Confused about QTLs

I understand phenotypic QTLs, but what is an eQTL? What is an eigengene?

eQTL are expression QTL where microarray probe expression is used as a phenotype (or RNA-seq counts)

Genomic data such as gene expression data and variant data have very high dimensionality, i.e. there are too many variables, and few data points. When you have a gene expression dataset, you may be interested in identifying groups of genes which show similar expression patterns.

One of the ways to do this is WGCNA or weighted gene coexpression network analysis. In simple terms, what you’re trying to do is identify genes which show similar expression patterns across samples or conditions. These gene groups are called modules. WGCNA identifies modules by using a type of Principle component analysis (PCA). Here, each module is represented by an expression value which belongs to the module ‘eigengene’. This value is identified from the PCA. None of the actual genes in the module need to actually have this expression value.

Since each eigengene represents a module, the distance a gene from the eigengene, and therefore the centre of the module, can be calculated. This tells us which module each gene lies in.

(from https://www.quora.com/What-are-eigengenes-and-gene-modules)

An “eigengene” is simply the first principal component of (the expression of) a set of genes. Since the first principal component is the first eigenvector it was called “eigengene” by Steve Horvath and colleagues.