T), which is a weighted sum of a genetic architecture part (S matrix) and the realized relationship matrix (G). The algorithm of BLUP|GA (BLUP-given genetic architecture) is provided and illustrated with real and simulated datasets. Predictive ability of BLUP|GA was validated with three model traits in a dairy cattle dataset and 11 traits in three public datasets with a variety of genetic architectures and compared with GBLUP and other approaches. Results show that BLUP|GA outperformed GBLUP in 20 of 21 scenarios in the dairy cattle dataset and outperformed GBLUP, BayesA, and BayesB in 12 of 13 traits in the analyzed public datasets. Further analyses showed that the difference of accuracies for BLUP|GA and GBLUP significantly correlate with the distance between the T and G matrices. The new strategy applied in BLUP|GA is a favorable and flexible alternative to the standard GBLUP model, allowing to account for the genetic architecture of the quantitative trait under consideration when necessary. This feature is mainly due to the increased similarity between the trait-specific relationship matrix (T matrix) and the genetic relationship matrix at unobserved causal loci. Applying BLUP|GA in WGP would ease the burden of model selection.Obtaining accurate predictions of unobserved genetic or phenotypic values for complex traits in animal, plant, and human populations is possible through whole-genome prediction (WGP), a combined analysis of genotypic and phenotypic data. Because the underlying genetic architecture of the trait of interest is an important factor affecting model selection, we propose a new strategy, termed BLUP|GA (BLUP-given genetic architecture), which can use genetic architecture information within the dataset at hand rather than from public sources. This is achieved by using a trait-specific covariance matrix ( With the availability of high-density single-nucleotide polymorphisms (SNPs) covering the whole genome of many animal and plant species, the genetic merit of a genotyped individual can be more accurately estimated via a combined analysis of phenotypes and genotypes. This method usually is termed genomic prediction . EquivalA critical concern in WGP is its predictive ability, which is usually measured as the correlation between the predicted genetic values and the true genetic/phenotypic values in a validation population  in the pIf the genetic architecture of a trait under consideration is unknown, it is hard to choose a proper WGP approach without a serial of laborsome model comparisons. These situations are quite common, such as with traits of low heritability, populations of small size, and novel traits with unknown genetic architecture. This increases the computing burden and uncertainty of implementation for WGP. Hence, a sophisticated model which blends the robustness of GBLUP and the advantage of BayesB appears attractive from an implementation point of view.G matrix) was replaced with a trait-specific variance-covariance matrix denoted as TA in  approach. Similarly, a systems genomic BLUP model, including two G matrices built with markers with known or unknown biological function, was proposed theoretically, which can account for and differentiate SNPs with known biological roles in the phenotypic or disease outcomes  is used to replace the A matrix in MME  isG matrix in our study is defined asM is an adjusted marker genotype matrix including m SNPs in columns and n individuals in rows. Here, the genotypes are coded as 0, 1, and 2 representing the copy number of the second allele, and then adjusted by 2ip in each column, where ip is the allele frequency of the second allele at the ith locus in the base population. Since the use of different allele frequencies ip does not affect the accuracy of prediction  to predict the breeding values of selection candidates for decades . ConventA . Recentlividuals ; e is thediction  we use uS matrix) now is extracted from the dataset at hand, rather than from prior GWAS results in the public domain. To run BLUP|GA, in the present study the G matrix in the standard MMEs , which is a key parameter in BLUP|GA, and denoted as ‘weight’ in the following. The S matrix used in the present study includes the following information sources: (1) a proportion of SNPs  selected according to their size of effect estimated in the training population; (2) possibly the n SNPs adjacent (right and left) to each of the top SNPs (nflank), which are included to account for linkage disequilibrium between the top SNP and its flanking SNPs; and (3) the corresponding sizes of marker effects for all selected SNPs. Correspondingly, the S matrix was defined asM1 represents the genotype matrix of m1 selected SNPs (top SNPs and their adjacent SNPs), which is a subset of M. D is a diagonal matrix, and its diagonal elements diag(D) contain as weights the estimated marker effects for the selected SNPs in M1. To ensure analogy of S and G, diag(D) was rescaled such that the mean of diag(D) was 1.In a previous study  was used to estimate variance components (weight (ω in top% (a proportion of top SNPs), and nflank (n SNPs adjacent to each of the top SNPs) need to be assigned. Both weight and top% range from 0 to 1, and 0 was assigned to nflank as default value accompanied with a maximum value of 10 in our calculation. In this study, we tentatively used a grid search strategy to identify the optimal parameters.By using an equivalent algorithm as proposed by ght ω in , top% , hence ‘folds’ and ‘replicates’ were used in this stage. The algorithm used in this study is as follows:G matrix with b top%, nflank, and ω, select the SNPs with the largest size of marker effect M1 and D, build Given Calculate top%, nflank, and ω, repeat steps 4 and 5 to predict the GEBVs of validation set, which is also a grid search of the optimal parameters for BLUP|GA within the current fold;Given different Repeat steps 1−6 within a cross-validation procedure by providing different folds of datasets and obtain the global optimal parameters by maximizing the average accuracy across all folds/replicates within the reference population;Apply the globally optimal parameters obtained from reference population to the full population to predict GEBVs of candidate population (never used in steps 1−7) by running steps 1−5 once.Z can indicate it correctly.The aforementioned algorithm obtains the optimal parameters from the reference population by applying CV and grid search via steps 1–7 (denoted as “training stage” in the sections to follow), and applies these parameters to the candidate population via step 8 (denoted as “application stage” in the following). It should be noted that the steps 1–5 are the core algorithm of BLUP|GA. Given a dataset, and given all parameters, GEBV solutions for BLUP|GA can be obtained from these five steps. It will not matter whether this dataset is a training / reference or both training / reference and validation / candidate set, since the matrix File S1 and File S2.A German Holstein genomic prediction population comprising 5024 bulls, provided by Vereinigte Informationssysteme Tierhaltung w.V., was used to validate our new strategy based on the BLUP|GA approach. All bulls were genotyped with the Illumina Bovine SNP50 Beadchip  the loblolly pine dataset . BecauseThe loblolly pine genomic selection dataset provided by This simulated livestock dataset  comprisehttp://qtl-mas-2012.kassiopeagroup.com/en/dataset.php. It includes 3000 training individuals in generation 1−3 and 1000 validation individuals in generation 4. The genome comprises five chromosomes and 4000 SNPs per chromosome. To generate the genetic effect, 50 QTL were selected randomly with their effects drawn from a gamma distribution . Three genetically correlated quantitative trait phenotypes were generated based on the 50 QTL for each of the 3000 training individuals. We predicted the genetic merit for 1000 validation individuals using the data from the training individuals.The third public dataset we analyzed is the 16th QTL-MAS Workshop dataset simulated by For the dairy cattle dataset, the full dataset was divided into two subsets, a reference population with randomly selected N bulls , and a candidate population with the rest (5024-N) bulls. In the training stage, a fivefold cross-validation procedure  was condFor the three public datasets, different validation procedures were used to make the results from the present study being comparable with those reported in the original studies, in which these public datasets were analyzed with several WGP methods (DP) For the loblolly pine dataset, one replicate of 10-fold CV was conducted to validate the BLUP|GA method, and hence only results from the training stage were reported. Similar validation procedures were used to assess several methods, such as BayesA, BayesCpi, RRBLUP, and BLASSO, in TBV) In each of the 10 GSA common datasets , the genThe 2012 QTL-MAS Workshop common dataset includes only one reference population and one candidate population , and somatic cell score , respectively. To ensure that the effects estimated from different traits and / or different population sizes were comparable, we rescaled the marker effects so that the average absolute value of marker effect was 1 for each scenario. It is clear that the marker with the highest estimated effect was found around DGAT1  for all scenarios in fat percentage . Although decreasing the population size (N) from 5024 to 125, the scaled peak value decreased from 60 to 9 for fat percentage , but no apparent decrease was observed for SCS . Similar effects on both the size and variance of SNP effects were reported in In addition, we compared the marker effects estimated from different population sizes for fat percentage , milk yircentage  and milkrcentage , from 26top%), overall weights assigned to the S matrix (weight), and the number of flanking markers selected accompanied with each top SNP (nflank). The reported accuracies achieved by the genomic selection methods BayesA, BayesB, BayesC, and RRBLUP in other studies are shown in To validate BLUP|GA in a variety of applications, we additionally analyzed three common datasets: loblolly pine dataset , and 201ω) decreased from trait Gall , and then predicted the genetic merit for 1,000 candidate individuals (application stage). In the two stages, accuracy of both GBLUP and BLUP|GA were calculated, respectively . Accordiectively . In addiectively .top% ranging from 0.05 to 10% and nflank = 6 is shown in weight 0.99, top% 0.05%) to 0.848 . In this calculation, inferiority of BLUP|GA performance was only observed when too large weight was given to a very small proportion of top SNPs, while for a wide range of parameter combinations  superior performance of BLUP|GA compared to BayesB was observed  in decreasing order, and finally plotted the cumulative proportion of genetic variance explained by the ordered SNPs for each scenario. The proportion of genetic