Three field experiments, using randomized complete block design with three replications, were installed in Goiânia-GO, in the 2002/03 season. Each experiment consisted of 36 treatments (6 common and 30 regular). Heritability estimates were: 74.6 and 36.1 (GFP); 51.9 and 19.9 (LR); 49.6 and 49.6 (PIPD) and 55.8 and 20.3 (PSS), in both the broad and narrow senses, respectively. Based on these results, we concluded that the best strategy for obtaining stink bug-resistant genotypes consists of selecting the PIPD trait in early generations (F 3 or F 4 ), followed by selection for the GFP, LR and PSS traits in generations with higher endogamy levels. Soybean genotypes resistant to stink bugs are derived from complex breeding processes obtained through indirect selection. The aim of the present work was to estimate genetic parameters for guiding selection strategies towards resistant genotypes, based on those traits associated with responses to pod-attacking stink bugs, such as the grain filling period (GFP), leaf retention (LR), percentage index of pod damage (PIPD) and percentage of spotted seeds (PSS). We assessed the parental lines IAC-100 (resistant) and FT-Estrela (susceptible), the progenies F Nezara viridula, Piezodorus guildinii and Euchistus heros. Through their piercing-sucking feeding habits, these insects cause damage mainly during pod formation, filling and maturation  30 F2:3 generation progenies from the bi-parental cross; c) 30 progenies from the second generation of respective inbred backcrosses, denominated BC1F2:3 and BC2F2:3. The cultivars BRS Celeste and MGBR-46 (Conquista) were used alongside the afore mentioned crosses. The experimental plot was installed on December 19th, 2002, in an experimental field at the Escola de Agronomia e Engenharia de Alimentos da Universidade Federal de Goiás , in Goiânia, Goiás. The experimental field was open to natural stink bug infestation through the absence of insect chemical control. In order to increase natural crop infestation by insect migration at the final maturation or initial harvesting stages, crops were sown lately. Evaluation of stink bug infestation was carried out between the R3 and R8 stages  were evaluated, these constituting the regular treatments. Common treatments were represented by sampling from F2 and F4 generations, the parent lines and the BRS Celeste and MGBR-46 (Conquista) cultivars. The plot consisted of one-meter lines, 0.5 m apart, with twelve plants apiece. Evaluation of the traits was undertaken in five plants per plot. The evaluated traits were: a) Grain filling period (GFP) - obtained by the difference in days between reproductive stages R7 and R5 (Nematospora coryli Peglion). Statistical analysis of the data for the groups of experiments consisted basically of the individual analysis of variance for each experiment in random blocks, followed by grouped analysis of all experiments  with three replications. Thirty F7 and R5  in the ceriments .Estimates of mean components were carried out by the joint-scale method proposed by 2 and F4 (as bulk), and F3 and the respective backcrosses in the second generation of inbreeding (BC1F2:3 and BC2F2:3), for those traits under investigation. Initially, it was predicted to use a simple genetic model of the dominant-additive type, involving the components m, [a] and [d], where, m is the average value between parents, [a] represents the algebraic sum of the additive effects of all distinct loci between the parents, and [d] represents the algebraic sum of dominance effects of all distinct loci between the parents. If the proposed model proves to be unsatisfactory for explaining genetic mechanisms controlling the traits being investigated, an alternative model may be used, this including non-allelic interaction parameters between pairs of loci, with the addition of components [aa], [ad] and [dd]. The additional components represent the epistatic interaction between homozygous loci from the additive x additive type, the epistatic interaction of the additive x dominant type and the epistatic interaction between heterozygous loci or of the dominant x dominant type, respectively. The proportion among the components m, [a], [d], [aa], [ad] and [dd], present in the evaluated generations, is shown in detail in Genetic models were adjusted to means of the parent lines IAC-100 and FT-Estrela and their segregating generations FApplication of the joint-scale method is as described by n) n(1-Fn) n) n) n is the endogamy coefficient for generation n  + 1/4 Σ(h2) which is equivalent to 1/2 D + 1/4 H. As an alternative and according to the notation proposed by Thus, an approximation of genetic variance to studied traits is represented by the sum of the components of the additive variance :Narrow sense heritability (%):A summary of individual analyses of variance for the investigated traits is presented in Tables S3 to S6. From this, it can be observed that the source of variation in treatment unfolds according to genetic group, thereby permitting recognition of the magnitude of variation in treatments within each group. This approach has allowed us to observe statistical differences among treatments for all investigated traits, thereby indicating the occurrence of genetic variability among genotypes. This result was expected, due to the presence of homozygous and segregating material in the treatments, and which showed a distinct response to the high level of stink bug infestation that occurred in the experimental area, crucially contributing to the differentiation and expression of genetic variability of the genotypes in their resistance- response.3 and R8 , demonstrating genetic variability between parent lines in those traits pertaining to stink bug complex resistance. This contributes to generating genetic variability in segregating populations, due to gene recombination in inbred populations originating from crosses and backcrosses between genotypes. Concerning group decomposition, it was observed that there were statistically significant differences (p < 0.01) between F2:3 progenies for GFP and PIPD. For LR and PSS, these were statistically significant at 5%. There were no significant differences found in progenies regarding LR and PIPD traits in the BC1F2:3 group. The absence of statistical significance in the F test between treatments in this group is an indication of little genetic variability among the genotypes for these traits. However, as to the remaining traits, statistically significant differences were observed between progenies  of a parental line in backcrosses induces lower levels of gene recombination in inbred generations. Consequently, the sampled progenies from backcrosses show a tendency towards presenting smaller differences one from the other.The parents FT-Estrela (G1) and IAC-100 (G2) differed for all investigated traits , IAC-100 (G2), FIn the group of experiments, statistically significant differences  were observed in the mean contrasts between the parental lines FT-Estrela (G1) and IAC-100 (G2) for all those traits associated to stink bug resistance , thereby2) test, the estimates of parameters, their significance and the errors associated to the estimates, are detailed in Genetic models adjusted to the generation means and their respective significance in the chi-square , the sum of the additive effect of the genes [a] and the sum of the dominance effect among the alleles [d]) was adequate to explain the behavior of the means of those generations used in the grouped scale test, assuming the probability of 5% for the χe traits .Estimates of parameter [a], refering to the sum of gene additive effects, were positive and significant for the traits GFP, LR, PIPD and PSS, thus indicating that additive genetic effects condition the increase in traits. With the exception of the trait LR, results indicate the absence of dominant effects among resistance traits against the investigated stink bugs .It has been observed that the estimates of parameter [d], which represents the sum of deviations caused by dominance among alleles, were significant exclusively for LR. Similar results were found by 4 or F5 on).In general, the heterosis effect occurs as a disturbing factor in selection processes, due to the difficulties it gives rise to in selecting really superior individuals at initial endogamy generation. Later, the effects of dominance are spread by the advance of inbred generations, as normally seen in soybean breeding programs. According to 3 or F4), due exclusively to the importance of additive gene effects on the expression of these traits. In contrast, for the LR trait which shows significant dominance effects, selection must be carried out in later generations with higher endogamy levels.Therefore, based on the genetic studies of the means from the afore-cited generations for GFP, PIPD and PSS traits, it is expected that genetic gains may be obtained by plant selection in early endogamy generations , followed by selection for GFP, LR and PSS in following generations with higher endogamy levels.Based on the observed results from genetic analyses of means and variances, as well as estimates of heritability coefficients, it can be concluded that the best strategy for obtaining stink bug resistant genotypes is selection of the PIPD trait in early generations .Table S4 - Summary of analysis of variance, with those mean squares associated to variation among the means and within plots from their respective sources of variation for the trait leaf retention (grade).Table S5 - Summary of analysis of variance, with those mean squares associated to variation among the means and within the plots from the respective sources of variation for the trait percentage index of pod damage in soybeans (%).Table S6 - Summary of analysis of variance, with those mean squares associated to variation among the means and within the plots from their respective sources of variation for the trait percentage of spotted soybean seeds (%).This material is available as part of the online article from http://www.scielo.br/gmb.


