at the expense of the translational goals of psychiatric research . This trend also seems to be reflected in the results of Collip et al. (p < 0.08). In models 3, 4, and 5, statistical evidence of interaction is generally weaker (p > 0.1), this is seemingly because adjustment for the confounding effect of stressful life events was not implemented in this set of analyses. In total, Collip et al. (r ≥ 0.80) were found to be the most consistent across all five models. Our own analytical design additionally factors-in cannabis-related characteristics of the cohort while cannabis does not feature in the models of Collip et al. , the theory of environmental confounding could explain why interactions mediated in the vicinity of rs1360780 showed poor consistency in the analyses of Collip et al . In the p et al. : in theip et al.  conductep et al. . Howeverp et al. , 32, we p values reported in this study have not been corrected for multiple-testing. The reasons for this are twofold: (i) a balanced penalization strategy should take into account the compelling evidence that made rs1360780 our preferred genetic candidate ; and (ii) the bulk of the additional testing relates to the formulation of our environmental model. For this we applied a principled approach, which sought to identify and use the most statistically relevant adverse childhood exposure in the cohort. We then explored the relationship between power and genetic outcome across all three cannabis measures. Finally, the study has been performed on a restricted  patient population within an inner-city area and controls were not randomly selected, though they were broadly matched across several demographic criteria . This may limit the generalizability of the findings. Future work could include further evaluation of our findings in more representative psychosis samples and community-based populations.This study has a number of methodological limitations that should be taken into account when interpreting these findings. We were unable to control for symptoms of depression in our cohort, because such data was not collected. Previously reported main and interaction effects of rs1360780 span the depression phenotype , 33, 34,FKBP5 on presence of psychotic disorder, the fact that our ability to detect this signal depended on controlling for environmental exposures suggests that FKBP5’s contribution may vary depending on the etiology relevant to each case. Translation of these findings into clinical practice might one day serve the need to factor individual profiles of exposure into calculations of personal risk. The ability to accurately pinpoint or discriminate the relevant genetic etiology based on a case-by-case understanding of environmental pathology, could provide an important clinical advantage by strengthening personalized medicine approaches within psychiatry.Although, we were able to detect the hypothesized effect of 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.http://www.frontiersin.org/Journal/10.3389/fpsyt.2014.00084/abstractThe Supplementary Material for this article can be found online at Click here for additional data file.


The biggest challenge for jatropha breeding is to identify superior genotypes that present high seed yield and seed oil content with reduced toxicity levels. Therefore, the objective of this study was to estimate genetic parameters for three important traits , and to select superior genotypes to be used as progenitors in jatropha breeding. Additionally, the genotypic values and the genetic parameters estimated under the Bayesian multi-trait approach were used to evaluate different selection indices scenarios of 179 half-sib families. Three different scenarios and economic weights were considered. It was possible to simultaneously reduce toxicity and increase seed oil content and weight of 100 seed by using index selection based on genotypic value estimated by the Bayesian multi-trait approach. Indeed, we identified two families that present these characteristics by evaluating genetic diversity using the Ward clustering method, which suggested nine homogenous clusters. Future researches must integrate the Bayesian multi-trait methods with realized relationship matrix, aiming to build accurate selection indices models. Jatropha curcas L.) has many economically interesting characteristics, and nowadays, it has been considered as the most important shrub for biodiesel production, mainly due to the large amount of oil content it produces . It is Phorbol ester was extracted according to procedure described by Makkar et al. . Milled The oil extraction was performed crushing seeds and albumens, and weighing epicarp and mesocarp separately. Analyses were performed according to Adolfo Lutz Institute protocols. Sample (200 g of seeds) for each plant and replicated twice. Soxhlet was used to extract the oil and the hexane was used as solvent.W100S, only the records of 2014 were used because SOC and PEC traits were recorded only in this specific year. Additionally, mean phenotypes were used for W100S, and these records were adjusted according to the number of replications within genotypes and blocks. Also, all analyses were carried out using 358 phenotypic records for each trait of the 179 half-sib families.Despite the five consecutive years of evaluations of MCMC) was tested by the Geweke criterion [SD) for estimated parameters were obtained from MCMC samples. Multi-trait mixed model was:yijkl is the lth = {1,2,…,358} phenotypic value of ith = {1,2,3} trait, on jth = {1,2,…,179} genotype, within kth = {1,2} blocks; μi is the overall mean of ith trait; and eijkl is the