variance explained by the top 1%, 10%, and 100% SNPs are shown in panels A, B, and C in Results in N) for all the three model traits in the dairy cattle dataset. By decreasing the population size from 5024 to 125, not only the size of estimated marker effects  decreased for all three traits. The same trend was observed for milk yield in another study within the German Holstein population , but it changed from 13 to 11% only for SCS .Additionally, we analyzed the proportion of genetic variance explained by top SNPs in scenarios with different population sizes . By decreasing the population size from 807 to 202 (~25%), the genetic variance explained by top 1% SNPs decreased from 18.5 to 16.4% for rust_bin , but no decrease was observed for rootnum_bin .To validate the explanatory power of the pattern observed in the cattle dataset, we plotted the proportion of genetic variance explained by top SNPs for Rust_bin and Rootnum_bin in the loblolly pine dataset  built for the three traits in the dairy cattle dataset . The largest regression coefficient was observed for the cattle dataset (2.17) while the smallest one was observed for the pine dataset (0.84).The results suggest that the advantage of BLUP|GA over GBLUP is the more pronounced the more the In the present study, we propose a new strategy of WGP to implement the BLUP|GA approach and validate this strategy in a variety of genetic architectures, including livestock, crop, and simulated datasets. Although many methods exist in this discipline, the new strategy of BLUP|GA provides a plausible alternative to established methods and is shown to flexibly adapt to the given genetic architecture of the trait of interest.Table S1). Because GBLUP and BayesB were suggested as standard approaches for method validation, our results strongly indicate that BLUP|GA is a promising approach that has the potential to flexibly account for effects of genetic architecture when they are relevant.BLUP|GA could effectively improve the predictive performance of WGP compared to GBLUP. We validated the performance of BLUP|GA and GBLUP in four different datasets . The valG matrix with a T matrix. Since the T matrix was a combination of genetic architecture part (S matrix) and the G matrix according to S matrix) and the way we build the T matrix  could effectively improve the prediction ability of the G matrix. The block structure of S for FP mainly reflects the three DGAT1 genotypes, which is a validated major gene affecting milk traits in dairy cattle. This finding suggests that the increase in accuracy is possibly due to the increased similarity between T and the genetic relationship at unobserved causal loci . Significant regression coefficients between them indicate that the T matrix used in BLUP|GA is the main explanation for the increased accuracy, and the amount of similarity between S and G matrices also affects the increment of accuracy. These observations together explain why we benefit from the S matrix for MY and FP but not for SCS. To understand the reason of increase in accuracy, we first investigated heat maps of these relationship matrices. The contrast between the heat maps of G matrix , togetheG matrix , strongle traits . In addiS matrix built from their inferred genetic architecture is similar to the averaged G matrix. This similarity might come from a (quasi) infinitesimal genetic background or might also arise for a trait that is controlled by a limited but not extremely small number of genes distributed across the genome. If this is the case, it is not hard to image why the G matrix is so robust in its prediction ability and why we can successfully apply the same G matrix or numerator relationship matrix  to geneT matrix ensures BLUP|GA being flexible to shift between the infinitesimal and major gene genetic architectures. The T matrix comes from a weighted sum of a realized / averaged information matrix (G) and a trait specific genetic architecture matrix (S) (defined in S is (1) small for infinitesimal model traits to shift the genetic model to be more similar to GBLUP, and (2) large for traits affected by major gene(s) to shift the genetic model to be more similar to BayesB. Expectedly, the actual selected optimal weights are relatively large for the traits fat percentage in cattle and rust resistance in pine, and small for the traits somatic cell score in cattle and PolyUnres in the GSA dataset , (2) the number of flanking SNPs adjacent each top SNP (nflank), and (3) the overall weight for matrix S (weight). The three parameters are determined to maximize the predicting ability of BLUP|GA by maximizing the similarity of T and the genetic relationship at unobserved causal loci. The first two parameters are used to select the subset of ‘important markers’ while building an S matrix. The parameter nflank is relevant to the global and local level and range of linkage disequilibrium in the dataset. Although nflank is defined as a parameter to capture the linkage disequilibrium among the top SNPs and their flanking SNPs, the contribution of linkage disequilibrium to additive variance is not considered in this approach  the proportion of top SNPs , and mainly dependent on the number of genotyped individuals and the training strategy used. The strategy proposed in this study to determine the optimal parameters for BLUP|GA might not be the most efficient one but is at least an effective way to obtain parameters that improve predictive ability, and similar strategies were used in other studies , the advantage of BLUP|GA over GBLUP exists . From these curves, it becomes evident that a high proportion of variance explained by a small proportion of top SNPs is indicative for the potential to outperform GBLUP by BLUP|GA or some other approach accounting for genetic architecture. A second diagnostic is the difference between the G and the S matrix, which can be expected visually (weight or top% being 0), and thus will “automatically” find the best model—which might be close to GBLUP in many cases—when calibrated. So, applying BLUP|GA would ease the burden of model selection in the practice of WGP.In most implementations of WGP, the GBLUP approach is recommended as a benchmarking method because of its proven robustness. Are there suitable diagnostics that can be derived from the data at hand, which indicate whether the performance of GBLUP can be improved upon by alternative models that take the genomic architecture into account? We suggest as diagnostics the plot of cumulative genetic variance curves (G) with a sample of evenly spaced markers first. Then, one could improve the prediction model of BLUP|GA by building an S matrix with the top SNPs extracted from the dataset in hand according to their effect size as proposed in this study, the significance of association (With the rapid reduction of sequencing cost, sequence data will soon be available for the use in breeding programs. In this case, if the number of individuals involved was less than the number of markers, WGP approaches based on some sort of genomic relationship matrix are computationally much more efficient than approaches based on the estimation of SNP effects (T and the genetic relationship matrix at unobserved causal loci. Given a subset of important markers that possibly locate in QTL regions and proper corresponding weights, genomic prediction could be successfully conducted with the BLUP|GA model in the four datasets analyzed in the present study and in most cases was found to be among the best methods for genomic prediction. The pattern of curves from cumulative proportion of genetic variance explained by top SNPs and the element wise standard deviation between G and T matrices might be a good diagnostic indicator for model selection.The new strategy applied for BLUP|GA is a favorable alternative to the standard GBLUP model, which better accounts for the genetic architecture of the quantitative trait under consideration. This feature is mainly due to the increased similarity between trait specific variance-covariance relationship matrix


Whole-genome regression methods are being increasingly used for the analysis and prediction of complex traits and diseases. In human genetics, these methods are commonly used for inferences about genetic parameters, such as the amount of genetic variance among individuals or the proportion of phenotypic variance that can be explained by regression on molecular markers. This is so even though some of the assumptions commonly adopted for data analysis are at odds with important quantitative genetic concepts. In this article we develop theory that leads to a precise definition of parameters arising in high dimensional genomic regressions; we focus on the so-called genomic heritability: the proportion of variance of a trait that can be explained (in the population) by a linear regression on a set of markers. We propose a definition of this parameter that is framed within the classical quantitative genetics theory and show that the genomic heritability and the trait heritability parameters are equal only when all causal variants are typed. Further, we discuss how the genomic variance and genomic heritability, defined as quantitative genetic parameters, relate to parameters of statistical models commonly used for inferences, and indicate potential inferential problems that are assessed further using simulations. When a large proportion of the markers used in the analysis are in LE with QTL the likelihood function can be misspecified. This can induce a sizable finite-sample bias and, possibly, lack of consistency of likelihood (or Bayesian) estimates. This situation can be encountered if the individuals in the sample are distantly related and linkage disequilibrium spans over short regions. This bias does not negate the use of whole-genome regression models as predictive machines; however, our results indicate that caution is needed when using marker-based regressions for inferences about population parameters such as the genomic heritability. Whole-genome regression (WGR) methods are being increasingly used for inferring the proportion of variance that can be explained by a linear regression on a massive number of markers, called ‘genomic heritability.’ However, the statistical assumptions involved in WGRs are somewhat at odds with important quantitative genetics concepts. We argue and show that the parameters of the statistical model used for data analysis typically bear a tenuous relationship with the quantitative genetic parameters of interest. We also study, using simulations, the extent of bias of likelihood-based estimates. We conclude that under certain circumstances estimates can have a sizable finite-sample bias; therefore, caution needs to be exercised when interpreting parameter estimates derived from WGR models. Whole-genome regression (WGR) methods  are becoBefore copious marker information became available, genetic analysis  was mainly based on mixed effects linear models applied to family data . In the The availability of genotype information on a large number of loci has made possible to assess kinship among nominally unrelated individuals –13. In tYang et al. 2010)  proposed010  propIn the literature on genomic analysis of complex traits published so far –6,14, geAn important contribution of this paper is to establish theory aiming at a precise definition of parameters arising in regression models using genomic data  as explanatory variables. Our approach is framed within the classical quantitative genetics paradigm. We discuss how these “instrumental model parameters” relate to “structural parameters” of an underlying conceptual QTL model. We also present stylized cases that shed light into the interpretation of the parameters of the instrumental model. Finally, we discuss potential estimation problems and provide a limited set of simulations where some statistical properties of likelihood-based estimates are assessed.In the first part of this section we develop the basis for a definition of genetic parameters arising in genomic regressions and in the second part of the section we describe two simulation studies conducted to assess some statistical properties of likelihood-based estimates of genomic parameters.QTL-model) assumes that a trait of interest measured on individual i  is affected by alleles at q QTL. Hereinafter, for ease of presentation, we assume that all loci are bi-allelic and that genotype codes  and phenotypes have been centered, so that E(yi) = 0 and E(zij) = 0 for all individuals and loci.In standard quantitative genetic theory –17 additgenetic value of an individual is defined as the expected phenotypic value given QTL genotypes, gi = E(yi|zi), where zi = {zi1, …, ziq} is a vector of genotype codes observed at the ith individual at each of the q QTL. The conditional expectation function maps from genotypes to expected phenotypic value. The genetic variance of a trait in the conceptual population is simply the average  squared deviation of the genetic values from the population mean. In our setting, because E(yi) = 0, the genetic variance becomes The ɡi = E(yi | zi), may not be linear on QTL effects. However, regardless of the genetic mechanism operating within or across loci, one can always define a linear regression model of the formα, a column vector of dimension q, whose elements are the regressions of phenotype on allelic content, represents the vector of additive effects of the QTL, or effects of allele substitutions . Using expression .N stands for a multivariate normal distribution, G is a genomic-relationship matrix and G matrix; further details about this are given in We focus our study on the G-BLUP procedure due to its widespread use and relative simplicity. In this method, phenotypes are regressed on markers using a linear model of the form G is computed using markers that are not necessarily QTL or that are in imperfect LD with QTL, the (co)variance patterns of additive effects and, consequently, the likelihood function, can be misspecified  = GMRK. However, even if this property were to hold, this does not imply that estimates of variance components derived using GMRK would be unbiased. Indeed, in each sample GQTL can differ from GMRK; if the differences in the proportion of allele sharing at markers and at QTL are large enough, misspecification of the likelihood function due to the fact that we use GMRK instead of GQTL, can induce a systematic bias.Goddard et al.  suggesteRecently Jiang et al.  examinedg et al.  and oursg et al.  focused g et al.  which weg et al.  indicateg et al. . Fourthlg et al.  the ratiSimulation studies using real human genotypes, including the one presented here, indicate that estimates of d et al.  argued td et al. ,36 presed et al.  yielded x replaced by its method-of-moments estimator X′ Xn-1. Indeed, when genotypes are centered,We have argued that the instrumental parameter c values  that is n et al.  one coulComplex traits are possibly affected by large numbers of small-effect QTL and the analysis of such traits requires fitting a large number of variants concurrently using a WGR approach such as the one proposed by . Close rS1 Text(DOCX)Click here for additional data file.S2 Text(DOCX)Click here for additional data file.S3 Text(DOCX)Click here for additional data file.S4 Text(DOCX)Click here for additional data file.S1 FigThe grey lines give the realized LD patterns for different blocks and the red dashed line gives the average (across block) LD pattern.(PDF)Click here for additional data file.


For community support please post questions to https://www.biostars.org/.Existing methods for identifying structural variants (SVs) from short read datasets are inaccurate. This complicates disease-gene identification and efforts to understand the consequences of genetic variation. In response, we have created Wham (Whole-genome Alignment Metrics) to provide a single, integrated framework for both structural variant calling and association testing, thereby bypassing many of the difficulties that currently frustrate attempts to employ SVs in association testing. Here we describe Wham, benchmark it against three other widely used SV identification tools–Lumpy, Delly and SoftSearch–and demonstrate Wham’s ability to identify and associate SVs with phenotypes using data from humans, domestic pigeons, and vaccinia virus. Wham and all associated software are covered under the MIT License and can be freely downloaded from github ( This is PLOS Computational Biology software paper.Whole-genome Alignment Metrics) effectively addresses these problems.Structural variation (SV) is a major source of phenotypic diversity –4 and huCurrent mapping based algorithms –16 use vde-novo and local. De-novo assembly can identify SVs with great accuracy [de-novo assembly. For example, synchronizing the coordinates of SVs present from de-novo assemblies across many individuals is not a trivial task. Multiple sequence alignments provide one approach, but this is computationally expensive and is itself subject to systematic errors [de-novo assembly, and alignment of reads to a reference genome remains problematic. Lastly, gains made possible by local and de-novo assembly are dependent upon higher read depths. Given finite resources, sequencing fewer individuals at a higher depth compromises power for conducting downstream association testing [Other approaches for identifying structural variants use sequence assembly methods in order to pinpoint SVs. There are two main assembly-based methods for SV detection: accuracy , but alsc errors . Anotherc errors –24. One  testing ,26.Wham’s joint SV identification and genotyping algorithms are tuned for association testing. As we show, Wham is able to pinpoint SVs in pooled and genotypic data associated with phenotypic variation. Wham thus fills the need for a fast, easy to use SV caller and association-testing tool that is compatible with most standard variant calling pipelines.Wham is designed for paired-end Illumina libraries with standard insert sizes (~300bp-500bp). Wham integrates mate-pair mapping, split read mapping, soft-clipping, alternative alignment and consensus sequence based evidence to predict SV breakpoints with single-nucleotide accuracy. Wham generates a combined pileup  for all BAM files provided. Reads from all individuals included in joint calling that are soft or hard clipped are hashed by position to identify shared breakpoints. Positions in the pileup where three or more primary reads share the same breakpoint are interrogated as a putative SV. The soft-clipped sequences that overhang the breakpoint are collapsed into a consensus sequence using a multiple sequence alignment (MSA) provided in the seqAn library . Wham apWham uses split-read (SR) alignments, mate-pair (MP) positional information, and alternative alignments to find the other SV breakpoint . Wham is unaware of past SV calls, therefore it outputs an SV call for the 5’ and 3’ breaks independently. Each split read entry in a BAM file reports the other supplemental alignments in the “SA” tag and alternative alignments are reported in the “XA” tag. Wham processes the cigar strings of the SA and XA tags to identify shared positions as candidate endpoints of the reported SV. Wham clusters all the candidate breakpoints and rounds their positions to the nearest tenth base pair. The position with the highest read support is reported. If the soft-clipped consensus sequence can be aligned to the putative breakpoint region using the Smith-Waterman algorithm, the breakpoint is further refined to the location of the consensus sequence alignment . The amoTranslocations and structural variants greater than 1 Mb undergo additional filtering. These classes of SVs can be highly deleterious genomic aberrations; therefore we require them to have additional support. Large intra-chromosomal SVs require that the other breakpoint (outside pileup position) have at least two reads supporting the exact breakpoint. This same filter is applied to putative translocations. Additionally, in the case of translocations, if the split reads in the pileup map to more than three different chromosomes, the SV is discarded. This filter removes many false positive SV calls resulting from inter-chromosomal mapping errors introduced by repetitive sequences.Genotyping is accomplished using a bi-allelic likelihood model ,30. RathFor best performance, we recommend using BWA mem  followedWham classifies the type of structural variant using a random forest of decision trees implemented in scikit-learn . This apWhen the “target” and “background” options are enabled, Wham quantifies the difference between the target and background allele frequencies using a likelihood ratio test (LRT) under a binomial likelihood model with one degree of freedom. The basic LRT used within Wham has been widely adopted for association studies ,29,35. HAFT) and background (AFB) groups have the same distribution, while the alternative hypothesis is that the allele frequencies of the two groups come from two separate distributions. The allelic counts in the model come from the genotype calls.The null model of Wham’s LRT assumes that the allele frequencies of both the target ) is parameterized by the number of successes n, the number of trials k, and the probability of success p. In the current application, n is the number of non-reference alleles in the target (NT), background (NB) and the target/background combined (NC). The parameter k is the number of alleles in the target (KT), background (KB) and the target/background combined (KC). The probability of success, p, corresponds to the target (AFT), background (AFB) and combined (AFC) allele frequencies. Wham reports the D statistic in the “LRT” info field. Larger LRT values can indicate that the null hypothesis should be rejected under the assumptions of the binomial model. A chi-squared