Existing software for quantitative trait mapping is either not able to model polygenic variation or does not allow incorporation of more than one genetic variance component. Improperly modeling the genetic relatedness among subjects can result in excessive false positives. We have developed an R package, QTLRel, to enable more flexible modeling of genetic relatedness as well as covariates and non-genetic variance components.34 body weight data that contains 688 individuals genotyped at 3105 SNP markers and identified 11 QTL. It took 295 seconds to estimate variance components and 70 seconds to perform the genome scan on an Linux machine equipped with a 2.40GHz Intel(R) Core(TM)2 Quad CPU.We have successfully used the package to analyze many datasets, including FQTLRel provides a toolkit for genome-wide association studies that is capable of calculating genetic incidence matrices from pedigrees, estimating variance components, performing genome scans, incorporating interactive covariates and genetic and non-genetic variance components, as well as other functionalities such as multiple-QTL mapping and genome-wide epistasis. Software that can model polygenic effects due to genetic relatedness includes TASSEL While other programs are available for calculating condensed identity coefficients from pedigrees , we provQTLRel can estimate variance components given the appropriate incidence matrices. QTLRel estimates these variance components using maximum likelihood. These estimates are nearly equivalent to those obtained by restricted maximum likelihood for typical sample sizes. The maximum likelihood estimates are found numerically using one of several methods. We default to Nelder-Mead since we have found it to be more numerically stable. QTLRel allows users to select variance components using a model selection procedure or perform statistical significance tests for them.Re-estimating variance components at each marker in a genome scan may not be computationally feasible. The approach used by QTLRel is to first estimate the correlation matrix due to polygenic, residual and other random effects, which is based on the estimated variance components, and then use this matrix as known to scan the genome. Testing fixed effects conditional on estimated random effects is a general approach in mixed-effect models ,3,8,9. OQTLRel implements two methods for estimating genome-wide significance thresholds. The first is a permutation test in which the genotypes are permuted while the phenotypes and incidence matrices are held constant. We have previously demonstrated that when polygenic effects are ignored in the model type I error rates are inflated when a permutation is used; however, when the model is appropriate, permutation performs well . The secQTLRel has been successfully used in an AIL to identify QTL for methamphetamine sensitivity , muscle QTLRel provides a toolkit for genome-wide association studies that is capable of calculating genetic incidence matrices from pedigrees, estimating variance components, performing genome scans, and estimating significance thresholds. It can model interactive covariates and multiple genetic and non-genetic variance components. Other functions include multiple-QTL mapping and genome-wide epistasis. QTLRel can perform interval mapping based on the Haley-Knott method  for markhttp://cran.r-project.org/web/packages/QTLRel for Windows, Linux and Mac machines under the GNU GPL license. A tutorial is available in the package as well as on the Palmer lab web page http://www.palmerlab.org/software.QTLRel is an R package. It is publicly available on R CRAN RC wrote the program, this paper and the tutorial and has made seminal intellectual contributions throughout this project. MA worked with the other authors and lent his considerable experience addressing similar issues in human populations such as the Hutterites. AAP initiated the projects that lead to the development of the software and has interacted extensively with all other authors. ADS worked with the other authors and lent his considerable experience with the analysis of animal breeding designs and helped to develop earlier versions of both this paper and the tutorial. All authors read and approved the final manuscript.


Challenges of satisfying parametric assumptions in genomic settings with thousands or millions of tests have led investigators to combine powerful False Discovery Rate (FDR) approaches with computationally expensive but exact permutation testing. We describe a computationally efficient permutation-based approach that includes a tractable estimator of the proportion of true null hypotheses, the variance of the log of tail-area FDR, and a confidence interval (CI) estimator, which accounts for the number of permutations conducted and dependencies between tests. The CI estimator applies a binomial distribution and an overdispersion parameter to counts of positive tests. The approach is general with regards to the distribution of the test statistic, it performs favorably in comparison to other approaches, and reliable FDR estimates are demonstrated with as few as 10 permutations. An application of this approach to relate sleep patterns to gene expression patterns in mouse hypothalamus yielded a set of 11 transcripts associated with 24 h REM sleep [FDR = 0.15 ]. Two of the corresponding genes, Sfrp1 and Sfrp4, are involved in wnt signaling and several others, Irf7, Ifit1, Iigp2, and Ifih1, have links to interferon signaling. These genes would have been overlooked had a typical a priori FDR threshold such as 0.05 or 0.1 been applied. The CI provides the flexibility for choosing a significance threshold based on tolerance for false discoveries and precision of the FDR estimate. That is, it frees the investigator to use a more data-driven approach to define significance, such as the minimum estimated FDR, an option that is especially useful for weak effects, often observed in studies of complex diseases. Their approach incorporates an estimator of the proportion of true null hypotheses, π0, which increases power over the original Benjamini and Hochberg  have become a widely used multiple testing strategy that is much less conservative than family-wise error rate (FWER) methods such as the Bonferroni and Šidák corrections when multiple null hypotheses are false , and T the number of rejected null hypotheses that are false (true discoveries). The goal is to estimate FDR for a fixed significance threshold, thus S, F, and T depend on that threshold. The null distribution for a test statistic can often be approximated using a permutation procedure where the data are permuted repeatedly, with a set of test statistics generated for each replicate permuted dataset. Permuted test results will be identified here with a * and a subscript, e.g., S*i denotes the count of positive tests for the ith permuted dataset of B permutations. By design there are no false null hypotheses for tests of permuted data, consequently,Table The principal assumption underlying most permutation testing approaches is exchangeability of observations under the null hypothesis, implying that the expected proportion of positive tests among true null hypotheses is the same in observed and permuted results that is,m1 − E[T]), corresponding to the lower right cell of Table m1 − E[T] = 0. Below, we show in simulated data and provide additional arguments that this approach yields a conservative estimator relative to the ST approach yet anti-conservative relative to Benjamini and Hochberg π^0=by Efron . The exp. Storey  showed t Storey, . Efron  estimator for FDR can be developed in a manner analogous to the approach commonly used for the odds ratio that is, an exponential back-transform with a normal approximation,It is important to note that the variance and thus the CI is undefined when the number positive test results in the permuted data is zero. When this occurs we take the conservative approach of setting this number to one for estimation of the CI.The development of the variance estimator relies on the assumption that the positive test counts follow a binomial distribution. Thus, tests are assumed to be i.i.d. Bernoulli variables. This assumption has two parts, (1) the tests are independent and (2) identically distributed that is, the probability of a positive result is the same for all tests.p. In theorem 1 of Appendix B, “variance inequality of a binomial sum,” we show that a cryptic binomial mixture may cause an upward but not a downward bias in the variance estimate, implying that a departure from exchangeability across tests could cause the variance estimator to be more conservative but not more anti-conservative. We also found in simulations that the binomial variance estimator is highly robust to departures, and that in extreme cases where substantial departures do occur, the estimator does indeed become more conservative (data not shown).The second property can be described as exchangeability across tests in the sense that each test is assumed to yield a positive outcome with the same probability On the other hand, the independence assumption (1) does present a major concern and is addressed here by modifying the variance estimator with an over-dispersion parameter to account for dependencies. This parameter can be estimated directly from counts of positive tests and thus does not require an additional analysis of the raw data or even the full set of test results. In contrast, Efron , 2010a pIn practice, most genomic datasets include dependencies between features that ultimately result in dependencies between tests, although the correspondence can be quite complex. For typical hypothesis tests that evaluate associations between molecular and phenotypic traits, positive or negative correlations between traits lead to positive correlations between tests causing over-dispersion in the variance of positive test counts Edwards, , which ia” indicates adjustment for dependencies.The over-dispersion parameter is used to scale the variance estimate for y Storey  for FDR Z-scores were simulated for 100 cases and 100 controls at 2000 “genes” with false null hypotheses created by adding a constant to case observations, as described by Efron  estimators, they were adjusted using 10 or 100 permuted datasets.We compared the proposed estimator with the ST and Efron  approachby Efron . The conB), implying that under these conditions little improvement is achieved by the order-of-magnitude increase in B. This result is consistent with Equation 11 that shows a small contribution in the variance due to permutations when the number of positive tests in permuted data is substantial.As expected, all methods were conservatively biased in all scenarios across a range of significance thresholds Figure . Also, rWhen the effects were weak (constant = 0.15) the ST estimator was more conservatively biased than the others between approximately FDR = 0.1–0.2, and this divergence increased with the increased number of permutations , the ST was less biased than the others across the entire range but the variance was greater over most of the range. This bias-variance tradeoff is also apparent in the difference between the JM and EB estimators with the JM substantially less biased over the approximate range FDR > 0.1 but with greater variance. From FDR = 0–0.1, JM and BE performed quite similarly, but ST bias was smaller and the variance was comparable.We compared our proposed variance estimator for by Efron  both undby Efron . SimulatFrom Figure Using the BE variance estimator, we constructed CIs as proposed in Equation 12 to compare this approach to the proposed JM CI estimator. The JM 95 percent CI estimator outperformed the BE estimator in both the independent and dependent testing scenarios , and the number of permutations was 100 . One hundred and one mice were hand scored for sleep at 11–13 weeks of age using electroencephalogram (EEG) and electromyogram (EMG) data collected over a 48 h period  sleep and transcriptome-wide gene expression variation in male mice from a genetically segregating back-cross population of inbred mouse lines, C57BL/6J and BALB/cByJ, both the breeding scheme and sleep measures described previously  or even a BH FDR equal 0.05 significance level. There is very little guidance in the literature regarding what to do when this happens, publish a negative finding? The problem here is that although there may be some evidence in the data of a true biological signal that signal may be too weak to achieve a Bonferroni or BH 0.05 significance level. However, using the proposed FDR CIs, the investigator is able to relax the significance threshold if necessary to capture and quantify evidence for relatively weak biological signals.For all 17,404 probes, p-value significance thresholds. Each permuted dataset was created by randomly permuting the individual labels corresponding to expression data. This approach preserves observed dependencies between transcripts. Ultimately, an investigator often choses a single “significance” threshold  and reports those findings that meet the