Best Prediction of the Additive Genomic Variance in Random-Effects Models

Abstract

The additive genomic variance in linear models with random marker effects can be defined as a random variable that is in accordance with classical quantitative genetics theory. Common approaches to estimate the genomic variance in random-effects linear models based on genomic marker data can be regarded as estimating the unconditional (or prior) expectation of this random additive genomic variance, and result in a negligence of the contribution of linkage disequilibrium (LD). We introduce a novel best prediction (BP) approach for the additive genomic variance in both the current and the base population in the framework of genomic prediction using the genomic best linear unbiased prediction (gBLUP) method. The resulting best predictor is the conditional (or posterior) expectation of the additive genomic variance when using the additional information given by the phenotypic data, and is structurally in accordance with the genomic equivalent of the classical additive genetic variance in random-effects models. In particular, the best predictor includes the contribution of (marker) LD to the additive genomic variance and possibly fully eliminates the missing contribution of LD that is caused by the assumptions of statistical frameworks such as the random-effects model. We derive an empirical best predictor (eBP) and compare its performance with common approaches to estimate the additive genomic variance in random-effects models on commonly used genomic datasets.

Empirical decomposition of the explained variation in the variance components form of the mixed model

“…which is similar to equation (3), has been observed by Schreck et al (2019) in several applications. This suggests a connection between the estimated genomic variance in (7) and the concept of the explained variation in the random effects model similar to model (2).…”

“…The decomposition of the total sum of squares derived in Theorem 5 and the associated natural extension of the classical coefficient of determination to the components form of the linear mixed model is in particular important in genomic applications. We have extended the best prediction approach introduced by Schreck et al (2019) from the random effects model to the linear mixed effects model. This enables an improved estimation of the additive genomic variance and the heritability for model (1).…”

“…it is a natural extension of the adjusted coefficient of determination from model (2) to model (1). We obtain the variance decomposition (8) in case of the random effects model (5), see also Schreck et al (2019). TheṘ 2 is an analytic function of the estimates returned after a model fit with restricted maximum likelihood so that its computation is straightforward and fast.…”

“…It has been widely stated that ratios similar to (6) should not be used to estimate the proportion of the variation explained by the genomic variance (Gianola et al, 2009;de los Campos et al, 2015). Recently, Schreck et al (2019) have introduced the empirical best predictoṙ…”

Temporal and genomic analysis of additive genetic variance in breeding programmes

“…Estimates of genetic variance from genome-based models pertain to the group of individuals for which the allele frequencies were computed—usually for the genotyped individuals or base population, both of which again do not have a clearly defined time point. In addition, the ‘genomic variance’ is estimating genetic variance only under some conditions (Gianola et al 2009 ; de los Campos et al 2015 ; Rawlik et al 2020 ; Schreck et al 2019 ). Therefore, we propose an alternative framework for temporal and genomic analyses of genetic variation.…”