lookup, with 1 df, can be used to convert the D statistic into a p-value.The binomial density function (Bhttp://zeeev.github.io/wham/).For instructions regarding the installation and use of Wham, refer to the wiki-page  data sets can be processed with Wham. Additionally, if two cohorts of genomes are provided (target and background), Wham can be used to conduct an association test. This provides means both to identify SVs with genotype-phenotype associations and to filter SV false positives. Wham also classifies types of SV . Classification is performed For a detailed description of the datasets used for the following analyses and software versions see the We first examined the performance of Wham’s SV detection heuristic and compared it to three other SV callers, Delly , Lumpy  and SoftWham, Lumpy, Delly, and Softsearch were run in their default modes across the simulated data to identify SV breakpoints. For the high-depth simulated dataset (50x), Wham and Lumpy have comparable sensitivity overall (0.94 and 0.90 respectively), while Delly has slightly lower sensitivity (0.84). Softsearch had the lowest sensitivity for the simulated dataset (0.74). The structural variant size drives the largest differences in sensitivity between the three tools . For exaNext we assayed the false discovery rate (FDR) of the four tools on the same simulated data. Wham has an FDR of 0.05 at 50x with 50 bp of slop see , which iTo assess the breakpoint accuracy of the tools, we removed the confidence intervals for deletions and then incrementally added 1–500 bp of bi-directional slop to both breakpoints . Wham haCollectively, these simulations show that Wham provides a robust means for SV identification. Compared to the other three tools, Wham excels at finding smaller structural variants across all simulated SV classes and has the highest breakpoint sensitivity. This is important as SVs are distributed geometrically with respect to length, and thus shorter SVs comprise the vast majority of real events ,43. As wpost hoc filtering prior to benchmarking against a truth set. For our human benchmarks, we started with NA12878, the best characterized human genome. For the truth set we used the 2,597 NA12878 non-reference genotype calls in the 1000 Genomes SV dataset  , downloaLumpy has the highest sensitivity (0.60) and lowest FDR (0.66) overall for NA12878 deletions. The sensitivity for all three tools starts at ~0.5–0.75 in the 150 bp to 1 kb interval and tapers off to ~0.25 for SVs greater than 10 kb . The FDRhttp://eichlerlab.gs.washington.edu/publications/chm1-structural-variation).For a second, independent, human benchmarking experiment we used the recently published single-molecule, real-time (SMRT) sequencing dataset of a hydatidiform mole cell line (CHM1) . The hydWham and Lumpy have similar sensitivities for CHM1 deletions, while Delly and SoftSearch lag behind . For SVsWe began to assay the genotype accuracy of the Delly, Lumpy (svtyper) and Wham by comparing their calls to Phase III NA12878 1kg deletions (genotyped by Genome STRiP ). SoftSeNext we used the Platinum trio of human genomes  to measure Mendelian violations for deletions. Wham had the lowest number of Mendelian violations followed by Lumpy and Delly .To ensure that Wham provides robust multi-sample genotype calls, we calculated the allele frequency spectrum for Chromosome 1 deletions in the CEPH 1463 pedigree . The CEPThe results from benchmarking on real data have several important implications. First, Wham achieves comparable performance relative to other commonly used structural variant callers for deletions. Importantly, Wham provides robust means for discovering small structural variants. Second, the low overlap between SV classes among the tools tested here supports the power of integrated SV call sets. Frameworks, like the approaches of bcbio, which acts by combining SV calls from a variety of callers (including Wham), can capture a greater swath of genetic diversity while also providing higher confidence for concordant allele calls across varying heuristic methods –19.Although Wham, Delly and Lumpy have similar sensitivities for NA12878 deletions, any critical appraisal of their performance must take into account the very high false discovery rates of all three tools. Using the NA12878 deletion data, for instance, Wham’s FDR is 0.78, Delly’s is 0.81 and Lumpy’s is 0.66. These values illustrate just how difficult SV discovery is using short read data. However, for purposes of genotype-phenotype association, high false discovery rates are tolerable so long as false positives are either randomly distributed across cases and controls , or are systematic . In both scenarios false positives will cancel out in an association test. Thus, given a reasonable true positive rate, robust association signals will be obtained even in the face of very high FDR.We first sought to test if Wham’s non-differential false discovery rate creates spurious signals of association. To examine this, we used a cohort of individuals with a high degree of genetic relatedness such that if they were assigned randomly into two groups for association testing, there should be little to no differentiation. We chose the CEPH/Utah Pedigree 1463, comprised of seventeen individuals across three generations ,50. ThisWhile Wham has a high false discovery rate for SV detection, Wham’s association-testing framework is robust to many of these errors as they are non-differential between the cases and controls. To demonstrate that Wham’s high FDR for SVs does not hinder association studies we used Wham on both genotypic (pigeon) and pooled  datasets. In the pigeon dataset, Wham was used to re-map a causative SV for the recessive red pigmentation trait and in the viral dataset we show that Wham reliably identifies the breakpoints of a duplication involved in viral adaptation.Tryp1, Sox10, and Slc45a2 –were recently identified that produce variation in melanin synthesis [Sox10 have reduced expression of Sox10 and its target Tyrp1, resulting in the ‘recessive red’ color phenotype . Using a previously generated WGS dataset, we examined the power of Wham’s association test to identify the e1 allele of recessive red, a 7.5-kb deletion on scaffold974 of the pigeon genome assembly . In conC_liv1.0 ) for SNPe1 allele as the best genome-wide candidate for recessive red using a likelihood ratio test  around the e1 allele are attributable to linkage disequilibrium since e1 is on a haplotype shared by all of the recessive red birds we tested. This linkage is even more pronounced in the SNP data, which have a much higher density of variants. The p-values from Wham’s association test fit a uniform distribution, suggesting little to no population stratification between the cases and controls in domestic pigeon  in DNA virus genomes provide a mechanism for rapid virus adaptation to host immune defenses –57. For We analyzed short-read sequencing data from viral genomes obtained from a virus population after ten passages and the parental ΔE3L strain for comparison. This analysis revealed areas of structural variation in the adapted viral population. Plotting read depth across genomic positions revealed a spike in read depth corresponding to the K3L locus that is only present in the adapted strain . This isWham analysis identified four SVs in the parental strain, and an additional two in the adapted strain. Notably, all six SVs map near the K3L locus or the E3L deletion . The twoSurprisingly, the other four breakpoints Wham identified with high read support map near the E3L deletion . This isTaking a closer look at Wham calls with mate-pair (MP) support in addition to SR calls, we discovered a complex set of breakpoints around one end of the E3L deletion. For the K3L breakpoint, Wham only called the two positions of the single breakpoint, whereas it called one additional position with high read support on one end of the E3L deletion . To deteIn addition to identification of SVs from sequencing individual genomes, this analysis demonstrates that Wham is able to detect variable structural changes within polymorphic populations. This provides an example of Wham’s utility as a tool for accurate detection of SVs in rapidly changing microbial populations. Gene amplification can play a major adaptive role in response to selective pressure in both viral –57 and bOf the four tools used in the benchmarks, Lumpy has the fastest runtime and lowest memory requirements, but with two important caveats. First, the preprocessing steps require reading through each BAM file at least once. Second, Lumpy’s genotyper, SVtyper, took three days to run with one CPU for NA12878 deletions compared to less than a day for Wham or Delly. Filtering out high coverage regions drastically improved SVtypers performance. SoftSearch was prohibitively slow in the human benchmarks. To successfully run SoftSearch we split the BAM files into smaller genomic regions. Delly and Wham do not have filtering steps and joint call samples, thereby allowing a more direct speed comparison . Wham’s Wham is a flexible SV caller that works on a broad range of data including pooled and diploid individuals. Wham’s SV detection compares favorably with other popular mapping based SV calling methods and performs well across a number of SV types in both simulated and real datasets. Like other SV calling tools, Wham suffers from high false positive rates, but we show that this is unlikely to affect the results of Wham’s association testing. Wham’s ease of use also makes it an ideal package for inclusion with integrated SV callers. By simply running Wham in its default association-testing mode, we were able to identify the causal SV allele of a recessive trait in pigeons. Similarly, Wham’s accurate breakpoint predictions were able to locate a copy number variant in viral populations relative to a parental strain with very high precision.https://github.com/zeeev/wham), documentation is on the wiki (http://zeeev.github.io/wham/). For community support please post questions to https://Biostars.org [Wham and all associated software can be found on github (tars.org .S1 File(DOCX)Click here for additional data file.S1 TableThese factors are found in the VCF info field under the “AT” key.(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.S1 FigLeft panel: The p-values for the structural variants that intersect with The 1000 Genomes Project Phase 3 dataset (within +/- 25 bp). Right panel: The p-values for structural variants that do not intersect with the phase III 1000 Genomes Project dataset. Both the true and false positive SV calls have very similar distributions.Quantile-quantile plots for Wham’s LRT statistic after conversion to p-values (y-axis). (PDF)Click here for additional data file.S2 FigWham has a linear relation between runtime and the number of samples run. The black line has a y-intercept of zero and slope of one.(PDF)Click here for additional data file.