residual term.Variance components and genetic parameter estimates were obtained under the Bayesian approach, via Gibbs sampling, using the Gibbs2f90 software, as described by Misztal et al. . We consriterion , using triterion , and CODriterion , implemeriterion . Posteriβ is the vector of a prior probability of systematic effects  is the vector of a prior probability of genotypic values, where I is the identity matrix and e = {eijkl}∼N is the vector of a prior probability of residual values with normal independent identical distribution; where x′ij and z′ij are incidence rows that relates systematic and genotypes effects within traits to the respective phenotypic value; and Under the Bayesian approach, the following joint distribution of data (likelihood function) were: from Eq ); g = {ga priori probability distributions for the location parameters of interest were given by:Vb is a diagonal matrix of the a priori variance of β, assuming Vb → ∞;The following G0 and R0 covariance matrices:Three-dimensional scaled inverted Wishart distributions are assigned as prior process for each of the Σg and Σe are scale matrices, and n = 5 is the degree of freedom parameter.Where The joint posterior density of all parameters, which are dependent on the genotypic effects of the corresponding matrix, but which take over prior independence, is given byD) matrix. In this study, we adopted the Mahalanobis distance, which can be defined as follows:A cluster analysis was carried out aiming to understand the genotypic relationship between traits, and to identify genotypes that expressed genetically similar performance. Hence, we intended to cluster homogeneous genotypes. The first step of cluster analysis is to calculate dissimilarity  is minimum. SSE of each cluster can be achieved as follows:nm is the number of individuals on mth cluster; and Thus, the Ward cluster hierarchy method was applied, and it was chosen aiming to maximize the homogeneity within clusters so that the sum of square of error  is the number of clusters; αj is the correspondence joint point to n − j + 1 clusters; Sα are the mean and the standard deviation of α′s; and ω is a constant equal to 1.25, as suggest by [Mojena criteria was used to set the optimal number of clusters, and the method is based on computing the highest amplitude between clusters that maximizes the quality of the clustering .αj>α¯+ωggest by .H) can by defined as:Selection indices procedures were constructed according to Hazel . Overallgi, i = {1,2,…,n} is the vector of genotypic values for the nth trait; and wi, i = {1,2,…,n} is the relative economic value.Where w) of the traits in the breeding goal were taken into account. In the first situation, all traits had weight of 1 monetary unit per genetic standard deviation. In the second situation, SOC received weight of 2 and 1 monetary units for the other traits. Finally, we set weight of 4 monetary units for SOC, 2 for W100S, and 1 for PEC, in the third scenario. Traits contemplated in these scenarios were defined to depict a situation in which an established breeding program already working on selection for SOC intends to incorporate W100S and PEC in its breeding goal. As a trait of major importance, only SOC was used as target in the first scenario. The next two scenarios gradually included W100S and PEC in selection indices.In this study, three different scenarios were used, and they included different traits in the selection indices. Additionally, three different weights variance between all components in a given scenario; covariance between traits of selection index and additive genetic values for traits of the breeding goal; and genetic (co)variance between traits in the breeding goal, respectively. Selection indices coefficients were calculated by b = P−1Gw, where w is the vector of relative economic weights expressed in monetary units per measurement units of the traits. Variances of the index (I) and of the H were calculated by The set up matrices G = (i)RIHσH, and the response to selection per generation (S) for each trait was calculated by:i is the selection intensity assumed to be 1.75, considering the selection of the 10% superior genotypes.Monetary overall genetic gain per generation was calculated by ΔSOC), weight of 100 seeds (W100S) and phorbol ester concentration (PEC) aiming to identify superior half-sib families under a Bayesian multi-trait model, using selection indices procedures.In this study, we evaluated 179 genotypes for the three important traits in jatropha breeding program: seed oil content  estimated the number of independent samples with information equivalent to that contained within the dependent sampling. Thus, it was observed that the length of the generated chain was adequate since the smallest ESS was 1991.Geweke convergence criterion indicates convergence for all dispersion parameters when generating 100,000 MCMC chains, 40,000 samples for burn-in and a sampling interval of 10, totaling 6,000 effective samples used for variance component estimate. Similar posterior mean, median and mode estimates were obtained for variance components, suggesting density with normal shape appearance. Effective sample size  . The genW100S presented the highest residual variance (lower certainty), possibly due to a scale effect, followed by SOC and PEC, respectively  for phenotypic and genotypic correlation, being the latter stronger than the former , accuracy of the index, and overall genetic gain among different scenarios and weights. The highest accuracy values were achieved under scenario 3  regardless of the assessed weights. A different trend was observed for the