ANGPTL 4 and ANGPTL 3 associated with obesity, FANOVA was able to identify both genes associated with obesity.While progress has been made in identifying common genetic variants associated with human diseases, for most of common complex diseases, the identified genetic variants only account for a small proportion of heritability. Challenges remain in finding additional unknown genetic variants predisposing to complex diseases. With the advance in next-generation sequencing technologies, sequencing studies have become commonplace in genetic research. The ongoing exome-sequencing and whole-genome-sequencing studies generate a massive amount of sequencing variants and allow researchers to comprehensively investigate their role in human diseases. The discovery of new disease-associated variants can be enhanced by utilizing powerful and computationally efficient statistical methods. In this paper, we propose a functional analysis of variance (FANOVA) method for testing an association of sequence variants in a genomic region with a qualitative trait. The FANOVA has a number of advantages: (1) it tests for a joint effect of gene variants, including both common and rare; (2) it fully utilizes linkage disequilibrium and genetic position information; and (3) allows for either protective or risk-increasing causal variants. Through simulations, we show that FANOVA outperform two popularly used methods – SKAT and a previously proposed method based on functional linear models (FLM), – especially if a sample size of a study is small and/or sequence variants have low to moderate effects. We conduct an empirical study by applying three methods  to sequencing data from Dallas Heart Study. While SKAT and FLM respectively detected  Advances in genotyping and sequencing technologies have revolutionized genetic studies of human diseases To identify additional genetic variants contributing to human diseases, efforts have been shifted from common variants of small effect towards uncovering rare variants of large effect. Benefiting from the recent high-throughput exome sequencing and whole-genome sequencing technologies, researchers were able to assess the spectrum of rare variants and comprehensively study their role in human diseases To improve the power of association analysis with sequencing data, burden tests, such as the weighted sum test analysis of variance fits perfectly with the paradigm of most case-control association studies, and has the advantage over an existing function-valued method It is now increasingly recognized that many variants jointly contribute to the observed phenotypic variation in complex human traits For both the currently proposed FANOVA approach and the FLM method of Luo et al. Before applying functional methods to perform an association test, we need to transform the discrete genotype profile of a subject  into smooth functions In functional data analysis, we denote a function, x-axis), which does not influence graphical representation of the data. Vertical dotted lines show “knots” – break points that divide the range of variant positions into segments along with two end points. Cubic B-splines The choice of basis functions is rather wide but can be narrowed to two popular options: Fourier basis system  optimization. Wood a priori assumptions about the direction and the magnitude of effects should be unaffected. Thus, we suggest a genotype relabeling algorithm to minimize the number of “flips” that, in turn, should decrease the number of noisy oscillations in smoothed data. 2 would obliterate the flip; the right panel shows the same data but genotype coding at the SNP2 position relabeled.The number of knots and the smoothing parameter aside, the functional fit to the data will depend on the variant coding. Single nucleotide polymorphism (SNP) genotype is usually coded “0” for homozygote with respect to the major allele, “1” for heterozygote, and “2” for homozygote with respect to the minor allele. The power of functional procedures may depend on the linearity of the functional fit. That is, if in the original sequence data the pattern 0-2 (or 2-0) is persistent, which can be expected with a negative pairwise LD between biallelic variants, a smoother is going to have a high frequency of oscillations. Negative LD is expected to be common based on the population genetics theory Once the continuous functions are obtained, the question remains how to perform statistical inference with functional data. Here, we propose a functional analysis of variance approach and provide an overview of the methods based on functional linear models by Luo et al. Suppose we have We wish to test if the mean genotype functions vary among A number of test statistics were proposed to perform the above test e.g., . For exaUnder the Gaussian assumptions, it can be shown that the numerator of The distribution of Shen and Faraway The method proposed by Luo et al. We now have to estimate the infinite-dimension function The coefficient vector It should be noted that in Luo et al. The sequence kernel association test (SKAT) was proposed by Wu et al. We performed simulation studies to evaluate FANOVA and compare its size and power to FLM and SKAT. The genetic data were simulated using the 1,000 genome project Two disease models were considered. First, we ran simulations for a model with both deleterious and protective causal variants. Therefore, the effect, To explore the effect of smoothing on functional procedures, we considered three different smoothing strategies:1. The number and the position of knots were chosen to concur with recommendations in Luo et al. 2. A knot was placed in every other genetic position and cubic B-splines were used as basis functions. As illustrated by 3. A knot was placed in every genetic position and an optimal smoothing parameter, unctions .https://sph.uth.edu/hgc/faculty/xiong/software-F.html. The sequence kernel association test proposed by Wu et al. The functional data were estimated using the fda Under the null model with no casual variants, empirical type I error rates are reported in jth iteration and Finally, via anonymous review of this article, we were encouraged to check the FANOVA performance at a nominal We started our simulations by examining the impact of the proposed genotype relabeling method on power of functional procedures. The results are summarized in As expected, genotype relabeling drastically increases power of functional procedures if penalized cubic B-splines are used to obtain smooth curves (note the difference between thick and thin blue lines). In the case of a small number of cubic spline basis functions, the relabeling does not have much of an effect because the resulting smoothed function are “too smooth” and are insensitive to SNP relabeling. Similarly, in the case of a large number of cubic spline basis functions, the relabeling does not have much of an effect due to high oscillation in the fitted curves. Based on the comparison of Taking these results into consideration, in the remainder of the article we used penalized cubic B-splines after genotype relabeling and the asymptotic test for the FANOVA method. We believe that penalized splines with the “optimal” amount of smoothing for each subject chosen through GCV is the most adequate way to represent genetic data out of the three different smoothing strategies that we considered. Additionally, parametric test has approximately the correct size and satisfactory power along with the best computational efficiency.Simulations were then conducted to evaluate power of the three methods under the two different disease models  and varied percentage of causal variants. To validate that FANOVA is also appropriate for GWAS data, we ran additional simulations in which we tested for an association a set of only common variants and a dichotomous phenotype. These results are available in ANGPTL3, ANGPTL4, ANGPTL5, and ANGPTL6. The four genes are members of the ANGPTL family, with variants found contributing to plasma triglyceride levels ANGPTL4 could be potentially associated with BMI We used FANOVA, FLM and SKAT to test for an association between body mass index (BMI) and ANGPTL 3; 94 individuals for ANGPTL 4; 147 individuals for ANGPTL 5; and 103 individual for ANGPTL 6), as well as genetic variants that had information for less than 70% of subjects . After multiple imputation and omitting variants with no variation, the total numbers of variants were 50, 70, 52, and 45 for ANGPTL3, ANGPTL4, ANGPTL5, and ANGPTL6 genes, respectively. We examined the phenotypic association with BMI obesity by splitting the individuals into two groups: BMI≤30 and BMI>30. The sample sizes were: 1,307 subjects (ANGPTL 3), 1,596 subjects (ANGPTL 4), 1,739 subjects (ANGPTL 5), and 1,365 subjects (ANGPTL 6). Genomic positions were available for all variants but for those from the ANGPTL 5 gene. For this gene, we assumed that sequencing variants were equally spaced over the genomic region. ANGPTL 4 with BMI obesity. In addition, FLM  and FANOVA  detected a marginal association between ANGPTL 3 and BMI obesity. No association evidence has been found for ANGPTL5 and ANGPTL6, which may suggest that these two genes make no contribution to BMI obesity, although the FANOVA method produced the smallest p-value of the approaches considered. After the Bonferroni adjustment for four tested genes, only the ANGPTL4 association (by SKAT and FANOVA) remains significant. Nevertheless, unajusted p-values for ANGPTL3 and ANGPTL4 genes appear to confirm previous findings, considering that both genes have been linked to obesity and related phenotypes in prior studies that employed independent data sets Although one of the strengths of functional approaches is that missing data are efficiently handled, software implementation of FLM by Luo et al. We have presented a new method based on functional analysis of variance for detecting an association of multiple genetic variants with a dichotomous phenotypic trait. The FANOVA framework is a natural strategy for the case-control study design that exploits the correlation structure among variants. Functional data analysis (FDA) methods, including both FANOVA and FLM, effectively utilize position and LD information over sequenced data which can result in increased power over competing methods like SKAT. Furthermore, we have found that if the sample size or the magnitude of the majority of the effects is small, our procedure has substantially higher power than that of both FLM and SKAT. FANOVA surpasses these methods in a common situation when there are multiple susceptibility variants within a gene but statistical power to detect any particular variant by itself is insufficient.We investigated different strategies for fitting functional objects to sequenced data. The typical FDA paradigm is that the smoother the original data are, the better, so that passing a smoother on each curve can effectively recover the true sample curves. If data jitter, the observations may contain additional random errors that need to be accounted for. As might be imagined, the typical FDA paradigm does not readily fit typical sequenced data. By using our flipping method of a reference allele, we tailored the genetic data to the FDA techniques which can result in a gain in power. To achieve better performance with our flipping method, the smoothing technique should be taken into careful consideration. With a typical approach based on a B-spline basis, a higher number of basis functions may result in an abundance of noise inherited by the smoother and subsequently may not lead to a power gain. To help overcome this noise, the number of basis functions can be truncated but the resulting fit may be overly smooth which would also not result in a gain in power. We recommend the use of penalized B-splines, in which the “optimal” amount of smoothing is based on the generalized cross validation algorithm. Our empirical findings demonstrated that our flipping method with the penalized B-splines greatly increased power of our procedure.The functional analysis of variance method provides access to other potentially useful extensions. It allows for a follow-up test A useful area for improvement would be an extension of our methodology to a multiple phenotype case as well as the ability to adjust for other covariates. If the additional phenotype and covariates are factors , then multifactorial ANOVA for functional data provides a solution. Similar to Eq. 2, test statistics for the main-effect and for the interaction effect functions could be based on the We believe that functional analysis of variance is a promising method for efficient locus-wide inference. As we saw in our application, FANOVA is capable of delivering powerful results with interpretable conclusions. We hope that this paper will promote research on development and implementation of FDA methods for genetic studies.Figure S1Empirical power of the three methods, only common variants,  subjects, first disease model . Left panel: . Right panel: .(TIFF)Click here for additional data file.Figure S2Empirical power of the three methods, only common variants,  subjects, second disease model .Left panel: Right panel: (TIFF)Click here for additional data file.Figure S3Empirical power of the three methods, only common variants,  subjects, first disease model .Left panel: Right panel: (TIFF)Click here for additional data file.Figure S4Empirical power of the three methods, only common variants,  subjects, second disease model .Left panel: Right panel: (TIFF)Click here for additional data file.Figure S5Empirical power of the three methods, only common variants,  subjects, first disease model .Left panel: Right panel: (TIFF)Click here for additional data file.Figure S6Empirical power of the three methods, only common variants,  subjects, second disease model .Left panel: Right panel: (TIFF)Click here for additional data file.