criterion, considering these to be “discoveries” that are worth further investigation. Unlike FWER control, where a universal threshold such as.05 can function as a single interpretable criterion to define significant features and quantify uncertainties, applying a FDR estimation approach may yield a range of thresholds over which p < 0.0001 p-values are more likely to be true discoveries. In view of the small differences in Figure p-values are secreted Frizzled-related proteins, Sfrp1 and Sfrp4 , known to be involved in wnt signaling , which is not directly related to the magnitude of Not only were suggestive links found in the literature between REM sleep and gene expression for the set of 11 genes whose expression was significantly associated with 24 h REM sleep, but the signal-to-noise ratio was also quantified in the form of FDR, along with a measure of uncertainty in the estimate. From the sleep data analysis, it is clear that there is evidence of association between gene expression and REM sleep, and we are able to identify many of the genes likely to be involved. If a typical FWER approach or a BH FDR approach had been applied to these data, the investigator would have failed to reject the global null hypothesis of no association between gene expression and REM sleep. Though 11 genes may seem like a small number, it is important to remember that these associations reflect chronic differences in expression and sleep between individuals  as distinct from detecting genes that cycle with sleep state changes. Also, we set out to identify genes that explain normal sleep variation in individuals who are relatively healthy, unlike many differential expression studies that are conducted by comparing a diseased or perturbed population, e.g., sleep deprivation, to a healthy one.http://cran.r-project.org/web/packages/fdrci/index.html) where permutations can be used to estimate FDR including CIs in a fully non-parametric approach, which is computationally parsimonious and robust to dependencies among tests.The migration to non-parametric approaches in genomic analyses may be inevitable as investigators are faced with seemingly insurmountable challenges of satisfying parametric assumptions in the context of many thousands of sample distributions. In addition, the typically stringent significance thresholds used in multiple testing on a genomic scale results in the need to draw inferences based on the extreme tails of an assumed distribution, which are notoriously inaccurate. Permutation-based approaches are attractive in their flexibility and accuracy but are computationally expensive. We have described a method (with software freely available as an R package, “fdrci”: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


We compared the genetic architecture of thirteen maize morphological traits in a large population of recombinant inbred lines. Four traits from the male inflorescence (tassel) and three traits from the female inflorescence (ear) were measured and studied using linkage and genome-wide association analyses and compared to three flowering and three leaf traits previously studied in the same population. Inflorescence loci have larger effects than flowering and leaf loci, and ear effects are larger than tassel effects. Ear trait models also have lower predictive ability than tassel, flowering, or leaf trait models. Pleiotropic loci were identified that control elongation of ear and tassel, consistent with their common developmental origin. For these pleiotropic loci, the ear effects are larger than tassel effects even though the same causal polymorphisms are likely involved. This implies that the observed differences in genetic architecture are not due to distinct features of the underlying polymorphisms. Our results support the hypothesis that genetic architecture is a function of trait stability over evolutionary time, since the traits that changed most during the relatively recent domestication of maize have the largest effects. Genetic architecture is of broad interest in evolutionary biology, plant and animal breeding, and medicine, because it influences both the response to selection and the success of trait mapping. Results from the most rigorously studied genetic systems suggest a similar genetic architecture across all species and traits studied, with many loci of small effect. A few strongly selected traits in domesticated organisms show unusual genetic architecture, for reasons that are unclear. We compare maize inflorescence, flowering, and leaf traits and show that inflorescence traits have distinct genetic architectures characterized by larger effects. Female inflorescences (ears) have larger effects than male inflorescences (tassels) even though the two structures have similar developmental origins. Analysis of pleiotropic loci shows that these larger effects are not inherent features of the underlying polymorphisms. Rather, maize inflorescences appear to be exceptionally labile, with female inflorescences more labile than male inflorescences. These results support the canalization hypothesis, which predicts that rapidly changing traits will have larger effects. We suggest that maize inflorescence traits, and ear traits in particular, have larger effects than flowering or leaf traits as a result of strong directional selection during maize domestication. The genetic architecture of a complex trait is defined by the number, effect size, frequency, and gene action of the quantitative trait loci (QTL) that affect it. A comparison of studies from flies, mice, and humans shows that genetic architecture is remarkably consistent among these species, with many loci of small additive effect Fisher A few traits exposed to strong, recent selection show distinct genetic architectures not characterized by many loci of small additive effect. For inbred dogs, three loci explain 38% of the variance in body weight among diverse breeds Arabidopsis thaliana than in maize, an outcrosser Mating system also appears to influence genetic architecture. Flowering time QTL effects are much larger in the inbreeding species Zea mays ssp. mays) was domesticated from teosinte (Zea mays ssp. parviglumis) 5,000 to 10,000 years ago in southwest Mexico 2 progeny from a maize-teosinte cross appear maize-like. Two of these mutations have been identified: teosinte branched1 (tb1) causes an increase in apical dominance and reduction of lateral branching and teosinte glume architecture (tga1) causes “release” of the nutritious grain from bony, enclosing glumes Plant and animal domesticates provide opportunities to compare genetic architecture between selected and unselected traits in populations exposed to the same demographic effects Maize is a monoecious plant with an apical male inflorescence, the tassel, and an axillary female inflorescence, the ear . Maize aTasselseed phenotypes are characterized by failure to abort female development in the tassel, and can be induced by mutation or epigenetic change The maize tassel and ear, despite their differences, share a common developmental origin and are nearly indistinguishable from each other during early development. Tassel and ear become distinct through the formation of long branch primordia and the abortion of female floral organs in the tassel, and through the abortion of male floral organs in the ear. Several mutant phenotypes support a close developmental relationship between tassel and ear. Branches are usually only found in the tassel, but a number of mutations produce branched ear phenotypes nested association mapping (NAM) population, a set of 4892 recombinant inbred lines (RILs) derived from 26 biparental families that capture much of the genetic diversity of maize In this study we compare the genetic architecture of thirteen maize morphological traits, including seven inflorescence traits reported here and three leaf and three flowering traits reported previously The four tassel traits and three ear traits measured are shown in We mapped loci controlling maize inflorescence variation using joint linkage and GWAS analyses in the NAM population of ∼5000 RILs as described previously 2 = 0.127 for joint linkage and r2 = 0.233 for GWAS). Scaling by the total heritable variation reduced this correlation considerably , and ear traits have larger effects than tassel effects (Kolmogorov-Smirnov test p = 0.004 for joint linkage and p<10−15 for GWAS). The few large-effect flowering QTL are contributed by anthesis-silking interval .Since ear QTL have larger effects, we reasoned that the subset of QTL for other traits that show evidence of pleiotropy with ear traits might also have larger effects. To address this hypothesis, all pleiotropic GWAS SNPs were grouped according to whether they showed pleiotropy within or between trait categories  encodes a squamosa-binding-protein (SBP)-domain transcription factor teosinte branched1 (tb1) encodes a TCP-domain protein fea2 and td1 loci , but are not associated with variation in branch number.Induced and spontaneous mutations in many maize genes cause dramatic inflorescence phenotypes . We constd1 loci -top. SBPtd1 loci -middle. Low-frequency SNPs found in four families or fewer account for most of the largest GWAS effects . Lack ofLarger QTL effects may reflect either larger effects of individual causal variants or greater linkage disequilibrium between causal variants with effects in the same direction. The latter phenomenon is expected to be most prevalent for SNPs found in a single family. However, the difference in magnitude between inflorescence and flowering/leaf effects holds true across the entire range of SNP frequencies , suggestZea populations of large-effect variants for DA and DS due to the fitness cost of flowering too early or late relative to the rest of the population. In contrast, ASI may be a much “younger” trait specific to the apically-dominant architecture of the maize plant. Our scaling procedures may also have inflated effects for ASI. The development and maintenance of inbred lines by self-fertilization strongly selects for synchronous male and female flowering , reducing the total heritable variation in ASI and increasing our scaled ASI QTL effects.Three flowering traits show a disjunct distribution of effect sizes, with days to anthesis (DA) and days to silking (DS) effects much smaller than anthesis-silking interval (ASI) effects . StabiliThe utility of GWAS studies is contingent on their ability to predict phenotypes. In this study we show that simple additive models containing several hundred SNPs explain over 50% of the phenotypic variation in a set of 4892 RILs for most of the 13 maize morphological traits . SNP numWe observe several pleiotropic relationships consistent with previous developmental genetic work. Negative pleiotropy between spike length (SL) and branch number (BN) indicates a trade-off between the two, consistent with the finding that a given meristem in the maize inflorescence acquires the fate of either a long indeterminate branch or a short indeterminate spikelet pair liguleless1 (lg1) locus, which is associated with variation in both leaf angle lg1 encodes an SBP-domain transcription factor. The association of lg1 with leaf angle is supported by its mutant phenotype lg1-linked leaf angle and branch number QTL in NAM are not correlated, suggesting that different polymorphisms may be responsible for the effects of lg1 on leaf and tassel traits. Since structural mutations in a gene are more likely to have effects wherever the gene is expressed, lg1-linked variants for leaf angle and branch number might be cis-regulatory variants operating independently of each other in specific tissues In a biparental family, close linkage of genes cannot be distinguished from pleiotropic effects of a single gene. Assessment of pleiotropy in NAM is made possible by testing correlations between vectors of QTL or SNP effects across the 26 families of RILs. This analysis will only detect pleiotropy when the same polymorphism or haplotype is consistently associated with phenotypic effects on different traits. Another less stringent definition of pleiotropy would allow a single gene to control variation in different traits through different polymorphisms. A possible example of this type of pleiotropy is the Only a small degree of overlap is observed between the location of cloned maize inflorescence development genes and SNPs significant for inflorescence traits . OverlapZea is characterized by a shift in the entire distribution of effect sizes, with many more effects of intermediate size and many fewer small effects. Although unusual genetic architectures observed in domesticates are sometimes attributed to human preference for novelty, which may preserve unadaptive, large-effect mutations The genetic architecture observed for maize inflorescence traits is novel. Very large effect sizes for a few major loci are commonly observed in plant and animal domesticates, including maize-teosinte segregants Maize domestication released cryptic genetic variation for inflorescence traits Maize ear and tassel traits have distinct genetic