BackgroundCurrently, association studies are analysed using statistical mixed models, with marker effects estimated by a linear transformation of genomic breeding values. The variances of marker effects are needed when performing the tests of association. However, approaches used to estimate the parameters rely on a prior variance or on a constant estimate of the additive variance. Alternatively, we propose a standardized test of association using the variance of each marker effect, which generally differ among each other. Random breeding values from a mixed model including fixed effects and a genomic covariance matrix are linearly transformed to estimate the marker effects.ResultsThe standardized test was neither conservative nor liberal with respect to type I error rate (false-positives), compared to a similar test using Predictor Error Variance, a method that was too conservative. Furthermore, genomic predictions are solved efficiently by the procedure, and the p-values are virtually identical to those calculated from tests for one marker effect at a time. Moreover, the standardized test reduces computing time and memory requirements.The following steps are used to locate genome segments displaying strong association. The marker with the highest − log(p-value) in each chromosome is selected, and the segment is expanded one Mb upstream and one Mb downstream of the marker. A genomic matrix is calculated using the information from those markers only, which is used as the variance-covariance of the segment effects in a model that also includes fixed effects and random genomic breeding values. The likelihood ratio is then calculated to test for the effect in every chromosome against a reduced model with fixed effects and genomic breeding values. In a case study with pigs, a significant segment from chromosome 6 explained 11% of total genetic variance.ConclusionsThe standardized test of marker effects using their own variance helps in detecting specific genomic regions involved in the additive variance, and in reducing false positives. Moreover, genome scanning of candidate segments can be used in meta-analyses of genome-wide association studies, as it enables the detection of specific genome regions that affect an economically relevant trait when using multiple populations.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2105-15-246) contains supplementary material, which is available to authorized users.
An individual tree model with additive direct and competition effects is introduced to account for competitive effects in forest genetics evaluation. The mixed linear model includes fixed effects as well as direct and competition breeding values plus permanent environmental effects. Competition effects, either additive or environmental, are identified in the phenotype of a competitor tree by means of 'intensity of competition' elements (IC), which are non-zero elements of the incidence matrix of the additive competition effects. The ICs are inverse function of the distance and the number of competing individuals, either row-column wise or diagonally. The ICs allow standardization of the variance of competition effects in the phenotypic variance of any individual tree, so that the model accounts for unequal number of neighbors. Expressions are obtained for the bias in estimating additive variance using the covariance between half-sibs, when ignoring competition effects for row-plot designs and for single-tree plot designs. A data set of loblolly pines on growth at breast height is used to estimate the additive variances of direct and competition effects, the covariance between both effects, and the variance of permanent environmental effects using a Bayesian method via Gibbs sampling and
BackgroundEpistasis marker effect models incorporating products of marker values as predictor variables in a linear regression approach (extended GBLUP, EGBLUP) have been assessed as potentially beneficial for genomic prediction, but their performance depends on marker coding. Although this fact has been recognized in literature, the nature of the problem has not been thoroughly investigated so far.ResultsWe illustrate how the choice of marker coding implicitly specifies the model of how effects of certain allele combinations at different loci contribute to the phenotype, and investigate coding-dependent properties of EGBLUP. Moreover, we discuss an alternative categorical epistasis model (CE) eliminating undesired properties of EGBLUP and show that the CE model can improve predictive ability. Finally, we demonstrate that the coding-dependent performance of EGBLUP offers the possibility to incorporate prior experimental information into the prediction method by adapting the coding to already available phenotypic records on other traits.ConclusionBased on our results, for EGBLUP, a symmetric coding {−1,1} or {−1,0,1} should be preferred, whereas a standardization using allele frequencies should be avoided. Moreover, CE can be a valuable alternative since it does not possess the undesired theoretical properties of EGBLUP. However, which model performs best will depend on characteristics of the data and available prior information. Data from previous experiments can for instance be incorporated into the marker coding of EGBLUP.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1439-1) contains supplementary material, which is available to authorized users.
Background Metafounders are pseudo-individuals that encapsulate genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses the estimation and usefulness of metafounder relationships in single-step genomic best linear unbiased prediction (ssGBLUP).ResultsWe show that ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, such as fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals and pedigree. Simple methods for their estimation include naïve computation of allele frequencies from marker genotypes or a method of moments that equates average pedigree-based and marker-based relationships. Complex methods include generalized least squares (best linear unbiased estimator (BLUE)) or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer coefficients from marker data have not been developed for related individuals. We derived a genomic relationship matrix, compatible with pedigree relationships, that is constructed as a cross-product of {−1,0,1} codes and that is equivalent (apart from scale factors) to an identity-by-state relationship matrix at genome-wide markers. Using a simulation with a single population under selection in which only males and youngest animals are genotyped, we observed that generalized least squares or maximum likelihood gave accurate and unbiased estimates of the ancestral relationship parameter (true value: 0.40) whereas the naïve method and the method of moments were biased (average estimates of 0.43 and 0.35). We also observed that genomic evaluation by ssGBLUP using metafounders was less biased in terms of estimates of genetic trend (bias of 0.01 instead of 0.12), resulted in less overdispersed (0.94 instead of 0.99) and as accurate (0.74) estimates of breeding values than ssGBLUP without metafounders and provided consistent estimates of heritability.ConclusionsEstimation of metafounder relationships can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships reduces bias of genomic predictions with no loss in accuracy.
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