monetary overall genetic gain per generation (ΔG), which was higher when adopting w3  strategies. Additionally, it was possible to obtain simultaneous economically interesting response to selection in scenarios 1 and 2, considering different weighting strategies.Boxplot analysis was carried out to verify how phenotypic data were distributed among blocks. Previous phenotypic analyses are always important for the understanding of each trait, and it helps the researcher in choosing the best way of data evaluation.SOC) and phorbol ester concentration (PEC) presented low magnitudes. Different authors have shown the absence of genetic diversity between accessions [Phenotypic variance estimates for seed oil content . Rosado et al. [SOC, and consequently its low heritability. Thereby, selecting superior genotypes based on phenotypic values would not provide an expected overall genetic gain since approximately 83% of the phenotypic variance is not genetic. Thus, it is necessary the adoption of appropriate methodologies to accurately predict genetic effects. Therefore, based on these results and on previous researches, we suggest that the Bayesian multi-trait analysis is more appropriate than ANOVA to perform analysis and select superior genotypes for jatropha breeding, since the Bayesian model can capture minor genetic differences between families, while ANOVA cannot.Genetic and environment parameters estimated under the Bayesian multi-trait approach were similar to o et al. , while co et al.  used infSOC and W100S  would be the key to improve the accuracy of selection, to reduce the time per cycle, and to decrease the costs per cycle.Jatropha is a perennial plant which has been used to produce biofuel, and it has been reported that it is possible to increase its performance by selecting plants based on genetic information. Indeed, the use data of traditional jatropha breeding techniques, novel statistics methods, and molecular markers  is likely to increase efficiency of breeding programs by shortening the duration of the breeding cycle. Today, progeny testing phase could potentially be omitted, since breeders are able to carry out early selection for yet-to-be observed phenotypes at seedling stage. This early selection would then allow selected individuals being immediately propagated, if micropropagation protocols are available for the immediate establishment of optimized clonal trials with several years of anticipation, compared to the classical breeding scheme [In future researches, the use of too long . Based og scheme .IBS) information [Integration between genomic selection and multi-trait Bayesian approach can increase prediction accuracy. Therefore, selection indices will be more powerful and reliable. Moreover, the identification of chromosome regions that are related to genetic control of multiple traits (pleiotropic genes) would be a useful tool aiming to increase the overall genetic gain during selection. Additionally, the use of molecular data will provide the realized genetic diversity among families since the evaluation will be based on the identical by state (ormation .PEC) and to increase seed oil content (SOC).The Bayesian multi-traits analysis integrated with selection indices allowed obtaining selection gain for all traits simultaneously, i.e., it is possible to reduce Jatropha seeds toxicity caused by phorbol ester concentration Click here for additional data file.S2 Table(DOCX)Click here for additional data file.


However, this appears to be determined by the effect size of the SNP on the phenotype. This bivariate association method applied to longitudinal data improves genetic signal for quantitative traits when the effect size of the variant is moderate to large.Statistical genetic methods incorporating temporal variation allow for greater understanding of genetic architecture and consistency of biological variation influencing development of complex diseases. This study proposes a bivariate association method jointly testing association of two quantitative phenotypic measures from different time points. Measured genotype association was analyzed for single-nucleotide polymorphisms (SNPs) for systolic blood pressure (SBP) from the first and third visits using 200 simulated Genetic Analysis Workshop 18 (GAW18) replicates. Bivariate association, in which the effect of an SNP on the mean trait values of the two phenotypes is constrained to be equal for both measures and is included as a covariate in the analysis, was compared with a bivariate analysis in which the effect of an SNP was estimated separately for the two measures and univariate association analyses in 9 SNPs that explained greater than 0.001% SBP variance over all 200 GAW18 replicates.The SNP 3_48040283 was significantly associated with SBP in all 200 replicates with the constrained bivariate method providing increased signal over the unconstrained bivariate method. This method improved signal in all 9 SNPs with simulated effects on SBP for nominal significance ( Traditional analyses of genetic variants influencing complex diseases focus on phenotypes and covariate measurements from a single time point. However, the majority of human epidemiologic studies collect information from multiple measurements. This, coupled with the knowledge that many quantitative phenotypes correlated with complex disease change with age or environmental confounders, suggests that inclusion of a temporal component may allow for increased understanding of complex diseases. Given the nature of these longitudinal data, methods jointly using multiple time points when performing association may have increased