architectures even though they have shared genetic control: pleiotropic loci with effects on both tassel and ear show larger effects on the ear. This is the expected pattern if these pleiotropic loci had phenotypic effects in male but not female inflorescences in teosinte. Following maize domestication, they would act as newly-released cryptic variants in maize ears but not tassels. Maize domestication moved the ear from an axillary position to an apical position in the primary branch, which may have brought it under the control of an apical dominance network The process of domesticating maize from teosinte transformed plant architecture. The long lateral branch of teosinte with multiple, axillary, two-rowed female inflorescences was reshaped into a short, unbranched structure bearing a single, apical, multi-rowed ear. We present evidence that this process also transformed genetic architecture, creating a state of increased genetic lability in the maize ear that humans have cleverly exploited. Because only a few thousand generations have elapsed since the maize ear was created, ear traits still show a larger range of effect sizes than tassel, flowering, and leaf traits, for which maize and teosinte are phenotypically much more similar.Future advancements in medicine and agriculture will benefit from an improved understanding of the forces that shape the genetic architecture of complex traits. The most rigorous study to date comparing the genetic architecture of traits within a species The creation of the NAM population of RIL families has been described previously Trait transformations were performed using the boxcox function in R with lambda ranging from −10 to +10 in increments of 0.1, where lambda values of 0 and 1 are equivalent to log and linear transformations, respectively. Branch number and ear row number traits had maximum likelihood values of lambda of 0.3 and 0.4 respectively. Box-cox transformed values of these traits were used to calculate BLUPs. BLUPs were calculated in SAS using PROC MIXED and a model with location, set(location), family, family*location, and entry(family) as random effects.The genotypic dataset consisted of 836 markers, representing the subset of 1106 markers that could be placed unambiguously on the physical map, scored on 4892 RILs. Missing data, consisting primarily of markers that were non-informative in particular families, were imputed as previously described Missing SNP data from the maize HapMap project QTL effects for each trait were divided by the standard deviation of BLUP values across a set of 282 diverse maize lines that included the 27 parental lines, and multiplied by the broad-sense heritability estimate for that trait. Since a minimum of 26 QTL were detected for each trait, a 26-QTL model was refit for each trait and used to determine effect sizes. This experiment used a reference design (26 inbred lines were each crossed to a common parent), meaning that QTL effect sizes are potentially biased for traits for which the common parent is an outlier. To circumvent this problem, for each QTL we calculated the predicted effects of all pairwise matings between the 26 parents , yielding a total of 325 (26 choose 2) effect sizes for each QTL, or a total of 6825 qtl effects per trait.(r) between the two effect vectors of length 26 is significant at p<0.01 if r exceeds 0.495 . The percentage of shared QTL between two traits is the sum of two fractions: the fraction of significant correlations when the model for trait 1 is applied to trait 2, and vice versa. Pleiotropy between pairs of traits in GWAS analysis has not been reported previously. First, the effects of all GWAS SNPs for each trait in each family were weighted by their RMIP values and averaged in sliding windows across the genome, in order to derive a vector of effect estimates for each trait in each window. Results presented here used a 5 cM window size and a 2.5 cM step, but similar results were obtained for larger and smaller windows. Second, for each pair of traits, only windows where the sum of RMIP values for each trait fell above a threshold (RMIP = 0.10 for the results presented) were considered. Finally, significance of Pearson correlation coefficients between effect estimates was calculated as for joint linkage analysis.Pleiotropy between pairs of traits in the joint linkage analysis was evaluated as described previously We considered only the top ten GWAS SNPs for each trait, ordered by decreasing RMIP value, on the assumption that these more robustly-selected SNPs should be more closely linked to the causal variants. To test for significant enrichment, the number of high-RMIP SNPs for a given trait that fell within 0.5, 1, and 2 cM of candidates was compared with a null distribution obtained by selecting an equivalent number of random genes (eg: 17 random genes for comparison to 17 SBP candidates), calculating their proximity to trait SNPs, and repeating this process 1000 times. Selection of random positions rather than random genes represents a far less stringent test, since genes are clustered in the maize genome.Figure S1Median scaled effects of joint linkage QTL for 13 traits regressed on broad-sense heritability (A) and on B73's phenotypic standard deviation from the mean in a panel of 282 diverse maize lines (B).(TIF)Click here for additional data file.Figure S2Median scaled effects of GWAS SNPs for 13 traits regressed on broad-sense heritability (A) and on B73's phenotypic standard deviation from the mean in a panel of 282 diverse maize lines (B).(TIF)Click here for additional data file.Figure S3Frequency distributions for scaled GWAS effects produced using the top 50 (A), 100 (B), and 500 (C) SNPs for each trait. Results are similar to those presented at the bottom of (TIF)Click here for additional data file.Figure S4Relationship between QTL frequency and scaled QTL effects in the joint linkage (A) and GWAS (B) analyses, as in (TIF)Click here for additional data file.Figure S5Relationship between RMIP and scaled effects (top), and between SNP frequency and RMIP (bottom).(TIF)Click here for additional data file.Figure S6Co-localization of GWAS SNPs and candidate genes. A: cloned inflorescence mutants (n = 26). B: SBP-domain genes (n = 17). C: TCP-domain genes (n = 24). The 10 GWAS SNPs with the highest RMIP values were tested for each of 13 maize morphological traits. The number of GWAS SNPs falling within 0.5, 1, and 2 cM of a candidate gene is indicated with black, grey, and white bars respectively. Significance at levels of p<0.05 (*) and 0.01(**) was obtained by selecting an equal number of random maize genes to the number of candidates, calculating their genetic distances to the top 10 GWAS SNPs, and repeating this procedure 1000 times. Significance levels differ greatly between traits due to differences in the genetic context of their GWAS SNPs. SNPs in regions of low recombination may fall within 1 cM of many more random genes than SNPs in regions of high recombination.(TIF)Click here for additional data file.Table S1Joint Linkage QTL.(XLS)Click here for additional data file.Table S2GWAS SNPs.(XLS)Click here for additional data file.Table S3Pleiotropy in joint linkage analysis.(XLS)Click here for additional data file.Table S4Pleiotropy in GWAS analysis.(XLS)Click here for additional data file.


Genotype-by-environment interaction (GxE) has been widely reported in dairy cattle. One way to analyze GxE is to apply reaction norm models. The first derivative of a reaction norm is the environmental sensitivity (ES). In the present study we conducted a large-scale, genome-wide association analysis to identify single-nucleotide polymorphisms (SNPs) that affect general production (GP) and ES of milk traits in the German Holstein population. Sire estimates for GP and for ES were calculated from approximately 13 million daughter records by the use of linear reaction norm models. The daughters were offspring from 2297 sires. Sires were genotyped for 54k SNPs. The environment was defined as the average milk energy yield performance of the herds at the time during which the daughter observations were recorded. The sire estimates were used as observations in a genome-wide association analysis, using 1797 sires. Significant SNPs were confirmed in an independent validation set (500 sires of the same population). To separate GxE scaling and other GxE effects, the observations were log-transformed in some analyses. Results from the reaction norm model revealed GxE effects. Numerous significant SNPs were validated for both GP and ES. Many SNPs that affect GP also affect ES. We showed that ES of milk traits is a typical quantitative trait, genetically controlled by many genes with small effects and few genes with larger effect. A log-transformation of the observation resulted in a reduced number of validated SNPs for ES, pointing to genes that not only caused scaling GxE effects. The results will have implications for breeding for robustness in dairy cattle. SNPs on the sex chromosome also were excluded. This data filtering was performed with PLINK ]. In contrast to classical sire models, the relationship among sires was ignored, which could be done because there was much progeny information available for each sire, and hence, the sire estimates were largely influenced by the progeny records and only very little by the pedigree. Indeed, preliminary results showed that the correlation between sire estimates with and without considering the pedigree in model (1) was >0.98 (not shown).In a previous study we applied a second-order sire model, which gave an improved fit compared with a first-order model. However, a first-order sire effect explained most of the variation of ES  and a validation data set (n = 500 bulls). In the second step of the statistical analysis, we performed genome-wide association analyses using the discovery data set. To do so, we applied the following mixed linear model:m = 0) and ES (m = 1). These estimates were taken from the results of model (1). The model was applied for the two traits (m = 0 for GP and m = 1 for ES) separately. The effect of the SNP k was modeled as a regression on the number of copies of the allele with the greater frequency , with A is the numerator relationship matrix calculated from high-quality pedigree information and k in turn, resulting in 41,349 association tests per trait. We declared each SNP with a pointwise error probability of P < 0.001 as significant. To judge how many false-positive results were among the significant associations we applied the false-discovery rate (FDR) technique. We calculated for each association test an FDR q-value by using the software QVALUE  provided an estimate of the proportion of false-positive results among the significant associations.The whole data set was randomly split into a discovery data set . Given the FDR q-values of the SNPs in the discovery set (In this study we attempted to identify and confirm SNPs for intercept (reflecting GP) and slope (reflecting ES) of milk traits in the German Holstein dairy cattle population. Numerous SNPs were identified and confirmed for both GP and ES. Many SNPs affecting GP also affect ES. We showed that ES of milk traits has a similar genetic architecture as GP and is a typical quantitative trait, genetically controlled by many genes with small effects and few genes with larger effect . Hence, these effects were completely removable by the log-transformation. It may be noted that the log-transformation is frequently applied, but maybe another transformation function  would be able to eliminate scaling effects more effectively. This was not investigated further in this study. The reduced correlation between intercept and slope when applying the log-transformation (We previously reported significant GxE resulting in substantial scaling effects (ormation  was alsoIntroduction, breeding for robustness for both milk production and health traits is an issue in dairy cattle. In this study only milk production traits were considered. On the basis of our results, it seems that simultaneously breeding for an increase in milk GP and a decrease in ES by applying marker-assisted selection is difficult because no SNPs showed opposite directions of the effects. Genomic selection can be seen as marker assisted selection on a genome-wide scale. It is currently implemented in many dairy cattle populations (i.e., on the number of genes affecting the trait and on the distribution of the effect size (As described in the ulations . ImproviWe presented GxE for milk traits resulting in substantial scaling effects. Many SNP clusters affecting GP and ES could be identified and validated. The effects of some SNPs for ES were not removable by a data transformation, indicating that these are not solely scaling effects. The positions of these clusters were often found in well-known candidate regions affecting milk traits. No validated SNP showed effects for ES and GP in opposite directions. We showed that ES of milk traits is a typical quantitative trait controlled by many genes with small and few genes with large effects.


