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

Abstract

The additive genomic variance, the chief ingredient for the heritability, is often underestimated in phenotypegenotype regression models. Various remedies, including different models and estimators, have been proposed in order to improve on what has been coined the "missing heritability". Recently, debates have been conducted whether estimators for the genomic variance include linkage disequilibrium (LD) and how to explicitly account for LD in estimation procedures.Up-to-now, the genomic variance in random effect models (REM) has been estimated as a parameter of the marginal, i.e. unconditional model. We propose that the genomic variance in REM should be predicted as a conditional random quantity based on the conditional distribution of β. This signifies a paradigm shift from the estimation to the prediction of the genomic variance. This approach is structurally in perfect accordance to the Bayesian regression model (BRM), where the posterior expectation of the genomic variance is estimated based on the posterior of β. We introduce a novel, mathematically rigorously founded predictor for the conditional genomic variance in (g)BLUP, which is structurally close to the Bayesian estimator. The conditioning of the novel predictor on the data is intrinsically tied to the inclusion of the contribution of LD and the predicted effects. In addition to that, the predictor shows much weaker dependence on distribution assumptions than estimators of other approaches, e.g. GCTA-GREML. Last but not least, the predictor, contrasted with the estimator in the unconditional model, enables an innovative approximation of the influence of LD on the genomic variance in the dataset.An exemplary simulation study based on the commonly used dataset of 1814 mice genotyped for 10346 polymorphic markers substantiates that the bias of the novel predictor is small in all standard situations, i.e. that the predictor for the conditional genomic variance remarkably reduces the "missing heritability".

HaploBlocker: Creation of Subgroup-Specific Haplotype Blocks and Libraries

“…Recent work by Schreck and Schlather (2018) has suggested that the direct estimation of the heritability using REML variance components is biased, so we use their proposed estimator. For the traditional estimates using REML estimates as proposed in a conference presentation by de los Campos (2017), we refer to Table S1.…”

On to the next chapter for crop breeding: Convergence with data science

“…Breeding values are often modeled as additive genetic variance (Holland, Nyquist, & Cervantes-Martínez, 2003;Mrode, 2000). As a consequence, the theoretical upper bound of predictive power in this model is equal to the narrow sense heritability of a given trait (Lourenço, Ogutu, & Piepho, 2019;Schreck, Piepho, & Schlather, 2019). For traits with high heritability, this approach works rather well (Figure 1).…”

Temporal and genomic analysis of additive genetic variance in breeding programmes

“…Estimates of genetic variance from genome-based models pertains to all genotyped individuals, which again does not have a clearly defined time point. In addition, the "genomic variance" is plagued with model "misspecification" (Gianola et al, 2009;de los Campos et al, 2015), see also Schreck et al (2019).…”