It is well known that genetic association studies are not robust to population stratification. Two widely used approaches for the detection and correction of population structure are principal component analysis and model-based estimation of ancestry. These methods have been shown to give reliable inference on population structure in unrelated samples. We evaluated these two approaches in Mexican American pedigrees provided by the Genetic Analysis Workshop 18. We also estimated identity-by-descent sharing probabilities and kinship coefficients, with adjustment for ancestry admixture, to confirm documented pedigree relationships as well as to identify cryptic relatedness in the sample. We also estimated the heritability of the first simulated replicate of diastolic blood pressure (DBP). Finally, we performed an association analysis with simulated DBP, comparing the performance of an association method that corrects for population structure but does not account for relatedness to a method that adjusts for both population and pedigree structure. Analyses with simulated DBP were performed with knowledge of the underlying trait model. Principal component analysis (PCA) and model-based estimation of ancestry are two widely used approaches for the detection and correction of population structure in admixed populations. The top principal components (PCs) from PCA can be used as covariates in a generalized linear model to protect against confounding resulting from population stratification in genetic association studies . IndividWe performed both supervised and unsupervised structure analyses for the GAW18 sample using the ADMIXTURE software. For the supervised structured analysis, proportional European, African, Native American, and East Asian ancestry was estimated using SNP genotype data for the odd-numbered chromosomes. There are 955 individuals in GAW18 who have available genotype data. We set the number of ancestral populations to 4 in the ADMIXTURE analysis, where the CEU and YRI samples of release 3 of phase III of the International Haplotype Map Project (HapMap)  were useet al [et al approach to general pedigrees by (a) selecting a set of genetically unrelated individuals and performing PCA on this unrelated set and (b) using the SNP weights from the unrelated set to obtain PCs for all remaining individuals in the sample. We name this approach R-PCA, where R indicates that this PCA method accounts for relatedness in the sample. We apply both sPCA and R-PCA to the GAW18 sample using 100,000 SNPs that were selected at random, without replacement, from the set of genotyped SNPs on the odd-numbered chromosomes.PCA has been shown to account for population stratification in samples with unrelated individuals. In samples with related individuals, however, the top PCs from standard PCA (sPCA) may not adequately account for population structure because of the complicated covariance structure of the genotypes among relatives. For genetic studies that contain nuclear families, Zhu et al  proposedKinship coefficients and identity-by-descent (IBD) sharing probabilities were estimated for all pairs of genotyped individuals in the GAW18 sample with the REAP (relatedness estimation in admixed populations) method . REAP giWe performed an association analysis with the first simulated replicate of DBP and SNPs that were genotyped on the odd-numbered chromosomes. We used the first time point for DBP and adjusted the DBP phenotype for age, sex, and current use of antihypertensive medications. The PLINK software was used to perform a linear regression association analysis, where the top 10 PCs, calculated from the EIGENSOFT software [There were 845 individuals in GAW18 for whom both SNP genotype data and phenotype information were available for simulated DBP, and we computed estimates of heritability using these sample individuals. Heritability estimates were calculated using a pedigree-based kinship coefficient matrix, an empirical matrix with REAP-estimated kinship coefficients, and a hybrid matrix of the two. The hybrid matrix uses REAP estimated kinship coefficients only for pairs of individuals who are related according to the available pedigree information. Individuals who are not related based on the pedigrees have a kinship coefficient value of 0 in the hybrid matrix, which corresponds to the same kinship coefficient value for the unrelated pairs in the pedigree-based kinship coefficient matrix. We implemented a restricted maximum likelihood estimation procedure to compute the variance components for heritability estimation.Figure Figure The individual ancestry results with ADMIXTURE illustrate that (a) an unsupervised analysis may not give appropriate proportional ancestry estimates in samples with related individuals and (b) a supervised ancestry analysis can give reliable individual ancestry estimates in related samples with ancestry admixture, as was previously demonstrated in an analysis of admixed population samples with relatedness .r2 = 0.92 . The top PC for sPCA, however, does not capture Native American ancestry as well as R-PCA, with an r2 value of 0.82. Using the top 10 PCs from sPCA as predictors in a linear regression model with Native American ancestry as the response yields an r2 = 0.86. The top 32 PCs from sPCA are needed as predictors in the regression model to match the proportional variance explained for Native American ancestry by the first PC from R-PCA. Proportional European ancestry explained by the top PC from R-PCA and PCs from sPCA are similar to the results for the Native American ancestry component because these two ancestry components are almost perfectly negatively correlated. The top 10 PCs from R-PCA have 2 rvalues of 0.74 and 0.69 for explaining proportional East Asian and African ancestry, respectively. In contrast, the top 10 PCs from sPCA have r2 values of 0.012 and 0.097, respectively, for East Asian and African proportional ancestry. Figure We find that the top PC from R-PCA is highly correlated with the Native American ancestry component from the supervised ADMIXTURE analysis discussed in the previous subsection; the linear regression model for predicting Native American ancestry from the top PC has an The vast majority of the REAP estimated kinship coefficients are consistent with the known pedigree relationships. There are, however, some cryptically related individuals from different families who were identified with REAP. Table p-values are systematically inflated for the expected null p-values that are less than 0.01. The genomic control inflation factor [p-values fall directly on or very close to the 45-degree line in the Q-Q plot until approximately p = 0.001. The large increase in the -log after this point corresponds to functional variants for the simulated DBP phenotype. Figure p-values for SNPs on the odd-numbered chromosomes. EMMAX identifies a number of highly significant associations with simulated DBP and SNPs in the functional region of the MAP4 gene on chromosome 3, where rs11711953, rs11706549, and rs11716779 are the three most significant SNPs with corresponding p-values of 1.2e-12, 1.4e-12, and 6.7e-10, respectively.Figure n factor , λ, for Heritability estimates of the first simulated replicate of DPB are remarkably close when using a pedigree-based kinship coefficient matrix, a REAP-estimated kinship coefficient matrix, and a hybrid of the two in the variance components analysis, where the corresponding heritability estimates  are 34.3% (21.7%-54.2%), 30.2% (18.3%-50.0%), and 33.1%(20.5%-53.4%), respectively. Estimation of heritability from variance components of pedigrees can lead to inflated heritability estimates resulting from confounding of shared environment of relatives. Recent work has been proposed to address this issue in GWAS samples by excluding relatives from a large-scale population study with empirical kinship coefficients that are greater than a specified threshold .Supervised individual ancestry analyses can give reliable proportional ancestry estimates in admixed population samples, provided that the surrogates for the ancestral populations are well represented in the analysis, but unsupervised individual ancestry methods perform poorly in this setting. We demonstrated that the top PCs in sPCA may not adequately reflect ancestry in samples with pedigrees from admixed populations. In contrast, our proposed method, R-PCA, can be used to obtain ancestry informative PCs in samples containing general pedigrees with known relatedness. Using the REAP relatedness estimation method, we obtained empirical kinship coefficients and IBD sharing probabilities in the GAW18 sample; we confirmed pedigree relationships and identified cryptic relationships that have not been reported. We also performed association testing with the first simulated replicate of DBP using the EMMAX association method, and genome-wide significant associations were detected with functional variants in the MAP4 gene on chromosome 3. Finally, we estimated the heritability of the first simulated replicate for DBP in the GAW18 pedigrees, and we found that the heritability estimates were remarkably similar when computing variance components with an empirical kinship coefficient matrix calculated with the REAP method, a pedigree-based kinship coefficient matrix, and a hybrid of the two kinship matrices.The authors declare that they have no competing interests.All authors participated in study design and analysis. TT drafted the manuscript, and all authors edited and approved the final manuscript.