For genetic association studies in designs of unrelated individuals, current statistical methodology typically models the phenotype of interest as a function of the genotype and assumes a known statistical model for the phenotype. In the analysis of complex phenotypes, especially in the presence of ascertainment conditions, the specification of such model assumptions is not straight-forward and is error-prone, potentially causing misleading results.In this paper, we propose an alternative approach that treats the genotype as the random variable and conditions upon the phenotype. Thereby, the validity of the approach does not depend on the correctness of assumptions about the phenotypic model. Misspecification of the phenotypic model may lead to reduced statistical power. Theoretical derivations and simulation studies demonstrate both the validity and the advantages of the approach over existing methodology. In the COPDGene study (a GWAS for Chronic Obstructive Pulmonary Disease (COPD)), we apply the approach to a secondary, quantitative phenotype, the Fagerstrom nicotine dependence score, that is correlated with COPD affection status. The software package that implements this method is available.The flexibility of this approach enables the straight-forward application to quantitative phenotypes and binary traits in ascertained and unascertained samples. In addition to its robustness features, our method provides the platform for the construction of complex statistical models for longitudinal data, multivariate data, multi-marker tests, rare-variant analysis, and others. In genetic association studies, individuals are often recruited based on case-control ascertainment conditions of the primary phenotype . For theWe present a more general approach that does not require any distribution assumptions for the secondary phenotype. We refer to the approach as the non-parametric population-based association test (NPBAT). The approach has a form similar to the Family Based Association Test (FBAT), a non-parametric test statistic that is frequently used in the family based setting -15. The The general concept of the proposed association-testing framework is to condition on the phenotype of interest and treat only the genetic data as random ,13,15. BWe illustrate the practical advantages of NPBAT by an application to the COPDGene study. The COPDGene study is a case-control study of the genetics of COPD in current or former smokers with at least 10 pack-years of smoking history . We testn unrelated study subjects have been recruited based on a predefined ascertainment condition. Let Xi denote the genotype of the individual i. The specific value of Xi will depend upon the genetic model under consideration. For instance, for an additive model, Xi = 0, 1, 2 for 0, 1, 2 disease alleles, respectively. Xi may also be a vector in order to test several alleles simultaneously. Let Ti denote the numerical trait information for individual i. For example, Ti could equal one for affected individuals and Ti could equal zero for unaffected individuals. Different coding functions are applied depending on the phenotype of interest. For binary and continuous traits, we will discuss efficient coding schemes below. First, we define a general class of test statistics as In a genetic association study, E(S) = 0 under the null hypothesis of no association between the genotype X and the phenotype Y. Constructing a conditional score test in which the genotype Xi is the dependent variable and we condition upon the numerical trait information Ti, the NPBAT statistic has the following form: Note that Ex denotes the expectation of the marker score/ genotype X under the null-hypothesis of no genetic association between the phenotype. The marker locus. Ex can be estimated based on the sample mean of the genotypes. The asymptotic distribution of the NPBAT statistic under the null-hypothesis depends on the estimation of Ex and on the specification of the trait information Ti, and is derived in the Appendix.where Ti. For the analysis of affection status, one could specify the coding function to be Ti = 1 or Ti = 0, depending on the disease status of the proband. However, as we show in the Appendix Appendix A: Offset choice when Y is binary, a more efficient way is to set There are various ways to code the phenotype of interest and define the coding function Yi is in fact normally distributed and Y on any covariates, then the NPBAT statistic is approximately the same as a t-statistic from a linear regression. In general, if the phenotype Yi is a continuous phenotype, we recommend Ti = Yi - μy where μy is the phenotypic mean in the general population.If the phenotype Ti = Yi - Yoffset where Yoffset is a constant. The choice of this constant is described in detail in the simulations sub-section and the asymptotic distribution of the NPBAT statistic is derived in the Appendix. Using this optimal offset choice, the NPBAT statistic has a substantial increase in power over other methods such as the NPBAT statistic when an offset choice of χ2 test and the genotypic χ2 test .Note that the statistic is maximized and has a standard normal distribution when n is only the number of cases and all summations are only over the number of cases since the phenotypic information is not available for the controls where as in Appendix Appendix B: asymptotic distribution when the secondary phenotype is available for both the cases and controls, n is the number of cases and controls and the summation is over both the number of cases and controls. Let E[X] since X is not associated with Y. Let text = cases or controls, meaning X1..Xn is the coded genotype of the cases but Here, we derive the asymptotic distribution of the NPBAT statistic for secondary phenotypes in case/control studies. Consider a case control study where genetic information is available for both the cases and the controls, but the phenotypic information is only available for the cases. Here then Zis are independent, E(Zi) = 0 and Zi, which ensures asymptotic normality of It is important to note that the ondition  for Zi, Zi has a discrete distribution, the Lindberg condition can only be fulfilled when the integration set {|Zi| ≥ ϵ} is empty for n → ∞. Since X is the coded genotype and Y is a biological quantity, assume Since n → ∞. Thus the Lindberg condition is always fulfilled when the regularity condition holds. Then the Lindberg theorem [Hence the integral in the Lindberg condition is always computed over a set that is empty for  theorem  implies Yoffset = E[Y]. Note that if Ex is based on the the controls and the phenotype information is only available for the cases, then the power is maximized when Yoffset ≈ E[Y].Then the NPBAT statistic is normally distributed with mean zero and variance given above. Note that the variance is always greater than or equal to one and equals one when https://sites.google.com/site/genenpbat/. In addition to NPBAT statistics, other population based statistics such as the Armitage Trend Test, Fisher Exact Test are also available. Currently, only two platforms are supported: linux64 and windows64. The NPBAT software package reads in genetic data through the PLINK style pedigree (ped), map (map) and phenotype (phe) files. The website provides detail information on how to use the software package.A software package implemented in C++ to compute both single phenotype and multiple phenotypes NPBAT statistics is available for download at the following website: COPD: Chronic obstructive pulmonary disease; FBAT: Family Based Association Test; FEV: Forced expiratory volume; FNDS: Fagerstrom nicotine dependence score; GWAS: Genome Wide Association Study; LRT: Likelihood ratio test; NPBAT: Nonparametric Population Based Association Test; PC: Principal component.The authors declare that they have no competing interests.SL derived the asymptotic distribution, performed the simulations studies and the data analysis. SL, WKY, JH, NL, and CL were involved in drafting the manuscript or revising it critically. CL made substantial contributions to conception of the method and assisted in the simulation studies. All authors read and approved the final manuscript.


