Identification of recombination events and which chromosomal segments contributed to an individual is useful for a number of applications in genomic analyses including haplotyping, imputation, signatures of selection, and improved estimates of relationship and probability of identity by descent. Genotypic data on half-sib family groups are widely available in livestock genomics. This structure makes it possible to identify recombination events accurately even with only a few individuals and it lends itself well to a range of applications such as parentage assignment and pedigree verification.hsphase, an R package that exploits the genetic structure found in half-sib livestock data to identify and count recombination events, impute and phase un-genotyped sires and phase its offspring. The package also allows reconstruction of family groups (pedigree inference), identification of pedigree errors and parentage assignment. Additional functions in the package allow identification of genomic mapping errors, imputation of paternal high density genotypes from low density genotypes, evaluation of phasing results either from hsphase or from other phasing programs. Various diagnostic plotting functions permit rapid visual inspection of results and evaluation of datasets.Here we present hsphase package provides a suite of functions for analysis and visualization of genomic structures in half-sib family groups implemented in the widely used R programming environment. Low level functions were implemented in C++ and parallelized to improve performance. hsphase was primarily designed for use with high density SNP array data but it is fast enough to run directly on sequence data once they become more widely available. The package is available (GPL 3) from the Comprehensive R Archive Network (CRAN) or from http://www-personal.une.edu.au/~cgondro2/hsphase.htm.The  Identification of recombination events and which chromosomal segments contributed to an individual is useful for a number of applications in genomic analyses including haplotyping, imputation, linkage disequilibrium , signatuhsphase, an R package that implements a fast, deterministic and robust method for half-sib family structures to identify recombination events, phase family groups, impute and phase un-genotyped sires and build a library of haplotypes [Here we present plotypes . The pachsphase or other phasing programs. hsphase will also generate a blocking structure of chromosomal segments that define which progeny carry segments identical by descent. This can be used to improve phasing of the paternal sequence data [Additional functions allow identification of genomic mapping errors, evaluation of phasing results generated by nce data ,9 and alnce data .hsphase seamlessly integrates into the R environment for pipelined analyses and provides a range of diagnostic plotting functions that permit rapid visual inspection of results and evaluation of datasets. Functions for pedigree checking, reconstruction and parentage assignment can be used independently or as part of phasing workflow. For phasing purposes, the main advantages of hsphase are that is it extremely fast in comparison to population based phasing methods, can be used with small datasets and it is not affected by sampling stratification. It also builds blocks of chromosomal inheritance in the half-sibs which makes it simple to impute when paternal sequence or higher density marker haplotypes are available. The package is sufficiently fast to be used directly on sequence data.hsphase package exploits the linkage disequilibrium found within a half-sib family and the information content of opposing homozygous SNP markers [The  markers . An oppohsphase implements four different methods to define the separability between related and unrelated individuals. The first method uses a pre-determined cut off based on the maximum number of expected opposing homozygotes in a family. The second approach uses the regression coefficients (slope and intercept) estimated from a large population of sheep half-sib families genotyped on the Ovine50k Illumina BeadChip; these are the default values based on a simple linear regression of the number of opposing homozygotes, but user defined coefficients better suited for a particular population can also be used. The third approach implements the method proposed by Calus et al.[hsphase uses opposing homozygotes to build blocks of haplotypic relationships in family groups, if an individual is not truly part of a group it will need a large number of recombinations to maintain Mendelian consistency with the other family members. These recombinations are of course not real but can be used to exclude a relationship (further details in the block structure section). To build the pedigree itself, the matrix of opposing homozygotes is used to calculate the Manhattan distance between all pairs of individuals. The algorithm then recursively builds a distance matrix and hierarchically clusters them into two groups using Ward’s minimum variance method. At each iteration, the groupings are checked against the separation criterion being used and if all individuals are below the threshold they are assigned to a family group; else the process is repeated.Consider, for example, a sire-offspring relationship, opposing homozygotes can be used to identify Mendelian inconsistencies which should not occur in a true relationship apart for genotyping errors or an unlikely mutation. Alternatively, between unrelated individuals the number of opposing homozygotes is much higher. This difference can be used to e.g. exclude a parentage relationship . The samus et al. based onseparation value which is the difference between the smallest number of opposing homozygotes found across all false sire-offspring relations  and the maximum number of opposing homozygotes in the correct sire-offspring pairs divided by the maximum number of opposing homozygotes found in the dataset . Figure t Figure . The sephsphase implements the method described in [block like structure across the individuals’ genome where each block reflects the inherited paternal haplotype . A detailed description of the algorithm implemented in hsphase and an evaluation of its performance is given in [Opposing homozygotes are also used for phasing and ribed in . Brieflye Figure . Paternagiven in . To imprhsphase was implemented as a package for the widely used R statistical programming environment and wrapper functions make it easy to use and facilitate integration with other R/Bioconductor packages. Programs such as snpQC[hsphase. Source code, compiled package, tutorial and example dataset are available from the project’s website . In the following section, the main components of the package are briefly described. as snpQC output fhsphase requires a SNP map file , a genotype data file  and a pedigree file . The latter can be generated from the data itself if no pedigree information is available or the pedigree is unreliable.ohg calculates a square matrix with the number of opposing homozygotes between all pairs of individuals; these are then used by rpoh to reconstruct family groups by iterative hierarchical clustering in the absence of pedigree data. If a pedigree file is available the function pedigreeNaming will match the inferred family groups with the most likely parents and can be used to correct pedigree errors or to evaluate efficiency of pedigree reconstruction. The accuracy of pedigree assignment decreases if individuals belong to overlapping generations with common ancestors. Results of pedigree reconstruction can be visualized with the hh function which generates a heatmap of the relationships for easy detection of pedigree errors in the original pedigree (if available) and evaluation of pedigree assignment . Function ohplot also uses the matrix of opposing homozygotes and a pedigree file to plot the separation value of the dataset and the sorted results of all pairwise comparisons . The function also reports average values for the number of opposing homozygotes expected in full and half-sib families and in unrelated individuals according to [These functions are not restricted to dense marker panels and can be used to assign parents using small parentage testing panels, for example. Function s Figure . ohplot rding to ; plus thbmh function creates the blocking structure for the half-sibs and splits them into two groups based on the chromosomal segments they inherited from either one of the sire’s haplotypes. Blocks for each chromosome are constructed by selecting the first opposing homozygous SNP on the chromosome and partitioning all members of a half-sib family into two groups according to their genotypes . Starting from this initial grouping the function steps through the SNP according to their map order to allocate individuals into one group or the other one, until the end of the chromosome is reached. At the end of the process each individual at each SNP will have been assigned to one of the two groups; the function returns a matrix of individuals by SNP coded as 1 and 2. Recombination between two adjacent SNP is an unlikely event, so from the second SNP onwards individuals are assigned to a group by minimizing the number of individuals that have to change groups in relation to the previous grouping (i.e. minimum number of recombinations). Recombinations are identified when an individual moves from one group to the other based on its opposing homozygous status. The bmh function performs a validation step for the recombination by checking if during the next steps (SNP) the individual does not return to the previous group. Recombinations occurring on both sides of a single SNP in a single individual are interpreted as a genotyping error and ignored. Group assignment is based on family relationships which makes bmh sensitive to pedigree errors [The e errors . In addihbp function can be used to compare an offspring’s haplotypes with its ancestor’s haplotypes. The function returns a matrix with the same block structure of bmh and can be used to evaluate phasing results of other programs – a single parent-offspring is sufficient in this case. Combined with the imageplot function . Averages are rounded to the nearest integer and assigned to the sire’s haplotypes.The function phf function phases the offspring and returns their paternal haplotypes. It uses the sire’s phased haplotypes as a reference and overlaps the block matrix to select which parts of the haplotypes each individual inherited. Once the paternal haplotypes of the offspring are created, the maternal ones are obtained by simply subtracting these haplotypes from the original genotypes.The impute imputes the paternal strand of half-sib families from low density genotypes to high density by using the sire’s haplotypes as a scaffold. Similarly to the function phf it simply uses the blocks to match the haplotypes of the offspring with the correct haplotype of the sire and fills the missing markers with the haplotypes of the denser panel.The function para function provides a parallelized wrapper to partition the job across multiple CPUs.For large datasets the hsphase package, a dataset of 106 brown Hanwoo Korean cattle genotyped on the Illumina 700 k BovineHD BeadChip SNP array was used. Individuals belonged to 14 half-sib family groups with family sizes ranging from 6 to 8. Genotypes for the 14 sires were also available and pedigree records were accurate. For reference purposes the Korean Hanwoo are a pure-bred heavily selected population with a small effective population size (Ne ~100) and there is some ascertainment bias in the chip which was not specifically designed for the breed. Population differences among unrelated individuals is expected to be lower than in populations with large Ne.To discuss the use of the hsphase implements four methods to define thresholds for pedigree reconstruction. Unfortunately no approach is robust across any scenario and the different methods will perform better or worse in different situations. The accuracy of reconstruction will depend on the sample size and genetic diversity in the population. A first look at the data using ohplot  for the 106 offspring was 0.981 (comparison of 50 K imputed to 700 k with the true 700 k haplotypes). The worst accuracy was 0.977 and the best 0.993. Note that the accuracies were high but they were probably biased upwards since the sires were phased using hsphase and there is some circularity in these values. In the absence of true phased sire data this issue cannot be resolved unambiguously. We also evaluated the accuracy of sire inference (comparison of inferred genotypes with the true genotypes of the sires). The average accuracy was 0.992, with the worst sire 0.985 and the best 0.997. Undefined regions were not called (average 16.5% of SNP). A comprehensive evaluation of the phasing method used in hsphase is given in [To test the accuracy of imputation from low to high marker density we selected 46,174 SNP – the SNP in common with the 50 k bovine panel – in the Hanwoo offspring and excluded the others. We built the block structures for this subset of SNP and then used the para function which allows jobs to run in parallel and acts as a wrapper for the main functions in hsphase. Although this population was reasonably large the time needed for the analysis without parallelization was ~55 seconds and with 8 cores this came down to ~28 seconds. The main reason for the nonlinear speed increase is that each individual analysis was fast and there is limited benefit from the parallelization . Speed hsphase is an R package for analysis and visualization of genomic structures in small half-sib groups. The package can be used to reconstruct pedigree, assign or verify parentage, impute and phase un-genotyped paternal ancestors, phase the half-sib groups and detect and quantify recombination events. Diagnostic plots assist identification of pedigree, mapping and phasing errors. Whilst designed for high density SNP arrays the algorithm is extremely fast and can be used directly on sequence data as it becomes available. Auxiliary functions to impute from low to high density markers and parse datasets are also included in the package.http://www-personal.une.edu.au/~cgondro2/hsphase.htm. Source code, compiled package, a tutorial and example dataset are available from the project’s website.The package is freely available (GPL 3) from the Comprehensive R Archive Network (CRAN) or from Project name: hsphase•Project home page:http://www-personal.une.edu.au/~cgondro2/hsphase.htm•Operating system(s): platform independent•Programming language: R [•guage: R  and C/C+Other requirements: the package depends on the R packages snowfall[Rcpp[RcppArmadillo[• snowfall, Rcpp[18fall[Rcpp and RcppArmadillo.License: GNU GPL 3•The authors declare that they have no competing interests.MF and CG designed the algorithm and experiments to test it. MF wrote the R package. SHL, JHJW and BPK advised on the experimental design to test the package. All authors read and approved the final manuscript.