The accuracy of genomic prediction depends largely on the number of animals with phenotypes and genotypes. In some industries, such as sheep and beef cattle, data are often available from a mixture of breeds, multiple strains within a breed or from crossbred animals. The objective of this study was to compare the accuracy of genomic prediction for several economically important traits in sheep when using data from purebreds, crossbreds or a combination of those in a reference population.The reference populations were purebred Merinos, crossbreds of Border Leicester (BL), Poll Dorset (PD) or White Suffolk (WS) with Merinos and combinations of purebred and crossbred animals. Genomic breeding values (GBV) were calculated based on genomic best linear unbiased prediction (GBLUP), using a genomic relationship matrix calculated based on 48 599 Ovine SNP (single nucleotide polymorphisms) genotypes. The accuracy of GBV was assessed in a group of purebred industry sires based on the correlation coefficient between GBV and accurate estimated breeding values based on progeny records.The accuracy of GBV for Merino sires increased with a larger purebred Merino reference population, but decreased when a large purebred Merino reference population was augmented with records from crossbred animals. The GBV accuracy for BL, PD and WS breeds based on crossbred data was the same or tended to decrease when more purebred Merinos were added to the crossbred reference population. The prediction accuracy for a particular breed was close to zero when the reference population did not contain any haplotypes of the target breed, except for some low accuracies that were obtained when predicting PD from WS and vice versa.This study demonstrates that crossbred animals can be used for genomic prediction of purebred animals using 50 k SNP marker density and GBLUP, but crossbred data provided lower accuracy than purebred data. Including data from distant breeds in a reference population had a neutral to slightly negative effect on the accuracy of genomic prediction. Accounting for differences in marker allele frequencies between breeds had only a small effect on the accuracy of genomic prediction from crossbred or combined crossbred and purebred reference populations. Genomic prediction refers to the prediction of genetic merit of selection candidates based on genome-wide marker genotypes using information from a reference population of individuals with both phenotypes and genotypes . Accuracet al. [et al. [According to theory, the improvement in accuracy of GBV for a specific breed based on using data from other breeds or crossbreds depends on the consistency of linkage phase between QTL and genetic markers across breeds and also on the similarity of QTL effects between breeds. Simulation results have shown either some  or no siet al.  reported [et al.  reported [et al. -10, beef [et al.  or sheep [et al. ,13. ThesIn a combined purebred and crossbred reference population, genomic predictions for a particular breed can be based on purebred data, on crossbred data, or on a combination of these. The question is how the use of data from multiple breeds affects prediction accuracies for a given breed. Adding information from unrelated breeds could have no impact, but the effect could also be negative, as marker effects may be averaged across breeds and marker allele frequencies may differ between breeds. The latter could also affect genomic relationships that are derived for genomic prediction. Furthermore, the contribution of using only crossbred animals for genomic prediction, which in some cases may be the only source of information, on the accuracy of genomic prediction of purebred individuals has not been addressed using real data.The objective of this study was to assess empirically and systematically the accuracy of genomic prediction based on purebred and crossbred data. The accuracy of genomic prediction was compared when using data from purebreds, from crossbreds, or from a combination of purebreds and crossbreds. Furthermore, we studied the effect of accounting for differences in marker allele frequencies between breeds on the accuracy of genomic prediction.et al. [et al. [The reference populations were data subsets extracted from a large reference population. The total reference population consisted of two research datasets known as the Sheep Cooperative Research Centre Information Nucleus Flock (INF) and the Sheep Genomics Flock (SGF). The INF consisted of nine flocks located across different sheep production regions in Australia that were linked by using common sires through artificial insemination. The SGF was a single research flock located in southern New South Wales, Australia. Both flocks used around 40% of sires from terminal breeds (Poll Dorset: PD and White Suffolk: WS), 20% sires from maternal breeds (Border Leicester: BL) and 40% Merino sires. Most dams used were purebred Merino (80%) or F1 crosses between Merino and BL (20%). The purebred Merino dams were used mainly in crosses with purebred Merino sires or BL sires. The crossbred dams were mated to PD or WS sires. As a result, the majority of progeny data were crossbreds and the main breed of purebred progeny was Merino. The complete reference population consisted of 10 772 animals genotyped and measured for the traits evaluated in this study. These animals were from 326 paternal half-sib families that varied in size from 10 to 216. Flock management and phenotypic recording schedules were similar across flocks. Furthermore, all data was acquired by “Sheep Cooperative Research Centre” and “Sheep Genomics Australia” under protocols that all had obtained appropriate ethical approval. Results of genomic prediction based on complete reference population are available in . More inet al.  and Whit [et al. , respectPrevious studies based on this data used the complete reference population consisting of multiple breeds ,13. Our The traits investigated were post-weaning weight (PWWT), post-weaning scanned eye muscle depth (PW-EMD) and post-weaning scanned fat (PW-FAT) measured between 125 and 300 days of age (standard deviation or SD = 52.4). Purebred Merinos were generally measured at an older age. Measurement of traits was performed based on defined recording schedules for the SGF and INF projects ,15. RecoA separate population was used to evaluate the accuracy of genomic predictions Table . These w−15). Furthermore, an individual sample was removed if the correlation of the genotypes  with another sample was equal or greater than 0.99. Following quality control, missing SNP genotypes within an animal were imputed using the Beagle software program [Animals from the reference and validation populations were genotyped using the 50 k Ovine SNP chip . The total number of SNP genotypes provided by this chip was 54 241, which decreased to 48 599 after applying quality control on genotyping data. Individual SNP genotype records were removed for call rates less than 95%, GenCal (GC) scores less than 0.6, and all genotypes for a given SNP were removed if the heterozygosity for the SNP deviated more than 3 SD from the population average heterozygosity, if the minor allele frequency was less than 0.01, for SNPs located on chromosomes X and Y and for SNPs that significantly deviated from Hardy-Weinberg equilibrium . Differences in accuracies resulting from different reference populations were tested using the Z-test statistic following .GBV were calculated based on genomic best linear unbiased prediction (GBLUP), replacing the pedigree-based numerator relationship matrix with a genomic relationship matrix ,19 basedy is a vector of phenotypes, b is a vector of fixed effects, g is a vector of random additive genetic effects, w is a vector of random maternal effects (fitted only for PWW), q is a vector of breed effects, s is a vector with sire by flock interaction effects and e is a vector of random residual effects. X, Z1 and W and Z2 are incidence matrices relating fixed, additive genetic, maternal, and sire by flock interaction effects to phenotypes. Q is a matrix with breed proportions for each animal. All random effects were assumed identically and independently distributed except for g, which was assumed distributed as: G is a genomic relationship matrix and In this model, GRM) used in GBLUP was calculated according to two methods, using Van Raden’s algorithm [GRM was calculated based on genotypes and the observed marker allele frequencies of all animals in the reference population based on the following equation: G1 = ZZ′/2 ∑ (pj)(1 − pj). In this equation Z = Mij − 2pj, Mij is the number of the second allele carried by animal i for SNP j, i.e. marker genotypes were represented as 0, 1 and 2, and pj is the frequency of the second allele for SNP j.The genomic relationship matrix /2 in which G21 and G22 refer to the GRM calculated based on each parental haplotype. Matrices G21 and G22 were calculated using the following equation: G2i refers to the GRM based on the paternal (i = 1) or maternal (i = 2) haplotype, Zi = Mij − pj, and Mij is the element of the incidence matrix (0/1) indicating the allele inherited for SNP j in the paternal or maternal haplotype for animal i. Matrices G2i were calculated using average frequencies of alleles present in that haplotype. To calculate G2, we derived phased genotypes using Beagle software program [In the second method (G2), the lgorithm , using G program  or a ped program . The latGRM (G1 and G2). Accuracies based on G2 using the two different phasing approaches were nearly identical. Thus, only results for G2 based on Beagle haplotypes are shown.Tables The GBV accuracy of Merino sires increased consistently with the size of the purebred Merino reference population for all three traits Tables , 4 and 5G1 and G2 for Merino sires based on prediction from combined purebred and crossbred Merinos, but there was no consistent pattern to these differences.The GBV accuracy of Merino sires when predicted from crossbred Merinos increased when data from purebred Merinos were added to the reference population. However, the accuracies were significantly lower compared to prediction from a similar number of purebred Merino haplotypes. For example, the GBV accuracy of PWWT based on 1000 to 3000 purebred Merinos ranged from 0.53 to 0.59 but ranged from only 0.41 to 0.54 when based on crossbred Merinos combined with those purebred Merinos , displaying values only for purebred Merino, BL, PD and WS validation sires. The figure shows that genetically the Merino breed is quite distinct from the other breeds , while the genetic differences between PD and WS are small.Figure The objective of this study was to compare the accuracy of genomic prediction for purebred sires based on purebred, crossbred, or combined purebred and crossbred reference populations. The results showed higher accuracy for predictions based on purebred data compared to crossbred data when the same number