The purpose of this work was to study the impact of both the size of genomic reference populations and the inclusion of a residual polygenic effect on dairy cattle genetic evaluations enhanced with genomic information.Direct genomic values were estimated for German Holstein cattle with a genomic BLUP model including a residual polygenic effect. A total of 17,429 genotyped Holstein bulls were evaluated using the phenotypes of 44 traits. The Interbull genomic validation test was implemented to investigate how the inclusion of a residual polygenic effect impacted genomic estimated breeding values.As the number of reference bulls increased, both the variance of the estimates of single nucleotide polymorphism effects and the reliability of the direct genomic values of selection candidates increased. Fitting a residual polygenic effect in the model resulted in less biased genome-enhanced breeding values and decreased the correlation between direct genomic values and estimated breeding values of sires in the reference population.Genetic evaluation of dairy cattle enhanced with genomic information is highly effective in increasing reliability, as well as using large genomic reference populations. We found that fitting a residual polygenic effect reduced the bias in genome-enhanced breeding values, decreased the correlation between direct genomic values and sire's estimated breeding values and made genome-enhanced breeding values more consistent in mean and variance as is the case for pedigree-based estimated breeding values. With the availability of the bovine genome sequence and the development of high-density arrays of single nucleotide polymorphism (SNP) markers, the accuracy of genetic predictions has improved compared to conventional breeding value estimations based on phenotypic data and pedigree -9. In orThe reliability of genomic predictions strongly depends on the number of genotyped bulls in the reference population that is used to estimate SNP effects ,18. The Holstein bulls from the German national genomic reference population originating partially from the national genome project GenoTrack and partially from routinely genotyped populations, were genotyped using the Illumina Bovine50k . The genotyping was conducted after ethnical review and approval by the project committee. Only SNP with a minor allele frequency greater than 1% and a call rate threshold greater than 95% i.e. 45,181 SNP were used for the analysis. Since male animals have only one allele for the 533 markers on chromosome X, the procedure to estimate marker effects developed for markers with two alleles was modified for these SNP. A genotyped animal was excluded if less than 95% of all SNP markers were called. Deregressed EBV (DRP) and effective daughter contributions (EDC) were obtained from the January 2010 German national conventional evaluation for all bulls. Forty-four traits from seven trait groups were analysed: milk production (three traits), udder health (one trait), functional longevity (one trait), calving (four traits), female fertility (six traits), workability (four traits) and conformation (25 traits). Table To investigate the impact of including an RPG effect on GEBV, another dataset was used, which originated from the EuroGenomics collaboration . This daIn the literature ,26, someThe following BLUP SNP model was applied to the DRP of reference bulls:qi is the DRP of bull i, μ is a general mean, νi is the RPG effect of bull i, p is the number of fitted SNP, zij is a genotype indicator (-1 or 1 for the two homozygotes and 0 for the heterozygote) of marker j of bull i, uj is the random regression coefficient for marker j, and ei is the residual effect of bull i. The total additive genetic variance, w is the proportion of additive genetic variance explained by the RPG effect, and additive genetic variance explained by the p markers w was assumed to vary across traits. The optimal w value was determined by applying the Interbull genomic validation test [qi was φi is the EDC for bull i. The RPG was fitted in the same way as in conventional genetic evaluations, i.e. using full pedigree and the same grouping procedures of phantom parents [Where n traits  and for n traits , and wasion test . Residua parents .Since the BLUP SNP model (1) has a large number of parameters, i.e. SNP effects that need to be estimated simultaneously, a Gauss-Seidel iteration with residual updating  was applTable When the genomic reference population for German Holstein cattle was switched from the German national to the EuroGenomics reference population, the number of reference bulls increased from 5,025 to 17,429. Additionally, the dependent variable DRP was derived from MACE EBV, which included phenotypic information from foreign countries, in contrast to German national EBV. In comparison to the validation results from the German national reference population in Table During the development of the German genomic evaluation system, a number of test runs were conducted over time, which enabled a comparison of the estimates of SNP effects across different reference populations. Table Table Estimated SNP effects from three scenarios using the EuroGenomics reference population were compared to the scenario with the lowest residual polygenic variance for milk yield Table . The corTable Following the Interbull genomic validation test procedure , convent2 values indicate the fraction of the sons' genetic variation that is explained by their sires and are shown in Figure 2 value was 0.42 for both DGV and the sum. As the residual polygenic effect increased to 20% of the total genetic variance, the R2 value between the DGV of the son and the EBV of the sire dropped below 0.20. In contrast to DGV, corresponding R2 values for the sum of DGV and RPG remained constant, regardless of the level of residual polygenic variance. Figure 2 values of the regression of DGV on the sires' EBV dropped from 0.29 for the scenario with a 0.02% residual polygenic variance to about 0.10 for the scenario with a 20% residual polygenic variance, suggesting a decreasing impact of the sires' EBV on the DGV of validation bulls. With increasing residual polygenic variances, R2 values decreased much less for combined GEBV of the validation bulls than for DGV alone, because in the combined GEBV the influence of sires was added back via the pedigree index. By fitting an RPG effect in the genomic model, the estimated DGV were less dependent on the sire's EBV, which was indicated by the lower R2 value of the DGV regression on sire's EBV. The two figures showed that fitting an RPG effect in a genomic model can reduce the correlation between sires' EBV and animals' DGV.A concern that under the genomic BLUP model, animals' DGV are highly correlated with the sires' EBV ,26 was aConvergence of the BLUP SNP model was improved when the SNP markers were processed in descending order of heterozygosity. The processing order was particularly important when some reference bulls with extremely high or low EBV happened to have extremely high EDC, because those extreme phenotypic values could lead to extreme regression estimates of SNP markers with a low heterozygosity and thus could cause a convergence problem in the estimation of SNP effects. For the currently and most widely used 54 K Illumina BeadChip , we observed that SNP effects did not converge as well as their sum, i.e. DGV. Due to higher LD, convergence of SNP effects could become even lower for a higher density chip, although the convergence of DGV should remain unchanged. An alternative modelling of marker information from high-density chips should be explored.The tremendous advances in conventional genetic evaluations during the last decades have formed a solid basis for genomic evaluation and selection in dairy cattle. Genomic validation studies worldwide have demonstrated that the genomic model proposed by Meuwissen et al.  is highlThe authors declare that they have no competing interests.ZL conducted the analyses and wrote the manuscript. FS prepared the genomic data. FR and SR helped check the results and suggested improvements. GT and RR coordinated the project, added valuable comments and suggestions. All authors read and approved the manuscript.


Until recently, genome-wide association studies (GWAS) have been restricted to research groups with the budget necessary to genotype hundreds, if not thousands, of samples. Replacing individual genotyping with genotyping of DNA pools in Phase I of a GWAS has proven successful, and dramatically altered the financial feasibility of this approach. When conducting a pool-based GWAS, how well SNP allele frequency is estimated from a DNA pool will influence a study's power to detect associations. Here we address how to control the variance in allele frequency estimation when DNAs are pooled, and how to plan and conduct the most efficient well-powered pool-based GWAS.array)] and pool-construction variance [var(econstruction)] contribute to the total variance of allele frequency estimation. This information is useful in deciding whether replicate arrays or replicate pools are most useful in reducing variance. Our analysis is based on 27 DNA pools ranging in size from 74 to 446 individual samples, genotyped on a collective total of 128 Illumina beadarrays: 24 1M-Single, 32 1M-Duo, and 72 660-Quad.By examining the variation in allele frequency estimation on SNP arrays between and within DNA pools we determine how array variance [var(earray) were similar, between 3-4 × 10-4 for normalized data. Var(econstruction) accounted for between 20-40% of pooling variance across 27 pools in normalized data.For all three Illumina SNP array types our estimates of var(earray), var(econstruction) is of less importance in reducing the variance in allele frequency estimation from DNA pools; however, our data suggests that on average it may be more important than previously thought. We have prepared a simple online tool, PoolingPlanner (available at http://www.kchew.ca/PoolingPlanner/), which calculates the effective sample size (ESS) of a DNA pool given a range of replicate array values. ESS can be used in a power calculator to perform pool-adjusted calculations. This allows one to quickly calculate the loss of power associated with a pooling experiment to make an informed decision on whether a pool-based GWAS is worth pursuing.We conclude that relative to var(e Catalog of Published Genome-Wide Association Studies . Unfort Studies ,4. To da Studies -12. Depe Studies . For a c Studies ,4, and f Studies .We know that in the process of estimating allele frequencies from DNA pools we introduce error, and these must be taken into consideration to plan an adequately powered experiment or to appropriately calculate association statistics ,16. WithHere we partition and estimate variance components using the approach described by MacGregor , which ehttp://www.kchew.ca/PoolingPlanner/). PoolingPlanner also accepts user-supplied values for variance estimates. ESS can then be used in one of the available power calculators, such as CaTS :In choosing to conduct a pool-based GWAS, one accepts a loss in power relative to a conventional GWAS. How much power is lost can be expressed in terms of the effective sample size . In two, it is expressed as the fraction of the total variance, (Vs + var(epooling)), explained by the binomial sampling variance, Vs. Vs is calculated as p(1-p)/2N, where p is the average minor allele frequency on the array, and N is number of individuals contributing to the DNA pool. If DNA pools have been constructed in replicate we let var(epooling)= var(epooling-1), otherwise we let var(epooling)= var(epooling-2). The two equations for RSS can then be equated and solved for N*. It is worth noting that because our calculation of RSS relies on our empirical estimates of var(epooling) (Equation 2), estimates which are based on contrasting allele frequencies in two DNA pools, the effects of unequal hybridization, which would typically thwart a direct comparison of a pooling-based and conventional genotyping experiment, cancels out .In one, the RSS of a DNA pool is expressed as the ratio of effective sample size to the actual sample size (pooling) by a factor of 1/k, where k is the number of replicate arrays [pooling) smaller the RSS and N* become larger. Effective sample size can then be used with one of the available power calculators, for example CaTS [http://www.kchew.ca/PoolingPlanner/).Replicate