Figure 1.
Overview of coefficient reparametrization for two phenotypes.
On the left, main effect and interaction parameters for two variants (var1 and var2) are derived from pairwise regressions (). The interaction coefficients are reparametrized as
and
on the right, which describe variant-to-variant influences that fit both phenotypes via indirect associations. For
the source variant is var1 and the target variant is var2, with the source and target reversed for
. The intercept and possible covariate terms are not shown. Note the main effects (
) are unchanged in the reparametrization.
Figure 2.
Overview of R/cape workflow and visualization tools using example data [1].
(A) Phenotypes are first decomposed into orthogonal eigentraits (ETs). Phenotype composition and global variance fraction are displayed for each ET, facilitating the selection of ETs for interaction analysis. In this study, the first two ETs were selected, which contained the correlated signal between all phenotypes and a divergence between phenotypes, respectively. (B) Pair-wise linear regression is next performed on each ET. Symmetric matrices of all marker pair interaction terms are displayed in matrix form, with gray and white bars along the axes to mark chromosome boundaries. The first two ETs for this study are shown. (C) Regression parameters are next reparametrized (Figure 1) to derive models of directed interactions between markers and from markers to phenotypes. In the adjacency matrix view (left), markers are designated as sources or targets of directed interactions, and marker-to-phenotype influences are in the rightmost columns. Only variants with significant main effect or interaction are shown, and gray dots mark pairs that were not included in the model due to linkage disequilibrium. In the network view (right), arrows are directed from source to target marker positions across all chromosomes. Red arrows indicate suppressive (negative) interactions. Main effects are represented below the variants with green indicating an effect that increases phenotype and gray indicating no significant main effect on phenotype.
Figure 3.
R/cape-derived interaction between Chromosome 1 and Chromosome 12.
(A) R/cape effect plots showing normalized phenotype values for each combination of the Chromosome 1 (D1Mit123) and Chromosome 12 (D12Mit150) genotypes. NON denotes a homozygous locus and Het denotes an NON/NZO heterozygote. Positive slopes correspond to Chromosome 1 effects, while differences between solid and dashed lines represent the Chromosome 12 effects. Positive and significant weight effects were detected for both loci, whereas effects on insulin were only significant for the Chromosome 1 marker. Neither locus had a significant effect on serum glucose. Significant epistasis was detected for weight, and appears as the convergence of solid and dashed lines for heterozygosity at the Chromosome 1 locus. Note that plotted data are not conditioned on maternal obesity, which was a covariate in the analysis. (B) Interaction network for variants on Chromosomes 1 and 12, extracted from Figure 2C, showing the significant suppressive interaction (red arrow) from the Chromosome 1 variant to the Chromosome 12 variant (gray circular nodes). Significant main effects (green arrows) link the source variants with the target phenotypes weight and insulin (square nodes labeled “I” and “W” respectively).