Residual propagation.

<p>A real data illustration of the necessity of non-genetic residual propagation for causal inference. Consider the causal model: , where denotes the QTL on Chrs 4, 5 and their interaction. Comparison of and shows correlation suggesting a causal reaction. If the residual variation did not propagate () then and are approximately independent.</p

Simulation results.

<p>Left: The correlation between metabolites and genetic multipliers, correlation indicates evidence of a QTL, the sign and magnitude indicate direction and size of the effect respectively. Center: metabolite correlation after conditioning on QTL. Right: The inferred causal graphical model estimated from the top ten graphs from MCMC. Edge weights indicate regression coefficients.</p

Aliphatic glucosinolate network reconstructions.

<p>The (A) homo-methionine, (B) dihomo-methioine and (C) hexahomo-methionine side chains were reconstructed independently. (D) The network was reconstructed from the entire panel of aliphatic metabolites and their QTL. Edge weights indicate regression coefficients.</p

Simulated pathway motifs.

<p>(A) Linear, (B) merging pathway via metabolic reaction, (C) merging pathway via independent paths, (D) branching pathway, (E) branching pathway with inhibition, (F) branching pathway with epistasis. represents a constant pool of metabolite taken up at a constant flux rate that is subject to a stochastic perturbation , represents the flux rate, is a genetic perturbation and denotes an upstream signal that is affecting the pathway.</p

Biosynthesis of aliphatic glucosinolates.

<p>The aliphatic glucosinolate biosynthetic pathway occurs in three stages: (1) side chain elongation, (2) formation of glucone moeity and (3) side-chain modification. The metabolites that are measured in the BaySha RIL population are indicated together with the facilitating enzymes.</p

Genome scans for the aliphatic metabolites.

<p>QTL mapping was performed for metabolites in the homo-methionine, dihomo-methionine and penta/hexa-methionine side-chains from the BaySha RIL population.</p

Enriched and depleted motifs in the CAPE genetic interaction network.

<p>The four possible motifs in the CAPE interaction network (<i>p</i> ≤ 0.01) are depicted in the top row. Variants A and B indicate the source and target QTL respectively in each motif type. Genetic interactions between QTL were either enhancing (positive) or suppressing (negative), and main effects were either coherent (same sign, positive or negative) or incoherent (opposite signs, one positive and one negative). Table cells show network motif count (top) and permutation-based enrichment <i>p</i>-value (bottom) for each motif type. Darker cells indicate greater significance of enrichment or depletion.</p

QTL interaction with IGF1.

<p>The effects of IGF1 are enhanced by QTL 9.2. IGF1 has a small positive effect on each phenotype in animals homozygous for the B6 allele at this locus. This can be seen in the positive slope of the blue line in each panel, which shows that each phenotype increases with increasing levels of IGF1. The effect of IGF1 on all phenotypes except femoral density is enhanced in heterozygotes (green line) and enhanced further in C3H homozygotes (purple line). For these genotypes, the increase in slope indicates that there is a more pronounced increase in phenotype as IGF1 levels increase. <i>Y</i>-axes represent rank normalized values of each phenotype, and <i>x</i>-axes represent rank normalized IGF1 levels scaled to range between 0 and 1. Shaded regions show 95% confidence interval for each slope.</p

<i>Kitl</i> as a negative regulator of IGF1 models how QTL 10.2 enhances IGF1 effect on femoral density.

<p>Kitl transcript expression is (A) significantly lower in C3H mice than in B6 mice (<i>p</i> = 0.012), and (B) negatively correlated with <i>Igf1</i> expression (<i>r</i> = −0.67, <i>p</i> = 0.018) [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005805#pgen.1005805.ref055" target="_blank">55</a>, <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005805#pgen.1005805.ref056" target="_blank">56</a>]. (C) Model of the relationships between the <i>Kitl</i> C3H allele (green circle), the <i>Kitl</i> and <i>Igf1</i> transcripts (teal pentagons), and femoral density. The C3H allele of <i>Kitl</i> decreases the gene’s expression resulting in the QTL 10.2 negative effect on femoral density. Independently, the <i>lit</i> mutation reduces the levels of <i>Igf1</i> transcript and circulating IGF1. Residual <i>Igf1</i> transcript is negatively regulated by the <i>Kitl</i> transcript in B6 mice, but the reduced <i>Kitl</i> transcript levels in C3H mice permit increased IGF1 effects on femoral density. This yields an incoherent enhancing genetic interaction from QTL 10.2 to IGF1 (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005805#pgen.1005805.g003" target="_blank">Fig 3C</a>).</p

Single-locus associations with phenotypes.

<p>LOD scores for each locus and each phenotype for both males (blue) and females (brown). There are significant QTL for each of the phenotypes, and males and females tend to share QTL.</p