Heritability estimates and predictive ability for pig meat quality traits using identity-by-state and identity-by-descent relationships in an F2 population.

Genomic relationships can be computed with dense genome-wide genotypes through different methods, either based on identity-by-state (IBS) or identity-by-descent (IBD). The latter has been shown to increase the accuracy of both estimated relationships and predicted breeding values. However, it is not clear whether an IBD approach would achieve greater heritability ( h 2 ) and predictive ability ( r ̂ y , y ̂ ) than its IBS counterpart for data with low-depth pedigrees. Here, we compare both approaches in terms of the estimated of h 2 and r ̂ y , y ̂ , using data on meat quality and carcass traits recorded in experimental crossbred pigs, with a pedigree constrained to only three generations. Three animal models were fitted which differed on the relationship matrix: an IBS model ( G IBS ), an IBD (defined within the known pedigree) model ( G IBD ), and a pedigree model ( A 22 ). In 9 of 20 traits, the range of increase for the estimates of σ u 2 and h 2 was 1.2-2.9 times greater with G IBS and G IBD models than with A 22 . Whereas for all traits, both parameters were similar between genomic models. The r ̂ y , y ̂ of the genomic models was higher compared to A 22 . A scarce increment in r ̂ y , y ̂ was found with G IBS when compared to G IBD , most likely due to the former recovering sizeable relationships among founder F0 animals.

Comparing Genomic Prediction Models by Means of Cross Validation.

In the two decades of continuous development of genomic selection, a great variety of models have been proposed to make predictions from the information available in dense marker panels. Besides deciding which particular model to use, practitioners also need to make many minor choices for those parameters in the model which are not typically estimated by the data (so called "hyper-parameters"). When the focus is placed on predictions, most of these decisions are made in a direction sought to optimize predictive accuracy. Here we discuss and illustrate using publicly available crop datasets the use of cross validation to make many such decisions. In particular, we emphasize the importance of paired comparisons to achieve high power in the comparison between candidate models, as well as the need to define notions of relevance in the difference between their performances. Regarding the latter, we borrow the idea of equivalence margins from clinical research and introduce new statistical tests. We conclude that most hyper-parameters can be learnt from the data by either minimizing REML or by using weakly-informative priors, with good predictive results. In particular, the default options in a popular software are generally competitive with the optimal values. With regard to the performance assessments themselves, we conclude that the paired k-fold cross validation is a generally applicable and statistically powerful methodology to assess differences in model accuracies. Coupled with the definition of equivalence margins based on expected genetic gain, it becomes a useful tool for breeders.

Phantom Epistasis in Genomic Selection: On the Predictive Ability of Epistatic Models.

Genomic selection uses whole-genome marker models to predict phenotypes or genetic values for complex traits. Some of these models fit interaction terms between markers, and are therefore called epistatic. The biological interpretation of the corresponding fitted effects is not straightforward and there is the threat of overinterpreting their functional meaning. Here we show that the predictive ability of epistatic models relative to additive models can change with the density of the marker panel. In more detail, we show that for publicly available Arabidopsis and rice datasets, an initial superiority of epistatic models over additive models, which can be observed at a lower marker density, vanishes when the number of markers increases. We relate these observations to earlier results reported in the context of association studies which showed that detecting statistical epistatic effects may not only be related to interactions in the underlying genetic architecture, but also to incomplete linkage disequilibrium at low marker density ("Phantom Epistasis"). Finally, we illustrate in a simulation study that due to phantom epistasis, epistatic models may also predict the genetic value of an underlying purely additive genetic architecture better than additive models, when the marker density is low. Our observations can encourage the use of genomic epistatic models with low density panels, and discourage their biological over-interpretation.

The effect of the H-1 scaling factors τ and ω on the structure of H in the single-step procedure.

BACKGROUND: The single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text]. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text], which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text]. Since the definition of this blending is based on the equation describing [Formula: see text], its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text]. RESULTS: Here, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. CONCLUSION: Our results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text].