Fig 1.
The main idea of our snQTL framework.
Our snQTL framework takes as input (i) gene expression read counts and (ii) genotypes of genetic markers from the same set of samples. The snQTL approach consists of three steps: (0) co-expression network construction, (1) snQTL identification via hypothesis testing using multilinear spectral statistics, and (2) joint differential network estimation at associated loci via sparse symmetric tensor decomposition. At each marker, the output includes (i) a p-value indicating the association significance between the co-expression network and the marker, and (ii) a joint differential network with nodes representing genes and edges representing associated effects.
Fig 2.
Synthetic datasets in three panels have the same parameter setup. (A) Absolute genetic correlation heatmaps among the markers in real F2 hybrid three-spined stickleback data [10] and synthetic data. Markers are ordered following their positions on the genome. Genetic correlations are measured by absolute sample Pearson correlation coefficients between the genotypes of two markers. (B) Density histograms for expression counts in real stickleback and synthetic data. The parameters in synthetic data generation are carefully chosen to mimic the real data. (C) Barplots comparing the snQTL identification performances for snQTL framework and local method (F-test for regression of pairwise co-expression onto genotype) on synthetic data with varying population size from 50 to 500. We set sparsity parameter R = p in snQTL for a fair comparison with the non-sparse local method. For results labeled “at snQTL", the y-axis is the observed for tests at the single true snQTL; for results labeled “at non-snQTL", the y-axis is the averaged observed
from three tests at randomly selected non-snQTL markers. True positive (or negative) rates for the tests at snQTL (or non-snQTL) are shown above the bars. All reported numbers are averaged across 50 replications for each population size.
Fig 3.
Identification of stickleback snQTLs via snQTL framework.
(A) Manhattan plot for snQTL testing with tensor statistics marks 21 stickleback snQTLs, mainly clustered in Chr 3, Chr 8, and Chr 18. The y-axis represents the natural logarithms of p-values. The snQTLs are deemed with testing p-values smaller than 0.05 (above the dashed line). (B) Strong genomic targets of selection with high population branch statistic (PBS) distribute around the outstanding snQTLs (markers X419, X423, and X425) in Chr 18. Values above the medial line represent higher PBS in Gosling Lake (blue); values below the line represent higher PBS in Roberts Lake (green). (C) Zoomed-in shadowed area in (B). Development regulation genes, lama4 an d ccn6, locate tightly around marker X419 with high selection speed. (D) Variance stabilized expressions (VSE) for ccn6 and lama4 in Gosling (GG) and Roberts (RR) lakes.
Fig 4.
Joint differential network analysis at snQTL X419 on Chr 18.
(A) Leverage scores for 10000 genes. Primary genes with top 10 leverage are highlighted with transcription IDs. Mitochondrial genome (MT) and scaffold region are coded as Chr 0 and Chr -1, respectively. (B-E) Networks for primary (red annotated nodes) and secondary (orange nodes) genes with top 100 leverages. The edge width indicates the connection strength between two genes; the diameter of node indicates the leverage of the gene; the color indicates enhancement (red) or reduction (blue) of the connection compared with average level. (B) Joint differential network at X419 with top 10% strongly connected edges. A wider edge implies a stronger genetic variation in the co-expression of the gene pair. Most genetic co-expression variations occur between the primary and secondary genes. (C-E) Co-expression networks corresponding to the genotypes GG, RG, and RR at X419, respectively. The linear changes in the colors of edges imply the nearly additive genetic effect to the co-expression networks. novel 1: ENSGACT00000018413; novel 2: ENSGACT00000026589; novel 3: ENSGACT00000017116.
Table 1.
List of primary genes with top 10 leverage scores in joint differential network at X419 on Chr 18.