Large-scale genomic prediction using singular value decomposition of the genotype matrix

Abstract

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.Electronic supplementary materialThe online version of this article (10.1186/s12711-018-0373-2) contains supplementary material, which is available to authorized users.

Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently

“…However, a major inconvenience of ssGBLUP is that the inverse of a dense genomic relationship matrix ( ) is required, which can be computed up to approximately 100,000 genotyped animals on current computers [ 6 ]. Thus, some methods were proposed to approximate the inverse of , such as the algorithm for proven and young animals (APY) [ 6 ], or to compute its inverse implicitly based on singular value decomposition (SVD) [ 7 ] or on the Woodbury decomposition [ 8 ]. Another approach to avoid the computation of the inverse of , or even itself, is to fit the SNP effects explicitly, or principal components obtained from a SVD of the genotype matrix, as random effects in the model.…”

“…Another approach to avoid the computation of the inverse of , or even itself, is to fit the SNP effects explicitly, or principal components obtained from a SVD of the genotype matrix, as random effects in the model. Several equivalent models were proposed in the literature that enable simultaneous modelling of genotyped and non-genotyped animals as in ssGBLUP [ 2 , 7 , 9 – 13 ]. Equivalent models that directly estimate SNP effects as random effects [ 2 , 9 – 13 ] will hereafter be referred to as single-step SNPBLUP (ssSNPBLUP).…”

Genomic selection for any dairy breeding program via optimized investment in phenotyping and genotyping

“…This implies that breeding programmes do not have to use all historical genotypes for prediction. The problem of a large number of genotypes can be alternatively solved by using methods with reduced computational costs, such as algorithm for proven and young [36] or singular value decomposition of the genotype matrix [37].…”

Temporal and genomic analysis of additive genetic variance in breeding programmes

“…pal component effects and σ 2 s is variance between principal component effects (Hastie and Tibshirani, 2004;Tusell et al, 2013;Ødegård et al, 2018). This model is structurally the same as the model (Eq.…”

“…MCMC on genome-based models with many individuals or markers can be time-consuming. To this end various dimensionality-reduction approaches have been proposed, for example, singular value decomposition (SVD) of marker genotypes where we fit a small number of principal components that capture majority of variance in marker genotypes (Tusell et al, 2013;Ødegård et al, 2018).…”