of haplotypes of that breed was present in the reference population, and very low to zero prediction accuracy when data was from another breed. Furthermore, the prediction accuracy tended to be the same or lower when data that contain haplotypes from other breeds were added. Nevertheless the results confirmed crossbreds of the target breed can be used in genomic prediction of purebred animals which is useful when purebred information is limited, or when the breeding objective is to improve crossbred performance.When predicting the GBV of purebreds, one would expect that data on crossbred animals of the target breed would provide less information than the same amount of data on purebreds from that breed, simply because the crossbreds (at least first crosses) contain only half the number of haplotypes of that breed. However, we found the accuracy from crossbreds to be lower also after accounting for the number of haplotypes, i.e. twice the number of crossbreds gave lower accuracy than purebreds. This may be because the Merino sires of the purebred Merino reference population are more related to the validation sires than the Merino ewes used as dams of crossbreds and hence the paternal haplotypes in Merino purebreds would be more informative in the prediction of GBV of the validation sires than the same number of maternal haplotypes in crossbreds. The mean and standard deviation of genomic relationships between paternal Merino haplotypes and the Merino validation set were 0.012 and 0.026, respectively, compared to 0.004 and 0.023 for maternal haplotypes. In our data, the dams of animals with records in the reference population were often breeding ewes from research flocks, whereas the sires were generally selected based on their relevance for commercial breeding flocks . AnotherThe reduction in GBV accuracy after adding data from another breed or from crossbreds to the reference population could also be explained by differences in marker effects between breeds as a result of differences in QTL-marker phase due to lack of LD between breeds, differences in QTL allele frequencies or different QTL effects in different breeds, in which the latter could possibly be also due to dominance and epistatic effects. These factors could lead to averaging of marker effects across breeds, resulting in less additive genetic variation explained than when effects are estimated within breed. Figure G2, could potentially alleviate this problem. However, G2 on average provided similar prediction accuracies as G1. Hence, using breed-specific allele frequencies in constructing the GRM had a limited impact on prediction accuracy. Makgahlela et al. [G1 and G2 was 0.94.Our results also showed that adding information from crossbreds that include distant breeds to a purebred reference population can in some cases lead to reduced accuracies. In addition to breeds having different QTL effects and marker-QTL LD, this could be explained by marker allele frequencies being different between breeds. If the GRM is based on average allele frequencies across breeds, then the genomic relationships within a breed could change if the GRM is derived from a multi-breed instead of the purebred population. Thus, rather than unrelated individuals providing no information, as in regular pedigree-based BLUP, adding animals from different breeds to a genomic evaluation could have a negative effect on accuracy. Figure a et al.  also repet al. [et al. [Our results, which are based on a 50 k marker density, suggest that different marker effects were estimated when using information from different breeds, which could be because of different marker-QTL LD or different QTL effects between breeds. This was also inferred by Daetwyler et al.  and Mogh [et al.  based on [et al. -11 show Marker panels with a higher density may provide higher LD and may overcome the problem of different marker-QTL LD between breeds. However, QTL effects may still differ between breeds, and between purebreds and crossbreds. Large numbers of phenotypes are required to estimate and test these differences.The accuracy of genomic prediction in purebred Merinos in this study was higher than theoretical predictions using Goddard’s methods , assuminThe results of this study show zero to small negative effects on genomic prediction accuracy in Australian sheep breeds when data from distant breeds were included in the reference population used to develop genomic predictions. This means that for predictions based on intermediate marker density (50 k) and GBLUP, it is currently necessary to use breed-specific reference populations. This problem might decrease when marker panels with higher density are used. However, information from crossbreds of the target breed can be used in genomic prediction of purebred animals, and this is particularly useful when there is limited information on purebreds.


Across animal species, offspring of closely related mates exhibit lower fitness, a phenomenon called inbreeding depression. Inbreeding depression in humans is less well understood because mating between close relatives is generally rare and stigmatised, confounding investigation of its effect on fitness-relevant traits. Recently, the availability of high-density genotype data has enabled quantification of variation in distant inbreeding in ‘outbred’ human populations, but the low variance of inbreeding detected from genetic data in most outbred populations means large samples are required to test effects, and only a few traits have yet been studied. However, it is likely that isolated populations, or those with a small effective population size, have higher variation in inbreeding and therefore require smaller sample sizes to detect inbreeding effects. With a small effective population size and low immigration, Northern Finland is such a population. We make use of a sample of ∼5,500 ‘unrelated’ individuals in the Northern Finnish Birth Cohort 1966 with known genotypes and measured phenotypes across a range of fitness-relevant physical and psychological traits, including birth length and adult height, body mass index (BMI), waist-to-hip ratio, blood pressure, heart rate, grip strength, educational attainment, income, marital status, handedness, health, and schizotypal features. We find significant associations in the predicted direction between individuals' inbreeding coefficient (measured by proportion of the genome in runs of homozygosity) and eight of the 18 traits investigated, significantly more than the one or two expected by chance. These results are consistent with inbreeding depression effects on a range of human traits, but further research is needed to replicate and test alternative explanations for these effects. Inbreeding is mating between related individuals, whereby offspring inherit two copies of the same ancestral gene (autozygosity). Because all members of a species are related to some degree, all individuals are likewise “inbred” to some degree, but there is variation between individuals in how closely or distantly related their parents are. It is widely observed across species that offspring of closely related mates tend to have lower fitness and fitness-related characters The theoretical relation of directional dominance to inbreeding depression is that purifying selection is less efficient at eliminating  recessive deleterious alleles than additive or dominant deleterious alleles, so that extant deleterious alleles tend to be more recessive than would be expected due to chance . When genetically related individuals mate, offspring are at an increased risk of inheriting two copies of recessive deleterious alleles, which would expose the offspring to the full  deleterious effects of those alleles, hence decreasing the fitness of the offspring.F) coefficients based on knowledge of pedigree. In many animals this methodology is feasible and many inbreeding effects have been demonstrated Until recently, inbreeding effects could only be tested using inbreeding (Froh) can be used to measure autozygosity and thus inbreeding Recently, the availability of high-density genotype information has enabled the estimation of inbreeding without any knowledge of pedigree, by looking at the proportion of the genome that occurs in stretches of homozygous DNA . Whereas any two individual alleles might be homozygous by chance , long ROHs are likely to represent two segments that are “autozygous”, or identical by descent from a common ancestor. As such, the proportion of the genome in ROHs  from a relatively isolated population  and a clinical examination (N = 6033) from the 31-year follow-up study obtained in 1997. At the time of the assessment the participants were between 29 and 33 years old (M = 31.3±0.4); this narrow age range obviated the need to control for age in our analyses. The cleaned genotypic dataset consisted of 5368 individuals, 2574 males and 2794 females, but sample sizes differ per variable. Informed consent for the use of the data and DNA was obtained from all subjects, and ethical approval was granted by the Ethics Committee of the Northern Ostrobothnia Hospital District in Oulu (Finland).The Northern Finland 1966 Birth Cohort (NFBC) is a longitudinal population-based birth cohort including 12,058 individuals born in 1966 in the two northernmost provinces of Finland (Lapland and Oulu), which comprised 96.3% of all births Various physical and psychological measures were obtained from the participants, some by means of questionnaire and others during a clinical examination. Continuous variables were winsorised at three standard deviations from the mean and standardised separately by sex to remove the effect of potential gender differences. Detailed information about the measures and the data cleaning steps per measure can be found in the Supplementary Methods in During a clinical examination individual's anthropometrical data, blood pressure, heart rate, and various physical fitness measures were obtained. For this study we used individual's measures on height, BMI, diastolic and systolic blood pressure, heart rate, waist-to-hip ratio, and grip strength.Participants filled out a mailed questionnaire with questions about their background, about physical exercise and performance capacity, occupation and working history, environment, health, gynaecology, the use of public health services and living habits. For the present study we used self-report data on marital status, household income, educational attainment, birth length, handedness, life satisfaction, self-rated health, lifetime health problems verified by a doctor, and schizotypal features  st or 2nd degree relatedness (Pi-Hat ≥ 0.20), and individual missingness , resulting in the removal of 178 individuals.DNA samples were collected in accordance with standard protocols and were genotyped on the Illumina 370 duo Chip >10 using PLINK Furthermore, we removed SNPs with a minor allele frequency (MAF) <0.05, with a Hardy–Weinberg equilibrium (HWE) test P<0.001, and a call rate <95% . We then pruned the SNP data lightly  by summing the total length of their genome that is in autosomal ROHs and divide that by the total SNP-mappable autosomal genome length (2.77 × 109).Based on the SNP data for each individual we obtained an index of the level of inbreeding in the individual's ancestry. Runs of homozygosity (ROHs) are homozygous stretches of DNA that can be observed in the offspring of even distant relatives In this study we defined ROHs  with each of the phenotypes described above. Sex differences in the phenotypic measures were controlled for in all analyses. We present results controlling for zero, 1, 5, and 10 ancestry-informative principal components (PCs) as obtained from GCTA Subsequently, we determined the correlation of inbreeding  and in the expected direction with eight of the 18 phenotypes, including: height, grip strength, household income, educational attainment, birth height, life satisfaction, Physical Anhedonia Scale, and Social Anhedonia Scale. This is significantly more than expected by chance (p = 1.1 *10-6). ). For all these traits higher levels of inbreeding are associated with low-fitness trait values. For one scale – lifetime health problems – we found a significant association with inbreeding in the opposite (unexpected) direction: individuals with higher Froh score lower on the lifetime health problems scale.We tested for a correlation between −3). When controlling for ancestry, the correlation between the inbreeding measure and the lifetime health problems scale remained significant (in the unexpected direction).Correcting for ancestry by controlling for 1, 5, or 10 ancestry-informative PCs tends to attenuate the associations; when controlling for 1 PC the relationships between the inbreeding measure and grip strength as well as life satisfaction are no longer significant, and when controlling for 5 PCs the relationship between inbreeding and birth length is no longer significant. Accordingly, when controlling for 5 or 10 ancestry PCs, five of the 18 traits  remain correlated significantly in the expected direction – this is more than expected by chance  would be associated with traits that have been under directional selection. For between five and eight of the 18 traits that we tested (depending on stringency of ancestry control), we detected significant inbreeding effects in the predicted direction: that is, higher inbreeding was associated with the lower-fitness ends of the traits. This proportion of significant inbreeding effects is significantly more than the one or two expected by chance due to multiple testing.Several of these traits, or similar traits, had been previously linked with inbreeding, either via estimates of consanguinity or genetic autozygosity. Shorter height had recently been linked with autozygosity Schizophrenia has previously been linked with inbreeding, both via consanguinity Inbreeding has previously been associated with lower intelligence (IQ) via consanguinity studies Nine of the 18 traits we tested did not show a significant association with inbreeding. This is not surprising even if true inbreeding effects were pervasive, because our sample is not large enough to afford sufficient power to detect all the existing effects if they are of the small size predicted in outbred populations negative association between inbreeding and lifetime health problems. One of the most straightforward predictions of inbreeding depression is a detriment to health, whereas we find greater inbreeding is associated with fewer doctor-verified health problems, both before and after controlling for ancestry stratification. Cancer, condyloma, and fractures were the only individual health problems that were significantly associated with inbreeding  – given that 32 health problems comprised the checklist, three significant effects could easily be due to chance. Similarly, the negative association of inbreeding with the overall health problems scale could be due to chance, but the observed pattern of results renders highly unlikely the predicted inbreeding depression effect on doctor verified health problems.A perplexing result is the significant Overall, our results are generally consistent with evolutionary genetic expectations regarding inbreeding depression in humans; however, the results should be interpreted with caution because of the aforementioned alternative explanations for certain traits, and the unexpected positive association of inbreeding with a scale measuring lifetime health problems. Nevertheless, our study is the first study testing the association of a genotype-based inbreeding measure with a range of physical and psychological traits in the same large sample. It therefore represents an important point of reference for further investigation of inbreeding depression in humans, which should investigate these and other traits in populations with different genetic structure and in samples that allow competing explanations to be tested.File S1Supporting Information File.Supplementary Methods. Detailed information about the measures and the data cleaning steps per measure. Supplementary Table S1. Information on the quality control procedure of the genotype data. Supplementary Table S2. Details of the parameters used for the runs of homozygosity analysis. Supplementary Material: Descriptive Statistics. Descriptive statistics of all phenotypic measures.(DOCX)Click here for additional data file.


Setaria italica) was one of the earliest cereal crops to be domesticated and served as a staple crop for early civilizations in China, where it is still widely grown today. In the present trial, a panel of foxtail millet elite varieties, which were released in the last sixty years in different geographical regions of China, was characterized using microsatellite markers (SSRs). A clear separation of two subpopulations corresponding to the two eco-geographical regions of foxtail millet production in China was identified by the dataset, which also indicated that in more recently released elite varieties, large quantities of accessions have been transferred from spring-sowing to summer-sowing ecotypes, likely as a result of breeding response to planting configurations. An association mapping study was conducted to identify loci controlling traits of major agronomic interest. Furthermore, selective sweeps involved in improvement of foxtail millet were identified as multi-diverse minor effect loci controlling different agronomic traits during the long-term improvement of elite varieties. Our results highlight the effect of transition of planting configuration and breeding preference on genetic evolvement of crop species.Crop improvement is a multifaceted micro-evolutionary process, involving changes in breeding approaches, planting configurations and consumption preferences of human beings. Recent research has started to identify the specific genes or genomic regions correlate to improved agronomic traits, however, an apparent blank between the genetic structure of crop elite varieties and their improving histories in diverse modern breeding programs is still in existence. Foxtail millet ( Setaria italica (L.) P. Beauv.) was one of the earliest crop species to be domesticated. It has been grown as a crop in China for more than 8,700 years and recent archeological evidence has pushed the earliest evidence for the domestication of this crop even further back to 11,500 years before present  and 2011 [E2]), Anyang  [E3] and Changzhi  [E4] during summer growing seasons of foxtail millet. Eight agronomic characters including plant height (PH), panicle length (PL), peduncle length (PEL), panicle diameters (PD), stem diameters (SD), heading date (HD), panicle weight (PW) and grain weight of single panicle (GW) were measured for each accession. Five individual plants from each accession were randomly selected for the measurement. All association tests were conducted with the mixed linear model [One hundred and ninety-three varieties released in the recent three decades were grown in Beijing (Geographic coordinate: N 39.93ar model  using TAar model  (“Trait ar model  (A modelar model .Fst (F statistics) values of microsatellite variations were used to detect genomic regions under selection pressures from landrace to elite varieties by using PowerMarker [http://www.phytozome.net/search.php), and overlapping genes were determined as candidates.erMarker  (A compuTable 2).All seventy-seven SSR markers were successfully amplified from DNA of all elite variety accessions, and all markers were polymorphic across the 348 accessions. A total of 1376 alleles were detected. The average allele number per locus was 17.87, with a minimum of 5 and a maximum of 34. The average number of genotypes observed per locus was 24.20, with a minimum of 8 and a maximum of 80. For gene diversity, the average number of each locus was 0.82, ranging from 0.47 to 0.95. The average PIC (Polymorphic index content) value for markers was 0.80, ranging from 0.44 to 0.95. Heterozygosity per locus on average was 0.03, ranging from 0 to 0.40. The average homozygosity per line was greater than 95%, which indicated that, as expected given foxtail millet’s naturally selfing reproductive habit, most of the elite varieties used in this study were nearly inbred lines . This implied that there might be two divergent subpopulations. According to the second-order statistics developed for STRUCTURE [S1B Fig). This result suggested that these foxtail millet varieties can be grouped into two populations, here designated as G1 and G2. For each inferred population, a second iteration of STRUCTURE analysis was conducted using the same approach. Our results indicated that G1 and G2 are both clearly divided into three (K = 3) subgroups . Here we designate the six subgroups identified as as G1-1, G1-2, G1-3, G2-1, G2-2, and G2-3.Admixture model-based calculations were conducted by varying K from 1 to 10 with 20 iterations per K. When we ran the STRUCTURE simulations using all 348 accessions, the LnP(D) value increased with K from 1 to 10, but showed an evident knee at K = 2 (TRUCTURE  to estimS1 Table). A principal component analysis (PCA) was conducted to further assess the population subdivisions identified using STRUCTURE . Plotting of the first three principal components  shows separation of the subpopulations inferred by STRUCTURE, and is also consistent with the neighbor-jointing tree of inferred subclusters .The G1 cluster was comprised of varieties cultivated in spring-sowing eco-regions and a few lines in the summer-sowing regions but developed prior to the 1980s. Most elite varieties in the G1 group are not used in grain production currently. The G2 cluster was composed of elite varieties collected from the summer-sowing eco-regions, and were mostly developed after 1980s (Table 3). Varieties in the G1 cluster possess higher levels of diversity, including higher number of alleles per