Technical note: Equivalent genomic models with a residual polygenic effect

Abstract

Routine genomic evaluations in animal breeding are usually based on either a BLUP with genomic relationship matrix (GBLUP) or single nucleotide polymorphism (SNP) BLUP model. For a multi-step genomic evaluation, these 2 alternative genomic models were proven to give equivalent predictions for genomic reference animals. The model equivalence was verified also for young genotyped animals without phenotypes. Due to incomplete linkage disequilibrium of SNP markers to genes or causal mutations responsible for genetic inheritance of quantitative traits, SNP markers cannot explain all the genetic variance. A residual polygenic effect is normally fitted in the genomic model to account for the incomplete linkage disequilibrium. In this study, we start by showing the proof that the multi-step GBLUP and SNP BLUP models are equivalent for the reference animals, when they have a residual polygenic effect included. Second, the equivalence of both multi-step genomic models with a residual polygenic effect was also verified for young genotyped animals without phenotypes. Additionally, we derived formulas to convert genomic estimated breeding values of the GBLUP model to its components, direct genomic values and residual polygenic effect. Third, we made a proof that the equivalence of these 2 genomic models with a residual polygenic effect holds also for single-step genomic evaluation. Both the single-step GBLUP and SNP BLUP models lead to equal prediction for genotyped animals with phenotypes (e.g., reference animals), as well as for (young) genotyped animals without phenotypes. Finally, these 2 single-step genomic models with a residual polygenic effect were proven to be equivalent for estimation of SNP effects, too.

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

“…The equivalence of GBLUP and SNP-BLUP models with RPG effects is demonstrated in Liu et al (2016), where the RPG is a separate effect in the SNP-BLUP model. According to Henderson (1984), 2 models are linearly equivalent when their phenotypic variance matrices Var(y) are equal and their fixed effect predictions are also equal.…”

“…For example, using an RPG proportion of 20% in multi-step genomic BLUP is known to improve the reliability of the prediction and reduce bias (Guarini et al, 2018). Liu et al (2016) showed that GBLUP and SNP-BLUP genomic models that include an RPG effect are equivalent, although inclusion of the RPG effect in the models increases the MME size by the number of genotyped animals. Hence, the reliability calculation requiring elements of the inverse of the MME coefficient matrix will become more computationally challenging in both models the more genotyped animals are included.…”

Short communication: Genomic prediction using different single-step methods in the Finnish red dairy cattle population

“…However, the matrix inverse needed in the regular ssGBLUP model is avoided and ssBR has the potential to be extended to variable selection models putting differential weight on individual markers (e.g., Bayes alphabet; Gianola et al, 2009). Only a few published studies have compared different single-step methods with a remaining polygenic effect included in the model (Liu et al, 2016). The objective of this study was to compare genomic predictions using a regular ssGBLUP model, APY methods with 2 different strategies of choosing core individuals, and an ssBR model based on records of 3 production traits of Finnish red dairy cattle.…”

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

“…A residual polygenic (RPG) effect is often included to account for the variance not captured by SNP markers. 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).…”