Using Monte Carlo method to include polygenic effects in calculation of SNP-BLUP model reliability

Abstract

An SNP-BLUP model is computationally scalable even for large numbers of genotyped animals. When genetic variation cannot be completely captured by SNP markers, a more accurate model is obtained by fitting a residual polygenic effect (RPG) as well. However, inclusion of the RPG effect increases the size of the SNP-BLUP mixed model equations (MME) by the number of genotyped animals. Consequently, the calculation of model reliabilities requiring elements of the inverted MME coefficient matrix becomes more computationally challenging with increasing numbers of genotyped animals. We present a Monte Carlo (MC)based sampling method to estimate the reliability of the SNP-BLUP model including the RPG effect, where the MME size depends on the number of markers and MC samples. We compared reliabilities calculated using different RPG proportions and different MC sample sizes in analyzing 2 data sets. Data set 1 (data set 2) contained 19,757 (222,619) genotyped animals, with 11,729 (50,240) SNP markers, and 231,186 (13.35 million) pedigree animals. Correlations between the correct and the MC-calculated reliabilities were above 98% even with 5,000 MC samples and an 80% RPG proportion in both data sets. However, more MC samples were needed to achieve a small maximum absolute difference and mean squared error, particularly when the RPG proportion exceeded 20%. The computing time for MC SNP-BLUP was shorter than for GBLUP. In conclusion, the MC-based approach can be an effective strategy for calculating SNP-BLUP model reliability with an RPG effect included.

Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling

“…We compared the MSE estimates obtained in this study to those reported in Ben Zaabza et al (2020a). Note that in our full-MC-SNP-BLUP approach, the size of the MME is determined by the number of MC samples, but in the MC-SNP-BLUP by Ben Zaabza et al (2020a), the MME size was determined by the number of markers plus the number of MC samples.…”

“…Routine genomic evaluations in animal breeding are usually performed using genomic relationship-based BLUP (GBLUP) or random regression-based SNP-BLUP models. These 2 models are equivalent and, thus, yield equal EBV and prediction error variances (PEV) at the animal level, regardless of whether or not a residual polygenic (RPG) effect is fitted (Strandén and Garrick, 2009;Liu et al, 2016;Ben Zaabza et al, 2020a). Genetic variation cannot be completely explained by SNP markers because of the incomplete linkage disequilibrium between the SNP markers used and the QTL.…”

“…Ben Zaabza et al (2020a,b) presented a Monte Carlo (MC) approach for the RPG effect in an SNP-BLUP model, in which the number of RPG effects was reduced from n to the number of MC samples. In this article, we describe a full MC-based SNP-BLUP approach that extends the approach in Ben Zaabza et al (2020a) to reduce the computational requirements in the calculation of SNP-BLUP genomic reliabilities. We compare the performance of the fully MC-based SNP-BLUP approach to GBLUP where the model has both SNP marker effects and RPG effects.…”

Snp_blup_rel: software for calculating individual animal SNP-BLUP model reliabilities

“…However, including an RPG effect into the SNP-BLUP model leads to an increase in the size of the MME by the number of genotyped animals (Liu et al 2016). This can be avoided by an approximation based on Monte Carlo (MC) sampling of pseudo markers that construct the relationships among animals (Ben Zaabza et al 2020).…”

“…If multiple traits (with different training population and/or variance components) need to be analyzed, then each trait will require its own inverse of the coefficient matrix of the MME. The snp_blup_rel program has been used in earlier studies (Liu et al 2017, Ben Zaabza et al 2020, but here we concentrate on describing the program itself. Firstly, we present some theoretical background and the algorithm used in the implementation.…”