Dust storm is one of the most important natural sources of air pollution in the Middle East that has caused a major concern in recent years. The aim of this study was to evaluate the respiratory tract function of people living in Ilam city (Iran) during dust storm.1), FEV1/VC, FEV1/FVC, peek expiratory flow (PEF), forced expiratory flow (FEF25-75%), forced expiratory flow (FEF25–75%), forced expiratory flow (FEF75–85%), forced mid flow time (FMFT) and maximum voluntary ventilation (MVV) were measured.A sample size of 250 people was selected and the cluster sampling was randomly used from 13 health centers in Ilam city. Pulmonary function test (PFT) was determined via a standard spirometry apparatus. Vital capacity (VC), Forced Vital capacity (FVC), FVC in first second  was more than females (19.6%). This could be related to more exposure (outdoor jobs) of males with dust storms.Mean values of respiratory capacities measured in all participants excluding FEVThe results also showed a negative significant relationship between duration of inhabitance in Ilam city and all respiratory capacities. Further studies are needed for confident confirmation of whether reduction of respiratory capacities among Ilamian people is only related to dust storms. In recent decades, air pollution in many parts of the world has caused increasing concerns about adverse effects on human health . Accordi10 and PM2.5  are the important constituents of dust storm (10 and PM2.5) over dust storm phenomenon, due to their deep penetration into the lower respiratory tract , has resulted in a range of illnesses and deaths  and southern west of Iran appear to be influenced by dust carried by the Shamal wind, a hot northwest wind that is dominant during the spring and carries large quantities of dust from Iraq deserts . In receThis study was conducted from August to September 2013 in Ilam city with population of 172000 people. Including criteria in this study were: 18 years old persons and more with at least 5 years inhabitance in Ilam city, no hereditary and familial history of respiratory diseases, no history of addiction and smoking, no direct contact with job inhaling pollutants, no history of acute respiratory infection in last two weeks and no usage of bronchodilators . A sampl1), FEV1/VC, FEV1/FVC, peek expiratory flow (PEF), forced expiratory flow at 25%, 50%, 75% of volume as a percentage of FVC , forced expiratory flow from 25–75% of the FVC (FEF25–75%), forced expiratory flow from 75–85% of FVC (FEF75–85%), forced mid flow time (FMFT) and maximum voluntary ventilation (MVV) parameters were measured. Then, the information achieved from the questionnaires and spirometry results were extracted and analyzed by SPSS version 16. A p-value of <0.05 was considered significant. In this research, the European community for coal and steel (ECCS) reference was used to evaluate the respiratory status of studied population (Pulmonary function test (PFT) was determined via a Vitalograph spirometry apparatus  . Accordipulation . T-test The anthropometric parameters values of the participants are shown in 1/VC, PEF and MVV in males and FVC in females (P<0.05). These values were located within 61.25%–128.95% of those derived from prediction equations values for ECCS of total subjects. The largest variations were for FMFT which was significantly higher (128.95%) and FEF75% which was significantly lower (61.25%) in males compared with the reference values. All the spirometric values  in males were greater than of females.The results of the pulmonary tests are indicated in The spirometric values also showed a moderate to strong positive correlation with height . But, thThe frequency of respiratory complications in Ilam city inhabitants based on spirometric tests is shown in The frequencies of abnormal symptoms during dust storm days are indicated by Pulmonary function among various communities considering genetics, environmental factors, and nutritional status is different . Compari1/VC and FMFT were less than predicted mean values by ECCS reference. Also, mean FVC is equal to the predicted mean value. Mean values of respiratory capacities measured in males and females was the same, except for FVC that was lower in males but it was not significant (p=0.196). FEV1/VC values in the current study among males did not show significant relationship with the predicted reference values (p=0.45), but they were significant among women as well as total participants. FVC, FEV1, and FEV1/FVC are pulmonary function parameters which are used in medical estimations for diagnosis of respiratory dysfunction . Also, values of FEF25-75%, FEF75-85%, FEF50% and FEF75% showed the most reduction compared to the predicted reference values. Results of spirometry tests showed that in 150 participants, FEF25-75% value was less than 80% and for 24 participants, it was less than 50% of the predicted reference values. In medical examinations, FVC is usually used to evaluate the large airways of lung and FEV1 shows the blockage of the small and large airways, while FEF25%, FEF50%, FEF75%, and FEF25-75% are used to show the function of small airways of lung . Other respiratory function parameters in females had reversed non-significant correlation with BMI. This may be related to higher BMI in participated females toward males. In the current study, there was no significant correlation between BMI and pulmonary function parameters for males. But, VC, FVC, FEV1 and long-term exposure with PM10 was also reported in a cross-sectional study in California (The results of this research showed a negative significant relationship between duration of inhabitance in Ilam city and all respiratory capacities. Evidences implied that pulmonary functions have been affected by long-term exposure with even relatively low levels of air pollution . A negatlifornia . Therefolifornia . Conside


Inferring population genetic structure from large-scale genotyping of single-nucleotide polymorphisms or variants is an important technique for studying the history and distribution of extant human populations, but it is also a very important tool for adjusting tests of association. However, the structures inferred depend on the minor allele frequency of the variants; this is very important when considering the phenotypic association of rare variants.Using the Genetic Analysis Workshop 18 data set for 142 unrelated individuals, which includes genotypes for many rare variants, we study the following hypothesis: the difference in detected structure is the result of a "scale" effect; that is, rare variants are likely to be shared only locally , while common variants can be spread over longer distances. The result is similar to that of using kernel principal component analysis, as the bandwidth of the kernel is changed. We show how different structures become evident as we consider rare or common variants. Inferring population genetic structure from large-scale genotyping of single-nucleotide polymorphisms (SNPs) or variants (SNVs), often performed using principal component analysis (PCA)  or modelThanks to the increasing availability of sequencing technology, it is possible now to identify very rare variants and to type them on large samples of individuals, extending the reach of the genome-wide association study design. However, methods for detecting population structure and for adjusting association tests accordingly, should take into account the fact that the population structures inferred depend on the minor allele frequency (MAF) of the SNVs; this is very important when considering the phenotypic association of rare variants .In this article we show evidence of different structures at different MAF levels. We propose that the difference is a result of a "scale" effect: rare variants are likely to be shared only locally , whereas common variants can be spread over longer distances. The result is similar to that of using kernel principal component analysis (KPCA)  because Using the Genetic Analysis Workshop 18 (GAW18) data set for 142 unrelated individuals, which includes genotypes for many rare variants, we show how different structures become evident as we consider rare or common variants and how these structures transform smoothly as we change the window of allowed MAF values. We suggest that such a procedure provides a more complete picture of the structure of the population.Private here refers to a variant that appears only once in the sample of 142 individuals. More of these variants can only make an individual more different from the others, whereas a shared variant can make 2 individuals more alike.)We selected at random a set of 82,594 SNVs from the odd-numbered autosomal chromosomes. The set is thin enough that linkage disequilibrium caused solely by proximity along the chromosome does not affect the results substantially. We dropped 133 SNVs that are monomorphic for the set of unrelated individuals, leaving 82,461 SNVs. We did not filter out those variants that appear in only 1 individual, even though they are less informative about the relationships between different individuals. It is important, though, to consider the number of such private variants for each individual, as that might add a linear dimension related to the total number of private variants. . One pairs is picked out by a component that corresponds to the eigenvalue path colored in green in Figure For MAF values above 0.02, the dominant feature corresponds to the eigenvalue path labeled in blue, except for an eigenvalue path that suddenly rises to prominence at MAF 0.09, even surpassing the blue curve briefly, and disappears equally suddenly at MAF 0.15 (colored in red). The "blue" eigenvalues correspond to a continuous axis, represented vertically in panels (6) through (9), while the "red" eigenvalues capture a clustering in the population into 2 clusters (plus 2 outliers). The colors in Figure Panel 1) in Figure  in FigurThe flares in panels 1) through (4) are dominated by a pair of individuals at the tip. These are set out from the rest of the group not because their genotype is different, but because they are more closely related to each other than to the rest. In other words, each of these "groups of 2" have reduced diversity, compared with the overall group. Each of these pairs form a feature that becomes more important when observed at a smaller scale. This corresponds to the appropriate eigenvalues rising to the top, and this pattern is evident in Figure  through As argued by Mathieson and McVean , it can The most intriguing feature to come out of our analysis is the separation in clusters that happens for values of MAF between 0.09 and 0.15. This feature is still present at other nearby frequencies, but the corresponding eigenvalue drops fast below the others. This clustering is not an artifact of the SNVs selected: When using a denser panel extracted from chromosome 11, the same feature arises, in the same furtive way (data not shown). It should be noted that this clustering does not become apparent when performing PCA using a panel of SNVs of all MAFs, or when restricted to common variants (MAF >0.05). Indeed, even logistic regression using the top 10 PCs does a poor job of replicating the separation of the clusters Figure . In othea posteriori for unequal distribution between the 2 clusters.We tried to match the cluster to the available phenotypic data, but none of the following factors matched: sex, status as sequenced versus genotyped-by-chip-plus-imputation, or pedigree membership.  