Studies that traverse ancestrally diverse populations may increase power to detect novel loci and improve fine-mapping resolution of causal variants by leveraging linkage disequilibrium differences between ethnic groups. The inclusion of African ancestry samples may yield further improvements because of low linkage disequilibrium and high genetic heterogeneity. We investigate the fine-mapping resolution of trans-ethnic fixed-effects meta-analysis for five type II diabetes loci, under various settings of ancestral composition , allelic heterogeneity, and causal variant minor allele frequency. In particular, three settings of ancestral composition were compared: (1) single ancestry (European), (2) moderate ancestral diversity (European and East Asian), and (3) high ancestral diversity . Our simulations suggest that the European/Asian and European ancestry-only meta-analyses consistently attain similar fine-mapping resolution. The inclusion of African ancestry samples in the meta-analysis leads to a marked improvement in fine-mapping resolution. Nonetheless, the joint effects of the loci identified to date have only accounted for a small proportion of the heritability of complex traits. Because of linkage disequilibrium (LD), many variants within identified loci have indistinguishable signals. This LD is beneficial to GWAS, as it increases the power to detect new associations, when the causal variant is not directly typed. However, the caveat to this is that it limits the potential of fine-mapping efforts to refine the location of causal variants.Numerous genome-wide association studies (GWASs) have been carried out, resulting in the identification of many susceptibility loci for a wide range of complex traits.3 The inclusion of African ancestry samples may yield substantial improvements in localisation of causal variants because of low LD and high genetic heterogeneity.4GWAS data from non-European populations are increasing in availability, and this provides the opportunity to meta-analyse GWAS across ancestrally diverse populations. Trans-ethnic meta-analysis may lead to an increase in power to detect novel loci and may improve fine-mapping resolution of causal variants by leveraging differences in the structure of LD between diverse populations.5 as well as in previously identified adiposity loci in a trans-ethnic meta-analysis of samples from European and African ancestries.6 Similarly, a refinement of signals was obtained at several lipid trait loci in a trans-ethnic fine-mapping study involving African-American, East Asian, and European ancestries.7 However, a comparison of study designs, where the ancestral composition of the samples varies in diversity whereas the same number of samples (and cost) is constant, has not yet been performed. Approaches to meta-analysis include a fixed- or random-effects model, as implemented in GWAMA  or MANTRA , that allows for heterogeneity in allelic effects between distantly related populations.9 We focussed on fixed-effects meta-analysis, as trans-ethnic studies of complex traits demonstrated relatively little evidence of heterogeneity in allelic effects at common variant loci. Moreover, MANTRA and fixed-effects GWAMA have been shown to have similar power when the variant has a non-null effect in all of the populations.10 Therefore, our objective is to examine different study designs with respect to ancestral composition, rather than statistical approaches to meta-analysis. There may be power and fine-mapping advantages in increasing the ancestral diversity among the samples while retaining the same number of samples and cost.Several trans-ethnic analyses have shown empirical improvements in fine-mapping resolution. Examples include a refinement of signals at several type II diabetes loci in an analysis involving samples of European, East Asian, South Asian, and Mexican and Mexican-American ancestry,We carried out an extensive simulation study to examine different study designs with respect to ancestral composition  to assess any power and fine-mapping advantages due to increasing ancestral diversity among samples while retaining the same number of samples and cost. The aim is to determine whether trans-ethnic meta-analyses offer fine-mapping resolution advantages over single ancestry meta-analyses, and whether or not any gains are due to the inclusion of African ancestry samples.IGF2BP2, CDKN2A/B, KCNQ1, FTO, CDKAL1). These loci were explicitly chosen as they have association signals present in multiple ethnic groups,11 and several of these loci have shown large differences in LD between ethnic groups . Such loci characteristics are likely to favour success for trans-ethnic meta-analyses.We focus on five established type II diabetes (T2D) loci ; and high ancestral diversity .In this simulation study, trans-ethnic meta-analysis was carried out by a frequentist fixed-effects meta-analysis that was implemented in GWAMA12 from 6 populations based on the 1000 Genomes June 2011 haplotypes:13 CEU, TSI (European reference panels (RPs)), CHB, JPT (East Asian RPs), LWK, and YRI (African RPs). Each cohort was composed of 1000 cases/1000 controls, and 1000 replications were used for each setting. These simulations represent directly typed data, and variants are referred to as perfect. They were then thinned down to GWAS density based on the SNPs in the Illumina 660-Quad array, and subsequently imputed via IMPUTE2,14 using the same cross-population 1000 Genomes reference panel, and effective population size Ne=20 000. A 500 kb up- and down-stream buffer was included in the imputation, and variants with SNPTEST proper information score below 0.4 were filtered out. Both perfect  and imputed data were analysed. Analysis of the perfect data illustrates an optimal scenario and provides the maximum possible power and refined fine-mapping resolution that may be attained, whereas the imputed data represent a more realistic setting.Sets of six cohorts were meta-analysed across five loci under various allelic heterogeneity models and ancestry compositions of the contributing cohorts. Data were simulated using Hapgen2Single ancestry (European): 6 CEU samples;Moderate ancestral diversity (European and Asian): 3 CEU+TSI samples, 3 CHB+JPT samples; andHigh ancestral diversity : 1 sample from each of CEU, TSI, CHB, JPT, LWK, and YRI.There were three general ancestry combinations considered for meta-analysis:1, it was selected to satisfy the MAF requirements in the CEU population frequency and to be nonmonomorphic in the other populations. A single causal variant c1 was considered for each of the single ancestry and moderate and high ancestral diversity scenarios.Within each locus, causal variants were selected within ±0.5% of one of three minor allele frequencies (MAFs): 5, 10, or 20%, with respective relative risks of 1.4, 1.3, and 1.2. As the MAF varies between the populations, when there was a shared causal variant c15 As put into practice in GWAMA,8 the frequentist fixed-effects meta-analysis of the single SNP summary statistics assumes that the allelic effect at SNP j is the same across all samples. This meta-analysis approach is highly computationally efficient, but has the limitation that it assumes a homogeneous effect size among all of the samples.Within each study sample, single SNP association tests were carried out with an additive model in a ‘missing data likelihood' framework, as implemented in SNPTEST v2.V) from each SNP were first converted to an approximate Bayes' factor (ABF):A measure of fine-mapping resolution was based on the construction of 95% credible sets using Bayesian theory, such that the sets were 95% likely to encompass the causal SNP. In order to form the credible sets, the association summary statistics  denotes that the random variable follows a Normal distribution with mean μ and variance σ2.16 For a case–control study and an additive model, a widely used default value is W=0.04.15 Evidence against the null hypothesis increases with the ABF value, and posterior probabilities were calculated from the ratio of the individual ABF value to the sum of the ABF values for all SNPs within the region. These posterior probabilities were then ranked in decreasing order and SNPs were consecutively collected to form a 95% credible set until the total of the posterior probabilities for the SNPs in the set first exceeded 0.95.17where P-value below a prespecified threshold in order to avoid the construction of sets consisting only of SNPs that are unlikely to be disease associated. The construction of credible sets based on lead SNPs with weak signals requires a larger number of SNPs to meet the criterion of a certain total posterior probability, as the individual SNP posterior probabilities tend to be small in this case. For computational efficiency, we focussed on a frequentist threshold for the decision of whether or not to construct a credible set. This avoided an additional computational step of ABF calculations that would not be required if it was inappropriate to construct a credible set.We only constructed 95% credible sets when the lead SNP had a In assessing any effect of ancestral diversity on fine-mapping resolution, the probability of the causal variant being a member of the 95% credible set was assessed among simulation scenarios in which all samples shared a causal variant. For each region, the median number of SNPs within credible sets that contained the true causal variant was considered in evaluating the refinement for localising the causal variant within the locus; a smaller number is indicative of higher fine-mapping resolution. As a means of combining the measures over the regions, we refer to the average of the region-specific medians as a summary statistic.2 for the Asian samples, such that it was of similar MAF, but in low LD (r2<0.2) with the European causal variant. In particular, for the moderate ancestral diversity scenario, we compared the setting of no heterogeneity, where c1 is the causal variant for both European and East Asian samples, with the allelic heterogeneity setting of causal variant c1 for European samples and causal variant c2 for East Asian samples.Effects of allelic heterogeneity were investigated by introducing a different causal variant c1 and c2 for the African samples; we refer to such cohorts as null. In these heterogeneity scenarios we examined the impact on power to detect the variant that is causal in the European samples. We compared the settings of no heterogeneity , allelic and locus heterogeneity , and locus heterogeneity . For both types of heterogeneity, comparisons are also made with the power to detect a causal variant in the single ancestry (European) composition to assess the power loss of trans-ethnic meta-analyses in the presence of heterogeneity.To reflect locus heterogeneity, in the high ancestral diversity set-up we assumed null associations at both cP-value threshold of 5 × 10−8 was employed. The probability that the 95% credible set contained the true causal variant was high across all five loci and there was no clear collective pattern between probabilities and degree of ancestral diversity. Upon collapsing the individual region results into averages over the regions, any differences were