statistical power over univariate association methods -6. HowevWe present a method for bivariate association using longitudinal data from the same phenotype in families using the Genetic Analysis Workshop 18 (GAW18) simulated single-nucleotide polymorphism (SNP) data for the phenotype systolic blood pressure (SBP) from visits 1 and 3. We have previously applied this method to the analysis of different phenotypic measures of heart rate (echo- and electrocardiograms) in American Indian participants of the Strong Heart Family Study  but wishThe GAW18 data set contains 959 individuals from 20 extended Mexican American pedigrees from the Type 2 Diabetes Consortium. Each of the 200 simulated data sets includes the following information for each individual for three time periods along with gender: age, SBP, diastolic blood pressure (DBP), hypertension status, blood pressure medication status, and smoking [p-valuebelow0.05. Measured genotype analysis was conducted for all available GAW18 polymorphic variants in which the number of minor alleles is added to the quantitative polygenic genetic model as a covariate to assess the effect of the SNP on the mean of the trait using the equationMaximum likelihood methods, taking into account relationships among family members, were used to determine association for the phenotypes SBP at visit 1 (SBP_1) and visit 3 (SBP_3) independently in a polygenic model available in the computer program Sequential Oligogenic Linkage Analysis Routines (SOLAR) . Covarias defines a variate for the ith SNP that takes the value, 0, 1, and 2 for the marker genotypes AA, Aa, and aa, respectively; α represents one-half the displacement between homozygous marker means; β represents fixed-effect regression coefficients for any measured covariates x; and g and e are random effects representing residual genetic effects and random environmental effects [α is different from 0 using a likelihood ratio test. Twice the difference in log-likelihoods is distributed as a where  effects . This moi and j, constraining the displacement in trait means (α) with each copy of the minor allele to be equal for both measures using the equationsWe also applied maximum likelihood methods accounting for familial relationships in bivariate association analyses. This bivariate method investigates two related phenotypes simultaneously, modeling genetic and environmental correlations between them . Our proi, and βj are fixed-effect regression coefficients and g and e are modeled through random effects with the bivariate model allowing for correlations between i gand j g(ρg) and between i eand j e(ρe). The difference between the log-likelihoods of a model in which the SNP effect is estimated versus one in which it is constrained to zero is then distributed as a where α, βp-values below For our bivariate analysis, we used the same covariates from the univariate analysis along with 9 variants that explained greater than 0.001 of SBP variance from the GAW18 answers.We then compared these results with univariate association models and a bivariate model in which the effect of genotype on the mean trait value of the two phenotypes was estimated separately, distributed as a g) for SBP over 200 GAW18 replicates between visits 1 and 3 was gvalue demonstrates that these two phenotypes are measures of the same genetic mechanism and therefore appropriate for our proposed bivariate association approach.The average genetic correlation , indicating no systematic inflation of p-values under the null (data not shown).When comparing the different methods, the bivariate method in which the effect of genotype on mean trait values of two phenotypes is constrained to be equal provided the most robust analysis, improving association for all 9 variants compared with the bivariate analysis in which these values were estimated separately and versus univariate analyses of exam 1 and 3 in cases where the The analysis of genetic variants using longitudinal data has the potential to be a valuable resource for determining biological and environmental factors affecting complex disease phenotypes over time. This type of analysis may provide increased power to detect rare genetic variants in complex diseases or to better understand when genetic components contribute to human development . In addiIn this paper, we present a bivariate approach to increase the genetic signal for a variant by constraining the effect of the SNP on the phenotype using a variance-component model. This model is predicated on the assumption that there is no gene- by-age interaction; however, the structure is general and is applicable to other issues in genetic epidemiology. As whole-genome data becomes more affordable for large-scale epidemiologic studies, an important consideration will be to maximize the ability to detect rare variants that have a large effect on complex disease. The easiest way to detect these rare variants will be through large pedigrees because they are amplified in families. However, the sample size of family studies is often small, making it difficult to determine association; therefore, methodologies that maximize the use of the genetic data and phenotypes from longitudinal studies may allow for an increased ability to identify genetic variants associated with complex disease. The model presented in this manuscript can be used as an early step in the analysis of longitudinal data and may lead to the development of more complex models.There are no competing interests.LA designed the overall study. PM conducted the analysis and drafted the manuscript. All authors read and accepted the final manuscript.


