Efficient Calculation of the Genomic Relationship Matrix

Schlather, Martin

doi:10.1101/2020.01.12.903146

Cited by 9 publications

(12 citation statements)

References 9 publications

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“…While the approaches of Jiang and Reif (2015) and Martini et al (2016) only capture the interactions whose products differ from zero (i.e., {22} genotype combinations for 0, 2 coded markers), our approach captures all possible genotype combinations ({00}, {02}, {20}, and {22}). Further, these epistasis relationship matrices and interaction effects were computed by bit-wise computations via the R-package miraculix (Schlather 2020), which carries out matrix multiplications about 15 times faster than regular matrix multiplications on genotype data in EpiGP R-package (Vojgani et al 2021). In the analyzed datasets containing up to 30′212 SNPs (and thus 456′397′578 interactions), the computing time required to set up the sERRBLUP relationship matrix was about 810 min out of which around 330 min was required to estimate all pairwise SNP interaction effects and 480 min was required to set up the sERRBLUP relationship matrix for selected proportion of interactions by utilizing the R-package miraculix with 15 cores on a server cluster with Intel E5-2650 (2X12 core 2.2 GHz) processors.…”

Section: Discussionmentioning

confidence: 99%

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

et al. 2021

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Key Message The accuracy of genomic prediction of phenotypes can be increased by including the top-ranked pairwise SNP interactions into the prediction model. Abstract We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from two European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested at six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings for predictions within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Across all studied traits, locations and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from −0.3 to + 27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP, with an average increase of 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for “sparse testing” approaches in which only a subset of the lines/hybrids of interest is observed at each location.

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Section: Discussionmentioning

confidence: 99%

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

et al. 2021

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“…The major concern in utilizing epistasis models has been the high computational load (Mackay, 2014) which has been reduced for the full model including all interactions by utilizing marker based epistasis relationship matrices (Jiang and Reif, 2015;Martini et al, 2016). In this work, epistasis relationship matrices were constructed by using the package miraculix (Schlather, 2020) which carries out matrix multiplications about 15 times faster than regular matrix multiplications on genotype data in R. In the analyzed datasets containing up to 30'212 SNPs, the computing time required to set up the sERRBLUP relationship matrix was about 810 minutes out of which around 330 minutes were required to estimate all pairwise SNP interaction effects and 480 minutes were required to set up the sERRBLUP relationship matrix for selected proportion of interactions by utilizing the R-package miraculix with 15 cores on a server cluster with Intel E5-2650 (2X12 core 2.2GHz) processors. Computing times for sERRBLUP scale approximately quadratic in the number of markers considered.…”

Section: Discussionmentioning

confidence: 99%

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

Vojgani

Pook

Martini

et al. 2020

Preprint

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We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested in six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Over all studied traits, locations, and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from −0.3 to +27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP. The average increase across traits and locations was 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for “sparse testing” approaches in which only a subset of the lines/hybrids of interest is observed at each location.Key MessageThe prediction accuracy of genomic prediction of phenotypes can be increased by only including top ranked pairwise SNP interactions into the prediction models.

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“…{22} genotype combinations for 0, 2 coded markers), our approach captures all possible genotype combinations ({00}, {02}, {20}, and {22}). Further, these epistasis relationship matrices and interaction effects were computed by bit-wise computations via the R-package miraculix (Schlather 2020), which carries out matrix multiplications about 15 times faster than regular matrix multiplications on genotype data in EpiGP R-package (Vojgani et al 2021). In the analyzed datasets containing up to 30'212 SNPs (and thus 456'397'578 interactions), the computing time required to set up the sERRBLUP relationship matrix was about 810 minutes out of which around 330 minutes were required to estimate all pairwise SNP interaction effects and 480 minutes were required to set up the sERRBLUP relationship matrix for selected proportion of interactions by utilizing the R-package miraculix with 15 cores on a server cluster with Intel E5-2650 (2X12 core 2.2GHz) processors.…”

Section: Discussionmentioning

confidence: 99%

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

Vojgani

Pook

Martini

et al. 2021

Preprint

View full text Add to dashboard Cite

We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from two European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested at six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings for predictions within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Across all studied traits, locations, and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from − 0.3 to + 27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP, with an average increase of 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for “sparse testing” approaches in which only a subset of the lines/hybrids of interest is observed at each location.

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Efficient Calculation of the Genomic Relationship Matrix

Abstract: Since the calculation of a genomic relationship matrix needs a large number of arithmetic operations, fast implementations are of interest. Our fastest algorithm is more accurate and 25× faster than a AVX double precision floatingpoint implementation.

Cited by 9 publications

References 9 publications

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

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