Thus, the true nature of the clustering remains a mystery and should be taken into account when analyzing the data for disease associations, possibly by including a component in the adjustment that separates the clusters, or by checking any potential discoveries This is an interesting question: If two individuals share a very rare variant, not only are they likely to be from the same locality, but they are also likely to be somewhat related. If this is the case, they will tend to share a higher proportion of common variants than other pairs of individuals. Why then would an analysis based on common variants not give the same information as one based on rare variants? A set of top PCs derived from common markers and the whole sample would pick up only large, continent-wide trends. A PC might pick up local correlation, but it would have a small eigenvalue.a posteriori for the possibility of spurious association with one or more of those PCs.There is an important consequence of the local nature of the components obtained from rare variants: many components might be needed to fully describe the population structure at the given scale. As an illustration, consider the following situation: Two components, derived from common markers, can be enough to capture the main genetic geographical structure on a continent . However, if we use components derived from rare alleles, being able to discriminate between neighboring villages, we would need a large number of components to distinguish all the villages. Thus, the following recommendation can be made: Instead of incorporating a large number of PCs derived from rare variants into the regression tests of association, one should check any discoveries We believe that a considerable amount of information can be gained by exploring the population structure at different values of MAF. Using rarer variants corresponds to looking at structures that arise at smaller scales, because rare variants are likely to be shared between individuals located near each other, whereas common variants can be shared at longer distances. We posit that population genetic structure is a multiscale phenomenon, and that to elucidate behaviors at different scales, it is useful to consider sets of variants grouped by MAF.The authors declare that they have no competing interests.ODC and PR designed the overall study, ODC conducted statistical analyses and drafted the manuscript. All authors read and approved the final manuscript.


To date, most genetic analyses of phenotypes have focused on analyzing single traits or analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power and improve our understanding of the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two genes in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large-scale simulations to calculate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare the power with multivariate pairwise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for epistasis analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 267 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has a much higher power to detect interaction than the interaction analysis of a single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes. The widely used statistical methods test interaction for single phenotype. However, we often observe pleotropic genetic interaction effects. The simultaneous gene-gene (GxG) interaction analysis of multiple complementary traits will increase statistical power to detect GxG interactions. Although GxG interactions play an important role in uncovering the genetic structure of complex traits, the statistical methods for detecting GxG interactions in multiple phenotypes remains less developed owing to its potential complexity. Therefore, we extend functional regression model from single variate to multivariate for simultaneous GxG interaction analysis of multiple correlated phenotypes. Large-scale simulations are conducted to evaluate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare power with traditional multivariate pair-wise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for interaction analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic GxG interactions. 267 pairs of genes that formed a genetic interaction network showed significant evidence of interactions influencing five traits. In the past several years, we have witnessed remarkable progresses in the development of methodologies for identification of epistasis that detect deviation from summation of genetic additive effects for a quantitative trait . The claThe classical statistical methods for interaction analysis have mainly tested association with single traits, one time analyzing one trait . HoweverPurpose of this paper is to develop a general analytic framework and novel statistical methods for simultaneous epistasis analysis of multiple correlated phenotypes. To unify the approach to epistasis analysis for both common and rare variants, we take a genome region (or gene) as a basic unit of interaction analysis and use all the information that can be accessed to collectively test interaction between all possible pairs of SNPs within two genome regions (or genes). Functional data analysis is used to reduce the dimension of next-generation sequencing data. Specifically, genetic variant profiles that will recognize information contained in the physical location of the SNP are used as a major data form. The densely typed genetic variants in a genomic region for each individual are so close that these genetic variant profiles can be treated as observed data taken from curves , 31. SinTo evaluate performance for multiple traits epistasis analysis, large scale simulations are used to calculate the Type I error rates of the MFRG for testing interaction between two genomic regions with multiple phenotypes and to compare power with multivariate pair-wise interaction analysis and single trait interaction analysis by functional regression (FRG) model. To further evaluate performance, the MFRG for epistasis analysis is applied to five traits: high density lipoprotein (HDL), low density lipoprotein (LDL), total cholesterol, systolic blood pressure (SBP), and diastolic blood pressure (DBP), from exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis.n individuals are sampled. Let yik, k = 1,2,…,K, be the k-th trait values of the i-th individual. Consider two genomic regions  and . Let xi(t) and xi(s) be genotypic functions of the i-th individual defined in the regions  and , respectively. Let yi = T be the vector of the trait values measured on the i-th individual. Let t and s be a genomic position in the first and second genomic regions, respectively. Define a genotype profile xi(t) of the i-th individual ast. Recall that a regression model for interaction analysis with the k-th trait is defined ask is an overall mean of the k-th trait, ζkd is the coefficient associated with the covariate νd, αkj is the main genetic additive effect of the j-th SNP in the first genomic region for the k-th trait, βkl is the main genetic additive effect of the l-th SNP in the second genomic region for the k-th trait, γkjl is an additive × additive interaction effect between the j-th SNP in the first genomic region and the l-th SNP in the second genomic region for the k-th trait; xij and zil are indicator variableS for the genotypes at the j-th SNP and the l-th SNP, respectively; εik, k = 1,..,K are independent and identically distributed normal variables with mean of zero and covariance matrix Σ.Assume that k0 is an overall mean, ζkd is defined as before, αk(t) and βk(s) are genetic additive effects of two putative QTLs located at the genomic positions t and s, respectively; γk is the interaction effect between two putative QTLs located at the genomic positions t and s for the k-th trait, k = 1,…,K, xi(t) and xi(s) are genotype profiles, and εik are independent and identically distributed normal variables with mean of zero and covariance matrix Σ. Consider covariates in the model (2) allows incorporating PCA scores for population stratification, sex, age, BMI and other biomarkers into the model.Similar to the multiple regression models for interaction analysis with multiple quantitative traits, the functional regression model for a quantitative trait can be defined asxi(t) and xi(s) are expanded in terms of the orthonormal basis function as:j(t) and ψl(s) are sequences of the orthonormal basis functions. The more number of variants in the genes the more accurate the eigenfunction expansion. If the number of variants is less than 3 the eigenfunction expansion of the genotypic profiles is impossible. MFRG can only be used for gene with more than 3 variants.We assume that both phenotypes and genotype profiles are centered. The genotype profiles In practice, numerical methods for the integral will be used to calculate the expansion coefficients. Substituting Eq  into Eq αkj, βkl and γkjl are referred to as genetic additive and additive × additive effect scores for the k-th trait. These scores can also be viewed as the expansion coefficients of the genetic effect functions with respect to orthonormal basis functions.The parameters Then, Eq  can be aTherefore, we transform the original functional regression interaction model into the classical multivariate regression interaction model by eigenfunction expansions. All methods for multivariate regression interaction analysis can directly be used for solving problem (5).The standard least square estimators of B and the variance covariance matrix Σ are, respectively, given byJL row of the matrix (WTW)−1WT by A. Then, the estimator of the parameter γ is given byDenote the last The vector of the matrix γ can be written asY, we obtain the variance