smoothed over and there were negligible differences between the probabilities for the various diversity settings at a given causal variant MAF  and at MAF 5% for FTO .Next, we examined the median number of SNPs in the credible sets for each region. Summary measures over the regions are provided in Within each region we used the Kruskal–Wallis rank sum test to assess the evidence for the null hypothesis that the median was the same in each ancestral setting group against the alternative that at least one group had a different median. If there was evidence of a difference, Dunn's test was then applied to test each of the pairwise comparisons for the null hypothesis that, with probability 0.5, a random SNP count from the first group is larger than one from the second group. This may be interpreted as a test for one group having a larger median than the other.P-value <10−5) that at least one ancestral setting had a median SNP count different from the others, with the exception of one region and MAF setting. Similarly high levels of significance  were attained for all imputed data settings.The Kruskal–Wallis test, applied to perfect data, resulted in strong evidence  of the high ancestral diversity group having a lower median than the single ancestry group. This was also true at the lower MAF for each region, except for only moderate evidence at CDKN2A/B . There was not a clear trend between the European and European/Asian meta-analyses, as either group was found to have strong support  for a larger median or no evidence  for a difference in medians for various MAFs and regions.In both perfect and imputed data, for each region with a causal variant having MAF 10% or 20%, Dunn's test gave strong evidence . Imputed data had similar levels of evidence  and considering 0.05 Bonferroni-corrected threshold of α=0.011 for the three pair-wise comparisons, this holds with strong evidence for MAF 10% . The results also suggested that the European/Asian trans-ethnic meta-analysis did not have a greater fine-mapping refinement than the European-only meta-analysis, except for moderate evidence in the low MAF setting of imputed data . There was moderate evidence for a higher median in European/Asian compared with European/Asian/African at MAF 5% .As each gene may differ in LD structure, we paired the medians of each ancestral diversity comparison according to gene, and then tested whether the region medians of lower ancestral diversity settings had a greater average than those of higher ancestral diversity via a paired P-value threshold of 5 × 10−8 , where three samples are taken from each of the LWK and YRI populations, we found that the proportion of 95% credible sets that contain the causal variant is similarly high for the various ancestral diversity settings. However, the standard errors of these probabilities are slightly higher for the African-only samples, as there are fewer replications in which the lead SNP passes the 5 × 10−8 . In addiFine-mapping resolution is most refined for African-only meta-analyses, suggesting that features of the African populations such as lower LD rather than ethnic diversity are the underlying source of improvement in the high diversity settings. The allele spectrum between the populations was also examined; for the various European causal variant MAF settings, the median MAFs for the East Asian and African samples are provided in IGF2BP2 in the high ancestral diversity setting and for the three MAF settings, identical power results of 1.0 were attained for perfect data.We also examined the effects of ancestral diversity on power to detect an association with a variant that was causal in all samples. At significance level 0.05, regardless of the level of ancestral diversity among the samples, a power close to or identically 100% was attained for both perfect and imputed data, respectively. Upon repeating the meta-analysis with random effects for FTO (4% lower) and in CDKN2AB (8% lower). In the presence of locus or allelic heterogeneity, there are also very few differences in power between imputed and directly typed causal variants; at MAF 5%, there is occasionally a power reduction near 10% when causal variants are imputed rather than directly typed. As the differences are not substantial, this subset of results from the imputed data is not provided.For imputed data, the causal variant may either be a tag SNP, so that it is directly typed, or it may be imputed. Among the replications for imputed data, upon examination of the power only at the imputed causal variants, there are not substantial differences compared with the power at directly typed variants. For instance, when the causal variant is the same across all ancestries and diversity settings, the power remains close to 1.0 at imputed-only causal variants, except that at MAF 5% the power is slightly lower for single ancestry in IGF2BP2 in the presence of allelic heterogeneity and for perfect data, there was a larger power reduction; fixed-effects meta-analyses yielded powers of 0.819, 0.886, and 0.865 at respective MAFs of 5, 10, and 20%, whereas the coinciding powers from random-effects meta-analyses were 0.73, 0.795, and 0.51.The effect of allelic heterogeneity on the power to detect a causal variant was assessed by comparing the moderate ancestral diversity scenario in which both Europeans and Asians shared the same causal variant, against the setting in which they had different causal variants in low LD with one another. In the moderate diversity setting, power losses from the presence of allelic heterogeneity in half of the samples ranged from 10% in perfect data up to 23% in imputed data, irrespective of MAF ; these s10 where a fixed-effects analysis of all populations attained a power of 99.7%, whereas the power dropped by 69.3% when African and East Asian samples were null strata. The power losses from the inclusion of samples with a null association at the variant suggest that locus heterogeneity may have a more profound effect on power compared with allelic heterogeneity. Similar power losses are observed in comparing the single ancestry scenario with any of the heterogeneity settings in the high diversity scenario, as there are negligible differences between the powers of the single ancestry and high diversity ancestral composition in the absence of heterogeneity.In the locus heterogeneity scenario, we found that null cohorts  had a dramatic impact on the power to detect the causal variant that was associated in only two (European) of the six cohorts . In bothIGF2BP2, as well as both allelic and locus heterogeneity in the high diversity scenario. Presence of the signal in only one group (Eu) resulted in very large 95% credible sets, consisting of at least 1500 variants (results not provided). Use of random effects rather than fixed effects reduced the size of the credible sets by ∼200 SNPs, but credible sets were constructed in <10% of the replications; few replications had a SNP that passed the genome-wide significance threshold.The manner in which the credible set is constructed makes the assumption of a common causal variant that does not hold in the heterogeneity settings, such that a low fine-mapping resolution is expected in these settings. As an illustration, credible sets were constructed when there is moderate diversity and allelic heterogeneity in 9 These results indicate that the meta-analysis of ancestrally diverse samples results in an improvement in fine-mapping resolution, provided that the composition includes those of African ancestry. For further investigation of this improvement, we examined African-only meta-analyses that displayed a high fine-mapping resolution, suggesting that increasing the sample size of African ancestry samples is more likely to improve fine-mapping resolution than increasing sample diversity. It would also be of interest to investigate the inclusion of Hispanic cohorts, given the current efforts in establishing large Hispanic cohorts, the admixing history, and ethnic diversity within such cohorts. Given the fine-mapping improvements observed from the inclusion of African ancestry samples, and that the LD levels in Hispanic samples tend to fall between those of Africans and Europeans/East Asian, inclusion of Hispanic samples is expected to contribute to refinement in fine-mapping over that of European and East Asian samples.There is a clear improvement in fine-mapping resolution when synthesising data across highly diverse samples (European/Asian/African) in comparison with the analyses of samples from the same ancestry (European). A clear trend of increased fine-mapping resolution is not apparent in comparisons between common ancestry meta-analyses and those consisting of samples of European and Asian ancestry. This may be because of individuals of European and Asian ancestry being more closely related with each other than with those of African ancestry, as had been illustrated in previous relatedness analyses.10 yet the impact of ancestral composition in study design has not previously been investigated. Although the conducted simulation studies are limited by taking place under an ideal scenario in which imputation reference panels consist of populations that are exact matches for the study samples, they act as a gauge for the performance of the various ancestral composition study designs. This study highlights the benefits of trans-ethnic meta-analysis for detecting novel complex trait loci and fine-mapping causal variants, when there is a shared causal variant. It also considers the effect on power from the inclusion of cohorts where the variant is null that may occur if it was discovered in African populations and did not segregate outside of Africa, or vice versa. In this case, the fixed-effects (and random-effects) meta-analysis is exposed to a dramatic power loss when the sample size is fixed over the different ancestral diversity scenarios. Therefore, when there is a restriction on sample size , careful consideration is needed in designing the ancestral composition for the meta-analysis, depending on the assumption of shared causal variants or locus heterogeneity.Methods for trans-ethnic meta-analyses have been compared in extensive simulation studies,Meta-analyses are often performed with an intention of maximising the number of available cohorts, with or without African ancestry cohorts. This is often owing to the restricted opportunities to include African cohorts, either because of GWAS data not existing or not readily available for sharing and for meta-analysis. Our simulation results indicate the importance of including African ancestry samples in fine-mapping studies, and that high gains in resolution are possible with their inclusion. Considering the high resolution in the African-only analyses, it may be beneficial to include a few small African cohorts  rather than an additional couple of large European cohorts . The possibility of deriving benefits that have a global impact may therefore be more likely by developing the capacity for genomic sciences in Africa, such that an increased number of African-focussed GWASs may be performed. This includes enabling and empowering more African researchers to carry out such studies in their populations.


