Dataset Information

A singular value decomposition Bayesian multiple-trait and multiple-environment genomic model.

ABSTRACT: Today, breeders perform genomic-assisted breeding to improve more than one trait. However, frequently there are several traits under study at one time, and the implementation of current genomic multiple-trait and multiple-environment models is challenging. Consequently, we propose a four-stage analysis for multiple-trait data in this paper. In the first stage, we perform singular value decomposition (SVD) on the resulting matrix of trait responses; in the second stage, we perform multiple trait analysis on transformed responses. In stages three and four, we collect and transform the traits back to their original state and obtain the parameter estimates and the predictions on these scale variables prior to transformation. The results of the proposed method are compared, in terms of parameter estimation and prediction accuracy, with the results of the Bayesian multiple-trait and multiple-environment model (BMTME) previously described in the literature. We found that the proposed method based on SVD produced similar results, in terms of parameter estimation and prediction accuracy, to those obtained with the BMTME model. Moreover, the proposed multiple-trait method is atractive because it can be implemented using current single-trait genomic prediction software, which yields a more efficient algorithm in terms of computation.

SUBMITTER: Montesinos-Lopez OA

PROVIDER: S-EPMC6460759 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature

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A singular value decomposition Bayesian multiple-trait and multiple-environment genomic model.

Montesinos-López Osval A OA Montesinos-López Abelardo A Crossa José J Kismiantini Ramírez-Alcaraz Juan Manuel JM Singh Ravi R Mondal S S Juliana P P

Heredity 20180817 4

Today, breeders perform genomic-assisted breeding to improve more than one trait. However, frequently there are several traits under study at one time, and the implementation of current genomic multiple-trait and multiple-environment models is challenging. Consequently, we propose a four-stage analysis for multiple-trait data in this paper. In the first stage, we perform singular value decomposition (SVD) on the resulting matrix of trait responses; in the second stage, we perform multiple trait ...[more]

PMID: 30120367

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Project description:BackgroundFor marker effect models and genomic animal models, computational requirements increase with the number of loci and the number of genotyped individuals, respectively. In the latter case, the inverse genomic relationship matrix (GRM) is typically needed, which is computationally demanding to compute for large datasets. Thus, there is a great need for dimensionality-reduction methods that can analyze massive genomic data. For this purpose, we developed reduced-dimension singular value decomposition (SVD) based models for genomic prediction.MethodsFast SVD is performed by analyzing different chromosomes/genome segments in parallel and/or by restricting SVD to a limited core of genotyped individuals, producing chromosome- or segment-specific principal components (PC). Given a limited effective population size, nearly all the genetic variation can be effectively captured by a limited number of PC. Genomic prediction can then be performed either by PC ridge regression (PCRR) or by genomic animal models using an inverse GRM computed from the chosen PC (PCIG). In the latter case, computation of the inverse GRM will be feasible for any number of genotyped individuals and can be readily produced row- or element-wise.ResultsUsing simulated data, we show that PCRR and PCIG models, using chromosome-wise SVD of a core sample of individuals, are appropriate for genomic prediction in a larger population, and results in virtually identical predicted breeding values as the original full-dimension genomic model (r = 1.000). Compared with other algorithms (e.g. algorithm for proven and young animals, APY), the (chromosome-wise SVD-based) PCRR and PCIG models were more robust to size of the core sample, giving nearly identical results even down to 500 core individuals. The method was also successfully tested on a large multi-breed dataset.ConclusionsSVD can be used for dimensionality reduction of large genomic datasets. After SVD, genomic prediction using dense genomic data and many genotyped individuals can be done in a computationally efficient manner. Using this method, the resulting genomic estimated breeding values were virtually identical to those computed from a full-dimension genomic model.

Project description:BackgroundBoth microarrays and quantitative real-time PCR are convenient tools for studying the transcriptional levels of genes. The former is preferable for large scale studies while the latter is a more targeted technique. Because of platform-dependent systematic effects, simple comparisons or merging of datasets obtained by these technologies are difficult, even though they may often be desirable. These difficulties are exacerbated if there is only partial overlap between the experimental conditions and genes probed in the two datasets.ResultsWe show here that the generalized singular value decomposition provides a practical tool for merging a small, targeted dataset obtained by quantitative real-time PCR of specific genes with a much larger microarray dataset. The technique permits, for the first time, the identification of genes present in only one dataset co-expressed with a target gene present exclusively in the other dataset, even when experimental conditions for the two datasets are not identical. With the rapidly increasing number of publically available large scale microarray datasets the latter is frequently the case. The method enables us to discover putative candidate genes involved in the biosynthesis of the (1,3;1,4)-beta-D-glucan polysaccharide found in plant cell walls.ConclusionWe show that the generalized singular value decomposition provides a viable tool for a combined analysis of two gene expression datasets with only partial overlap of both gene sets and experimental conditions. We illustrate how the decomposition can be optimized self-consistently by using a judicious choice of genes to define it. The ability of the technique to seamlessly define a concept of "co-expression" across both datasets provides an avenue for meaningful data integration. We believe that it will prove to be particularly useful for exploiting large, publicly available, microarray datasets for species with unsequenced genomes by complementing them with more limited in-house expression measurements.

Project description:The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices D(i)∈R(m(i) × n), each with full column rank. Each matrix is exactly factored as D(i)=U(i)Σ(i)V(T), where V, identical in all factorizations, is obtained from the eigensystem SV=VΛ of the arithmetic mean S of all pairwise quotients A(i)A(j)(-1) of the matrices A(i)=D(i)(T)D(i), i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λ(k)≥1. Equality holds if and only if the corresponding eigenvector v(k) is a right basis vector of equal significance in all matrices D(i) and D(j), that is σ(i,k)/σ(j,k)=1 for all i and j, and the corresponding left basis vector u(i,k) is orthogonal to all other vectors in U(i) for all i. The eigenvalues λ(k)=1, therefore, define the "common HO GSVD subspace." We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified.

Dataset Information

A singular value decomposition Bayesian multiple-trait and multiple-environment genomic model.

Publications

A singular value decomposition Bayesian multiple-trait and multiple-environment genomic model.

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