matrix of vec(Y):By the assumption of the variance matrix of Thus, it follows from Eqs  and 10)10) thatAn essential problem in genetic interaction studies of the quantitative traits is to test the interaction between two genomic regions (or genes). Formally, we investigate the problem of testing the following hypothesis:a1, b1] and  with K quantitative traits asH0: γ = 0, TI is asymptotically distributed as a central JL components are taken in the expansion Eq  at one gene:Finally, we consider the model with marginal genetic effects (additive model) at both genes:Pj and ql are frequencies of the alleles Aj and Bl, respectively, rpk and rqk are risk parameters of the k-th trait for the SNPs in the first and second genes, respectively, and randomly selected from 1.1 to 1.6, f0 is a baseline penetrance and set to 1 and ε are defined as before.To examine the null distribution of test statistics, we performed a series of simulation studies to compare their empirical levels with the nominal ones. We calculated the Type I error rates for rare alleles, and common alleles. To make simulations more close to real whole exome sequencing data, we generated 50,000 datasets consisting of 1,000,000 chromosomes randomly sampled from the NHLBI’s Exome Sequencing Project (ESP) with 2,016 individuals and 18,587 genes. Each dataset included randomly selected a pair of genes from sequenced 18,587 genes. We randomly selected 20% of SNPs from each gene as causal variants. The number of sampled individuals from populations of 1,000,000 chromosomes ranged from 1,000 to 5,000. For each dataset, we repeated 5,000 simulations. We presented average type I error rates over 50,000 randomly selected pairs of genes from whole exome sequencing ESP dataset.H pairs of quantitative trait loci (QTL) from two genes (genomic regions). Let H pair of QTLs. Let uijkl be the genotypes of the u-th individual with m-th trait. The following multiple regression is used as a genetic model for the m-th quantitative trait:h-th pair of QTLs for the m-th quantitative trait and εmu are distributed as To evaluate the performance of the MFRG models for interaction analysis of multiple traits, we used simulated data to estimate their power to detect interaction between two genes for two, four, five, six and ten quantitative traits. A true multiple quantitative genetic model is given as follows. Consider r varies from 0 to 1.Four models of interactions are considered: (1) Dominant OR Dominant, (2) Dominant AND Dominant, (3) Recessive OR Recessive and (4) Threshold model . We assuWe generated 2,000,000 chromosomes by resampling from 2,016 individuals of European origin with variants in random two genes selected from the NHLBI’s Exome Sequencing Project (ESP). Two haplotypes were randomly sampled from the population and assigned to an individual. We randomly selected 20% of the variants as causal variants. A total of 2,000 individuals for the four interaction models were sampled from the populations. A total of 1,000 simulations were repeated for the power calculation.The power of the proposed MFRG model is compared with the single trait functional regression (SFRG) model, the multi-trait pair-wise interaction test and the regression on principal components (PCs). For SNPs genotypes in each genomic region principal component analysis (PCA) were performed. The number of principal components for each individual which can explain 80% of the total genetic variation in the genomic region will be selected as the variables. Specifically, the principal component score of the i-th individual in the first and second genomic regions are denoted by The power of the MFRG is compared with the traditional point-wise interaction test which takes the following model:k1 SNPs, and the second gene has k2 SNPs, then, the total number of all possible pairs is k = k1 × k2. For each pair of SNPs, we calculated a statistic for testing pair-wise interaction Tmjpair. Finally, the maximum of Tmjpair: Tmax = max is computed.For a pair of genes, we assume that the first gene has Figs Figs Next we investigate the impact of the number of traits on the power. r = 0.05 for Dominant OR Dominant, Dominant AND Dominant, and Recessive OR Recessive, and r = 0.5 for Threshold models, respectively. Again, we observed that the power of the two-trait FRG was the highest.To investigate the impact of sample size on the power, we plotted −10. Population stratification may inflate the test statistics. To reduce the inflation, the standard strategy is to adjust for population stratification via principal components. All the tests were adjusted for sex, age and population stratification via 5 principal components.To further evaluate the performance, the MFRG for testing epistasis was applied to data from the NHLBI’s ESP Project. Five phenotypes: HDL, LDL, total cholesterol, SBP and DBP were considered with a total of 2,016 individuals of European origin from 15 different cohorts in the ESP Project. No evidence of cohort- and/or phenotype-specific effects, or other systematic biases was found . Exomes To examine the behavior of the MFRG, we plotted the QQ plot of the two-trait FRG test . The QQ −10 which were calculated using the MFRG model and simultaneously analyzing interaction of inverse normally transformed HDL and LDL  and high levels of triglycerides (TG > or = 180 mg/dl) [CSMD1 was associated with LDL and total cholesterol [Third, pairs of SNPs between two genes jointly have significant interaction effects, but individually each pair of SNPs make mild contributions to the interaction effects as shown in  network . The gentibility , LDL-chotibility , LDL is tibility , MAPK antibility , up-regutibility , PPARα htibility  and lecttibility , HDL redtibility , the Wnttibility , From th the HDL , CREBBP cription , PLTP wa and LDL , TMEM57 lesterol . It was 0 mg/dl) , associa0 mg/dl) . It was lesterol .Next we analyzed five traits: HDL, LDL, SBP, DBP and TOTCHOL. Again, for each trait, inverse normal rank transformation was conducted to ensure that the normality assumption of the transformed trait variable was valid. To examine the behavior of the MFRG, we plotted QQ plot of the test . The QQ −10 which were calculated using the MFRG model Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.S4 Fig(TIF)Click here for additional data file.S5 Fig(TIF)Click here for additional data file.S6 Fig(TIF)Click here for additional data file.S7 Fig(TIF)Click here for additional data file.S8 Fig(TIF)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(DOCX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.S6 Table(DOCX)Click here for additional data file.S7 Table(DOCX)Click here for additional data file.S8 Table(DOCX)Click here for additional data file.S9 Table(DOCX)Click here for additional data file.S10 Table(XLSX)Click here for additional data file.S11 Table(XLSX)Click here for additional data file.S12 Table(XLSX)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


Next-generation sequencing techniques, such as genotyping-by-sequencing (GBS), provide alternatives to single nucleotide polymorphism (SNP) arrays. The aim of this work was to evaluate the potential of GBS compared to SNP array genotyping for genomic selection in livestock populations.x) per individual from 0.01x to 20x or using SNP array genotyping; (ii) number of genotyped markers from 3000 to 300 000; and (iii) size of training and prediction sets from 500 to 50 000 individuals. The latter was achieved by distributing the total available x of 1000x, 5000x, or 10 000x per genotyped locus among the varying number of individuals. With SNP arrays, genotypes were called from sequence data directly. With GBS, genotypes were called from sequence reads that varied between loci and individuals according to a Poisson distribution with mean equal to x. Simulated data were analyzed with ridge regression and the accuracy and bias of genomic predictions and response to selection were quantified under the different scenarios.The value of GBS was quantified by simulation analyses in which three parameters were varied: (i) genome-wide sequence read depth  contains supplementary material, which is available to authorized users. Current applications of genomic selection (GS) in livestock are typically based on single nucleotide polymorphism (SNP) genotypes called from SNP array data. In practice, combinations of high and low-density SNP arrays along with imputation are used to reduce the costs of genotyping -3. Thesex). By increasing x, the proportion of correctly called genotypes increases but so do the costs. Since x varies along each sequenced genome, the number and quality of genotype calls also vary along the genome of each individual [Use of next-generation sequencing (NGS) techniques for genotyping could be a viable alternative to current low-cost SNP array strategies, with the potential to increase the fraction of the genome captured in a cost-efficient manner -8. Genotdividual -17. Thesdividual -20.x was sufficient to obtain accurate EBV without using imputation and error correction methods. This was in part facilitated by the low levels of heterozygosity in the individuals analyzed in these studies. However, the usefulness of GBS for GS in outbred livestock populations with higher levels of heterozygosity has not yet been evaluated. Algorithms and software for imputation and error correction of NGS data in livestock have yet to be developed to capitalize on their unique population structure and the available information . Therefore, for GBS to be a viable alternative to current genotyping approaches with SNP arrays in livestock, it needs to be competitive in the absence of imputation and error correction methods.GBS has been shown to be useful for GS of advanced breeding lines of wheat  and of dx) and fractions of genome covered. The results show that the accuracies of EBV obtained with non-imputed GBS data and of SNP array data were comparable when x was as low as ~1x and large fractions of genome were covered. In addition, decreasing x per individual enabled an increase in the response to selection by increasing both accuracy of prediction and intensity of selection through exploitation of the trade-off between the quality of genotyping and the number of individuals that could be genotyped.The objective of this research was to quantify the potential of GBS for GS in outbred populations of livestock in the absence of imputation and error correction methods. Specifically, using simulations, the accuracy and bias of predictions and response to selection were compared for various genome-wide sequence read depths  data on whole-genome sequence; (ii) the