arrays can be used to reduce var and 2.9 × 10-3 (raw data), see Table array). Three of these estimates, each from pair-wise array comparisons involving the same array, were extreme outliers in both the normalized and raw dataset  was 3.2 × 10-4  and 9.0 × 10-4 (raw data), see Table array)) and batch 2 (27 var(earray)) had mean estimates of array variance of 4.2 × 10-4 and 2.6 × 10-4, respectively. For the 660-Quad arrays, 7 pools were assayed using 72 arrays (6 or 12 arrays per pool), and mean array variance was 3.3 × 10-4 for normalized data, and 2.7 × 10-3 for raw data, see Table For the 1M-Single arrays 12 DNA pools were allelotyped using 24 arrays (2 arrays per pool), yielding 12 estimates of array variance, the mean of which was 3.8 × 10pooling) and var(econstruction) estimates for those pools on the 1M-Single array. For normalized data var(epooling-1) ranged from 3.2 × 10-4 to 5.5 × 10-4 and averaged 4.0 × 10-4. In comparison var(epooling-2) ranged from 3.5 × 10-4 to 7.0 × 10-4 and averaged 4.8 × 10-4. Var(econstruction-1) ranged from 0 to 6.7 × 10-5 and had a mean of 2.9 × 10-5 . Thus, for these pools var(econstruction-1) accounts for between 0 and 20%, or an average 7.5% of the pooling variance when using Type B derived values . Var(econstruction-2) ranged from 0 to 3.2 × 10-4 and averaged 1.0 × 10-4; thus, pool-construction variance accounted for between zero and 46%, or an average 20% of the pooling variance using Type C derived values . There does not appear to be any correlation between pool size and pool-construction variance, see Figure We estimate pool-construction variance for 27 DNA pools, discussed in order by Illumina array type. Six pools were allelotyped on the 1M-Single array, and for each, pools were constructed in replicate and allelotyped by two arrays. This allowed us to calculate and compare pooling variance and pool-construction variance estimates as calculated using Type B and Type C comparison values. Figure pooling-1) were approximately 8-fold higher than the normalized data. Estimates of var(econstruction-1) tended to be higher as well, averaging ~20% of the pooling variance. Var(epooling-2) estimates followed the same pattern, larger estimates of pooling variance and pool-construction variance (data not shown).Using raw data, estimates of var(epooling-2) each), and five using twelve replicate arrays (720 estimates of var(epooling-2) per pool. Figure pooling-2) and var(econstruction-2) estimates for these pools . Var(epooling-2) estimates ranged from 4.3 × 10-4 to 5.7 × 10-4, and averaged 5.1 × 10-4; meanwhile, the var(econstruction-2) estimates ranged from 1.0 × 10-4 (23%) to 2.4 × 10-4 (42%) and averaged 1.9 × 10-4 (35%). These estimates of pooling variance are very similar to those seen for pools on the 1M-Single array; however, the estimates of pool-construction variance are higher . For the raw data var(epooling-2) estimates ranged from 2.6 × 10-3 to 2.9 × 10-3, and averaged 2.7 × 10-3; meanwhile, the matched var(econstruction-2) estimates ranged from 0 to 2.6 × 10-4 (9%) and averaged 1.9 × 10-4 (2%).Pools allelotyped on the 1M-Duo and 660-Quad arrays were not constructed twice; hence, for these we estimated pool-construction variance based on Type C comparisons only. Seven DNA pools were allelotyped on the 660-Quad array, two using six replicate arrays (396 estimates of var(epooling-2) estimate is the average of 32 pair-wise array comparisons. Figure pooling-2) and var(econstruction-2) estimates for these pools . Var(epooling-2) was estimated at 5.6 × 10-4, 6.0 × 10-4 and 6.1 × 10-4. The matched var(econstruction-2) estimates were 1.5 × 10-4, 1.8 × 10-4, and 1.9 × 10-4 , or 26%, 31%, and 32% of the pooling variance for pools sized 122, 246, and 121 . These values reflect those seen for pools on 660-Quad and 1M-Single arrays. In comparison, the 1M-Duo batch 2 data deviated dramatically. This batch contained 5 pools, each also alleloyped by four replicate arrays. For these var(epooling-2) ranged from 1.8 × 10-3 to 3.7 × 10-3, and averaged 2.6 × 10-3, and var(econstruction-2) estimates ranging from 7.9 × 10-4 (43%) to 2.7 × 10-3 (72%) . For these pools the estimates of pooling variance are nearly 2-3 fold higher than those of batch 1 but the array variance remained low at 2.4 × 10-4, leading to high estimates of pool-construction variance (see discussion). For raw data batch 1 & 2 were analyzed combined using all possible array comparisons and var(earray) = 9.0 × 10-4. Estimates of var(epooling-2) ranged from 2.2 × 10-3 to 5.4 × 10-3 and averaged 3.4 × 10-3. Var(econstruction-2) estimates averaged at 51% of the calculated var(epooling-2).1M-Duo arrays were analyzed separately by batch using batch-specific estimate of array variance for normalized data. The 1M-Duo batch 1 data contained three DNA pools, each allelotyped by four replicate arrays; therefore, each var(earray), 2) var(econstruction), 3) pool size, and 4) allele frequency. Figure array) value as calculated based on our 660-Quad normalized data, 3.3 × 10-4, see Table construction) is 30% of the pooling variance, chosen to reflect values we observed. Var(econstruction) is entered into PoolingPlanner by specifying "Array:Construction Ratio = 7:3", as seen in Figure construction) can also be entered (30% of 3.3 × 10-4 would be 9.9 × 10-5). For allele frequency, by default PoolingPlanner uses HapMap CEU data (release 27) to set p to the average minor allele frequency (MAF) on the 1M-Single, 1M-Duo, or 660-Quad Illumina array. For the 1M-Single and 1M-Duo arrays p = 0.21 (>95% of SNPs had available HapMap data), and for the 660-Quad array p = 0.29 (87% of SNPs had available HapMap data). Estimates of p based on our pooled array data were similar . In this example the average MAF is set to 0.29, but the user can enter any value between 0 and 0.5. Once these values are entered the program calculates the relative and effective sample size of each DNA pool for a range of replicate array values, and provides a corresponding table of values as seen in Figure To demonstrate how to use PoolingPlanner we consider a hypothetical scenario. A researcher has a collection of samples including 300 cases and 1000 controls and wants to conduct a pool-based GWAS. The researcher needs to decide how many arrays to use, and wants to construct power curves that take into consideration the power loss concomitant with this cost-efficient strategy. They plan on using Illumina's 660-Quad array and normalizing their data. PoolingPlanner is used to calculate the effective sample size of each DNA pool using four input values: 1) var(erisk) is 29% (and in complete linkage disequilibrium with a SNP on the array), the power curves corresponding to a pooling experiment where 3, 6, 12, or 24 Illumina 660-Quad replicate arrays are used per pool is given in Figure risk is 0.29, and for comparison, when prisk is 0.1. Assuming individual genotyping, the MDOR at 80% power would be 1.32 when prisk is 0.29. Using 24 arrays per pool this value rises incrementally to 1.33. Using 12, 6, or 3 arrays per pool, the MDOR's further increase to 1.35, 1.38, and 1.44, respectively. Only when 3 arrays are used per pool does the MDOR dramatically differ between pooling and individual genotyping. Marginal improvements in MDOR should be considered in light of increasing experimental cost, and the percent cost of a pooling GWAS relative to a conventional GWAS is given in Table risk is 0.1. We note that as prisk gets smaller, the difference in the MDOR for a pooling versus individual genotyping experiment becomes more noticeable. For example, when 6 replicate arrays are used per pool and prisk is 0.29, the MDOR differs by 0.06 from individual genotyping, but this difference becomes 0.09 when prisk is 0.1. It is also worth noting in Table Figure S1). By conducting an analysis such as this a user can decide what power is forfeited by conducting a pool-based GWAS, and decide whether the approach makes practical sense in their situation.To perform pooling-adjusted power calculations, a pool's effective sample size, output by PoolingPlanner, is entered into a power calculator. We have used Quanto  for thisIn the first part of this study we set out to establish a range of experimentally observed values for array variance on Illumina's SNP-genotyping beadarrays. At the same time, we wanted to establish a range of values for pool construction variance. In the second part, we used these estimates to calculate the effective sample size of a DNA pool given a range of replicate array values, and provide an online tool to allow readers to do the same.array)= 1.1 × 10-4 ) for an Illumina HumanHap300 beadarray [array) estimates, centering around 3 × 10-4 for our normalized data, which is largely in keeping with the HumanHap300 result [At the time of our analysis we were aware of only one report that estimated array variance (var(eeadarray . Illumin0 result . We expe0 result . Reducedarray) estimates ~10-fold smaller than those of the Affymetrix HindIII 50K arrays (var(earray)= 1.26 × 10-3) analyzed by MacGregor [HindIII 50K arrays [The Illumina arrays analyzed here yielded var spanned 27 DNA pools, ranging in size from 74 to 446 individual samples, allowing us to sample a range of possible pool construction variances. First, in contrast to a previous report [construction) usually fell between 20 and 40% of the pooling variance. When calculations were based on the comparison of replicate DNA pools  our estimates were smaller, on average 7.5% of the pooling variance. There are several possible reasons for this. The adjustment for binomial sampling variance may not fully account for the variance arising from sampling, leaving variance that is then attributed to pool-construction in the Type C comparisons. As well, some estimates of pool-construction variance were negative, and these were set to zero, which would lead to overestimation of pool-construction variance. We conclude that relative to var(earray), var(econstruction.) is of less importance; however, our results suggest pool construction may account for more of the pooling variance than previously estimated [HindIII 50K arrays. On average we attribute 30% of pooling variance to pool construction when using Illumina arrays. This difference is what might be expected given the smaller var(earray) for Illumina arrays. Further reductions in array variance, for example, through improved normalization of array data, have the potential to further shift the proportion of an experiment's pooling variance that is attributed to pool-construction errors.Our estimates of var and var(econstruction) for a range of DNA pool sizes. We have also presented PoolingPlanner, a simple program to help translate these variances into their effect on sample size, information that can then be use in a power calculator to conduct pool-adjust calculations. PoolingPlanner may be helpful in quickly assessing theoretical best and worst-case scenarios for a DNA pooling GWAS. With this information the user can then make a more informed decision about how to carry out their pooling experiment to optimally balance cost with loss of power.We have provided empirical estimates of var(eThe authors declare that they have no competing interests.MAE performed all statistical analysis and drafted the manuscript. KC developed and implemented the online tool PoolingPlanner. MR and ABW participated in study design, coordination, and manuscript drafting. All of the authors have read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1755-8794/4/81/prepubAdditional Table S1.Click here for fileAdditional Table S2.Click here for fileAdditional Table S3.Click here for fileAdditional Table S4.Click here for fileAdditional Table S5.Click here for fileAdditional Figure S1.Click here for file