locus, higher gene diversity and PIC values and greater numbers of cluster-specific alleles, compared to elite varieties grouped into G2. The diversity difference between subgroups and phylogenetic relationship among them can also be seen from a neighbor-jointing tree of STRUCTURE inferred subclusters within each topmost hierarchy cluster . Pairwise estimates of Fst and genetic distance among six model-based subpopulations were also performed to infer genetic relationships among subgroups (Table 4). A neighbor-joining tree of the 348 varieties characterized in this study was concordant with the results of the STRUCTURE analysis .The genetic diversity was assessed per locus for each subgroup defined based on STRUCTURE, as well as for accessions grouped based on their released date , as can be seen especially in the three subclusters in G2. Varieties released by breeding programs conducted in Shanxi and Jilin were dissimilar from most other lines, suggesting unique germplasm was incorporated into these breeding programs.Varieties from the same breeding programs and similar eco-environmental conditions tended to be more closely related (Table 5). A total of 272 alleles  were identified as private alleles. Improved lines released in 1950s had the lowest allele count and the lowest genetic diversity in this analysis. In order to assess the significance of the differences observed between varieties released in different decades, FPTest was used to assess the statistical significance of differences in allele count between populations with different numbers of individuals. The results of this analysis indicated that allele number reductions of pairwise periods of 1990s/1970s, 1990s/1980s, and 2000s/1970s were significant at P<0.05, indicating a significantly loss of alleles accompanied progress in foxtail millet breeding progress in China.Varieties released in the 1970s had higher numbers of total alleles, gene diversity, PIC values and allele number per locus than varieties released in later decades . By grouping varieties by their release date, an obvious transition in genetic constitution of foxtail millet varieties becomes apparent when varieties are grouped by release date . In 1950s and 1960s, nearly all released varieties are spring-sowing ecotypes. Summer-sowing ecotypes begin to be released in 1970s and 1980s. In the recent two decades, the majority of newly released elite varieties are summer-sowing ecotypes, which was consistent with STRUCTURE inferred in S4A Fig) shows a clear decline of production area devoted to foxtail millet accompanied an increase in the production area devoted to maize production in China. In the last thirty years, the geographical distribution of foxtail millet growing areas has shifted greatly  which is correlated with the shift of germplasm foundation from primarily spring sowing ecotypes to summer sowing ecotypes in newly released improved varieties.Associations of varieties were characterized using PCA  analysis . Two-hundred-and-two (55.96%) of the significant marker/trait associations we detected were observed only in data from a single environmental condition, reinforcing the importance of genotype-by-environment interactions in the determining of morphological phenotypes in foxtail millet. Of the remaining marker/trait associations, 91 (25.21%) and 53 (14.68%) were identified simultaneously in two or three environments, respectively. Fifteen (4.15%) phenotype/marker associations were detected in all four environmental conditions, suggesting the alleles linked to these markers influence agronomic phenotypes in a largely environment independent manner (Table 6).Association analysis using the 193 elite varieties in our dataset which were primarily released in the most three decades was used to identify the molecular basis of variation in key agronomic traits in foxtail millet. A total of 361 significant marker-phenotype correlations were observed (P<0.05) for eight morphological characters scored under four different experimental conditions . The loss of diversity during the domestication and improvement process of S. italica shown in this study agrees well with other ancient crop species, such as maize [In this study, the genetic diversity of a set of Chinese foxtail millet varieties, released over the past six decades, was analyzed using DNA microsatellite markers. The average number of alleles per locus was higher than previous reports by Jia et al.  and Liu as maize  and riceas maize . This imas maize  and contas maize , which mS7 Fig). This result is concordant with the SNP result by Jia et al. (2013) [S8A Fig) from hybridization between local types and improved lines from summer sowing eco-regions. This probably led to the mixed genetic basis of elite varieties released in ESR and SR eco-regions of China that were generally designated as spring type in this study. Combined phylogenetic analysis of elite varieties and traditional landraces  also illustrate that more landraces from Summer-sowing eco-regions (SSSR) have been utilized in variety breeding programs. For instance, the development of Yugu1 in the early 1980s in Henan province has greatly changed the breeding situation of foxtail millet. With strong resistance to lodging, higher grain yield and superior quality, Yugu1 was not only the dominant elite variety in agricultural production, but also served as the main parent for pedigree breeding in most breeding programs from then on, including those institutes located in spring sowing regions . This meant many alleles from this summer sowing variety were incorporated into more recent spring sowing elite varieties and indeed, in this study we found that many elite varieties released after 1990s were in more genetically similar to the summer sowing type .Analyses of phylogenetic relationships in this trial suggest that varieties released in China are clearly divided into two groups, which correspond to the summer and spring ecotypes. Heading date differentiations of the two groups under diverse environmental conditions also support this conjecture (. 2013) , implyin. (2013) –36. Wang. (2013)  employed , implyi. (2013) . SecondlTable 3). Accessions released in the last two decades from the same breeding program are closely related and form distinct branches in the NJ tree . Dissemination of beneficial alleles across different breeding programs has the potential to catalyze the development of greatly improved elite varieties, reversing the declining rate of yield gain observed for foxtail millet since the 1990s.Although foxtail millet elite varieties still show high levels of diversity, the population structure and NJ (Neighbor Joining) classification presented here clearly indicate that the genetic diversity within individual breeding programs and institutes is decreasing . At that time, the dominant agricultural system was one year, one harvest, even in the North China Plain where the climate is such that two harvests per year are possible [Foxtail millet landrace collections and comparisons were mostly conducted between the 1950s and the 1970s in China  are different from previous analysis [Table 6) under three of the four environmental conditions and may represent valuable genomic regions contributed to this important morphological and grain-yield related agronomic trait.Association mapping analysis revealed that the majority of significant marker/phenotype correlations identified in this study were environment specific and acted only on a single trait, consistent with previous linkage analysis reports for foxtail millet , 19. Howanalysis  using woF-test between foxtail millet elite varieties and landraces revealed 11 SSR loci that had significantly (>97.5%) diversified between these two gene pools, owing to the long period of breeding selection or local adaptation . Two loci were localized in gene-coding regions (Si017865m and Si016673m), which are potentially important genes involved in different metabolic pathway or have played vital roles in foxtail millet improvement. All 11 genomic regions under selection were co-localized with significantly association loci controlling agronomically important traits in foxtail millet (S2 Table). These may be vital loci for morphological improvement of agronomic traits in foxtail millet. Results of the co-localization of selective sweep regions detected by SSRs and GWAS in this study implies that breeding of elite varieties of foxtail millet in China has been mainly focused on selection of multiple diverse minor-effect loci controlling different agronomic traits during long term breeding for improved varieties. This is dissimilar from domestication related selection where there can be rapid selection for large effect alleles which change plant morphology [An rphology . It can Raw data created in this trial could be found in supplemental materials as S1 Fig(A) Proper K inferred through the ad hoc procedure described in Pritchard et al. (2000); (B) The second order of statistics of Delta K based on methods developed by Evanno et al. (2005) for optimal K value determination.(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(A) and (B): Proper K identification by LnP(D) and delta K of G1; (C) and (D): Proper K identification by LnP(D) and delta K of G2; Phylogenic relationships among varieties (E) and subclusters (F) were indicated by colored lines.(TIF)Click here for additional data file.S4 FigA) Cropping area transitions of main cereal crops including rice, wheat, maize, foxtail millet, sorghum and barley during last six decades; (B) Changing of planting distributions of foxtail millet in China during last thirty years.((TIF)Click here for additional data file.S5 Fig(A) Venn plot of the numbers of significant (P<0.05) QTLs detected in this trial among four environments; (B) Relationship between number of significantly associated SSR markers and agronomic traits under diverse environmental conditions; (C) Relationship between numbers of traits associated with the same marker and amount of SSR loci.(TIF)Click here for additional data file.S6 Fig(A) and gene diversity, PIC values and heterozygosity (B) per locus detected in three panels of gene pools of Setaria identified using SSRs. Microsatellite diversity data were collected from Wang et al. (2012), Jia et al. (2013) and this study, which were analyzed using the same set of SSRs in the same lab; (C) Phylogenetic relationships between landraces (Blue)  and elite varieties (Green) sampled in this trial; (D) Phylogenetic analysis of four subclusters defined in landraces  and subgroups inferred in this study.Allele and genotype no. (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.S9 FigBootstraps across loci were repeated for 1000 times and the 97.5% up border is indicated by broken lines.(TIF)Click here for additional data file.S1 Table(DOC)Click here for additional data file.S2 Table(DOC)Click here for additional data file.S3 Table(XLS)Click here for additional data file.