pedigree structure for a livestock population; (iii) causative loci affecting phenotypes; and (iv) marker genotypes. These simulated data were in turn used in the analyses described below.8 base pairs. Chromosomes were simulated using a per site mutation rate of 2.5 × 10−8, a per site recombination rate of 1.0 × 10−8, and an effective population size (Ne) that varied over time. Based on estimates for the Holstein cattle population [Ne = 100 in the final generation of simulation, to Ne = 1256 for 1000 years ago, to Ne = 4350 for 10 000 years ago, and to Ne = 43 500 for 100 000 years ago, with linear changes in between. The resulting sequences had approximately 1.7 million segregating sites in total.Sequence data were generated using the Markovian Coalescent Simulator (MaCS)  and Alphpulation , effectiAfter the sequence simulation, several pedigrees of two generations were simulated. Chromosomes of individuals in the first generation were sampled from the 1000 simulated base haplotypes and those in the second generation were sampled from the parents’ chromosomes by recombination . Different pedigrees were simulated by mating each of the 25 sires with 20 dams , with 500, 1000, 5000, 10 000, 20 000, or 50 000 progeny per generation by varying the number of progeny per mating.Quantitative trait loci (QTL) were selected as a sample of 9000 segregating sites in the base population, with the restriction that 300 were sampled from each chromosome. These QTL had their allele substitution effect sampled from a normal distribution with a mean of 0 and standard deviation of 1.0 divided by the square root of the number of QTL. QTL and their effects were in turn used to compute true (simulated) breeding values to simulate complex trait phenotypes with a heritability of 0.25.The fraction of genome covered by the different genotyping platforms was represented by a variable number of markers, which was selected as a random sample of 3000 (3 K), 9990 (10 K), 60 000 (60 K), and 300 000 (300 K) segregating sites in the base population, with the restriction that equal numbers were sampled from each chromosome. These markers were assumed to be available for all individuals and their genotypes were called via processes similar to those used for either SNP arrays or GBS. With SNP arrays, genotypes were called from sequence data directly without error. With GBS, genotypes were called from sequence data based on the principle and simulation procedure described in the following.n sequence reads is the same as observing two different outcomes among n draws from a Bernoulli distribution. Such an event has a probability of 1-2/2n. The probability of calling a heterozygous genotype from n sequence reads of a locus is therefore equal to 0.00 for n = 1, 0.50 for n = 2, 0.75 for n = 3, 0.875 for n = 4, etc. However, the number of sequence reads per locus varies along the genome, thus, for an (average) genome-wide sequence read depth (x), the realized number of sequence reads per locus i of an individual j  was assumed to be distributed according to a Poisson distribution with mean equal to x, i.e., In the absence of sequencing errors, a single sequence read of a locus provides discriminative calls for homozygous but not heterozygous genotypes, which can be called only when multiple sequence reads are available. Calling a heterozygous genotype in diploids from x across the sequenced fraction of the genome: 0.01x, 0.02x, 0.05x, 0.10x, 0.20x, 0.25x, 0.50x, 1.00x, 1.50x, 2.00x, 3.00x, 4.00x, 5.00x, 10.00x, and 20.00x. These values represent the average number of sequence reads at genotyped loci per individual and is often referred also as “coverage” in the literature, e.g., [n and one of the homozygous genotypes with a probability of 1/2n. For example, with two reads at a heterozygous locus, the probability to call each of the homozygous genotypes was 0.25 and the probability to call the heterozygous genotype was 0.50. Uncertainty in the calling of genotypes was neglected, i.e., the collected data were discrete genotype calls and not genotype probabilities or derived allele dosages. It was assumed that all selected SNP sites could be sequenced in all individuals and that sequencing errors were absent. If there was no read for an individual at a particular locus, the genotype was set equal to twice the allele frequency of the allele coded as 1. Allele frequencies were assumed known.GBS genotypes were called from sequencing data with the following range of e, e.g., . If one Training and prediction sets were extracted to test the accuracy of EBV using GBS or SNP array genotype data. The training set comprised all individuals in the first generation  that were genotyped and phenotyped. The prediction set comprised a random subset of 500 genotyped individuals from the second generation, with the restriction that all families were equally represented, i.e., an equal number of progeny per dam was sampled.i–th individual, α is the intercept, βj and xi,j are the allele substitution effect and genotype call of the j-th marker, and Statistical analysis was based on the ridge-regression model -26, as ix in both training and prediction sets; (A2) using different x in training and prediction sets; (A3) reducing x to expand the training set; and (A4) reducing x to expand the prediction set. For each of these analyses, all marker densities were used to quantify the effect of the fraction of genome covered.The simulated data were analyzed in several ways to quantify the effect of: (A1) using the same x in both training and prediction sets was quantified by training the prediction model on the 1000 individuals with phenotype and genotype information from the first generation and predicting EBV of 500 individuals with genotype information that were randomly sampled from the second generation. In this analysis, GBS data with the whole range of x and SNP array data were tested (see Subsection “(A1) The effect of using the same x in training and prediction sets was quantified by using the same setting as in (A1), except that all combinations of x in training and prediction sets were analyzed .(A2) The effect of using different x per individual in order to expand the training set was quantified by training the prediction model on different numbers of individuals with phenotype and genotype information in the first generation  to predict EBV of 500 individuals with genotype information that were randomly sampled from the second generation. Three different x per individual were used, such that the total available x of 1000x, 5000x, or 10 000x was spread across all individuals in the training set and kept constant across all sizes of training sets. More precisely, with the total of 1000x, 5000x, or 10 000x  1000 individuals at 1x, 5x, or 10x; (iii) 5000 individuals at 0.2x, 1x, or 2x; (iv) 10 000 individuals at 0.1x, 0.5x, 1x; (v) 20 000 individuals at 0.05x, 0.25x, or 0.5x; or (vi) 50 000 individuals at 0.02x, 0.1x, or 0.2x. The prediction set was genotyped either with SNP arrays, to remove confounding with the quality of genotyping, or with GBS with the same x as the training set to maintain consistency.(A3) The effect of reducing x per individual to expand the prediction set was quantified by calculating the response to selection (in units of standard genetic deviations) using the breeders’ equation, e.g., [x as the training set in (A3), such that the total available x in the prediction set was equal to 1000x, 5000x, or 10 000x  1000 individuals at 1x, 5x, or 10x; (iii) 5000 individuals at 0.2x, 1x, or 2x; (iv) 10 000 individuals at 0.1x, 0.5x, 1x; (v) 20 000 individuals at 0.05x, 0.25x, or 0.5x; or (vi) 50 000 individuals at 0.02x, 0.1x, or 0.2x. Response to selection was calculated in two ways based on the accuracies obtained from the various scenarios in (A1) and (A3). Accuracies from the scenarios in (A1) were used when the training set  had SNP array data and the prediction set had GBS data with the same x as training set in (A3). This set of scenarios was chosen to remove confounding with the quality of genotyping in the training set and to maintain consistency. Accuracies from the scenarios in (A3) were used when both the training and prediction sets had the same x. This set of scenarios was chosen to show the potential of expanding both the training and prediction sets by reducing x per individual.(A4) The effect of reducing n, e.g., . It was x and marker density when x was the same in the training and prediction sets, as well as by the interaction between these two factors  the accuracy was close to 0 and ranged from −0.01 for 3 K markers to 0.03 for 300 K markers. However, the accuracy increased quickly with small increases in x, especially for the higher marker densities. With 300 K markers, the asymptote of accuracy (0.54) was obtained with 2.0x and most of this was obtained with 1.0x (0.53) or 0.5x (0.51). With 60 K markers, the asymptote of accuracy (0.53) was obtained with 3.0x and most of this was obtained with 2.0x (0.52) or 1.0x (0.50). With less than 60 K markers, the asymptote was reached at higher x, i.e. 5.0x for 10 K markers and 10.0x for 3 K markers. At a sufficiently large x (10x and above), accuracies were comparable between GBS and SNP array data, i.e. 0.48 with 3 K, 0.52 with 10 K, 0.53 with 60 K, and 0.54 with 300 K markers.A1) The accuracy of EBV calculated using GBS data was strongly influenced by both  The accux and marker density when x was the same in the training and prediction sets , biases were comparable between GBS and SNP array data, i.e. 0.89 with 3 K, 1.01 with 10 K, 1.06 with 60 K, and 1.07 with 300 K markers.Bias of EBV using GBS data was also strongly influenced by s Figure . In genex between the training and prediction sets revealed several interactions between x and marker density that impacted the accuracy of EBV  but accuracy improved progressively more with increasing marker densities . When x was intermediate or high (~1.0x and above) in the training set, increasing x in the prediction set did not improve accuracy for higher marker densities (60 K or 300 K), since the asymptote was largely reached, while there was still some improvement for lower marker densities. Among the tested combinations of x in the training and prediction sets, no particular ratio provided substantial benefits, e.g., with 300 K markers, the accuracy was equal to 0.52 with 0.5x in the training set and 1.0x in the prediction set and also with 1.0x in the training set and 0.5x in the prediction set  Varying V Figure . Increasx and marker density in the training and prediction sets for the bias of EBV  with a lower x in the training