Research on genetic influences on human fertility outcomes such as number of children ever born (NEB) or the age at first childbirth (AFB) has been solely based on twin and family-designs that suffer from problematic assumptions and practical limitations. The current study exploits recent advances in the field of molecular genetics by applying the genomic-relationship-matrix based restricted maximum likelihood (GREML) methods to quantify for the first time the extent to which common genetic variants influence the NEB and the AFB of women. Using data from the UK and the Netherlands , results show significant additive genetic effects on both traits explaining 10% (SE = 5) of the variance in the NEB and 15% (SE = 4) in the AFB. We further find a significant negative genetic correlation between AFB and NEB in the pooled sample of –0.62 . This finding implies that individuals with genetic predispositions for an earlier AFB had a reproductive advantage and that natural selection operated not only in historical, but also in contemporary populations. The observed postponement in the AFB across the past century in Europe contrasts with these findings, suggesting an evolutionary override by environmental effects and underscoring that evolutionary predictions in modern human societies are not straight forward. It emphasizes the necessity for an integrative research design from the fields of genetics and social sciences in order to understand and predict fertility outcomes. Finally, our results suggest that we may be able to find genetic variants associated with human fertility when conducting GWAS-meta analyses with sufficient sample size. Recent research within both biology –4 and deAn ideal design to examine the genetics of fertility would be a direct estimate using single nucleotide polymorphisms (SNPs) across the entire genome for unrelated individuals who do not share the same micro environment, which was first applied to height as a model complex trait ,16. Thisgenomic-relationship-matrix restricted maximum likelihood (GREML) methods to quantify for the first time the extent to which common genetic variants influence both the NEB and the AFB of women. We applied both uni- and bivariate models to these traits producing unbiased estimates of their common SNP heritability and the extent to which the association between earlier AFB and higher lifetime fertility (NEB) is due to a (negative) genetic correlation between AFB and NEB [The current study exploits recent advances in the field of molecular and quantitative genetics by applying  and NEB . This noIn contrast to twin and family designs, the GREML approach is free of confounding from shared environmental effects between close relatives because the method can be applied in a sample of unrelated individuals ,16. The The most successful and popular design to detect the approximate location of genetic variants associated with a complex trait is the meta-analyses of genome-wide association studies (GWAS) from multiple samples. In lieu of this, our assessment of the genetic effects of common SNPs based on the pooled samples shape the expectations to find individual variants when conducting a GWAS. We account for population stratification effects by adjusting for the first 20 principal components in our GREML models. Population stratification refers to allele frequency differences due to systematic ancestry differences. Population stratification can cause spurious associations if not adjusted properly . We furThis study has several important implications for research in demography, genetics and biology. We know surprisingly little about genetic effects on human fertility on a population level, yet it is crucial for our understanding of fertility, the interpretation of related social science research in this field ,22,29–31The term ‘fertility’ takes on different meanings in demography, reproductive medicine and biology . In demoIn the last decades, industrialized societies have experienced massive changes in both the postponement of AFB and drop in the total number of offspring, which cannot mainly be attributed to genetic or biological factors ,37. RathPrevious research has successfully demonstrated that there is a genetic component to reproduction with over 70 genome-wide association studies (GWAS) published for 32 traits and diseases associated with reproduction found in . This inA bivariate twin model in a study by Rodgers and colleagues  suggestsIf the quantum of fertility in the form of NEB is at least partly genetically influenced, this implies that certain SNPs have a higher chance to be successfully transmitted to the next generation than others, and by extension that the allele frequency might change due to natural selection, indicating evolution. If the negative relationship between AFB and NEB is partly genetic, this would indicate that the AFB was under natural selection during the Twentieth century and that more recent birth cohorts may carry a higher genetic predisposition for an earlier AFB.Using a family-design, findings from the Framingham Heart Study demonstrated that the same genes influencing NEB are negatively correlated with the AFB . The autWritten informed consent has been given by each TwinsUK and Lifelines participant. This research was approved by the Department of Sociology’s Departmental Research Ethics Review Committee both at the University of Groningen and the University of Oxford. All data had been anonymized before we received it.For the Netherlands, we use data from the LifeLines cohort study, a multi-disciplinary prospective population-based cohort study examining in a unique three-generation design the health and health-related behaviours of 167,729 persons living in the North of The Netherlandsincluding genotype information from more than 13,000 unrelated individuals . It emplFor the UK, we use data from TwinsUK, the largest adult twin registry in the country with more than 12,000 respondents . Due to Since genotyping had been performed using different chips in the UK and the Netherlands, we use imputed data to aid the alignment of both datasets. The HapMap3 imputation panel has been shown to be reliable for GREML analysis .−6 for both datasets. We merged the TwinsUK and the Lifelines samples and quality controlled the merged dataset in the same way again. On average 1,017,420 SNPs could be utilized to estimate the GRM between individuals. We used the software Plink [We received genotype data from TwinsUK and Lifelines, which we imputed according to the 1000 genome panel after which we selected HapMap3 SNPs with an imputation score larger than 0.6. For quality control (QC), we excluded the SNPs with a larger missing rate than 3%, lower minor allele frequency than 1% and which failed the Hardy-Weinberg equilibrium test for a threshold of 10re Plink  for the Number of children ever born measures the number of children a woman has given birth to including stillbirths. This has been asked directly in the twinsUK (“How many children have you given birth to?”) or we constructed it using questions about the year of childbirth of each child. In Lifelines, respondents have been asked to list the birth and death date of children from their current and previous partner with up to 6 children in both categories. For the Lifelines and part of the TwinsUK questionnaires information for the date of death of the children was given. In both datasets less than 0.2% of the children had not reached reproductive age and the correlation of number of children ever born and number of children reaching reproductive age was >0.98.Since fertility is strongly age dependent, we focus on women with completed fertility history in reference to the phenotype. In general the end of the woman’s reproductive lifespan occurs around the age of 45 , thus, wTo calculate the AFB, we used information on the year of childbirth of the first child and year of birth of the mother. In TwinsUK, information from an additional behavioral questionnaire directly asking for the age at first birth in 2005 was available. Childless individuals have been set to missing in the analysis.h2) as the proportion of the genetically caused variance VP)) [The genetic component underlying a trait is commonly quantified in terms of heritability ) :Whereas the phenotypic variance is the sum of genetic and environmental The methods we applied have been detailed elsewhere –17. BrieA is the genetic relationship matrix (GRM) estimated from SNPs, I is an identity matrix. The variance components are estimated using the restricted maximum likelihood (REML) approach. The NEB is not normally distributed ) is an estimate that standardizes the genetic covariance between two traits Cov by the genetic variance of both traits:The genetic correlation  is the sum of genetic and environmental influences shared across traits and can be estimated like this:r is the environmental or residual correlation between the traits  and the NEB has been log transformed to approach normal distribution  estimated from the univariate models for AFB and NEB. Both traits have a significant genetic component, with h2SNP for NEB of 0.10 (SE 0.05) and for the AFB of 0.15 (SE 0.04). These results suggest that additive effects of common SNPs explain 10% of the variance in the NEB and 15% of the variance in the AFB of women.Using recently developed analytical techniques from molecular genetics we provide direct evidence for a genetic component underlying the AFB and NEB of women in the UK and the NL born during the Twentieth century. Moreover, genetic effects on the tempo (AFB) and quantum (NEB) of human reproduction co-vary, which partly explains why women who start reproducing at an earlier age, have higher fertility.This genetic association between AFB and NEB can have different origins. Both traits might simultaneously be influenced by the same genetic effects (pleiotropy) or genetic effects on the NEB could be mediated via the AFB—as well as a combination of both. To further examine the causal relations between these factors, actual measured genotypes important for these traits might be integrated in the statistical models  in appliAlthough our results seem to raise a paradox, they are well in line with studies on natural fertility populations, such as from Milot and colleagues  who obseThe discrepancy between observed changes and those predicted by evolutionary processes show parallels to the case of human height. Although natural selection has disinclination for taller individuals at least in US populations ,58, peopA second potential—and largely interrelated—explanation for the fact that AFB is postponed despite selection towards genes favoring earlier birth is that genes and the environment interact across birth cohorts. Previous twin studies have in fact shown differences in heritability estimates across cohorts and environments in both NEB  and AFB The genetic effects estimated in this study represent narrow sense heritability estimated from SNP data. As can be expected , they armeasure of fitness. It would be better to have information on the number of children who entered reproductive age or even more appropriate, the number of grandchildren entering reproductive age to have a more precise measure of how far genes have been successfully transmitted across generations. However, the NEB has been shown to be a good measure of reproductive success  due to see also . Second,see also , it is ssee also ,63. Chilsee also  or ordersee also  to integsee also .To date, thousands of genetic variants have now been successfully linked to physical or psychological traits in the past years ,69, as wS1 Fig(DOCX)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.