In pig breeding, selection is usually carried out in purebred populations, although the final goal is to improve crossbred performance. Genomic selection can be used to select purebred parental lines for crossbred performance. Dominance is the likely genetic basis of heterosis and explicitly including dominance in the genomic selection model may be an advantage when selecting purebreds for crossbred performance. Our objectives were two-fold: (1) to compare the predictive ability of genomic prediction models with additive or additive plus dominance effects, when the validation criterion is crossbred performance; and (2) to compare the use of two pure line reference populations to a single combined reference population.We used data on litter size in the first parity from two pure pig lines (Landrace and Yorkshire) and their reciprocal crosses. Training was performed (1) separately on pure Landrace (2085) and Yorkshire (2145) sows and (2) the two combined pure lines (4230), which were genotyped for 38 k single nucleotide polymorphisms (SNPs). Prediction accuracy was measured as the correlation between genomic estimated breeding values (GEBV) of pure line boars and mean corrected crossbred-progeny performance, divided by the average accuracy of mean-progeny performance. We evaluated a model with additive effects only (MA) and a model with both additive and dominance effects (MAD). Two types of GEBV were computed: GEBV for purebred performance (GEBV) based on either the MA or MAD models, and GEBV for crossbred performance (GEBV-C) based on the MAD. GEBV-C were calculated based on SNP allele frequencies of genotyped animals in the opposite line.Compared to MA, MAD improved prediction accuracy for both lines. For MAD, GEBV-C improved prediction accuracy compared to GEBV. For Landrace (Yorkshire) boars, prediction accuracies were equal to 0.11 (0.32) for GEBV based on MA, and 0.13 (0.34) and 0.14 (0.36) for GEBV and GEBV-C based on MAD, respectively. Combining animals from both lines into a single reference population yielded higher accuracies than training on each pure line separately. In conclusion, the use of a dominance model increased the accuracy of genomic predictions of crossbred performance based on purebred data.The online version of this article (doi:10.1186/s12711-016-0220-2) contains supplementary material, which is available to authorized users. The effect of dominance, a non-additive genetic effect, has traditionally been ignored in genetic evaluation of livestock populations. There are three reasons for this: 1) lack of informative pedigrees, typically requiring large full-sib families for accurate estimates of dominance effects  lack of . The recIn some livestock production systems, including pigs, crossbred animals are used in commercial production to exploit heterosis and complementary effects. The aim of selective breeding programs in these systems is to maximize crossbred performance, where selection is carried out within pure lines using data from purebred animals . Howevers than 1 , 11. Genmentclasspt{minimaOne of the challenges of implementing genomic selection in crossbreeding programs is to determine whether marker effects should be predicted from pure line or crossbred data. When non-additive genetic effects or G × E exist, purebred performance is likely to be a poor predictor of performance in crossbred descendants, which has led to suggest the use of a training dataset consisting of crossbred animals , 13, 14.ominance . Previouominance , 16. IncWe used data on litter size at first parity from two pure pig lines (Landrace and Yorkshire) and their reciprocal crosses Fig. . The datLitter sizes of 489,523 Landrace and 316,127 Yorkshire sows were used to calculate corrected phenotypic values for litter size for each line separately (see details below). Corrected phenotypic values for litter size at birth (LSc), rather than raw observations, were used as response variables for genomic prediction and to estimate additive and dominance genetic variances. The reason for using LSc as response variable was to reduce noise by removing non-genetic effects, which could be estimated much more accurately using a large dataset that includes all contemporaries and relatives, rather than using only genotyped animals. Contemporary group effects were estimated using a traditional pedigree-based linear model including herd–year–season, month at farrowing and effects of hybrid indicator (0 = pure litter and 1 = hybrid litter), age at first farrowing (linear covariate), artificial insemination (AI) , along with random effects of service sire, animal additive genetic effects, and residuals. The LSc was computed as the original observations of litter size adjusted for all non-genetic effects from this model.−7). For SNPs with less than 2 % missing genotypes, the most common genotype at each SNP was identified within each population and assigned to the missing genotypes. Animals with more than 10 % missing SNP genotypes were also removed. After editing, 34,216 and 35,135 SNPs remained for 2085 Landrace and 2145 Yorkshire sows, respectively. More details about the data are in [A total of 2740 Landrace pigs (2085 sows and 655 boars) and 2325 Yorkshire pigs (2145 sows and 180 boars) were genotyped using the Illumina PorcineSNP60 BeadChip . Quality control of the genotype data consisted in removing SNPs with a call rate less than 90 %, SNPs with a minor allele frequency (MAF) less than 1 %, SNPs with more than 2 % missing genotypes, and SNPs that deviated strongly from Hardy–Weinberg equilibrium  and 2030 Yorkshire × Landrace (sire–dam) and were born between 2009 and 2012. Pedigrees were available for both purebred and crossbred animals and all crossbred animals could be traced back to their purebred parents. Similar to the purebred Landrace and Yorkshire data, litter size of crossbred animals were calculated by adjusting for estimates of non-genetic effects obtained from a traditional animal model with a pedigree-based relationship matrix. The model included herd-year-group, month at farrowing and a linear covariate of age at first farrowing and, as well as random animal additive genetic effects and residuals .The purebred genotyped animals were split into training and validation datasets to evaluate the accuracy of genomic prediction for crossbred performance Fig. . The LanTwo models for genomic prediction were evaluated. The first model included only additive effects (MA) and was used to estimate the additive effect associated with each SNP:The second model (MAD) included both additive and dominance effects associated with each SNP and was as follows:The definition of the elements in this model is analogous to that in model MA. In addition, raftery.diag function of the R package Coda [The BayesC method proposed by Habier et al.  was usedage Coda . Convergage Coda .jth SNP of the ith individual, with jth SNP in breed jth SNP and Genomic estimated breeding values (GEBV) were calculated as the expected genotypic value of the offspring of a boar. From the estimates of additive marker effects  and GEBV for crossbred performance (GEBV-C). GEBV were calculated as the expected genotypic values of the offspring of a boar carrying a certain set of SNP genotypes, when this parent is mated at random to its own line (GEBV) or to the other pure line (GEBV-C). Thus, from the estimates of both additive . Thus, for animal pjŕ and qjŕ, which are the frequencies of alleles A and a for the jth SNP in line For crossbred offspring, the expected genotype frequencies of the offspring of a parent depend on the allele frequency in the other pure line  value in the training dataset. The superiority of MAD over MA was tested by a likelihood ratio test.Predictive ability of a model (with respect to accuracy and unbiasedness) was evaluated by comparing the GEBV of the boars in the validation dataset with the mean corrected phenotypes of their crossbred offspring. Unbiasedness of GEBV was assessed by regressing mean corrected phenotypes of crossbreds on the GEBV of the boars in both lines. A necessary condition for unbiased predictions is that the regression coefficient does not deviate significantly from 1. Prediction accuracy of GEBV was measured as the correlation between GEBV of boars in the pure lines and mean corrected crossbred-progeny performance. This correlation was divided by the average accuracy of mean-progeny performance, i.e. the mean of entclass1pt{minimaMAD had better predictive ability than MA for both the Landrace and Yorkshire lines Table . IncludiEnlarging the training dataset by combining Landrace and Yorkshire animals into a single training population increased the prediction accuracy of MA and MAD models for both lines Table  with theThe MAD model improved data fit over the MA model for both the Landrace and the Yorkshire data Table . A lowerCoefficients of regression of corrected phenotypes of crossbreds on the predicted breeding values of boars in both lines show that, for the Landrace line, the variance of the GEBV was overestimated, i.e. most regression coefficients were less than 1.0 Table . When trEstimates of additive genetic variance and heritability obtained with the pedigree-based model differed from those obtained with the genomic models Table . The estWe tested whether including dominance effects in genomic prediction models increased the prediction accuracy of purebred animals for crossbred performance. We provide evidence that supports this premise by showing that including dominance increased the prediction accuracy for litter size for both the Landrace and Yorkshire lines. We also found that combining the data from the two lines into a single reference population improved prediction accuracy for both lines. Therefore, a dominance model can be used to increase the accuracy of genomic predictions for crossbred performance.We showed that crossbred performance was predicted more accurately and with less bias by including dominance in genomic models, although only small amounts of dominance variance were detected in both the Landrace and Yorkshire lines. A possible explanation for higher prediction accuracy in spite of the small amount of dominance variance may be that the dominance variances have been underestimated. Also, in our study, the validation criterion was crossbred performance. To determine whether inclusion of dominance also increased the prediction accuracy of purebred performance, we compared the additive and dominance models by training and validation based on the performance of sows within each pure line, using five-fold cross-validation. For each line, sows with both phenotype and genotype data were split randomly into five sets. In each run, four sets were used for training and the remaining set was used for validation. The results showed that including dominance in the genetic model improved prediction accuracy also within pure lines; prediction accuracy for sow performance was improved by 11 and 9 % for the Landrace and Yorkshire lines, respectively, by including dominance  and 43 (Yorkshire) boars were in the top 50 for both. This indicates that ranking of boars would be different for purebred and crossbred performance and, therefore, breeding for GEBV-C is expected to result in greater progress in performance of crossbred animals.For both lines, we found that GEBV-C had better predictive ability than GEBV based on the dominance model. The improvement in prediction accuracy based on GEBV-C was achieved by including dominance effects in the model and using allele frequencies of the opposite line when computing GEBV-C. Dekkers et al.  also shoTo estimate GEBV-C for purebred boars, we used SNP allele frequencies on the genotyped sows of the opposite line. However, a more accurate approach would be to use SNP allele frequencies for the selection candidates of the opposite line. For instance, to estimate GEBV-C for Landrace boars, SNP allele frequencies could be calculated on the 2450 Yorkshire sows that were mated to the Landrace boars to produce the crossbred progeny. However, since these sows were not genotyped, we used SNP allele frequencies for the sows of the relevant generation, which correspond to SNP allele frequencies estimated for the selection candidates.In this study, we used the BayesC method to estimate the additive and dominance effects of SNPs [for the distribution of estimated effects . To investigate the possible reasons for these differences, we carried out additional analyses. First, we compared the within-line prediction accuracy based on the MA and MAD models for each line by using sows for training and validation. The mean prediction accuracies for within-line performance of sows were equal to 0.15 and 0.22 for the Landrace and Yorkshire lines, respectively. The higher prediction accuracy for sow performance of Yorkshire sows may explain the higher prediction accuracy for crossbred performance for this line compared to the Landrace line. Second, we compared the variance of the off-diagonal elements of the genomic relationship matrix of training animals for the two lines and found these to be very small for both lines but larger for Yorkshire (0.0069) than for Landrace (0.0031) animals. This larger variation in genomic relationships may also explain the greater prediction accuracy for Yorkshire animals compared to Landrace animals. Third, we compared the average genomic relationship between boars and sows of the same line and found a higher relationship between boars and sows for the Yorkshire line (0.0014) than for the Landrace line (~0). These three reasons could all contribute to the higher observed prediction accuracy for the Yorkshire than for the Landrace boars.Combining animals from pure lines into a single training set improved prediction accuracy for both Landrace and Yorkshire lines for all models. Combining populations into a common reference dataset is often argued to be an obvious way of increasing GEBV accuracies , 29. HowWe used a breeding  model rather than a genotypic model to estimate additive and dominance variances, similar to Vitezica et al. . The breFor both lines, estimates of additive variance based on pedigree data differed from those based on genomic information, probably because animals used to estimate genomic variances represented a small proportion of all the animals. Based on the present data, the estimated dominance variance was 15 and 18 % as large as the estimate of additive variance for the Landrace and Yorkshire lines, respectively. In pigs, significant contributions of dominance genetic variance have been reported. Lopes et al.  found raDominance models resulted in higher prediction accuracy of crossbred performance for purebred animals than additive models. This is probably because the dominance model accounts for part of the deviation from 1 of the genetic correlation between crossbred and purebred performance in crossbreeding programs. Furthermore, we found that combining animals from the two lines into a single reference population improved prediction accuracy in the two lines.