set and there was little variation due to x in the prediction set , accuracies of EBV were generally maximized by using large training sets that comprised individuals with a low x, rather than by generating small training sets that comprised individuals with a high x  or even decreased (with 1000x) when expanding the training set , but was 0.73 with 10 000 individuals , 0.78 with 20 000 individuals , and 0.78 with 50 000 individuals  , 20 000 individuals when using 5000x , or 20 000 individuals when using 10 000x   Keeping the total available x Figure . The onlt Figure a. With 3x was used, so that the number of individuals in the training set could vary, the bias of EBV increased with larger sets of individuals with lower x per individual  instead of SNP array data.When a fixed total available l Figure . Howeverl Figure . This inx in the prediction set, the highest response to selection was obtained by generating large prediction sets that comprised individuals with high marker density and low x because the high selection intensity compensated for lower accuracy of EBV , response to selection was equal to 1.11 when training was on SNP array data with 1000 individuals, and equal to 0.73 when training was on GBS data with the same number of individuals and x as in the prediction set. Spreading the equivalent of 10 000x across 50 000 individuals  gave a response to selection of 1.87 when training was done on SNP array data and a response to selection of 2.56 when training was done on a larger GBS dataset  For a fixed V Figure d. At lowx is not necessarily needed to obtain high accuracies. With high marker densities, almost all of the prediction accuracy that can be obtained with high-quality SNP arrays of the same density can be recovered with low x . Furthermore, NGS approaches provide the user with the opportunity to tailor the quantity and quality of the genotype information to their requirements and some flexibility regarding the number of individuals and genotype quality in both the training and prediction sets. Expanding the training set at the expense of reducing the sequencing depth  for each individual led to higher overall accuracy of EBV. Expanding the prediction set at the expense of reducing the quality of genotyping for each individual led to lower overall accuracy of EBV, but it enabled a higher selection intensity, which in turn resulted in a higher response to selection. Thus, from the perspective of maximizing genetic gain in the next generation, the results suggest that the optimal use of sequencing resources requires an increase in the number of individuals in both the training and prediction sets, at the expense of quality of genotyping. However, at very low x, the resulting EBV were biased. This was particularly evident for very low x with high marker densities, which conversely are scenarios that, for a fixed amount of financial resources, maximize accuracy and response to selection in the next generation. Biased breeding values may not impact the response to selection in the next generation, but they can impact the long-term response to selection when the value of the breeding value is proportional to the number of genetic contributions that each individual is allowed to make to the next generation.The results of this study show that GBS can be as accurate as SNP array genotyping for GS in livestock populations and that a high x GBS data used to genotype a training population. In this example, at each marker locus approximately 10% of the individuals will have one of their alleles genotyped. The individual and the allele will be sampled at random and this sampling at each marker position will be independent. Thus, the sample of individuals from the population that is used to estimate the phenotypic effect of an allele will be different at each locus. If there is a correlation between alleles at adjacent loci, the sampling of different phenotypes may enable a statistical algorithm to better separate the effects of these loci. Thus, on the one hand, it may be possible to reduce sequencing depth considerably for the construction of very large training populations before the net benefit of assembling larger datasets with low-coverage becomes negative. On the other hand, the quality of genotyping may be much more important for the prediction set. Although reducing the sequencing depth in the prediction set can result in greater selection intensity, it may also be necessary for the genotype of a selection candidate to be much more accurate than that of a training individual. This was clearly observed when marker density was high and with a low x in the training set, i.e., prediction accuracy increased greatly when x in the prediction set increased. These results are in line with those reported for human populations, which show that low-coverage sequencing (low x) of a large number of individuals provides more power for complex trait association studies than deep sequencing (high x) of a smaller subset [x. Extrapolating all these results to whole-genome sequencing for GS suggests that low-coverage sequencing of a large number of individuals could be a viable alternative to deep sequencing of a limited set of “key” individuals of a population [The finding that low-coverage GBS data can lead to accurate EBV in livestock populations, even in the absence of imputation, is perhaps surprising given that the livestock breeding community has placed major emphasis on ensuring genotype data is accurate. A possible explanation for this finding can be illustrated with the example of 0.1r subset ,18,19. Tr subset , which spulation ,29.A drawback of the low-coverage approach is that heterozygous loci will often be called as homozygous, which limits the use of such data for analyzing the dominance effects. This is not a major limitation for inferring the additive genetic effects, because randomness in calling one or the other allele at a locus provides enough population-wide information to obtain estimates of the allele substitution effects. However, imputation is expected to improve the usefulness of low-coverage data for the analysis of dominance variation by increasing the amount of genotypic information. This information can then be used in the analysis either as discrete genotypes in the case of perfect imputation or as genotype probabilities in the case of imperfect imputation.x , which, when coupled with high marker densities , would result in accurate EBV and high response to selection in the next generation. In addition, imputation may lead to high levels of accuracy with levels of x that are much lower than 0.5x to 2x, perhaps 0.05x to 0.2x. From an imputation perspective, properties of GBS data differ from those of SNP arrays that have been commonly used in livestock to date. For example, the density of GBS can be very high, but the information content at each marker position is variable or even missing due to variable x along the genome. In addition, some individuals can have mutations in restriction enzyme cut sites, which results in missing genotype calls due to this rather than due to the stochastic nature of the sequencing process. In contrast, SNP array genotypes are called with a high degree of certainty, almost all of the markers that are missing have a certain structure , and the density from which imputation is to be undertaken is much lower . For these reasons, the imputation algorithms that have been designed for application in livestock datasets [This study did not apply imputation algorithms to increase the information content in GBS data, although if it had there could be much less data missing and the effective coverage of each marker could be much higher -20. Incres i.e., 0 K, wouldatasets  are not datasets . Unlike es i.e., 0 K, wouldatasets . Thus, ax sequencing of one individual with a genome size of approximately 3 Gb, which can be assumed to scale linearly with x  and the proportion of the genome sequenced. Therefore, GBS-like approaches could be even cheaper since they only sequence a small proportion of the genome. In this study, the total available x was spread across different numbers of individuals, which implicitly only includes the actual sequencing costs and thus, assumes that sample library preparation costs are negligible. These assumptions are simplistic, but the purpose of this study was to evaluate the potential of GBS with varying number of individuals, without putting much consideration on costs. Development of imputation algorithms specific to livestock NGS data will substantially reduce sequencing costs per individual and thus the scenarios studied in this work will become realistic.Given that accurate EBV and high response to selection can be obtained with GBS, it represents an attractive alternative to SNP array technology for animal breeders if the cost of generating and using such data is reasonable. Full costs for GBS are difficult to determine and are continually changing with the rapid progress in sequencing technologies and few publications provide a clear breakdown of costs and, in some cases, do not report the full economic impact. Similarly, the cost of SNP array genotyping declines steadily. A recent study on the use of GBS in wheat indicated that future costs per individual would be as low as $10 . Howeverin lieu of SNP array genotyping, and simulation studies such as this cannot easily account for these. First, GBS approaches typically sequence the flanking regions of restriction enzyme cut sites, which is equivalent to sequencing subsections of the genome taken at random. While the proportion of the genome sequenced can be tailored through the choice of frequent or rare cutting enzymes, or the use of multiple enzymes, it is a stochastic process and only a proportion of the sequenced sites will contain polymorphic markers. Therefore, to achieve a target marker density, it will be necessary to sequence many more sites, some of which will be uninformative, and this limits the number of samples that can be multiplexed to achieve a target x. In addition, the random nature of the sequencing process leads to an uneven x across sites and across individuals. Despite equal amounts of input DNA from an individual, there is substantial fluctuation in x per individual, with knock-on consequences for genotype quantity and quality per individual [a priori in limited subsets of individuals and therefore do not suffer from the ascertainment bias that affects SNP arrays, e.g., [There are a number of practical limitations to the GBS approach dividual -17. Howedividual . In addis, e.g., -14, and x the accuracy of genotype calls is more than 