The identification of genetic variants influencing gene expression (known as expression quantitative trait loci or eQTLs) is important in unravelling the genetic basis of complex traits. Detecting multiple eQTLs simultaneously in a population based on paired DNA-seq and RNA-seq assays employs two competing types of models: models which rely on appropriate transformations of RNA-seq data (and are powered by a mature mathematical theory), or count-based models, which represent digital gene expression explicitly, thus rendering such transformations unnecessary. The latter constitutes an immensely popular methodology, which is however plagued by mathematical intractability.