A spectral framework to map QTLs affecting joint differential networks of gene co-expression

Studying the mechanisms underlying the genotype-phenotype association is crucial in genetics. Gene expression studies have deepened our understanding of the genotype → expression → phenotype mechanisms. However, traditional expression quantitative trait loci (eQTL) methods often overlook the critical role of gene co-expression networks in translating genotype into phenotype. This gap highlights the need for more powerful statistical methods to analyze genotype → network → phenotype mechanism. Here, we develop a network-based method, called snQTL, to map quantitative trait loci affecting gene co-expression networks. Our approach tests the association between genotypes and joint differential networks of gene co-expression via a tensor-based spectral statistics, thereby overcoming the ubiquitous multiple testing challenges in existing methods. We demonstrate the effectiveness of snQTL in the analysis of three-spined stickleback ( Gasterosteus aculeatus ) data. Compared to conventional methods, our method snQTL uncovers chromosomal regions affecting gene co-expression networks, including one strong candidate gene that would have been missed by traditional eQTL analyses. Our framework suggests the limitation of current approaches and offers a powerful network-based tool for functional loci discoveries. Significance statement This work addresses a key gap in understanding the mechanistic foundations for genotype-phenotype associations. While existing expression quantitative trait loci (eQTL) methods identify candidate loci affecting gene expression variants, they often neglect the crucial role of gene co-expression networks. Here, we develop a network-based QTL framework to map genetic loci affecting the gene co-expression network. Utilizing a tensor-based spectral approach, our snQTL method estimates the differential co-expression patterns and effectively identifies the associated genetic loci. Application of snQTL to three-spined sticklebacks revealed candidate loci missed by standard methods. This work suggests the limitations of current approaches and highlights the potential of network-based functional loci discovery.