99% [The impact of sequencing errors was not quantified in this study. Sequencing errors typically occur at 0.5 to 1.0% per raw base and vary somewhat between sequencing approaches ,33, e.g.than 99% . Howeverthan 99% . If low-than 99% ,19,35.x, on average all heterozygous loci were called as homozygous, while at 2x, on average half of the heterozygous loci were called as homozygous. At 0.5x, on average half of the loci were not called at all and the other half had all heterozygous loci called as homozygous. With 0.1% erroneous base reads, the amount of wrong genotype calls would not increase drastically and would therefore not invalidate the main conclusions of this study. A more efficient approach than calling genotypes would be to calculate genotype probabilities conditionally on the observed sequence reads from each individual and its relatives and sequence error rates [Applying an error rate of 0.1% to the simulations performed in this study would result on average in 3, 10, 60, and 300 markers with erroneous base reads per individual for marker densities of 3 K, 10 K, 60 K, and 300 K, respectively. These errors would add some additional noise to the genotype calls, which were already quite noisy with low-coverage GBS. Note that at 1or rates ,19,35; tx) is as low as ~1x and large numbers of markers are available. The ability to vary the quality of genotyping per individual (by varying the sequencing effort) makes it possible to reduce the cost of genotyping of a large number of individuals and therefore to increase the accuracy of prediction and selection intensity. Similar strategies could be developed for low-coverage sequencing of whole genomes. Further developments in sequencing and imputation techniques are necessary to improve the cost effectiveness of such strategies for their application to real populations.In conclusion, NGS techniques used for genotyping such as GBS have potential advantages for genomic selection in livestock. Our results show that genomic prediction using unimputed GBS data gives comparable accuracies to using SNP array data with the same number of markers, even if the genome-wide sequence read depth (


Limb bone length is an economically important trait in pigs, because it is negatively correlated with backfat thickness, and is also a determinant to the yield of hip and loin. Moreover, abnormal growth of the limb bone leads to leg structural weakness. Until now, the genetic architecture of the pig lime bone length remains poorly understood. The object of this study was to map genomic loci for limb bone length by genome-wide association study (GWAS) on 4 pig populations.2 intercross, Erhualian, Laiwu and Sutai populations, respectively. We genotyped the 2004 pigs for 62,163 single nucleotide polymorphisms (SNPs) on the Porcine SNP60 BeadChip, and performed GWAS and a GWAS meta analysis in the 4 populations. In total, we identified 12 and 4 loci associated with the limb bone lengths at suggestive and genome-wide significant levels respectively, of which 4 loci were reported for the first time. The most prominent locus was identified in a 924-kb (kilo base pairs) linkage disequilibrium block on Sus Scrofa chromosome (SSC) 7, and High Mobility Group AT-hook 1 (HMGA1) appears to be a strong candidate gene in this region. Another promising locus is located in the middle of SSC4, and Pleiomorphic Adenoma Gene 1 (PLAG1) is a functionally plausible candidate gene underlying the locus. Because the lengths of the 5 limb bones are highly correlated to each other, most of significant loci were associated with all of the 5 traits; however, several loci showed specific effect on the length of one limb bone, such as the locus at the proximal end of SSC2 associated with only the scapula length.We measured the lengths of five limb bones including scapula, humerus, ulna, femur and tibia that were dissected from the right-side carcass of 925, 331, 314 and 434 animals from White Duroc × Erhualian FHMGA1 and PLAG1 are two appearing candidate genes for pig limb bone lengths, which warrant further investigations.To our knowledge, this study was the first GWAS meta analysis for limb bone lengths in pigs. As expected, the meta analysis is more powerful to identify genomic loci. A total of 16 loci were identified in this study, including four novel loci. The online version of this article (doi:10.1186/s12863-015-0257-1) contains supplementary material, which is available to authorized users. Limb bone length is a major factor influencing body height in pigs. It has been reported that body height is negatively correlated with backfat thickness, and is also a determinant to the yield of hip, loin, picnic shoulder and shoulder butt , 2. AbnoIn humans, body height is positively and highly correlated with limb bone length, with correlation coefficients from 0.66 to 0.88 , 5. The 2 population produced by a Large White × Minzhu intercross[Limb bone length is a multi-factorial trait in pigs. To date, a total of 39 quantitative trait loci (QTL) for limb bone length have been identified across the pig genome –10. With2 intercross, Chinese Erhualian, Laiwu and Sutai pigs.The aim of this study was to identify genomic loci for the lengths of limb bones including scapula, humerus, ulna, femur and tibia by GWAS and a meta GWAS analysis in four pig experimental populations: a White Duroc × Erhualian FP < 0.05) in males than in females across those populations. An additional table shows the phenotypic correlation coefficients among the 5 measured traits related to limb bone length [see Additional file P < 0.0001).Descriptive statistics of phenotypic traits measured in the four pig populations are shown in Table Z test to detect the association between SNPs and limb bone lengths in the GWAS meta analysis. The Kolmogorov-Smirnov test results showed that all of the statistics followed the standard normal distribution except the one of the ulna length (P = 0.0448) [see Additional file In this study, we used a 2 (n = 925), Erhualian (n = 331), Laiwu (n = 314) and Sutai (n = 434) populations, respectively [see Additional file After quality control, 39461, 28094, 36585 and 41320 SNPs were retained for GWAS on the F2 population, but the other populations had a certain level of population stratifications, especially in Erhualian and Sutai pigs [see Additional file The principal component analysis showed that no population stratification existed in the FThe individuals were clustered into four groups according to their genetic distances [see Additional file 2 we detected two loci associated with all of the 5 traits at 1 % genome-wide significant level. One was around 35 mega base pairs (Mb) on SSC7, and the other was in the middle of X chromosome. For the analysis in the Erhualian, we detected three QTL. One for all of the 5 traits was mapped around 35 Mb on SSC7. Another one for the three front-limb bone lengths was detected around 66 Mb on SSC4. The third one for the ulna length was identified around 103 Mb on the X chromosome. For the Laiwu, only one locus at the distal end of SSC1 was significantly associated with the lengths of scapula and tibia. Another region around 77 Mb on SSC4 had an association with the lengths of femur and ulna almost reaching the suggestive significant level  than the suggestive level were listed in an additional table [see Additional file Since Bonferroni-corrected thresholds are very conservative, using the Bonferroni correction will decrease the detection power. To overcome it, some loci with significant levels slightly lower  block in the F2, on SSC4 and 7 in the Erhualian, and on SSC1, 4 and 7 in the meta analysis. The unmapped SNP ss107830715, which tightly links to the SNP ss107865741 at 15.10 Mb on SSC17, added an associating signal to the tibia length on SSC17 in the meta analysis.There were 20 unmapped SNPs associated with limb bone lengths at the suggestive significant level [see Additional file In this study, we conducted GWAS and GWAS meta analyses in four pig experimental populations. In total, we identified 16 loci significantly associated with the limb bone lengths, of which 12 confirmed the QTL previously reported on SSC1, 2, 3, 4, 7, 13, 14, 15, and X –10, and 2 population [2 population. The lower power of GWAS could be explained by the following factors. First, the Bonferroni-corrected thresholds in GWAS are more conservative than those obtained from the permutation test used in QTL mapping studies. Second, the error variance is smaller in the QTL mapping study than in the GWAS. When perform genome scan for QTL, the detected QTL in the previous rounds are included in the model as fixed effects, so their variances are removed from the error variance [Our previous QTL mapping study detected 35 QTL for the five traits on 11 chromosomes in the Fpulation . In thisvariance . HoweverP < 0.001, corrected by genomic control), we didn’t detected more locus in the F2 [see Additional file When we used a looser stringent threshold , and the locus with small effect can be unveiled by single-population analysis. The meta analysis utilizes information from multiple independent studies and can increase the detection power. It not only detected 8 more regions than the single population analyses, but also confirmed all loci identified in the four populations separately except the locus at the proximal end of SSC3.To our knowledge, this is the first GWAS meta analysis of limb bone lengths in pigs. We used a common set of informative SNPs in the four populations to conduct the GWAS meta analysis. Although the SNP density in the GWAS meta analysis is lower than that used in a single population, the meta analysis is more powerful to identify chromosomal regions associated with limb bone lengths than the single-population GWAS. In the single-population GWAS, the detection power is limited by the small population size  [HMGA2 was also reported associated with human’s height [HMGA1 is a strong candidate gene for limb bone lengths on SSC7.The locus around 35 Mb on SSC7 showed the most significant effect on the length of all limb bones. This locus has a pleiotropic effect on multiple traits, including the gait scores of front and rear legs , fat acie HMGA1) , which ie HMGA1) . Anothers height . TherefoOn chromosome X, the top associated SNPs of the five traits covered a 64.1-Mb region (from 43.4 to 107.5 Mb). It was probably caused by the extremely low recombination rate and low SNP density in this region. This region encompasses a big recombinant cold spot , in whic2 population [see Additional file PLAG1) locates about 600 kb away from the top SNP and has been reported to be associated with