An approximate Bayesian significance test for genomic evaluations

Abstract

Genomic information can be used to study the genetic architecture of some trait. Not only the size of the genetic effect captured by molecular markers and their position on the genome but also the mode of inheritance, which might be additive or dominant, and the presence of interactions are interesting parameters. When searching for interacting loci, estimating the effect size and determining the significant marker pairs increases the computational burden in terms of speed and memory allocation dramatically. This study revisits a rapid Bayesian approach (fastbayes). As a novel contribution, a measure of evidence is derived to select markers with effect significantly different from zero. It is based on the credibility of the highest posterior density interval next to zero in a marginalized manner. This methodology is applied to simulated data resembling a dairy cattle population in order to verify the sensitivity of testing for a given range of type-I error levels. A real data application complements this study. Sensitivity and specificity of fastbayes were similar to a variational Bayesian method, and a further reduction of computing time could be achieved. More than 50% of the simulated causative variants were identified. The most complex model containing different kinds of genetic effects and their pairwise interactions yielded the best outcome over a range of type-I error levels. The validation study showed that fastbayes is a dual-purpose tool for genomic inferences - it is applicable to predict future outcome of not-yet phenotyped individuals with high precision as well as to estimate and test single-marker effects. Furthermore, it allows the estimation of billions of interaction effects.

Keywords: SNP; conditional expectation; dominance; epistasis; genetic architecture.

Figure 1

Example of a highest posterior density interval tangent to zero with arbitrary parameters mentioned within the graph

Figure 2

Results of analyzing the mouse data set ($p=8,797$ SNPs, $n=1,521$ individuals): estimated additive and dominance effects of SNPs using the fastbayes (A) and vbay (C) approach; gray dots indicate significant loci. Measure of evidence related to fastbayes (B) and posterior probability of nonzero effects related to vbay (D) reflect the significance of effects. SNP index equals SNP number for additive effects and SNP number plus p for dominance effects

Figure 3

Results of analyzing the mouse dataset ($p=8,797$ SNPs, $n=1,521$ individuals): significance of additive and dominance effects of SNPs was inferred using fastbayes and (A) measure of evidence (MOE) ⩽0.05 or (B) Bayes factor (BF) >3. SNP index equals SNP number for additive effects and SNP number plus p for dominance effects