Genomic selection has become a standard tool in dairy cattle breeding. However, for other animal species, implementation of this technology is hindered by the high cost of genotyping. One way to reduce the routine costs is to genotype selection candidates with an SNP (single nucleotide polymorphism) panel of reduced density. This strategy is investigated in the present paper. Methods are proposed for the approximation of SNP positions, for selection of SNPs to be included in the low-density panel, for genotype imputation, and for the estimation of the accuracy of genomic breeding values. The imputation method was developed for a situation in which selection candidates are genotyped with an SNP panel of reduced density but have high-density genotyped sires. The dams of selection candidates are not genotyped. The methods were applied to a sire line pig population with 895 German Piétrain boars genotyped with the PorcineSNP60 BeadChip.Genotype imputation error rates were 0.133 for a 384 marker panel, 0.079 for a 768 marker panel, and 0.022 for a 3000 marker panel. Error rates for markers with approximated positions were slightly larger. Availability of high-density genotypes for close relatives of the selection candidates reduced the imputation error rate. The estimated decrease in the accuracy of genomic breeding values due to imputation errors was 3% for the 384 marker panel and negligible for larger panels, provided that at least one parent of the selection candidates was genotyped at high-density.Genomic breeding values predicted from deregressed breeding values with low reliabilities were more strongly correlated with the estimated BLUP breeding values than with the true breeding values. This was not the case when a shortened pedigree was used to predict BLUP breeding values, in which the parents of the individuals genotyped at high-density were considered unknown.Genomic selection with imputation from very low- to high-density marker panels is a promising strategy for the implementation of genomic selection at acceptable costs. A panel size of 384 markers can be recommended for selection candidates of a pig breeding program if at least one parent is genotyped at high-density, but this appears to be the lower bound. Genomic selection refers to the use of large numbers of single nucleotide polymorphisms (SNPs) spread across the genome for breeding value estimation and subsequent selection of individuals based on genomically enhanced breeding values ,2. This One way to reduce routine costs is to genotype selection candidates with an SNP panel of reduced density -10. MissMany SNPs of the available chips have unknown chromosomal positions. For example, the PorcineSNP60 BeadChip contains > 62 000 SNP, of which 30% have no known position on the porcine genome sequence (build 7 version) [The aim of the present study was to evaluate different strategies for genomic selection in a sire line pig population using low-density marker panels. The strategies included methods for the approximation of SNP positions, for the selection of SNPs to be included in the low-density panel, for genotype imputation, and for the estimation of the accuracy of genomic breeding values. The methods were validated using genotype imputation error rate, imputation accuracy, correlation between direct genomic values (DGV) and BLUP breeding values (EBV), and approximate accuracies of DGV.Genotypes and EBV of 895 German Piétrain boars were available from breeding organizations. Boars were genotyped with the PorcineSNP60 BeadChip [The boars were progeny tested with a varying number of offspring. Conventional EBV were available for 14 growth, carcass and meat quality traits from the routine animal evaluation centre  of every individual from the validation set was in the training set. The individuals of the validation set were chosen from the latest delivered genotypes. In order to avoid a possible bias due to overfitting the model, we excluded these 100 boars (i.e. their EBV and their genotypes) from all evaluations done during the development of the imputation method.Gm to be the vector of genotypes of the individuals for marker m and MAFm the MAF of this marker. We constructed equivalence classes of marker sets such that markers from the same equivalence class are expected to belong to the same chromosome. Two markers m′ and m″ belong to the same equivalence class if a chain m1,..., mn of markers exists, starting with marker m1 = m′ and ending with marker mn = m″, such that the absolute value of the correlation of the genotypes for adjacent markers in the chain is larger than a threshold value of 0.4. That is,In order to also use markers with unknown physical position for imputation, their positions were approximated using LD information, as described below. Let k = 2,..., n − 1. The threshold value 0.4 was chosen to avoid equivalence classes to cover multiple chromosomes. Correlations of genotypes  were used and not the LD measure r[m′ with unknown position on the identified chromosome was then set equal to the known position of a marker m from the same chromosome that maximized with measure r, becauselocm be the location in megabases (Mb) and Chrm the chromosome of SNP m. In the first step, we defined a distance measure d between two SNPs m′ and m″ as d = ∞ if Chrm′ ≠ Chrm″, and if Chrm′ = Chrm″ thenFrom the set of markers, four subsets consisting of 384, 2 · 384 = 768, 3 · 384 = 1152 and 3000 SNPs were selected based on equidistant location, high MAF, and low correlation of genotypes, as described in the following three steps. Let κ = 5. Following this, we have λ < 1 (λ = 1) if the markers were separated by less than (more than) κ = 5 Mb. Hence, for closely linked loci (λ < 1), the correlation between the genotypes contributed to the distance measure. This was done so that two markers at similar genomic positions could be included in the low-density panel if they were not in LD and, hence, the correlation between their genotypes was low.where m based on its MAF (MAFm):In the next step, a score was calculated for each marker um = 1 if marker m had a known physical position in build 10.2 and if the position did not change during the editing of the marker map, and um = 0.8 if the position of the marker was estimated as described in the previous section, i.e. the latter markers were penalised in the construction of the low-density panels. In the third step, markers were selected based on their scores and the distance measure d. If n markers were already included in the low-density panel, then marker mn+1 was chosen such that mn+1 was chosen from the largest gap, provided that a marker in the gap had a high score.where Scorem = 1), κ was close to zero, and only markers with known physical positions were included. This resulted in low-density panels with approximately equally spaced markers since they were subsequently chosen from the centre of the largest gap.For comparison, we also considered a naïve approach in which all markers had the same score . If the alleles have a different origin t between DGV and EBV was estimated for each trait t. The parameter of most interest, however, is the correlation between DGV and true breeding values (TBV), which will be referred to as the accuracy of the DGV. Since the breeding values for individuals in the training set and the validation set were taken from the same genetic evaluation, there is a substantial correlation of prediction errors among individuals for the EBV that were computed using the complete pedigree. Thus, the frequently used formula to derive the accuracy of DGV, i.e.The individuals were divided into a training set and a validation set as described above. For individuals in the validation set, the correlation is expected to provide estimates that are substantially biased upwards . Hence, n randomly chosen traits, the correlation cort has been estimated. These estimates have been obtained for different mean accuracies Suppose that for a0 and the regression coefficients a1 and a2 are fixed effects, and the errors et are normally distributed. Note that for where the intercept et on t can be estimated asFor simplicity we assumed that possible dependency of the error Table Table Figure Table Table Figure The results presented in this paper showed that imputation caused only a small decrease in accuracy of the DGV, even for very low-density marker panels (384 SNPs across the genome). This might be due to the performance of the genotype imputation method proposed in this study. The method uses both LD and family information. It is tailored to a situation in which at least one parent of the selection candidates is genotyped at high-density. This might be a typical situation in livestock breeding schemes that apply genomic selection with low-density panels. Compared to imputation error rates reported in most other studies, the error rates obtained in this study Tables  and 3 weHuang et al.  estimatem and the haplotype h with the largest score was used to impute the maternal haplotype i of the individual in the neighbourhood of m. The score of a haplotype h depends not only on the length of the interval in which h coincides perfectly with haplotype i, but also on the mismatches at nearby SNPs. This increases the robustness of the method with respect to sporadic haplotyping errors that occur from data phasing. Moreover, inclusion of the additive relationship into the score has the effect of favouring haplotypes of closely related individuals for imputation. This is an advantage because for unrelated individuals the low-density haplotypes can by chance coincide in the neighbourhood of m.For the imputation approach, all haplotypes of the haplotype library were scored for every low-density marker Other methods such as Beagle , LDMIP , IMPUTE2Imputation error rates could be reduced by genotyping at high-density more close relatives of the low-density genotyped individuals Table . A furthLm to be the length of the chromosome that contains marker m. The score may be multiplied with a factor of the form ((1 − λ)Lm + λ max (L))/Lm in order to ensure that more markers from the low-density panel are placed on short chromosomes. In some cases, it may be desirable that the markers from the low-density panel explain part of the additive variance. The approach can be generalized to this situation. For example, the score of a marker may be defined as its average contribution to the additive variance of traits that are standardized to have the same additive variance. That is, the score could be m, averaged over all traits. Another possibility is to let the score of a marker depend on the p-values obtained from an association study, such that markers with small p-values have a higher score. It is also possible to choose more markers from the chromosome ends by modifying the distance measure.Markers for the low-density panels were selected based on their scores and their distances to the markers already included in the low-density panel. The MAF of the marker was used as the score. An alternative procedure for marker selection that takes MAF and distances of adjacent markers into account was proposed by Wang et al. . Our appThe correlations between DGV and EBV Table  were subs could be obtained by splitting the data into a training set, a validation set and an omitted set. Care should be taken so that the mean accuracies of the EBV in the validation sets vary between replicates and that the mean accuracies in the training sets are approximately equal to the average accuracy of all EBV. For these replicates the linear model a2 could be omitted if only one trait is considered.The regression approach used a linear model to predict the regression function outside the range of the data. Since the linearity assumption might be violated, this approach should be evaluated in more detail with simulated data, where the true accuracies are known. The regression approach used results from multiple traits with heterogeneous accuracies of the EBV Table . This apMethods for genomic selection using low-density marker panels were introduced and applied to a dataset from a sire breeding line in pigs. It was shown that imputation from low- to high-density marker panels is a promising strategy, even if the low-density panel contains less than 1000 markers. A number of 768 markers can be recommended, but 384 markers may be sufficient if at least one parent is genotyped at high-density. Careful selection of low-density markers is essential. The proposed regression method for obtaining unbiased estimates of the accuracy of genomic breeding values in a cross-validation setting showed promising results but has to be evaluated in more detail.The authors declare that they have no competing interests.RW developed the methods and did the statistical analysis. RW and JB conceived and designed the experiment and wrote the paper. SP and KW generated the genotypes. JH and ET generated the conventional BLUP EBV. All authors read and approved the final manuscript.The table shows the genotype error rate and imputation accuracy per chromosome for the 384 marker panel.Click here for file