The power of the genome wide association studies starts to go down when the minor allele frequency (MAF) is below 0.05. Here, we proposed the use of Cohen’s h in detecting disease associated rare variants. The variance stabilizing effect based on the arcsine square root transformation of MAFs to generate Cohen’s h contributed to the statistical power for rare variants analysis. We re-analyzed published datasets, one microarray and one sequencing based, and used simulation to compare the performance of Cohen’s h with the risk difference (RD) and odds ratio (OR).The analysis showed that the type 1 error rate of Cohen’s h was as expected and Cohen’s h and RD were both less biased and had higher power than OR. The advantage of Cohen’s h was more obvious when MAF was less than 0.01.Cohen’s h can increase the power to find genetic association of rare variants and diseases, especially when MAF is less than 0.01.The online version of this article (doi:10.1186/1471-2164-15-875) contains supplementary material, which is available to authorized users. The prevailing hypothesis in genome-wide association studies (GWASs) of genetic diseases is “common disease, common variant” , 2. The Many strategies have been developed to analyze disease-associated rare variants, e.g. the collapsing method , 15, theThe aim of this study was to examine the distributions and properties of Cohen’s h , and comn1 and n2 allele counts, respectively. Let p1 = P(A|D) be the MAF of the case group and p1 - p2, and the estimator is p1 and p2, respectively. The definition for Cohen’s h is For biallelic SNPs with minor allele A, and major allele a, the case (group D) and control  Φ denotes the cumulative normal distribution and zα/21 -  was the 100(1-α/2)-th percentile. The power for H0 : OR = 1 vs. H1 : OR = c could be determined provided that the MAF in the control group, p2, and c were known according to the above formula where the MAF in the case group could be calculated as p1 = (OR * p2)/(OR * p2 - p2 + 1). In the case of Cohen’s h, the association test can be set as H0 : h = 0 vs. H1 : h = δ, and the power formula is c values for OR of 1.8, 2, and 3, and δ values of 0.08, 0.1, and 0.13 for Cohen’s h were considered for p2 < 0.05. We used a nominal significance level of 5 × 10-8 to calculate the statistical power of a GWAS.The derivations of the asymptotic distributions of estimators and their applications to the calculation of the p-values were described in Additional file -7 in shared controls and (4) allele frequency difference test based on two samples proportion test P value <5.7 × 10-7 between 58C and NBS. A total of 413,059 SNPs consisting of 52,220 (12.64%) rare SNPs (MAF < 0.05) and 360,839 (87.36%) common SNPs (MAF≧0.05) passed this filter.We obtained genotyping data of 1,988 CAD patients and 3,004 shared controls  and 1,500 from UK Blood Services sample (NBS)) from the WTCCC archive. The majority of subjects were of European descent. All individuals were genotyped using Affymetrix GeneChip 500 K arrays. Details of the study samples were described in the original report [To assess statistical properties of ES measures in terms of bias, MSE, and type I error rate, we performed simulations of a pseudo case–control study using the two shared controls. We randomly selected 1,480 subjects from pooled shared controls as pseudo-cases and kept the remaining 1,458 samples as pseudo-controls. For every replication, we calculated the ES estimate by each measure and tested the association for each SNP. The bias was calculated as the mean deviation of estimates from 0 per replication, and the MSE was the mean of the square of the bias. The fraction of times that the p-values of the association tests were less than 0.05 was the empirical type I error rate. These three indices for rare and common variants on each autosome were shown in Additional file http://code.google.com/p/simrare/). SimRare uses the forward-time simulation program to generate sequence data. Evolution parameters used were: (1) an additive multi-locus model with selection coefficient distribution by Kryukov [-8, and (3) the effective population sizes were 8,100, 8,100, 7,900, 900,000 with 500, 10, 370 generations, respectively. Fifty replications of fixed gene lengths including 250, 500, 1,000, 2,000, and 5,000 base pairs were simulated. The longer gene length produced a larger number of rare variants. The corresponding mean numbers of rare variants were 46.2, 96, 187.5, 377.7 and 944.3. For the setting of risk simulations, we assume a model with a disease prevalence rate of 1% and 2,000 cases and 2,000 controls. The power was assessed at OR = 0.5 for protective mutations and OR = 3 for detrimental mutations with an additive mode of inheritance over 1,000 replications. For CMC, WSS and VT, p-values were obtained empirically through 1,000 permutations for each replication . For single-marker testing methods such as RD, Cohen’s h and OR, the smallest p-value for testing the rare variant was recorded for each replication. We defined the unadjusted power for