DOCK3 (p = 0.0090), ARMC8 (p = 1.29E-5), KCNAB1 (p = 5.8E-4), and MYRIP (p = 5.79E-6). DOCK3 and MYRIP are newly discovered. Incorporating linkage scores as weights was found to help identify rare causal variants with a large effect size.We conducted linkage analysis using the genome-wide association study data on chromosome 3, and then assessed association between hypertension and rare variants of genes located in the regions showing evidence of linkage. The rare variants were collapsed if their minor allele frequencies were less than or equal to the thresholds: 0.01, 0.03, or 0.05. In the collapsing process, they were either unweighted or weighted by the nonparametric linkage log of odds scores in 2 different schemes: exponential weighting and cumulative weighting. Logistic regression models using the generalized estimating equations approach were used to assess association between the collapsed rare variants and hypertension adjusting for age and gender. Evidence of association from the weighted and unweighted collapsing schemes with minor allele frequencies ≤0.01, after accounting for multiple testing, was found for genes  Linkage studies have high power to detect loci that have variants with large effect size, although they often are rare in the population . In contp value < 10-4) test. The Hardy-Weinberg equilibrium test was performed using PLINK 1.07 [−4) were further excluded by the MERLIN 1.1.2 computing package [Linkage analysis was conducted on chromosome 3 GWAS data. A total of 65,519 single-nucleotide polymorphisms (SNPs) were genotyped on chromosome 3 for 959 individuals from 20 original pedigrees; of these individuals, 344 had hypertension and 506 did not. As a result of the limitations of our computing facility for linkage analysis, PedCut [i with LOD score i zwas weighted by i and by, otherwise. Here, m is the total number of rare variants per gene, i = 1,..., m. For individual k, his or her collapsed rare variants (CRVs) were then equal to km. The association between hypertension and the CRVs was assessed by logistic regression models adjusted for age and gender. The GEE approach implemented in the SAS computing package  was used to account for within-family correlations in the association analysis based on the original 20 families under an exchangeable covariance structure. Multiple testing corrections were made using the false discovery rate (FDR) as implemented in SAS.Linkage screens on chromosome 3 GWAS data were conducted using MERLIN 1.1.2; linkage evidence was assessed based on nonparametric linkage (NPL) log of odds (LOD) scores by Kong and Cox  where idZNF621 . The effect is from the single variant, rs34412695, with MAF = 0.00096. This association should be interpreted with caution because the significance resulted from only 1 rare variant with 1 minor allele. A larger sample size is required to reexamine this finding. The risk variant(s) in gene ATR (LOD score = 7.0) had MAFs between 0.01 and 0.03, hence the CRV is significant (p = 0.024) for the MAF ≤0.03 category only. The CRV for gene DOCK3 has a risk effect (p = 0.0090) comprised of 51 variants with MAF ≤0.01. The significance was reduced after collapsing with other variants (p = 0.043 for the MAF ≤0.03 category and p = 0.056 for the MAF ≤0.05 category). The CRV for the ARMC8 gene (with 6 variants collapsed) had a significant protective effect (p = 2.27E-5). The CRV (with 16 MAF ≤0.01 variants combined) for the KCNAB1 gene had a significant positive effect (p = 0.00058); the significance is reduced when collapsing with more variants . The CRV of the MYRIP gene in the MAF ≤0.01 category had a significant protective effect (p = 1.39E-5), which was not present in the other 2 categories. In the present study, the power to detect the collapsed causal variants with a large effect size from ARMC8 and MYRIP genes, was improved when incorporating linkage scores as weights based on the GEE approach. We did not observe an improvement in power for the collapsed variants with small effect sizes. Regardless, the ZNF621 (FDR <1E-30), DOCK3 (FDR = 0.031), ARMC8 (FDR = 0.00013), KCNAB1 (FDR = 0.0025), and MYRIP (FDR = 0.00012) genes remained significant after a multiple testing correction, regardless of the weighting schemes--the FDRs provided are for the unweighted CRV.Figure ZNF621 with an effect size of −0.44 (SE = 0.021) under MAF ≤0.01 resulted from only a single allele. The effect size changed to 0.045 (SE = 0.057) and became insignificant after collapsing with the other 2 variants under MAF ≤0.03 or ≤0.05. This observation suggested the necessity to carefully reexamine and interpret the significant result that was based on only a few rare variants.Linkage scores from GWAS data can be useful to narrow down regions for detecting rare variants associated with disease. Therefore, using linkage scores as weights for collapsing rare variants may improve the power of detection. Although in the present study, the effects of rare variants were assumed to be in the same direction during collapsing, it is important to take the directions of effects into consideration during collapsing, as the effects of significant variants can be diluted or eliminated when collapsed with other variants having neutral or opposite effects. One way to eliminate this problem is to test the variation of individual variant effects, rather than their mean effects, in mixed-effects models . StudyinDOCK3, ARMC8, KCNAB1, and MYRIP. KCNAB1 was the only gene previously identified in a GWAS, specifically for being associated with blood pressure. The other 3 genes were novel for hypertension/blood pressure in the present association analysis. Our proposed method focused on rare variant detection; common variants were not analyzed in the association analyses. Therefore, we did not expect to have a large proportion of replicate findings from GWAS.Accounting for multiple testing, the CRVs from the following 4 genes were identified for hypertension: KCNAB1 gene became insignificant, whereas the genes GBE1 and GK5 were significant under the unweighted scheme, accounting for multiple testing. In such conditions, it may be helpful to apply a statistical method to select an appropriate variance-covariance structure [The 20 families varied in size and ranged from 22 to 86 individuals, so it may not be reasonable to use an exchangeable correlation structure in the GEE approach. However, independent and exchangeable correlation structures involving less covariance parameters were better options than others given such a small number of families. An exchangeable correlation structure was adopted here as it is often a more appropriate correlation structure for a family study than other structures . GEE apptructure . This poIn summary, it is helpful to apply linkage analysis to GWAS or sequencing data, and then incorporate the linkage information into association analyses under certain scenarios. The benefits of using this method were seen particularly in cases where the collapsed variant had a large effect size. A powerful collapsing method should consider the effect size and direction of a rare variant, as well as the threshold of MAF during collapsing. We are currently systematically studying and modifying this proposed method under different scenarios to improve its power to detect functional rare variants.The authors declare that they have no competing interests.YFC, RHC, LH, and FCH made contributions to the study design, statistical analysis, interpretation, and draft of the manuscript. HYK and CYL performed the data analysis. All authors read and approved the final manuscript.