Genome-wide association studies revealed single nucleotide polymorphisms (SNPs) on chromosome 5D significantly associated with flour yield, Alveograph P (dough tenacity), and Alveograph W (dough strength). Additionally, SNPs on chromosome 1D were associated with Alveograph P and W, SNPs on chromosome 1B were associated with Alveograph P, and SNPs on chromosome 4A were associated with Alveograph L (dough extensibility). Predictive abilities based on genomic best linear unbiased prediction (GBLUP) models ranged from 0.50 for flour yield to 0.79 for Alveograph W based on a leave-one-out cross-validation strategy. Predictive abilities were negatively affected by smaller training set sizes, lower genetic relationship between lines in training and validation sets, and by genotype–environment (G×E) interactions. Bayesian Power Lasso models and genomic feature models resulted in similar or slightly improved predictions compared to GBLUP models. SNPs with the largest effects can be used for screening large numbers of lines in early generations in breeding programs to select lines that potentially have good quality traits. In later generations, genomic predictions might be used for a more accurate selection of high quality wheat lines.Use of genetic markers and genomic prediction might improve genetic gain for quality traits in wheat breeding programs. Here, flour yield and Alveograph quality traits were inspected in 635 F Glu-A1, Glu-B1, and Glu-D1 and the low molecular weight glutenins (LMWGs) Glu-A3, Glu-B3, and Glu-D3 [Hardness locus on chromosome 5D, consisting of the genes Pina-D1, Pinb-D1, and Gsp-1 [Baking quality of wheat is a complex trait controlled by many genes with minor effects and few genes with larger effects ,2. The ad Glu-D3 . Millingnd Gsp-1 .Breeding for improved wheat quality is challenging, because phenotyping of most quality traits requires laborious analyses of relatively large amounts of grain using expensive equipment. Baking tests can be used for evaluating the quality of wheat lines by determining bread loaf volume and texture. However, breeding programs typically do not have the resources to perform baking tests with large numbers of lines . AnotherThose in Denmark are allowed to use more nitrogen for the cultivation of wheat for bread production if certain criteria are fulfilled. The cultivar must be on a list that has been approved by The Danish Agricultural Agency. For a cultivar to be approved, it must have a bread volume and a Zeleny sedimentation value of, at minimum, 90% of the average of the cultivars that have already been approved, and it must not have sticky dough. In addition, the grain used for bread production should, as a minimum, have a test weight of 78 kg/hL, a falling number of 275 s, and a protein content of 11.5% ,22. TherThe use of DNA markers to predict quality traits can reduce costs and enable higher selection intensities compared to having to do the phenotypic measurements. Thereby, higher numbers of wheat lines might be tested in breeding programs. Marker assisted selection based on few DNA markers can be effective for traits that are controlled by few QTL with large effects . HoweverThe aims of the present study were to identify SNPs affecting the baking quality traits flour yield and Alveographs P, L, and W and to evaluate and compare genomic prediction models in order to facilitate implementation of genomic selection for baking quality traits in breeding programs.6 winter wheat lines from two breeding cycles in the Danish plant breeding company Nordic Seed A/S  were used in this study. The 321 lines of the first breeding cycle (set2014) were harvested in 2014, and the 314 lines of the second breeding cycle (set2015) were harvested in 2015. Six out of 96 crossing parents were used for both sets (years), while the remaining 90 crossing parents were used for one of the sets only. Each line was grown in an unreplicated 9.9 m2 plot at Lolland, Denmark, following standard Danish agricultural practices. Approximately 180 kg of nitrogen were applied per hectare during the growth season, and no irrigation was used.In total, 635 FPhenotyping was done at the Wheat Chemistry and Quality Laboratory at International Maize and Wheat Improvement Center (CIMMYT), Mexico. Grain samples were conditioned to 13.5% moisture content and then milled one time using a Brabender Quadrumat Jr. . Flour yield was measured as the percentage of refined flour obtained from each grain sample after the bran fraction was sieved away through a 75 µm mesh sieve. A Chopin Alveograph  was used to obtain the Alveograph traits P, L, and W  using a modified version of the American Association of Cereal Chemists (AACC) method 54-30A ,43. FlouDNA extraction was performed with a modified cetyl trimethylammonium bromide (CTAB) method  using ley is a vector of observed phenotypes, X and Z1 are design matrices, b is a vector of fixed effects (mean and year/set), iw is the vector of genotypes of the thi SNP coded as 1, 0, −1, ia is the additive genetic effect of the thi SNP, u is a vector of additive genetic effects of the lines , where G1 is a G-matrix (genomic relationship matrix) and gσ2 is additive genetic variance), and e is a vector of random residual effects , where I is an identity matrix and eσ2 is the residual variance). Model effects and variance components were estimated by restricted maximum likelihood using the software package DMU [Genome-wide associations were studied using single marker regression. The following model was run for each of the 10,802 SNPs:kage DMU .ip is the MAF of thi marker, Z2 = M − P, M is a matrix with the marker alleles coded as 1, 0, -1, and P is a matrix where the thi column contains the MAF of SNP i calculated as 2(ip – 0.5). Missing genotypes were set to 0 in matrix 2Z.For each chromosome, a G-matrix was calculated based only on the SNPs mapped to the remaining chromosomes and then used to correct for structure when analyzing the SNPs mapped to the excluded chromosome. This was done so that the SNP effect was not included twice in the model. G-matrices were calculated using the first method proposed by Van Raden :(2)G=Z2ZIF, were calculated for each trait by dividing the observed median value of the chi-squared statistic for the SNPs with the expected median value [IF was used to correct the p-values for inflation by dividing the chi-squared statistic with λIF and then re-calculating the p-values. The significance threshold was set using a Bonferroni correction: 5% divided by number of SNPs .Genomic inflation factors, λan value . The infChinese Spring, IWGSC RefSeq v1.0 [DNA sequences surrounding the significantly associated SNPs were blasted against the annotated reference genome of the bread wheat variety Seq v1.0 , using tSeq v1.0 .y is a vector of observed phenotypes, b is a vector of the mean + year/set effect with design matrix X, Z3 is a matrix of the alleles of the SNPs coded as 0, 1, 2, u is a vector of additive genetic SNP effects, and e is a vector of residual effects. The prior distribution of SNP effects was specified as an exponential power distribution [m is the number of markers, and β is shape parameter to control the sparsity, which affects the shrinkage of the SNP effects. Setting β to 1 makes the model equivalent to a standard Bayesian Lasso model. If β is set to less than 1, the difference between large and small marker effects can be increased [β of 0.2, 0.4, 0.8, and 1.0 were run, and the Deviance Information Criterion was used to determine the optimal β for each trait [RP,λ were assigned flat prior distributions. Model parameters were estimated using Markov Chain Monte Carlo with a length of 100,000 with 30,000 cycles as burn-in. The tool pbayz supplied with Bayz was used to compute posterior means, and the R package CODA was used to check for convergence to the posterior distribution [A Bayesian Power Lasso model where all SNPs were fitted simultaneously was also used for genome-wide association analyses in the Bayz software :y = Xb ribution :(4)p(u)=ncreased . Models ch trait . Residuaribution .y is a vector of observed phenotypes, X and Z4 are design matrices, b is a vector of fixed effect (mean and year/set), u is a vector of additive genetic effects (u ~ N(0 G2G2 is a G-matrix computed as above (2) using all SNPs, e is a vector of random residual effects ).Genomic predictions based on all 10,802 SNPs were conducted using the Bayesian Power Lasso model (3) and using a GBLUP model:2G)d, Model effects and variance components for the GBLUP and Bayesian Power Lasso models were estimated by DMU and Bayz packages, respectively. For the GBLUP models, the narrow-sense genomic heritability corresponding to records of single plots was calculated as:The following cross-validations (CVs) were used to study the effectiveness of possible strategies for implementing genomic selection in breeding programs:Leave-one-out (LOO): The GEBV of each line was predicted from the rest of the lines. The training set used in the LOO strategy was as large as possible (634 lines), and the genetic relationship between lines in the training and validation set was higher compared to the other CV strategies.Leave-family-out (LFO): The GEBVs of lines in each half-sib family were predicted from lines of the remaining families. The average size of the half-sib families was 46 lines. Using this strategy, the effect of the genetic relationship between the lines in training and validation sets was studied.Leave-set-out (LSO): The GEBVs of lines in each set were predicted from lines from the other set. The training set sizes were 314 or 321 lines. The LSO CV strategy was used for studying the predictive ability when GEBVs of lines from one breeding cycle were predicted from lines from another breeding cycle.k-fold: The lines were randomly divided into k folds  of equal size. The GEBVs of lines in each fold were predicted from lines in the other folds. The training set sizes were approximately 318 lines for the 2-fold, 508 lines for the 5-fold, and 572 lines for the 10-fold. Approximately half of the lines in the training sets were from set2014 and half from set2015. The k-fold CV strategy was used for studying the effect of the training set size.Furthermore, the effect of the training set size was studied by selecting from 10% to 90% of the 635 lines as a training set for genomic predictions using LOO CV. The lines were randomly selected, and selection and predictions were repeated 100 times for each 10% interval.Correlations between observed phenotypes corrected for fixed effects and GEBVs were calculated to determine predictive abilities of the models and were compared with the maximum correlation (the square root of the narrow-sense genomic heritability). Biases of the genomic predictions were calculated as the deviation from the expectation of the slope (1.0) of the regression line of the corrected phenotypes on the GEBVs.p-value in the GWAS. The most significant SNPs were used for one G-matrix, and the remaining SNPs were used for the other. The following thresholds for number of SNPs to include in the group of most significant were tested: 5, 10, 50, 100, 500, 1000, 3000, 5000, 7000, 10,000, and all 10,802 SNPs. The following model was used for the genomic predictions:y is a vector of observed phenotypes, X, Z5, and Z6 are design matrices, b is a vector of fixed effect (mean and year/set), s and n are vectors of additive genetic effects  using significant (sG) or nonsignificant (nG) SNPs, e is a vector of random residual effects .Genomic feature models with two G-matrices were tested in order to possibly utilize the most significant SNPs better ,54. The 6 winter wheat lines from two different breeding cycles (set2014 and set2015) were phenotyped for the quality traits flour yield and Alveos P, L, and W  interactions ,37,38. TAdvanced breeding material was used in the present study. The breeding program has, until now, focused more on increasing yield rather than improving baking quality due to restrictions in application of nitrogen fertilization to the fields in Denmark, which have made it challenging to grow high quality bread wheat lines. Nevertheless, variation was observed for the quality traits, indicating that both high and low quality wheat lines were used as crossing parents for the studied lines, and that genetic variation was maintained throughout the breeding program , Table 2Pina-D1 and Pinb-D1 have a large effect on grain hardness. These genes are located on chromosome 5D and can affect several quality traits [Pinb-D1 alleles with a positive effect on wheat quality were identified [QTL for wheat quality traits were identified across the genome ,2,17. Hoy traits ,57. Seveentified ,59. Howeentified , thus adGlu-D1 is located on chromosome 1D and has a large influence on wheat baking quality [Glu-B1 and Glu-B3, which are located on chromosome 1B, can affect quality. No SNPs on chromosome 1A were significantly associated with the Alveograph traits. The loci Glu-A1 and Glu-A3 are also known to affect wheat quality traits [Glu loci [Glu- and Pin loci in the breeding material could be useful for more accurate estimation of their effects and consequently more accurate predictions of the baking quality traits [For Alveo P and Alveo W, significant SNPs were also identified on chromosome 1D. The HMWG loci  quality . Similary traits . Thus, tGlu loci . Therefoy traits ,38,58.The GWAS indicated that only few QTL with large or intermediate effects controlled the quality traits. The identified QTL only explained a relatively small proportion of the total genetic variance. This indicates that the traits were also controlled by many QTL with small effects. Identification of such minor QTL is challenging, especially if they have a low MAF or if they are located near major QTL. Lines with the positive alleles of the four largest QTL for Alveo W had considerably higher dough strength than lines with negative alleles of any of the QTL . HoweverSince only a relatively small proportion of the genetic variance could be explained by the identified QTL, genomic predictions based on a large number of genome-wide markers could be useful. The different CV strategies showed that the predictive abilities were affected by size of the training set, by the genetic relationship between lines in training and validation sets, and by the G×E interactions . The LSOThe predictive abilities of the Bayesian Power Lasso models were slightly higher compared to the GBLUP models for flour yield, Alveo P, and Alveo W . In the Glu-1 loci as fixed effects resulted in improved accuracies. For each trait, Glu-1 loci were included if the locus explained more than 5% genetic variance [Other studies of genomic selection for wheat quality traits using breeding material have reported predictive abilities in similar ranges as in the present study ,37,64. Tvariance .In the present study, an alternative approach using one G-matrix computed from the most significant SNPs and another G-matrix computed from the remaining SNPs could slightly improve predictive abilities . HoweverImplementation of genetic markers and genomic predictions in breeding programs could likely lead to increased genetic gains for the wheat quality traits. Resources needed for phenotyping could be reduced, and the selection intensity could be increased. The identified SNPs with large effects might be used for screening large numbers of lines early in the breeding program and selecting lines that potentially have good quality traits. Genomic predictions could be used for a more accurate selection of lines with good quality in later generations.Pina-D1 or the Pinb-D1 on chromosome 5D and the Glu-D1 loci on chromosome 1D. Furthermore, SNPs associated with Alveo W were identified on chromosome 1B, and SNPs associated with Alveo L were identified on chromosome 4A. Additive genetic variance explained by a single SNP was up to 13.3% (SNP on 5D for flour yield). The identified SNPs can be used in early generations of breeding programs to screen large numbers of lines. In later generations, it would be advantageous to use a large number of SNPs to ensure accurate prediction of breeding values. Predictive abilities of GBLUP models were 0.50 for flour yield, 0.75 for Alveo P, 0.79 for Alveo W, and 0.64 for Alveo L based on the LOO CV. Predictive abilities were lower when using smaller training sets but were still moderate when using only 10% of the 635 lines as the training set. Furthermore, predictive abilities were significantly lower when using LSO and LFO CV strategies because of reduced genetic relationship between lines in training and validation sets and because of G×E interactions. Predictive abilities were similar or slightly higher based on Bayesian Power Lasso and genomic feature models. Thus, GBLUP models could be used for genomic prediction of wheat quality traits with moderate to high predictive ability. Other models might give slightly higher predictive abilities for traits where major QTL are present in the breeding material.SNPs significantly associated with flour yield, Alveo P, and Alveo W were identified on chromosome 5D. For Alveos P and W, associated SNPs were also identified on chromosome 1D. Likely candidate genes could be the


The domesticated yak is among the most important livestock species on the Qinghai-Tibet Plateau. Breeders have the task of developing varieties that provide growth performance and disease resistance. Traditional breeding processes rely on complete family pedigree information and large numbers of data records. However, there are inevitably records that are missing, including incomplete pedigrees and long-term data tracking, resulting in prolonged breeding cycles, reduced breeding efficiency, and the lack of economic benefit. Genome selection (GS), also known as whole genomic selection (WGS), can significantly reduce the selection cycle of quantitative traits and accelerate genetic progression while displaying appropriate prediction accuracy (PA). It combines a reference population and single nucleotide polymorphism (SNP) loci rather than pedigrees to estimate the effect of all SNPs. Then breeding values of target traits are predicted. The key for GS is genomic prediction (GP) and an assessment of PA.The aim of this study was to explore the possibility of applying GP to important economic traits in the domesticated yak, thus providing theoretical support for its molecular breeding. A reference population was constructed consisting of 354 polled yaks, measuring four growth traits and eight hematological traits related to resistance to disease (involved in immune response and phagocytosis). The Illumina bovine HD 770k chip was used to obtain SNP information of all the individuals. With these genotypes and phenotypes, GBLUP, Bayes B and Bayes Cπ methods were used to predict genomic estimated breeding values (GEBV) and assess prediction capability. The correlation coefficient of the association of GEBV with estimated breeding value (EBV) was used as PA for each trait. The prediction accuracy varied from 0.043 to 0.281 for different traits. Each trait displayed similar PAs when using the three methods. Lymphocyte counts (LYM) exhibited the highest predictive accuracy (0.319) during all GP, while chest girth (CG) provided the lowest predictive accuracy (0.043). Our results showed moderate PA in most traits such as body length (0.212) and hematocrit (0.23). Those traits with lower PA could be improved by using SNP chips designed specifically for yak, a better optimized reference group structure, and more efficient statistical algorithms and tools. The polled yak is a newly cultivated breed that provides meat, milk, and other products to local people on the Qinghai-Tibet Plateau . CompareThe majority of important economic traits of yaks are affected by multiple genes . ConventIn recent years, with the development of molecular genetics, molecular markers have been defined for marker-assisted selection (MAS) in the breeding of cattle to improve the accuracy of selection . HoweverGenomic selection has been utilized on a large scale in major economic animals such as dairy cattle , pig 1111, sheepThe relationship between relevant blood traits and the resistance of yak to disease has been discussed in earlier studies and therefore will not be repeated here. Production performance and hematological traits play vital roles in the process of intensive farming of the domesticated yak . HoweverIn this study, by selecting a reference population and obtaining SNP chip genotyping, the genomic prediction of a yak growth performance index and blood biochemical index was conducted to verify the application of GS in the yak population and to explore related optimization methods.This study was approved by the Chinese Academy of Agricultural Sciences Laboratory Animal Ethics Review with accession number CAAS 2017-115. All procedures were in compliance with the guidelines for the care and use of experimental animals. The experiment station, Qinghai Datong Breeding Farm is located in Datong County, Xining City, Qinghai Province, China , with an average elevation of 3450 m. Datong County has a plateau continental climate and an average annual temperature of 4.9 °C.The animal population used in this study comprised of 354 polled yaks selected from the Datong breeding farm in Qinghai Province, China. They were all healthy female individuals born between March and May 2017. These yaks were scattered across three breeding farms and were grazed naturally.The phenotypic traits of the 18-month-old yak reference population were obtained in October 2018, including direct measurement of performance data, withers height, body length, body weight, chest girth  and eight hematological traits obtained from non-anticoagulated blood, namely, red blood cell count, hemoglobin, hematocrit, platelet count, lymphocyte count, medium white blood cell count, distribution of platelet width, and mean platelet volume , as described in a previous study . Twelve −6 were removed. Those individuals with an individual detection rate <0.1 and Mendelian errors >5% were also removed. Only SNPs and individual yaks that satisfied the quality control requirements described above were selected for subsequent research and analysis.Genomic DNA was extracted and genome-wide single nucleotide polymorphism (SNP) loci scanned using an Illumina Bovine HD 770K chip, as described in detail in a previous study . PLINK sMethods of calculation of genome prediction are divided into two categories. One is the method of directly estimating breeding value, based on the genetic relationship matrix (G matrix) that predicts genomic breeding value . The othy, X, b, Z, g, and e are the phenotype vector, matrix relating the fixed effects to each animal, fixed effects vector, correlation matrix of random additive genetic effects, random additive genetic effects vector , and the residual vector, respectively. Prediction of GEBVs and the assessment of accuracy of GBLUP were conducted using the GAPIT function set [www.r-project.org) [The technique used for directly estimating genomic breeding value is the genomic best linear unbiased prediction (GBLUP) method, based on the best linear unbiased prediction (BLUP) method . Genome-tion set  in R proect.org) .y is a phenotypic vector, X is a fixed-effect correlation matrix, b is a fixed effect vector, m is the total number of SNP sites, and e is the random residual effect vector. Z is a haplotype correlation matrix of n × m, where n is the number of individuals. In fact, the number of quantitative trait loci (QTLs) affecting the target trait is also limited, consistent with the theoretical hypothesis of the Bayes B method [In a previous study, a number of SNP loci associated with eight hematological traits were explored through GWAS . DifferiB method .Bayes Cπ is an improvement on the Bayes B method. In a Bayes A-based model, the mean of the inverse chi-square distribution can be determined by information such as additive genetic variance of the trait, thereby estimating the ratio π of the non-effector site . SimilarThe π in the Bayes Cπ model is not a constant, but assumes that the prior distribution obeys a uniform distribution denoted as Uniform  and that its posterior distribution is a beta distribution ,30. In tIn this study, the mrMLM package (version 3.1)  available in R project software was used to evaluate genetic parameters, including the additive genetic effect, the error effect and the fixed effect . DiffereIn general, calculation of accuracy is required in order to evaluate the predictive capability in different models and different traits . In thisFive-fold cross validation was performed to assess the accuracy of GP in this study. All individuals were randomly divided into 5 groups on average, of which 4 were used as a training group to estimate parameters, and the other group used to test the group .From the filtering process described above, the following quality control (QC) results were obtained, as shown in After filtering, the 96,087 SNP loci and 354 individuals remaining were used for GS.All phenotype data were processed as described above, displaying a symmetric distribution, as detailed in By using the mrMLM package in the R project with exisiting data, all genetic parameters were estimated, as summarized in In this study, GBLUP, Bayes B, and Bayes Cπ were selected as methods to predict the GEBVs of 12 target traits with processed data, including phenotype and genotype data. The accuracy of prediction of GBLUP, Bayes B, and Bayes Cπ is listed in As can be seen from −6). In addition, 636,289 SNPs were removed due to the minor allele frequency that is less than 0.01 (<0.01) in the majority of all removed SNPs. Furthermore, all yaks had less than 10% missing genotype data so no one was removed. The fact that so many loci with a minor allele frequency of less than 0.01 were removed may be because of the use of bovine chips instead of a specific yak chip and that these SNP genotypes are rare in the entire population.In this study, GBLUP, Bayes B, and Bayes Cπ methods were used for GS and assessment of PA in a yak population. A bovine HD chip was used to scan the yak genome and all SNPs were cleaned through a defined process . As can When estimating the effect of an SNP, it is necessary to combine observed phenotypes and genotypes. However, various errors may occur in actual situations. Using probability theory, the greater the number of experiments performed, the more frequently these errors occur . TherefoThe premise of GS is that it predicts quantitative traits from multiple linkage disequilibria (LD) for each quantitative trait locus (QTL), which is influenced by the number of SNPs in a gene chip. That is to say, the greater the number of markers, the higher the accuracy. Calus et al. believe that the larger the rate of linkage, the greater the accuracy . That isFor simulation studies of different species, Bayes methods have been demonstrated to be better than GBLUP. The results of this study confirm this conclusion. Sun et al. analyzed the simulation data from the 14th QTL-MAS Workshop, the results indicating that the accuracy of Bayes Cπ was approximately 6% higher than that of GBLUP ,42. EdriThe present study was the first time GP has been applied to the domesticated yak population, which assessed prediction accuracies of 12 important traits using GBLUP, Bayes B, and Bayes Cπ. The three methods presented approximate prediction capability. Several traits such as BL, WH, and BW exhibited moderate prediction accuracy (>0.1), demonstrating that it is possible to apply GP/GS in yak breeding. Unfortunately, GP/GS demonstrates a tiny effect on CG and RBC, with low accuracy (<0.1).


Anopheles gambiae mosquitos are the main vectors of malaria, threatening around half of the world’s population. The bacterial symbiont Wolbachia can interfere with disease transmission by other important insect vectors, but until recently, it was thought to be absent from natural A. gambiae populations. Here, we critically analyze the genomic, metagenomic, PCR, imaging, and phenotypic data presented in support of the presence of natural Wolbachia infections in A. gambiae. We find that they are insufficient to diagnose Wolbachia infections and argue for the need of obtaining robust data confirming basic Wolbachia characteristics in this system. Determining the Wolbachia infection status of Anopheles is critical due to its potential to influence Anopheles population structure and Plasmodium transmission. Wolbachia  is an intraovarially transmitted symbiont of insects able to exert striking phenotypes, including reproductive manipulations and pathogen blocking. These phenotypes make Wolbachia a promising tool to combat mosquito-borne diseases. Although Wolbachia is present in the majority of terrestrial arthropods, including many disease vectors, it was considered absent from Anopheles gambiae mosquitos, the main vectors of malaria in sub-Saharan Africa. In 2014, Wolbachia sequences were detected in A. gambiae samples collected in Burkina Faso. Subsequently, similar evidence came from collections all over Africa, revealing a high Wolbachia 16S rRNA sequence diversity, low abundance, and a lack of congruence between host and symbiont phylogenies. Here, we reanalyze and discuss recent evidence on the presence of Wolbachia sequences in A. gambiae. We find that although detected at increasing frequencies, the unusual properties of these Wolbachia sequences render them insufficient to diagnose natural infections in A. gambiae. Future studies should focus on uncovering the origin of Wolbachia sequence variants in Anopheles and seeking sequence-independent evidence for this new symbiosis. Understanding the ecology of Anopheles mosquitos and their interactions with Wolbachia will be key in designing successful, integrative approaches to limit malaria spread. Although the prospect of using Wolbachia to fight malaria is intriguing, the newly discovered strains do not bring it closer to realization. Wolbachia is an obligate intracellular, intraovarially transmitted bacterium living in symbiosis with many invertebrates .tebrates . Depending males . One of ng males , has beeng males , 5. BidiWolbachia can also provide infected individuals with fitness benefits: nutrient provisioning  project . We used the data released in the course of phase 1 AR3, namely, Illumina sequences of 765 wild-caught mosquitos from eight African countries  Phylogenetic reconstruction of Anopheles species based on ITS2 alignment of previously published data and all ITS2 contigs present in the meta-assembly of all libraries from SAMEA3911293. Sequences recovered from this library are highlighted in blue. (B) Phylogenetic reconstruction of Anopheles based on mitochondrial COI. Sequences from the SAMEA3911293 meta-assembly are highlighted in blue. (C) Phylogeny of Wolbachia supergroup B based on concatenated core genome alignments of all strains with a (draft) genome in the NCBI database. Again, the strain isolated from SAMEA3911293 is highlighted in blue. Download FIG S1, PDF file, 0.04 MB.Phylogenetic assessment of Copyright © 2019 Chrostek and Gerth.2019Chrostek and GerthCreative Commons Attribution 4.0 International license.This content is distributed under the terms of the Wolbachia infections required improved diagnostics. This prompted Shaw et al. to modify the wSpec PCR protocol by including a nested pair of primers and increasing the number of cycles to a total of 72 , potentially amplifying the initial 16S rRNA template over 1021 times  genes, has also been challenging  assay . The robi et al. ) were nenopheles , 39. Ampllenging , 29–31, nging 29– or the unging 29–, 27. OveWolbachia symbiont of A. gambiae, despite several attempts at generating and extracting such data. One common feature of all of them is an extremely low titer, at the limit of detection of PCR-based methods. Even from the few data available, it is obvious that there is no single Wolbachia strain associated with Anopheles gambiae    40). In. InWolbaWolbachia DNA in A. gambiae samples may be explained not only by a stable Wolbachia-Anopheles symbiosis but also in several alternative ways. First, the signal may stem from Wolbachia DNA insertions into an insect chromosome , once amplified to high concentration in the lab, the contaminating templates may spread. This is especially true for extractions and PCR amplifications performed under field conditions and for labs that routinely amplify Wolbachia from other sources.Part of the PCR signals observed throughout the studies reporting natural Wolbachia infections in A. gambiae, together with similar reports suggesting Wolbachia infections in species previously considered uninfected, e.g., A. stephensi  reads being classified as Wolbachia (0.000063%)  alone is not sufficient to conclude that an intracellular, inherited symbiont is present in a sample.Importantly, contamination from any of the mentioned sources cannot be ruled out with the data currently available. The previously mentioned sequencing of two 000063%) . For a hxception –55. Contception –, such asmunities , 29–31).Wolbachia is a symbiont of Anopheles gambiae and assembly of complete genomes has not been achieved due to low sequence abundance, other hallmarks of symbiotic interactions between the taxa can be used to support this claim.While sequence data alone are insufficient to determine whether Wolbachia. The only published image of natural Wolbachia infections from A. gambiae is a combination of fluorescence in situ hybridization (FISH) and immunofluorescence. In this experiment, Wolbachia was detected with a combination of a Cy3-labeled probe, anti-Cy3 mouse antibody, and anti-mouse Alexa448 secondary antibody   and paternal wSpec sequence transmission. These experiments would help to confirm that A. gambiae is infected with an intracellular, transovarially transmitted symbiont and, together with the PCR evidence, diagnose a stable Wolbachia infection.Second, fspring) . HoweverWolbachia phenotypes similar to those observed in other insect hosts may have a huge impact on wild Anopheles populations and malaria transmission. Reproductive manipulations and fitness benefits may increase the proportion of biting females spreading the disease, while pathogen blocking may limit Plasmodium prevalence in the wild mosquito populations. Understanding Anopheles gambiae biology is crucial for the design of effective strategies aiming at limiting Plasmodium transmission.Wolbachia-based Plasmodium control strategies, similar to the ones used for dengue and Zika virus control, are also exciting prospects. However, they are not reliant on Wolbachia symbionts naturally associated with Anopheles. Insect populations may equally well be suppressed by the release of males carrying incompatible Wolbachia strains by bidirectional CI on an infected population or by unidirectional CI on an uninfected one. The same applies to Wolbachia-induced pathogen blocking. Existing initiatives to control dengue and Zika virus with Wolbachia-conferred antiviral protection use naturally uninfected Aedes aegypti mosquitos that were artificially transinfected with Wolbachia from a different insect species , it wasasmodium , 29. As asmodium –59 and h gambiae . Howeverdetected . ReliablWolbachia to fight malaria has been eagerly anticipated, naturally occurring Wolbachia strains in Anopheles were never an absolute requirement for this to be successful. Even now, their presence, phenotypes, and suitability for deployment in disease control remain to be confirmed. However, they should be studied, as understanding Anopheles gambiae biology and ecology, including its interactions with other micro- and macroscopic organisms, is crucial for designing effective malaria elimination programs.In summary, although using Wolbachia infections in Anopheles gambiae is currently limited to a small number of highly diverse, very low-titer DNA sequences detected in this important malaria vector. Further efforts toward characterization of the interaction between Wolbachia sequences and A. gambiae are required to establish that this is a true symbiotic association. Demonstrating the presence of intracellular bacterial cells and their intraovarian transmission are prerequisites to diagnose a symbiosis. Additionally, genomic data may shed light on the features of these Wolbachia and may reveal the origin of the sequences and the ecological interactions that caused their acquisition by A. gambiae mosquitos. Finally, ascertaining phenotypes associated with these Wolbachia sequence variants will improve our understanding of Anopheles gambiae biology, and as such inform future strategies aimed at limiting malaria spread and eventual disease eradication. Given that both Shaw et al. and Gomes et al. report the establishment of the wSpec-positive A. gambiae laboratory colonies (The evidence for natural colonies , 29, theWolbachia sequences were encountered multiple times by independent groups of researchers clearly indicates present or past, direct or indirect ecological interactions between Wolbachia and Anopheles gambiae across Africa. While in-depth investigations of these interactions will be interesting from a basic biology, evolutionary, ecological, and disease control perspective, current data indicate that the postulated natural Wolbachia infections in Anopheles will be of limited use for application in fighting malaria with Wolbachia.The fact that


G) or phenotypic (RFIP) partial regression coefficients. The posterior distribution of the FCR’s breeding values was derived from the posterior distribution of “fixed” environmental effects and additive genetic effects on ADFI and ADG.This study aimed at (1) deriving Bayesian methods to predict breeding values for ratio  or linear  traits; (2) estimating genetic parameters for average daily feed consumption (ADFI), average daily weight gain (ADG), lean meat percentage (LMP) along with the derived traits of RFI and FCR; and (3) deriving Bayesian estimates of direct and correlated responses to selection on RFI, FCR, ADG, ADFI, and LMP. Response to selection was defined as the difference in additive genetic mean of the selected top individuals, expected to be parents of the next generation, and the total population after integrating genetic trends out of the posterior distribution of selection responses. Inferences were based on marginal posterior distributions obtained from the Bayesian method for integration over unknown population parameters and “fixed” environmental effects and for appropriate handling of ratio traits. Terminal line pigs (n = 3724) were used for a multi-variate model for ADFI, ADG, and LMP. RFI was estimated from the conditional distribution of ADFI given ADG and LMP, using either genetic (RFIP, and RFIG, respectively. Selection against RFIG showed a direct response of − 0.16 kg/d and correlated responses of − 0.16 kg/kg for FCR and − 0.15 kg/d for ADFI, with no effect on other production traits. Selection against FCR resulted in a direct response of − 0.17 kg/kg and correlated responses of − 0.14 kg/d for RFIG, − 0.18 kg/d for ADFI, and 0.98% for LMP.Posterior means of heritability were 0.32, 0.26, 0.56, 0.20, and 0.15 for ADFI, ADG, LMP, RFIP resulted in unexpected responses in production traits.The Bayesian methodology developed here enables prediction of breeding values for FCR and RFI from a single multi-variate model. In addition, we derived posterior distributions of direct and correlated responses to selection. Genetic parameter estimates indicated a genetic basis for the studied traits and that genetic improvement through selection was possible. Direct selection against FCR or RFI In swine breeding programs, efficiency of nutrient use is a significant factor because of its economic and environmental importance. Classically, feed efficiency is defined as output over input, for instance, milk yield, or milk components yield over dry matter consumption in dairy cattle, or body weight gain over feed consumption in pigs. However, in swine breeding programs, feed conversion ratio (FCR) is primarily used, defined as average daily feed intake (ADFI) over average daily body weight gain (ADG).The distribution of ratio traits such as FCR depends on the joint distribution of two normally distributed variables. The distribution of a ratio trait is easily determined if the mean of each random variable and the correlation between them are equal to zero. However, complexity arises as the variables’ means and correlation deviate from zero , 2. The To circumvent the problems of ratio traits, residual feed intake (RFI) was proposed by Koch et al.  as a betBayesian methodology, as illustrated by Sorensen et al. , provideThe aims of this study were to (1) derive methods for the Bayesian prediction of breeding values for phenotypic and genetic RFI and for FCR, without invoking unrealistic distributional assumptions for FCR; (2) estimate genetic parameters for the production traits of growth, feed intake, and lean meat production, and for the derived traits of RFI and FCR; and (3) derive Bayesian estimates of direct and correlated responses to selection for feed efficiency, measured either as RFI or FCR, and for production traits.Animal care and handling were performed as part of a routine commercial breeding program. Animals were reared using standard procedures in a commercial Irish pig farm and therefore, no further approval of animal care and handling procedures was necessary. The dataset used for this study was collected as routine feed intake records from 2007 to 2014. Pigs  originated from Hermitage Genetics  and were selected on an index comprising feed conversion ratio, days to achieve 110 kg, and lean meat percentage (LMP). Animals went on trial at 52 kg  and daily feed intake records were collected until they reached 110 kg  of BW. During the test period, pigs were kept in mixed-sex pens of 12 pigs each, equipped with IVOG electronic feeders . Pig were fed ad libitum using a standard wheat and barley-based Irish finisher diet with 13.7 megajoules of digestible energy, 17% crude protein, and 0.97% standard ileal digestible lysine per kg of feed. The test period lasted a maximum of 8 weeks. Raw data contained records from each entry to the feeder during the test period. Feed intake errors in single visits to the feeding station were identified following the algorithm developed by Casey et al. [yADFI, yADG and yLMP are vectors of phenotypic records for ADFI, ADG, and LMP, respectively; vectors bADFI, bADG, and bLMP contain “fixed” effects of year-quarter, gender, and sow parity for ADFI, ADG and LMP, respectively; bADFI and bADG are “fixed” regressions for start body weight for ADFI and ADG, respectively; bLMP is the “fixed” regression for end body weight for LMP; aADFI, aADG, and aLMP, pADFI, pADG, and pLMP, eADFI, eADG, and eLMP are vectors of animal additive genetic, pen, and residual effects for ADFI, ADG, and LMP, respectively. The permanent environment effect of litter of origin had a small effect based on an initial likelihood ratio test and therefore was not included in the model. Matrices X are design matrices for year-quarter, gender, and parity effects; xs is a vector of start body weights for each animal and xe is a vector of end body weights. Matrices Z and S are the corresponding design matrices for additive genetic animal effects  and the permanent environmental effect of pen  for the three traits. Average BW was not included in the model because animals were tested over a fixed weight interval; therefore, all animals had the same average weight. A full Bayesian analysis was conducted and, therefore, priors were specified for all parameters. Prior distributions for all random vectors were multivariate normal distributions with a mean of zero, and R0 is a 3 × 3 matrix of residual (co)variances, A is the additive genetic relationship matrix, G0 is a 3 × 3 matrix of additive genetic (co)variances, and genetic values are ordered by individual; and K0 is a 3 × 3 matrix of pen (co)variances. The random effects of a, p, and e were considered independent of each other. The prior distributions for the covariance matrices G0, K0, and R0 were inverse Wishart distributions and priors for all dispersion and for all “fixed” location parameters were taken as flat priors.Tri-variate analysis was used for ADFI, ADG, and LMP traits using the following models:The Bayesian estimation method via Gibbs sampling was used to obtain posterior distributions for all parameters that were included in the trivariate models (1), (2), and (3), including the matrices of variances and covariances. The Gibbs sampler was run for 1.1 million rounds, with the first 100,000 rounds considered burn-in, and after the burn-in, every 250th sample was saved for posterior analysis. The RJMC module in the DMU software package by Madsen and Jensen  was usedA total of 4000 samples from the joint posterior distribution of all location and (co)variance parameters from the trivariate models (1)–(3) were saved for post-Gibbs analysis. The BOA package of Smith  in the Rsi be the vector of all model parameters in sample i from the marginal posterior distribution of s. Any feature or function of the distribution can be obtained using the ergodic theorem shown by Geyer [g(.) is an appropriate operator, μ is any function or feature of the marginal distribution of s, and m is the number of samples obtained. For more details on how to use this to estimate response in selection experiments, see Sorensen et al. [Let by Geyer  and Smitby Geyer :4\documen et al. . Then, wP) using phenotypic partial regression coefficients to ensure that phenotypic covariances are zero; and (2) genetic RFI (RFIG), conditioning breeding values of ADFI by breeding values for ADG and LMP using genetic partial regression coefficients, ensuring that the genetic covariances between RFIG and production traits (ADG and LMP) are zero. In other words, the breeding values for ADFI are corrected for ADG and LMP using either genetic or phenotypic regression coefficients. In this section, we present the derivation of variance parameters and breeding values for both RFI forms, which are both linear combinations of the traits included in the analysis. In each individual sample (s), derivation of both the distribution and the breeding values of the RFI traits are straightforward because they are conditional on the (co)variance components, and all elements are from multivariate normal distributions. These derivations are used on all samples obtained from the Gibbs sampler to obtain the posterior distributions of (co)variances and breeding values for the two RFI definitions. Across the posterior samples, the distribution is, however, not necessarily normal.RFI was defined as (1) phenotypic RFI  for ADG and LMP were computed from the genetic (co)variance matrix, while for RFIP the partial phenotypic regression coefficients (bP) were from the phenotypic (co)variance matrix. Within a posterior sample, both RFI definitions involved conditional normal distributions, resulting in the following straightforward derivations: let G0 the genetic (co)variance matrices of the traits involved, which are subdivided in:For RFIbP) and genetic (bG) regression coefficients was obtained as:Pp and Gp are 2 × 2 matrices of phenotypic and genetic (co)variance for the production traits of ADG and LMP from P0 and G0, respectively. Matrices Pp,ADFI and Gp,ADFI are the phenotypic and genetic covariances, respectively, of the production traits ADG and LMP with ADFI.Bayesian estimation of partial phenotypic (aADFI), conditional of breeding values for ADG (aADG) and LMP (aLMP), using either phenotypic (bP) or genetic (bG) partial regression coefficients. A sample from the posterior distribution of breeding values for phenotypic variance. As a result, the breeding value for FCR depends on “fixed” location parameters, since it depends on the mean of ADFI variance available for selection at a given time point is:mentclasspt{minimaThe Bayesian estimate of the superiority of a selected group is the difference between the mean of the breeding values in the selected group and the mean of the breeding values of all animals corrected for the genetic trend. This yields an expression of the superiority of the selected group in every sample from the posterior distribution, depending on the selection rule.j when selecting on trait j′ can be calculated as:j on animal i, conditional on the genetic trend; n is the total number of animals; and ns) when ordering breeding values for trait j′. If j′. Six traits were investigated in this study and thus, six scenarios were developed to compare direct and correlated responses to selection for feed efficiency and production traits. The number of individuals ranked for analysis was decided based on truncation selection of the top 5 to 30% of animals. Here, only the results of truncation selection of the top 10% are presented, since the results and conclusions were consistent across various truncation selection percentages.The mean of the selected group for trait Posterior means and standard deviations (PSD) of heritability and genetic variances for the two entclass1pt{minimaPosterior means (with PSD) of genetic and phenotypic correlations for the two The genetic (co)variance available for selection was obtained for all traits based on Eq. . The obtPosterior means of genetic trends of the traits of interest are presented in Fig. The posterior mean of the direct and correlated superiority of the selected groups under various selection scenarios are in Table In this study, a Bayesian method for estimating genetic parameters for y et al.  to derivIn this study, a Bayesian approach was used to derive a posterior distribution of all parameters of interest, which enables computation of the probabilities that the parameter lies between specified values. The Bayesian method integrates over all unknown model parameters, including “fixed” and random effects, and properly handles ratio traits that do not have standard distributions.cov = cov − bgvar(yp), which is equal to cov − cov(1 − hp2)/hp2), as also shown by Kennedy et al. [Residual feed intake is a partial measure of feed efficiency, for which the average components of feed efficiency related to production and maintenance are excluded, and which is obtained through the conditional distribution of feed intake to production traits and metabolic body weight. Many studies have used linear regression of the phenotype of feed intake onto phenotypes of the production traits, e.g., Mrode and Kennedy . Some sti et al.  and Shiri et al. . Some sti et al. . This aph et al. . The mety et al. . Phenotyy et al. . The nony et al. . To obtay et al. . Variatiy et al. , Shiraliy et al. , and theTraditionally, FCR is derived by dividing the phenotype of feed intake by BW gain. This definition ignores the fixed and environmental effects that influence the component traits of the ratio trait. The Bayesian analysis presented here considers the uncertainties in the fixed effects and avoids approximations due to unknown distributional properties of a ratio trait and its component traits.The current study shows substantial genetic variance in y et al.  because terature , 21.The percentage of genetic variance in ADFI that was explained by genetic i et al.  and Shiri et al.  reportedThe considerably lower posterior mean of heritability for genetic Posterior means of heritability and genetic variance for ADG and LMP obtained here were larger than those for Danish Duroc pigs that were reported in Shirali et al. . The larThe substantial deviation from 1 of the posterior mean of the genetic correlation between genetic and phenotypic n et al.  and in tn et al. . The posn et al.   in the breeding program. This disproportionate selection pressure on component traits can be explained by genetic correlations between ADFI, ADG, and LMP and their heritabilities. A large reduction in ADFI, which is the numerator of FCR, may be due to the heritability of ADFI being higher than that of ADG, in addition to a large positive posterior mean of the genetic correlation between these traits. The low posterior mean of the genetic correlation between FCR and ADG indicates a smaller change in ADG due to selection for FCR, while a large negative posterior mean of the genetic correlation between FCR and LMP explains the indirect genetic response from selection against FCR. The substantial reduction in ADFI through direct selection on FCR could also be due to a correlated response on LMP, since increased lean meat growth is one of the underlying biological reasons for improved FCR. Therefore, selection for FCR is not an efficient strategy because, first the improvement in this trait can be due to improvement in lean meat growth rather than improvement in efficiency of nutrient utilization per se; and second the relative improvements can change over generations as the means of the underlying trait change. Shirali et al.  reportedGunsett  reportedIn a selection index context, single-trait selection against genetic g et al.  showed ty et al.  showed tA Bayesian procedure for analysis of response to selection on linear versus ratio traits was developed and applied to feed efficiency in pigs. The Bayesian methodology allowed prediction of breeding values for ratio and linear definitions of feed efficiency from a multi-variate model for the traits measured. The Bayesian method allowed prediction of breeding values for FCR without the need for approximations. Posterior means of genetic parameters indicated that the traits were influenced by genetics and that genetic improvement through selection was possible. Direct selection against FCR or


Genetic studies of psychiatric disorders often deal with phenotypes that are not directly measurable. Instead, researchers rely on multivariate symptom data from questionnaires and surveys like the PTSD Symptom Scale (PSS) and Beck Depression Inventory (BDI) to indirectly assess a latent phenotype of interest. Researchers subsequently collapse such multivariate questionnaire data into a univariate outcome to represent a surrogate for the latent phenotype. However, when a causal variant is only associated with a subset of collapsed symptoms, the effect will be challenging to detect using the univariate outcome. We describe a more powerful strategy for genetic association testing in this situation that jointly analyzes the original multivariate symptom data collectively using a statistical framework that compares similarity in multivariate symptom-scale data from questionnaires to similarity in common genetic variants across a gene. We use simulated data to demonstrate this strategy provides substantially increased power over standard approaches that collapse questionnaire data into a single surrogate outcome. We also illustrate our approach using GWAS data from the Grady Trauma Project and identify genes associated with BDI not identified using standard univariate techniques. The approach is computationally efficient, scales to genome-wide studies, and is applicable to correlated symptom data of arbitrary dimension. However, even in studies involving thousands of subjects, identification of specific common trait-influencing polymorphisms remains a challenge. To discover new associations, much attention has been spent on improving genotyping and sequencing technologies to interrogate more genetic variation; however, comparatively less attention has been afforded to thorough characterization of the underlying psychiatric phenotypes that are considered for genetic analysis.Evidence indicates that common genetic variants should explain a sizeable role of the variation in many psychiatric disorders. For example, common variants are estimated to explain 40% of the heritability for bipolar disorder9. Meanwhile, in studies of depression, many studies attempt to measure the phenotype using multiple symptom measurements from the Beck Depression Inventory-II (BDI). The BDI is a 21-item questionnaire with each question developed to correspond to DSM-IV diagnostic criteria for major depressive disorder. The answers to each question are scored from 0 to 3, with higher scores indicating more severe depressive symptoms10.In genetic analyses of a psychiatric phenotype, we often envision our outcome of interest as a single, measurable entity. In practice, we are rarely able to measure the outcome of interest directly and instead attempt to capture the true, latent phenotype via several connected but discrete measurements. As an example, psychiatric genetic studies attempt to account for the heterogeneity of symptoms found in a single psychiatric disorder by measuring the symptoms from several angles via a questionnaire or exam. For example, in studies of post-traumatic stress disorder (PTSD), researchers often measure the outcome using the PTSD Symptom Scale (PSS), which is a 17-item questionnaire for assessing and diagnosing PTSD according to the DSM-IV. Each item corresponds to a PTSD symptom and is rated from 0 to 3, with higher scores indicating greater symptom frequency/intensity11. Nevertheless, practical use of such multivariate symptom data in genetic analysis is complicated by the fact that standard statistical techniques for genetic analysis are generally univariate and designed to handle a single outcome at a time. To improve analytical utility, many questionnaires like the BDI and PSS were designed so that the multivariate symptoms are collapsed into a univariate phenotype for analysis. The simplest and most common collapsing method is unweighted summation of each question’s score14 into a univariate cumulative score. The cumulative score can then be treated either as a continuous outcome, or cutoffs can be applied to indicate presence/absence of disease symptoms.Data captured by the PSS, BDI or other questionnaires can actually be considered a collection of interrelated multivariate phenotypes that, in the case of symptom scales, are usually ordinal in nature. The view of a mental disorder as a constellation of multiple correlated symptoms is aligned with the National Institute of Mental Health’s (NIMH) Research Domain Criteria (RDoC), which emphasize basic functional dimensions or mechanisms involved in psychopathology  rather than DSM or ICD diagnostic categoriesAn important issue with applying a univariate cumulative score in genetic analysis is that reducing multivariate information to univariate data nearly always comes at a cost. Carefully defining a phenotype is as vital in a GWAS as reliable genotyping; any association between gene and trait may be diluted by phenotypic heterogeneity. For example, if a gene were associated with a subset of the BDI questionnaire outcomes  but not other subsets , the magnitude of the overall effect size of the gene would be attenuated if the two subsets were combined into a univariate outcome measure.et al.17, the three primary assumptions that must be met are: (1) the correlation between all questions in the questionnaire must be explained by a single (latent) phenotype; (2) the genetic effect must be on the latent phenotype; (3) the genetic effect—acting through the latent phenotype—must have identical effects on all of the questions in the questionnaire. For applied psychiatric phenotypes, it is more plausible that the assumptions are violated than maintained, a perspective that is supported by NIMH’s focus on RDoC. Depressive symptoms identified by the BDI might come from multiple sources , violating the first assumption. The causal genetic effect might directly increase somatic symptoms of depression such as changes in appetite and sleep, but not impact mood, violating the second assumption. Alternatively, a variant might in fact affect each trait identified by every question, but have slightly different effect sizes on different questions. If any of these assumptions are not met, association analysis using the cumulative score will result in a substantial loss of power19.A few key assumptions must be met in order for a univariate cumulative score to sufficiently summarize multivariate ordinal data. As noted by van der Sluis 21. However, PCA-based strategies that consider only high-variance principal components were recently shown to be generally suboptimal22. As an alternative, van der Sluis et al.17 presented a multivariate gene-based association test by extended Simes procedure (MGAS) that combines the P-values obtained from standard, single-SNP association tests for each outcome to produce a single multivariate gene-based P-value. However, MGAS relies on permutations to establish significance, which make genome-wide analyses of psychiatric phenotypes cumbersome. Alternatively, Basu et al.23 introduced a rapid multivariate multiple linear regression method (RMMLR), which operates on a MANOVA-based platform. However, while RMMLR establishes significance analytically, it cannot incorporate the important ordinal outcomes commonly measured in questionnaires and surveys.A few alternatives have been presented to model the complex multivariate data captured within questionnaires. A popular type of approach is a data reduction method like principal component analysis (PCA), which relies on identifying a linear combination of the set of questionnaire responses that maximizes response variance across questions. Once the top few principal components are identified , association testing is performed between those top principal components and genotype28 method called the Gene Association with Multiple Traits (GAMuT) test29, to assess association between high-dimensional symptom data and multiple variants (common or rare) in a gene. The framework is designed to test whether pairwise similarity in questionnaire responses is independent of pairwise genotypic similarity in a region of interest. The framework allows for an arbitrary number of categorical questions within the questionnaire as well as an arbitrary number of genotypes, thereby permitting gene-based or pathway-based testing of genetic variants. The method allows for covariate adjustment and is a closed-form test that yields analytic P-values, thus scaling easily to genome-wide analysis. GAMuT is therefore well-suited to facilitate research that is directly aligned with RDoC’s goal of encouraging investigation of biological, cognitive-behavioral, and self-report data using multivariate methods11.To allow computationally-efficient and powerful genetic analysis of multivariate symptom data, we show in this paper that we can use a kernel distance-covariance (KDC)32. We finish with concluding remarks and discuss potential extensions to our approach.The remainder of this manuscript is organized as follows. We first provide a short overview of the GAMuT method and its features. We then present simulation work to demonstrate that the framework can be considerably more powerful than the standard univariate test based on a cumulative score derived from a questionnaire. We then illustrate the approach using a GWAS study of BDI scores collected as part of the Grady Trauma Project29 here and relegate the technical details of the procedure to the Supplementary Methods section online. For a sample of N unrelated subjects, GAMuT examines the relationship between a set of Q questions  and a set of V genetic variants within a gene or pathway of interest. GAMuT is motivated by the idea that, for a pair of individuals, increased genetic similarity at trait-influencing loci across a gene should lead to increased similarity of their questionnaire outcome data. Consequently, GAMuT constructs two different similarity matrices; one similarity matrix for the questionnaire outcomes and the other similarity matrix for the genetic variation within a gene. Each similarity matrix has N rows and N columns with individual elements of the matrix denoting the similarity (phenotypic or genetic) among different pairs of subjects. GAMuT creates a test statistic that evaluates whether the pairwise elements in the similarity matrix of questionnaire outcomes is independent of the pairwise elements in the genetic similarity matrix. The resulting test follows a known asymptotic distribution, which leads to easy and rapid calculation of P-values. GAMuT allows for questionnaire outcomes of arbitrary dimension and can further adjust for covariates.We provide a brief overview of the GAMuT methodsignal transducer and activator of transcription 3 (STAT3), a gene on chromosome 17q21.31, and leucine rich repeat and fibronectin type III domain containing 5 (LRFN5), a gene on chromosome 14q21.1 recently identified as possibly involved in major depressive disorder33 . We generated simulated genotypes for all SNPs identified in HapMap within these genes , but applied the testing approaches only to those SNPs that would be typed on standard genotyping arrays .We conducted simulations to verify that GAMuT properly preserves type-I error  and to assess power of GAMuT relative to standard association tests that treat questionnaire responses as a univariate outcome variable resulting from summing the responses into a continuous score. We briefly summarize the simulation design here and provide more comprehensive details in the Supplementary Methods section online. We considered sample sizes of either 1,000 or 2,500 independent subjects. We performed simulations based on SNPs and LD patterns located within 2 kb up- and down-stream from two genes: We simulated multivariate questionnaire data to mimic the BDI questionnaire results obtained from Grady Trauma Project participants. The BDI consists of 21 groups of statements that reflect various symptoms and attitudes associated with depression. Each group includes 4 statements, which correspond to a scale of 0 to 3 in terms of intensity. The BDI is scored by summing the ratings given to each of the 21 items, yielding a cumulative score ranging from 0–63. To mimic the BDI, we generated 21 ordinal responses using the observed distributions and correlations of these responses within the GTP BDI dataset. We show the correlation matrix among ordinal responses in Supplementary Fig. STAT3 and LRFN5, we applied GAMuT to 10,000 null simulated datasets to estimate empirical size. To investigate the performance of GAMuT under confounding and to assess whether the approach can successfully adjust for relevant covariates in this setting, we also tested empirical size by simulating questions under a confounding model where question responses were independent of genotype, but both questions and genotype were associated with a continuous covariate. For power models, we simulated data sets in which each of the SNPs within the particular gene was modeled as being causal  with effect size of the causal SNP on each question resulting in mean effect sizes with modest effect on the overall cumulative score. We varied the number of questions associated with the causal SNP, considering situations where 18/21, 12/21, and 6/21 questions were actually associated with the causal SNP.For both 34. Standard linear regression considers individual SNPs for analysis. KMR tests, on the other hand, jointly model multiple SNPs within a gene. KMR can be thought of as a specialized version of GAMuT that considers only one phenotype (the univariate cumulative sum of symptoms/questions) rather than the observed multivariate phenotypes. For KMR, we modeled genotypic similarity in a fashion analogous to GAMuT by using a weighted linear kernel with weights based on sample MAF. Thus, comparison of GAMuT to KMR helps highlight the benefit of considering a multivariate questionnaire phenotype over a traditional cumulative-based score for gene-based analysis.Using the simulated data, we evaluated GAMuT using either projection matrices or linear kernels to model phenotypic similarity and using weighted linear kernels to model genotypic similarity (with weights based on sample MAF). We compared GAMuT to two standard approaches that use the univariate cumulative questionnaire score for inference: standard linear regression and kernel machine regression (KMR)35. This study has been carried out according to protocols approved by the IRBs of Emory University School of Medicine and Grady Memorial Hospital. Participants in the GTP are served by the Grady Hospital in Atlanta, Georgia, and are predominantly urban, African American, and of low socioeconomic status. GTP staff approach subjects in the waiting rooms of Grady Primary Care, Obstetrics and Gynecology, and other clinics, obtaining their written informed consent to participate. In addition to collecting an Oragene salivary sample for DNA extraction, GTP staff conduct an extensive verbal interview, which includes demographic information, a history of stressful life events, and several psychological surveys, including the BDI.Data used in our analyses were collected as part of the Grady Trauma Project (GTP), which investigates the role of genetic risk factors for psychiatric disorders such as PTSD and depressionThe GTP initially genotyped participants on the Illumina HumanOmni1-Quad array to permit GWAS analyses. Applying standard GWAS quality control filters left 4,607 African-American subjects with good quality genotype data. Further removal of subjects who did not report at least one past trauma, subjects with missing BDI scores, or subjects with incomplete covariate data  yielded a final sample size of 3,520 subjects.38. For comparison, we also applied SNP-based linear regression and gene-based univariate KMR to the cumulative BDI score. For KMR, we applied the same genotype weighting schemes as used for the GAMuT analyses.For our sample, we used the support files provided by Illumina to identify 765,580 common genetic variants (MAF > 5%) that fell within 19,609 autosomal genes. We applied GAMuT to the BDI data using a linear kernel to measure pairwise phenotypic similarity in multivariate symptom scores. To measure genetic similarity, we used a linear genotype kernel within GAMuT and performed unweighted analyses as well as weighted analyses, with weights based on variants’ MAF or the variants’ estimated log odds ratios derived from external and independent GWAS studies of MDD, bipolar disorder, and schizophrenia that are available from the Psychiatric Genomics ConsortiumSTAT3. We also present empirical type-I error rates for the STAT3 gene at three nominal significance thresholds in the top half of Table LRFN5 likewise produced results indicating that GAMuT, KMR and linear regression all properly control for type-I error  were treated as causal in turn. Therefore, in situations where the causal SNP is not typed, we rely on correlation of the causal SNP with observed typed SNPs in the gene to gain statistical power. GAMuT offers considerably more power than the two competing univariate methods using cumulative scores for each of the three simulation models considered. For STAT3, when approximately half of the questions (12/21) are associated with the causal SNP, both KMR and linear regression observe less than 30% power to detect all 27 causal SNPs; by comparison, GAMuT using a projection matrix to model phenotypic similarity maintains power greater than 80% for 26 of the 27 causal SNPs, while GAMuT using a linear kernel for modeling phenotypic similarity maintains power greater than 50% for 7 of the causal SNPs. When only six questions are associated with the causal SNP, the univariate methods using cumulative scores show nearly zero power for detecting effects across all SNPs, whereas GAMuT employing a projection matrix maintains power greater than 60% for 25 of the 27 causal SNPs.Figures LRFN5, when 12 of 21 questions are associated with the causal SNP, both KMR and linear regression show less than 20% power for detecting all 127 causal SNPs; whereas GAMuT employing a projection matrix observes greater than 80% power to detect 55 of the causal SNPs and greater than 50% power to detect 96 causal SNPs. For the LRFN5 simulations, when only 6 of the 21 questions have an association with the causal SNP, the univariate methods have almost zero power for detecting all 127 causal SNPs, while GAMuT with a projection matrix maintains greater than 50% power for detecting 57 of the causal SNPs.Similarly, for 41. Regardless, our power results demonstrate the benefits of modeling the questionnaire data in a multivariate framework like that employed by GAMuT rather than using a traditional cumulative score.We observe a slight drop in power using GAMuT when nearly all of the questions are associated with the causal variant  on the cumulative BDI score.−6). Thus, the study-wise significance threshold differed depending on the particular genotype weights used, ranging from a threshold of 0.05/16,716 = 2.99 × 10−6 for PGC MDD weights to 0.05/19,609 = 2.55 × 10−6 for MAF-based weights and no weights. For all GAMuT and KMR analyses we considered P-values less than P < 1 × 10−4 as suggestive. For SNP-based linear regression, we tested 775,255 SNPs across the genome. While we could apply the standard GWAS significance threshold of 5 × 10−8, we note that this threshold is more conservative than a Bonferroni correction based on the number of SNPs tested. Thus, for linear regression, we instead used a study-wise significance threshold of 0.05/775,255 = 6.45 × 10−8, and we considered P-values less than P < 1 × 10−6 as suggestive.Since GAMuT and KMR analyze genes whereas linear regression analyzes SNPs, the multiple-testing adjusted significance thresholds differ between the former tests and the latter test. For each GAMuT and KMR analysis, we set a stringent study-wise significance threshold corresponding to a Bonferroni correction based on the number of genes tested , when using genotype weights based on estimated log odds ratios from the PGC GWAS for schizophrenia. We present QQ and Manhattan plots for this particular analysis in the first column of Fig. ZHX2 was also found to be highly suggestively associated with BDI when employing genotype weights based on the PGC GWAS of MDD (P = 8.59 × 10−6). Previous research suggests a possible link between ZHX2 and autism spectrum disorder42. In comparison with the GAMuT analyses, KMR of cumulative BDI did not identify ZHX2 as having even suggestive association , it is imperative to employ powerful statistical tests that maximize the possibility of novel genetic discoveries. Here, we have shown that multivariate methods like GAMuT are substantially more powerful for gene mapping of multivariate symptom data than standard methods that typically summarize such symptoms into a single univariate cumulative score for analysis. Methods like GAMuT that jointly model individual questionnaire outcomes are robust to phenotypic heterogeneity, in which a genetic risk factor only affects a subcategory within the questionnaire. In standard cumulative approaches, including KMR and linear regression, phenotypic heterogeneity can dilute the association between gene and trait, making the association extremely difficult to detect. While we focused here on gene-based studies of common variants, we note that our findings are generalizable to studies of rare genetic variation as well as studies of methylation patterns throughout the genome.ZHX2 (P = 2.73 × 10−6), which previous research suggests might be associated with autism spectrum disorder42. In comparison, univariate KMR and linear regression did not identify ZHX2 or SNPs within it to be associated with BDI, at even suggestive levels. This demonstrates through use of real-world data the capacity for multivariate methods like GAMuT to detect genotype-phenotype associations that would be missed using standard cumulative univariate approaches.We applied GAMuT to the GTP dataset to test for associations between the BDI questionnaire and up to 19,609 genes. After controlling for important covariates, GAMuT found a strong association between BDI and P-values based on Davies’ exact method, thereby improving computational efficiency and permitting application of the approach on a genome-wide scale. Like the popular KMR framework for univariate analysis, our approach allows for inclusion of prior information, such as biological plausibility of the SNPs under study. We provide R43 software implementing the approach on our website (see Web Resources). Computation run times for GAMuT are primarily dependent on sample size. Using an R script running single-threaded on a 1.7 GHz Intel Core i7 CPU processor, the time required for GAMuT to analyze 10 phenotypes for 1,000, 5,000, and 10,000 subjects is 0.52 seconds/gene, 13.2 seconds/gene, and 68.6 seconds/gene. Thus, genome-wide implementation is feasible particularly when high-performance cluster services are available.GAMuT derives analytic https://github.com/epstein-software.Epstein Software: http://www.omim.org.OMIM: Supplementary Information


In biological processes, it is common that a single gene controls two or more traits, leading to a high genetically correlation between many traits in human beings and livestock. Genome-wide association study (GWAS) is a popular method for mapping causal genes or regions related to studied traits. Taking the advantage of genetically correlation among traits, a combined analysis of two or more traits can improve the power of detection in GWAS analysis. In this study, we prove the improvement of multiple-traits GWAS through theoretical derivation, simulated dataset and real dataset, respectively. In addition, using this approach, we successfully identified a candidate gene for presoma muscle development in cattle that were not be found in the average association analysis. In summary, we conclude that multiple-trait GWAS is an effective method to explore genetic factors of traits, which have high correlations.MCHR2, which was associated with presoma muscle development in cattle. In summary, PCA-based multiple-trait GWAS is an efficient model for exploring pleiotropic QTNs in quantitative traits.Principal component analysis (PCA) is a potential approach that can be applied in multiple-trait genome-wide association studies (GWAS) to explore pleiotropy, as well as increase the power of quantitative trait loci (QTL) detection. In this study, the relationship of test single nucleotide polymorphisms (SNPs) was determined between single-trait GWAS and PCA-based GWAS. We found that the estimated pleiotropic quantitative trait nucleotides (QTNs)  Disease and quantitative traits usually follow a polygenic model , in whicnp × np in size , with a time complexity of O(n3p3·t). Some researchers [A plausible approach for exploring pleiotropy is the multiple-trait GWAS model in comparison with single trait GWAS, which has been shown to be an effective method to detect shared QTL . Althougearchers ,10,11 haearchers ,13. PCA-earchers , as wellearchers . Compareearchers . HoweverIn livestock breeding, fine mapping of pleiotropic QTL for objective traits, such as milk yield, milk fat yield, and milk protein yield in dairy cattle ,18, as wIn this study, we considered two types of pleiotropy, namely a single causal variant model and a colocalizing effect model. Specifically, the colocalizing effect model is defined as different causal variants that affect distinguishing phenotypes with high linkage disequilibrium (LD), resulting in variants displaying signals in association with different traits. We first theoretically describe the relationship between a PCA-based multiple-trait GWAS model and single-trait model for pleiotropic QTL mapping. Next, we demonstrate a powerful PCA-based model based on three sets of simulation data under three situations . Finally, we use real GWAS data of three meat cut traits to explore candidate genes associated with presoma development in cattle. The analytical strategies are visually outlined in We firstly decomposed the phenotypes into several principal components scores (PCS) according to eigenvectors, and then treated PCS as pseudo traits to carry out multiple-trait GWAS. To show the improved power of PCA-based GWAS, we theoretically explored the relationship of the estimated effects between PCA-based multiple-trait GWAS and single-trait GWAS. In this study, two situations were considered as follows.X is the genotype matrix for a single marker, defined as 0 for the heterozygote and −1 and 1 for the two homozygotes. Two traits were observed (represented by y1 and y2) and included in single-marker GLM tests as follows:β1 and β2 represent the marker’s effect on trait one and trait two, respectively. Therefore, β1 and β2 are estimated byIn GWAS analysis, the standard approach usually uses a mixed linear model (MLM), in which polygenic effects are treated as random effects . For a cy1) = 0 and E(y2) = 0 after phenotype normalization. We conducted principal component analysis (PCA) between phenotypic traits in two steps. First, we constructed the covariance matrix S:n is the number of phenotyped individuals. Second, we created a pseudo trait weighting of the first eigenvector (μ):The phenotypes followed E with two traits effects (β1 and β2) to explain the increasing power using the pseudo trait. SinceHere, we compared the pseudo trait effect (Putting Equation (12) into Equation (5) we gotλ was the eigenvalue corresponding to μ, we hadBecause Putting Equation (13) into Equation (5) we gotλ into right-hand side, we gotBy letting X. The residual error can be considered to be independent of the marker indicator matrix β* estimation:w1 and w2 represent elements of the eigenvector μ.Therefore, putting Equation (17) into Equation (16), we obtained the For pleiotropic SNPs, this result indicated that the PCA-based multiple-trait model had a high chi-square statistic for the tested SNP compared to the single-trait model.X1 and X2 are the normalized genotypes, with E(X1) = E(X2) = 0 and Var (X1) = Var (X2) = 1. Similarly, the effects of marker 1 on trait one, marker 2 on trait two, and marker 1 on a pseudo trait are β1, β2, and β*, respectively, as in Equations (3)–(5).As shown in Sinceβ* as in the single causal variant model—Equations (13)–(16). Therefore, we hadNext, we performed a derivation to estimate αi is the ith quantitative trait nucleotide (QTN) effect followed by a gamma distribution with a shape parameter of 0.4 and scale parameter 1.66. The polygenic effects vector g was formed by We simulated phenotypes based on real data that included 1000 samples and 120,710 SNPs on five chromosomes. The principle of phenotypic simulation is as follows:h2 = 0.05 and r = 0. When simulating environmental correlation traits, we set the parameters as h2 = 0.5 and r = 0.25.When simulating low heritability traits, we set the parameters as In the GWAS analysis, a total of 1141 Simmental beef cattle born between 2008 and 2014 composed the experimental population. All cattle were from more than 30 families and were fattened for 8–12 months in a similar environment with the same feed, and slaughtered following the Standard Wholesale Cuts of American Beef guidelines. The phenotypes of three meat cut traits, including the clod weight (CW), fore shank weight (FSW), and heel muscle shank weight (HMSW), were collected during slaughtering. DNA was extracted from the blood samples and genotyped using an Illumina BovineHD BeadChip .p-Value of Hardy–Weinberg equilibrium < 10−6. Finally, a total of 1111 individuals and 608,761 SNPs were left for subsequent analysis. In this study, all phenotypes followed normal distribution and GWAS analyses were implemented using a mixed linear model (MLM). PCA was performed by SAS  software version 9.4  and genetic parameter estimations were conducted using GCTA  [Quality control was conducted as follows: (1) Individuals with a call rate < 0.95 and SNPs with a call rate < 0.9 were removed, (2) minor allele frequency < 0.05, and (3) nalysis) .Based on the simulated phenotypes, the power and FDR were calculated under different significant thresholds using a single-trait model and PCA-based multiple-trait model. Power was evaluated as the proportion of QTNs that passed the significance threshold. FDR was defined as the proportion of the non-QTN markers among the identified markers that exceeded the threshold, where the non-QTN markers were markers that were not located 10 Kb upstream or downstream of the QTNs. A total of 100 replicates were conducted for each group, and the average of the 100 replicates was reported.h2 = 0.5. Their positions and effect sizes are listed in p) and effect standard error (Se Eff) for each QTN are shown in p) of the chr1:132347489 locus in PCA-based GWAS was 6.16, and the corresponding values in the two single-trait GWASs was 4.57 and 5.85. If the significant threshold was p < 10−6, this locus could be found using PCA-based GWAS, rather than single-trait GWAS.We first simulated one set of pleiotropic traits with 10 shared QTNs and h2 = 0.5), low heritability (h2 = 0.05), and environmental correlation . h2 = 0.534, 0.052, and 0.580) compared with the second dimension . As shown in To facilitate the comparison of the two association strategies, we compared the power and FDR between them in three situations: Medium heritability . In each set of simulations, we first randomly simulated pairwise traits by the pleiotropic QTNs regardless of MAF, and then set a significance threshold of the GWAS results  to define significant SNPs. The power for each SNP was defined as whether there were significant SNPs harbored by this SNP . Lastly, based on the power and MAF for each QTN, we fitted trendlines for the two strategies . Overallr = 0.7, PCA-based GWAS had a similar power/FDR to single-trait GWAS.In the colocalizing effect model, to prove Equation (21), we explored the relationship between the capacity of QTL mapping and linkage disequilibrium (LD) of pleiotropic QTNs. Because the value of power/FDR reflects the statistical power of the GWAS model, we found that the capacity of detection was reduced with decreasing LD of pleiotropic QTNs . For pleThree meat cut traits, clod weight (CW), fore shank weight (FSW), and heel muscle shank weight (HMSW), are found in presoma muscles and reflect presoma development in cattle. The heritabilities of the three traits ranged from 0.56 to 0.62, and all three traits had a high phenotypic correlation from 0.76 to 0.82, and genetic correlation from 0.90 to 0.94. The details of the descriptive statistics of the three traits are shown in −7 and 10−5, respectively. For CW, only one significant SNP  was detected on chromosome 4, and no SNPs exceeded the suggestive significance threshold. For FSW, two significant SNPs , one of which was also identified in CW, were detected on chromosomes 1 and 4, respectively. For HMSW, a total of 24 significant SNPs were found (10−7 > p >10−5) on chromosomes 5, 6, and 15. In an approximately 3.5 Mb region (chr6:38550000-42180000), 22 SNPs were associated with the HMSW phenotype, and the most significant SNP was rs137121021, with a p-Value of 1.6 × 10−7.GWAS analyses for the three traits were conducted using the single-trait GWAS and PCA-based multiple-trait GWAS strategies . The genp1, p2, and p3), which explained 86.0%, 8.2%, and 5.8% of the total variance, respectively  was also found in CW- and FSW-GWASs. Another four associated SNPs, which exceeded the suggestive significance threshold, were located on chromosomes 9 and 14. For the p3 GWAS, in the region (chr6:38550000-42180000) where the HMSW trait was associated with 22 SNPs, a total of 31 significant SNPs were found. Another significant SNP, rs134637644 (3.42 × 10−6), on chromosome 5 was also detected by HMSW. In the PCA-based GWAS analysis, the three pseudo traits were combined as new phenotypes  → h2 instead of cov → 1 when the environmental correlation equals 0. However, GLM is approximately equivalent to MLM when analyzing unrelated individuals, and traits with genetic correlation show high phenotypic correlation, indicating that the environmental correlation contributes more. In a pleiotropic trait simulation involving medium heritability, low heritability, and environmental correlation, each pairwise trait shared 10 common QTNs that followed a gamma distribution. We found that multiple-trait GWAS outperformed single-trait GWAS in all three situations, which provides some clues that this approach can be applied to a range of pleiotropic traits. In livestock, detection of pleiotropic QTNs has facilitated the biological understanding of commercial traits, particularly in highly related traits, such as birth weight and weaning weight, as well as milk fat yield and milk protein yield. Additionally, due to taxonomic and binary traits in practical breeding programs, we should further optimize the PCA-based multiple-trait model to combine quantitative traits, taxonomic traits, and binary traits.The conception of PCA-based QTL mapping was first introduced by Weller in 1996 , in whic and β2^ . We admir > 0.7, PCA-based multiple-trait GWAS was more powerful than single-trait GWAS in detecting QTL regions , our results indicated that PCA-based GWAS has significant advantages in pleiotropic QTNs detection when the MAF of QTN is greater than 0.2, while the power improvement gradually reduced when the MAF was less than 0.2. Specifically, for uncommon and rare alleles, the PCA-based strategy had little advantage over the single-trait strategy. In the colocalizing effect model, the estimated effect of a pseudo trait is proportional to the level of linkage disequilibrium (LD) (Equation (21)), and the simulation data supported this view . Under t regions . AssuminNCAPG [LAP3 [KCNIP4 [LCORL [FBXO45, SLIT2, SMCO1, TCTEX1D2, UBXN7, and WDR53, which had not been previously reported in growth-associated studies. Only one additional gene, MCHR2, was identified in multiple-trait GWAS. Although single-trait GWAS has annotated more genes, it’s result may not be reliable. For example, rs134385681 is a prominent SNP found only in FSW-GWAS which is located in a gene-enriched region, so is likely to be a false positive based on gene annotation. However, MCHR2 has been reported to be associated with human obesity [On the real data, we detected 46 SNPs that were significantly associated with the three traits . A totalNCAPG ,26, LAP3PG [LAP3 ,28, KCNI [KCNIP4 , and LCO4 [LCORL . In cont obesity  and a ca obesity , making MCHR2, which is associated with presoma muscle development in cattle.In this study, a PCA-based multiple-trait GWAS model proved to be effective in exploring pleiotropic QTNs in theory and practice. Using this method, we found a plausible candidate gene,