Genomic prediction of agronomic traits as targets for selection in plant breeding programmes is increasingly common. The methods employed can also be applied to predict traits from other sources of covariates, such as metabolomics. However, prediction combining sets of covariates can be less accurate than using the best of the individual sets.We describe a method, termed Differentially Penalized Regression (DiPR), which uses standard ridge regression software to combine sets of covariates while applying independent penalties to each. In a dataset of wheat varieties, field traits are better predicted, on average, by seed metabolites than by genetic markers, but DiPR using both sets of predictors is best.DiPR is a simple and accessible method of using existing software to combine multiple sets of covariates in trait prediction when there are more predictors than observations and the contribution to accuracy from each set differs. Increasingly large amounts of data are being collected in crop science experiments. These come from two sources. Firstly, high densities of genetic markers are now available for the major crop groups . SecondlA major application for high density genetic markers is to predict traits for selection in breeding programmes ,6. TheseGenetic marker data aside, to date the large amounts of data collected have primarily been from physiological and biochemical analyses of crops rather than for use directly in breeding. An exception is  which prTriticum aestivum var aestivum) varieties which were studied to determine the extent of diversity in the content and composition of bioactive components ' is a vector of phenotypes for n lines or individuals.Y = [y1b2 … bm]’ is a vector of m fixed covariate effects.b = [ bX is the (n x m) design matrix for covariates and assigns values at each covariate to the individual phenotypes in Y.I is a unit matrix with the same dimensions as X’X.λ is a positive real number.Iλ to X’X allows estimates of b to be made for all markers simultaneously. If λ is zero, the ridge regression elements reduce to the ordinary least squares solution (which will fail if there are more columns in X than rows in Y). Estimating b from equation The addition of the penalty term i-∑bjxij)2, is identical to that minimized in ordinary least squares and corresponds to the squared deviation of observed values (yi) from expected (∑bjxij). The second part, λ∑bj2, penalizes the sum of squares of the regression coefficients (bj) themselves. The appropriate value of λ can be determined by cross-validation or, for markers, is often set equal to σe2/ σb2 where σe2 and σb2 are the residual variance and the variance of the marker effects, respectively [is minimized. Equation ectively ,25. In tWe have extended ridge regression to take into account two independent sets of predictors; here metabolites and markers. If markers and metabolites are included together in a standard ridge regression model, both sets will be penalized by a common value of λ. However, if one set has more predictive power it may be over-penalized (shrunk too much) and the other set under-penalized. Similarly, if one set has more covariates than the other it may dominate in estimating λ. Consequently, it is possible that the combined set of predictors will be less accurate than the best set on its own. To avoid this, working on standardized variables, we fit a model in whichj and b*k are regression coefficients for the two sets of covariates, x and x* with m and m* covariates respectively, each with separate penalties of λa and λb. The separate penalties ensure that each set of variables is penalized independently. Equation is minimized. The bIn this form, there is a single penalty, λ, for both sets of variables, but with separate weighting factors w and (1-w) where w varies between 0 and 1. The weighting factors can be regarded as additional scaling factors for the standard deviation of the two groups of covariates since a regression on x with an estimated regression coefficient b will give an identical fit to a regression on wx with a regression coefficient b/w. Rescaling by w and 1-w allows fitting of equation As far as we are aware, this form of ridge regression, which for convenience we term Differentially Penalized regression (DiPR) has not been described. In this paper, all models were fitted with the R package Penalized  using thhttp://www.niab.com/pages/id/326/Resources.Data used in the analyses are available from


Motivation: For many classes of disease the same genetic risk variants underly many related phenotypes or disease subtypes. Multinomial logistic regression provides an attractive framework to analyze multi-category phenotypes, and explore the genetic relationships between these phenotype categories. We introduce Trinculo, a program that implements a wide range of multinomial analyses in a single fast package that is designed to be easy to use by users of standard genome-wide association study software.Availability and implementation: An open source C implementation, with code and binaries for Linux and Mac OSX, is available for download at http://sourceforge.net/projects/trinculoSupplementary information:Supplementary data are available at Bioinformatics online.Contact: lj4@well.ox.ac.uk Of the many associations discovered by genome-wide association studies, a large number are shared across multiple traits  Calculates a single Bayes factor for each variant that summarizes the evidence of association across all categories. Users can specify a prior covariance on effect sizes, an independent-effects prior (default) or an empirical prior calculated across all variants.Generates a marginal likelihood for each possible sharing model, where a sharing model specifies which categories the variant is and is not associated with. The module can calculate Bayes factors in favour of, or against,a variant being shared across categories or uniquely associated to one (see use case below), or posteriors on particular sharing models (if provided with priors on models).Efficiently simulates genotypes from a multinomial model under ascertainment for given sample sizes and allele frequency. This allows the user to undertake power calculations for the above analyses.Supplementary Materials.All of these modes can include principal components (to control for population stratification) or other covariates, and can include other SNPs as covariates to test for independent effects or carry out stepwise regression. More details on these use modes, and technical details on their implementation, can be found in Trinculo is written in C and is supported on linux and Mac OS X. Models are fitted using Newton’s method, which, after optimization of the second derivative calculation, we find to be much faster than the BFGS method used by other implementations. Like other genetic association software, Trinculo also lends itself readily to parallelization, either by splitting the data up into chunks and running each chunk on a separate core, or through inbuilt multithreading capacity in the software itself.Trinculo can carry out an omnibus frequentist multinomial association scan for a reasonably sized genome-wide association study  on a laptop (1.7 GHz Intel Core i7) in under 10 h. A very large study (100 000 samples across five categories with 50 000 controls) would take 16 h on 24 cores. The fastest R implementation, NNET (on, NNET ,would taon, NNET  would taWe applied the Bayesian model selection mode, using an empirical prior, to data from 193 inflammatory bowel disease risk variants (Trinculo is a fast, flexible and easy-to-use tool for multi-category genetic association studies. By providing a wide range of use options, it allows the user to tailor their analysis to their data and experimental design. For instance, if the user wishes to carry out model selection at a risk variant, but wishes to account for the effect of a second risk variant in linkage disquilibrium, then Trinculo’s conditional regression option will handle this automatically. Other use cases not discussed here, such a multinomial fine-mapping or ordinal logistic regression, are also included in the software. We hope that these features will allow researchers to use multinomial logistic regression to answer their own biological questions as easily as they currently use binary logistic regression.