pig body length [A region around 82 Mb on SSC4 was detected to be associated with the limb bone lengths in the GWAS meta analysis  were bought from Laiwu Stock Seed Farm in Shandong province from 2012 to 2013. Those pigs were derived from 11 sire and 45 dam families and covered almost all lineages of the Laiwu breed. Both Erhualian and Laiwu are Chinese indigenous breeds, the former is famous for its high prolificacy, and the latter is well known for its high intramuscular fat content. Erhualian and Laiwu boars were castrated before weaning, and females were intact. The Erhualian and Laiwu pigs at the age of 60 ± 3 days were transported from their original farms to Nanchang Guohong Ecological Farm in Jiangxi province. During the fattening period, both Erhualian and Laiwu pigs accessed ad libitum to the fresh water and a consistent feed, which met the pig’s needs for energies, amino acids, vitamins and minerals. Both Erhualian and Laiwu pigs were harvested at the age of 300 ± 3 days.A total of 2004 pigs were used in this study including 925, 434, 331 and 314 animals from Fications , 26. In ian sows . Erhuali2 and Sutai populations and at 300 ± 3 days in the other two populations. The lengths of these limb bones were measured according to the method described in Mao et al. [Scapula, humerus, ulna, femur and tibia were dissected from the right side carcass after the animal sacrificed at 240 ± 3 days in Fo et al. . BrieflyP < 0.000001), and the animals with call rate <95 % were removed. A common set of SNPs that passed quality control across the four populations were used in the GWAS meta analysis.Genomic deoxyribonucleic acid (DNA) was extracted from ear or tail tissues under a standard phenol/chloroform protocol. All DNA samples were qualified and diluted to a concentration of 50 ng/μl. All of the animals from the four populations were genotyped by the porcine 60 K SNP Beadchip on an iScan System  following the manufacturer’s protocol. The SNP positions were determined according to the pig genome assembly Sscrofa10.2. The unmapped SNPs were assigned to chromosome 0, and their positions were arbitrarily given by the rule described in the reference . SNPs weDescriptive statistics of the measured traits were calculated by the MEANS procedure. Phenotypic difference between sexes was tested by the TTEST procedure of SAS9.0 . The CORR procedure was used to compute phenotypic correlation coefficients, and the MIXED procedure was engaged to determine the fixed effects and the covariates for the GWAS model. Sex and batch were included as fixed effects, and body weight at harvest was included as a covariate in the GWAS model for all traits. To remove the effect of the population stratification, a random polygenic effect estimated with a genomic kinship was included in the GWAS model , 28. TheP values for suggestive, 5 % and 1 % genome-wide significant levels were one, 0.05 and 0.01 divided by the number of informative SNPs, respectively.The GenABEL in the R package was used to conduct individual population GWAS using an additive model . The famwi) for the ith population is calculated by the following formula:si is the standard error of the allele effect in the ith population.The inverse variance pooling method was applied to perform a GWAS meta analysis of the four populations . The weiβ) and its standard error (s2) are calculated by the following formula:βi is the allele effect in the ith population.Then, the pooled estimate of the effect (Z-test was calculated by the below formula under the assumption of the linkage phases being same across populations, and a Kolmogorov-Smirnov test was used to determine whether the statistic follows the standard normal distribution.A statistic of βi and its absolute value to calculate the pooling β and Z values under the assumptions of the linkage phases being same and different across the populations, respectively. A Bonferroni correction was used to obtain the P values for suggestive, 5 % and 1 % genome-wide significant levels in the meta GWAS analysis.We used 2 population [The linkage between the mapped and unmapped associative SNPs was determined by two-point linkage analysis using CRI-MAP in the Fpulation . Two SNPpulation , and linpulation .


Although genome-wide association studies have successfully identified thousands of variants associated to complex traits, these variants only explain a small amount of the entire heritability of the trait. Gene-gene interactions have been proposed as a source to explain a significant percentage of the missing heritability. However, detecting gene-gene interactions has proven to be very difficult due to computational and statistical challenges. The vast number of possible interactions that can be tested induces very stringent multiple hypotheses corrections that limit the power of detection. These issues have been mostly highlighted for the identification of pairwise effects and are even more challenging when addressing higher order interaction effects. In this work we explore the use of local ancestry in recently admixed individuals to find signals of gene-gene interaction on human traits and diseases.We introduce statistical methods that leverage the correlation between local ancestry and the hidden unknown causal variants to find distant gene-gene interactions. We show that the power of this test increases with the number of causal variants per locus and the degree of differentiation of these variants between the ancestral populations. Overall, our simulations confirm that local ancestry can be used to detect gene-gene interactions, solving the computational bottleneck. When compared to a single nucleotide polymorphism (SNP)-based interaction screening of the same sample size, the power of our test was lower on all settings we considered. However, accounting for the dramatic increase in sample size that can be achieve when genotyping only a set of ancestry informative markers instead of the whole genome, we observe substantial gain in power in several scenarios.Local ancestry-based interaction tests offer a new path to the detection of gene-gene interaction effects. It would be particularly useful in scenarios where multiple differentiated variants at the interacting loci act in a synergistic manner.The online version of this article (doi:10.1186/s12863-015-0283-z) contains supplementary material, which is available to authorized users. Advances in high-throughput genotyping technologies have enabled large-scale studies of genetic variation, from genome-wide association studies (GWAS) to inference of population history. The most notable use of high-throughput genotyping has been in GWAS where researchers have reproducibly identified thousands of genetic variants associated with many complex traits and common diseases. Despite the great success in identifying variants that contribute risk to disease, the majority of the genetic component of human traits and diseases remains unexplained. A potential source for this missing heritability is gene-gene interactions that alter disease risk in a coordinated fashion, for example when several genes are acting synergistically on a trait. Although of potential great interest, robust identification of gene-gene interactions has largely remained elusive, and despite numerous studies only a few interaction effects have been detected in human data –3. Most The development of accurate methods for discerning population structure have allowed for studies across different ethnicities including admixed populations (i.e. populations with recent ancestry from more than one continent such as African Americans). In addition to the standard linkage disequilibrium (LD) between nearby markers  admixed populations exhibit another form of correlation among variants at a coarser scale due to chromosomal segments of distinct ancestry that is commonly referred to as admixture-LD . This en12 pairs for a standard GWAS of 2.5 million SNPs), we propose to test interaction only between pairs of local ancestries (on the order of 5×105 pairs for recent admixtures). By performing a much smaller number of statistical tests, our approach solves the computational bottleneck and reduces the multiple testing correction burden. We derive the analytical formulation for our test assuming a single causal variant for each interacting locus and investigate its performance across a wide range of parameter values. Motivated by recent works that show ever-increasing evidence for multiple causal variants per locus , so that the minimum squared-correlation was 0.09. A correlation of 1 corresponding to the highest potential increase in power that can be achieve, since it will be equivalent to testing the interaction with the true causals while dramatically reducing the multiple testing corrections.For the test see further section on simulation). For ease of computation, we considered the number of causal SNPs per segment to be equal between the two interacting loci. The βi were randomly drawn from a left-truncated normal (cut at 0) distribution with mean 0 and variance 1. The causal alleles were chosen to be minor in one of the populations so that all effects go in the same direction in one population. We considered scenarios including 1 to 5 causal SNPs per locus, and selected the variants so that correlation between local ancestry and each SNP was either >0.1, >0.2 or >0.5, assuming low, moderate or high differentiation at the causal SNPs, respectively.We used models from equation  and 2)  2) and gj that maximizes K causal variants at locus i, where ρjk is the correlation between the tag SNP Gj* and the causal variant Gk) and then test only the product of that genotype with the best tag genotype at the second locus. Power was defined as the number of replicates for which the pairwise SNP interaction is significant at nG the number of SNPs tested equals 1 M when including genotyped SNPs only and equals 10 M when including common imputed SNPs from 1000 Genomes. For the local ancestry-based test, the threshold was nL = 1, 000 local ancestry segments.We perform both the local ancestry interaction and the pairwise SNP interaction test in a standard linear regression. However, instead of testing all combination of SNP, we first find the best combined tag in each locus (i.e. the single SNP −8 chance of recombination. At a recombination event, the next haplotype was selected with a 20 % chance of being European and an 80 % chance of being African to reflect the estimated admixture proportions in the literature [Similar to previous work , we simuterature , 28. Hapterature  with defAll supporting data are included as additional files.