single marker testing methods as the proportion of replicates with minimum p-values < =0.05. Furthermore, we used Bonferroni correction and the Benjamin-Hochberg procedure [To better compare the performance of Cohen’s h with other methods including Combined Multivariate and Collapsing Method (CMC) , Weighte Kryukov , (2) therocedure  to adjus-7. The sequence based T1D dataset was retrieved from http://www.sciencemag.org/content/early/2009/03/05/science.1167728/rel-suppl/62c4d688b3668c3c/suppl/DC1. A total of 179 rare variants (defined as MAF < 3%) in 10 candidate genes were used in the current study [We compared the three measures described above on one microarray typed (CAD)  and one 70.05/41,59. The sTable Table α =10-8, the power of Cohen’s h remained higher than that of OR at α =5 × 10-8 for SNPs with MAF < 0.001 (data not shown).Generally, the statistical power is related to the magnitude of the ES, the sample size, and the variance of the estimator of ES. The variance of each of the ES measures except Cohen’s h is related to the MAF in cases and controls  was needed to achieve 80% statistical power to detect the effect at a genome-wide significance level of 5 × 10-8. However, the statistical power of Cohen’s h was approximately 85% with the same sample size. Additionally, the power ratio of the power based on Cohen’s h versus that of OR was consistently larger than 1  which were shown to be associated with T1D in the previous study were also identified by RD, Cohen’s h and OR. Another SNP, ss107794716 residing within the AIRE gene, was identified by both of RD and Cohen’s h but not OR . The association of this region and the AIRE gene with T1D was documented [The distributions of ES values for rare variants reflected the magnitude of rare variant-disease associations. We further explored the ES distributions of Cohen’s h and OR with regard to robustness and interpretation using the GWAS data. The two panels in Figure p2, and the OR. We found that the relationship between the MAF and Cohen’s h for rare SNPs was similar to that for common SNPs. As MAF increases, the magnitudes of Cohen’s h turned out to be greater at fixed OR. As such, we determined thresholds for Cohen’s h according to the average value of varying MAFs. For common SNPs, the values at 1.2 and 1.5 for OR are comparable to thresholds at 0.075 and 0.15 for Cohen’s h, respectively. As for rare SNPs, Cohen’s h had thresholds 0.05 and 0.1 corresponding to mild and moderate effects of OR at 1.5 and 2. One can choose dynamic thresholds for Cohen’s h with varying MAFs; however, this approach is not practical in comparison to using the p value of the calculated h. Using the above criteria, we further subdivided all common SNPs into the mild, moderate, and larger effect categories  were more biased and exhibited greater MSE for rare variants than RD and Cohen’s h, as was reported , 24. In Second, we compared the empirical distributions of ORs and Cohen’s h for common and rare variants corresponding to the null hypothesis of WTCCC GWAS with ~2000 cases and 3000 controls. To the best of our knowledge, most studies used significant or susceptible SNPs from GWAS findings to examine the distributions of ORs for common and rare variants , 12, 25.Third, our finding also showed that Cohen’s h could uncover rare disease-associated variants missed by OR based analysis. The arcsine square root transformation stabilized Cohen’s h so its asymptotic variance did not depend on the allele frequency. Accordingly, its power to detect a genetic association was relatively robust at low MAF. The data presented here suggest that test based on Cohen’s h is an appropriate substitute for OR Table . The vasUsing simulated and publically available data, our results suggested that Cohen’s h, a difference-type measure based on the arcsine square root transformation of minor allele frequencies, was less biased and substantially more powerful than OR in detecting the association of rare variants and complex genetic diseases. Our method offers a useful option for researchers who wish to quantify rare variants associated with diseases.Additional information of sampling distributions of RD, Cohen’s h and OR.(PDF 246 KB)Additional file 1:Biases and MSEs for RD, Cohen’s h and log(OR) for 22 chromosomes.(PDF 116 KB)Additional file 2:Type I error rates for RD, Cohen’s h and log(OR) for 22 chromosomes.(PDF 91 KB)Additional file 3:Box-plot of effect sizes for rare SNPs based on two shared controls in WTCCC data. Panel A: RD; Panel B: Cohen’s h; Panel C: log(OR). (PDF 262 KB)Additional file 4:Box-plot of effect sizes for common SNPs based on two shared controls in WTCCC data. Panel A: RD; Panel B: Cohen’s h; Panel C: log(OR). (PDF 353 KB)Additional file 5:Proportions of mild, moderate, and large effect for common SNPs in CAD. Grey bar represents OR and Black bar denotes Cohen’s h. (PDF 254 KB)Additional file 6:Proportions of mild, moderate, and large effect for rare SNPs in CAD. Grey bar represents OR and Black bar denotes Cohen’s h. (PDF 250 KB)Additional file 7: