Abstract
BackgroundThe quantitative genetics theory argues that inbreeding depression and heterosis are founded on the existence of directional dominance. However, most procedures for genomic selection that have included dominance effects assumed prior symmetrical distributions. To address this, two alternatives can be considered: (1) assume the mean of dominance effects different from zero, and (2) use skewed distributions for the regularization of dominance effects. The aim of this study was to compare these approaches using two pig datasets and to confirm the presence of directional dominance.ResultsFour alternative models were implemented in two datasets of pig litter size that consisted of 13,449 and 11,581 records from 3631 and 2612 sows genotyped with the Illumina PorcineSNP60 BeadChip. The models evaluated included (1) a model that does not consider directional dominance (Model SN), (2) a model with a covariate b for the average individual homozygosity (Model SC), (3) a model with a parameter λ that reflects asymmetry in the context of skewed Gaussian distributions (Model AN), and (4) a model that includes both b and λ (Model Full). The results of the analysis showed that posterior probabilities of a negative b or a positive λ under Models SC and AN were higher than 0.99, which indicate positive directional dominance. This was confirmed with the predictions of inbreeding depression under Models Full, SC and AN, that were higher than in the SN Model. In spite of differences in posterior estimates of variance components between models, comparison of models based on LogCPO and DIC indicated that Model SC provided the best fit for the two datasets analyzed.ConclusionsOur results confirmed the presence of positive directional dominance for pig litter size and suggested that it should be taken into account when dominance effects are included in genomic evaluation procedures. The consequences of ignoring directional dominance may affect predictions of breeding values and can lead to biased prediction of inbreeding depression and performance of potential mates. A model that assumes Gaussian dominance effects that are centered on a non-zero mean is recommended, at least for datasets with similar features to those analyzed here.
Highlights
The quantitative genetics theory argues that inbreeding depression and heterosis are founded on the existence of directional dominance
The classical theory of quantitative genetics [9] argues that inbreeding depression and heterosis are based on the presence of directional dominance and this contrasts with the assumption of symmetry of the above-described procedures
There is a broad corpus on the specification of skewed distributions [14, 15] and, among them, the family of skew-elliptical distributions defined by Sahu et al [16] can be implemented in Bayesian regression using Markov chain Monte Carlo (MCMC) techniques [17]
Summary
The quantitative genetics theory argues that inbreeding depression and heterosis are founded on the existence of directional dominance. The classical theory of quantitative genetics [9] argues that inbreeding depression and heterosis are based on the presence of directional dominance (i.e., a higher percentage of positive than negative dominance effects) and this contrasts with the assumption of symmetry of the above-described procedures. This discrepancy can be overcome in at least two ways: (1) by assuming that the mean of dominance effects differ from zero, which leads to the inclusion of a covariate for the average individual homozygosity in the statistical model, and (2) by using skewed distributions for the regularization of dominance effects. There is a broad corpus on the specification of skewed distributions [14, 15] and, among them, the family of skew-elliptical distributions defined by Sahu et al [16] can be implemented in Bayesian regression using Markov chain Monte Carlo (MCMC) techniques [17]
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