Studies of the genetic loci that contribute to variation in gene expression frequently identify loci with broad effects on gene expression: expression quantitative trait locus hotspots. We describe a set of exploratory graphical methods as well as a formal likelihood-based test for assessing whether a given hotspot is due to one or multiple polymorphisms. We first look at the pattern of effects of the locus on the expression traits that map to the locus: the direction of the effects and the degree of dominance. A second technique is to focus on the individuals that exhibit no recombination event in the region, apply dimensionality reduction (e.g., with linear discriminant analysis), and compare the phenotype distribution in the nonrecombinant individuals to that in the recombinant individuals: if the recombinant individuals display a different expression pattern than the nonrecombinant individuals, this indicates the presence of multiple causal polymorphisms. In the formal likelihood-based test, we compare a two-locus model, with each expression trait affected by one or the other locus, to a single-locus model. We apply our methods to a large mouse intercross with gene expression microarray data on six tissues. KEYWORDS eQTL; pleiotropy; multivariate analysis; data visualization; gene expression T HERE is a long history of efforts to map the genetic loci [called quantitative trait loci (QTL)] that contribute to variation in quantitative traits in experimental organisms, particularly to learn about the etiology of disease (Broman 2001;Jansen 2007). But it remains difficult to identify the genes underlying QTL (Nadeau and Frankel 2000). There has been much interest recently in measuring gene expression in disease-relevant tissues in QTL experiments as a way to speed the process from QTL to gene (Jansen and Nap 2001;Albert and Kruglyak 2015). The genetic control of gene expression is itself of great interest.Expression quantitative trait loci (eQTL) analysis attempts to find the genomic locations that influence variation in gene expression levels [messenger RNA (mRNA) abundances]. eQTL near the genomic location of the influenced gene are called local eQTL, and eQTL far away from the influenced gene are called trans-eQTL. When a genomic region influences the expression of many genes, the region is called a trans-eQTL hotspot.eQTL hotspots have been observed in many genetic studies (e.g., Brem et al. 2002;Schadt et al. 2003;Yvert et al. 2003;Chesler et al. 2005), and they are of particular interest because gene expressions mapping to the same location may indicate the existence of a genetic regulator.Batch effects (artifacts arising from technical or environmental factors) are common in microarray experiments. This has led to the development of a number of methods to control for underlying confounding factors (Leek and Storey 2007;Kang et al. 2008;Listgarten et al. 2010;Stegle et al. 2010;Fusi et al. 2012;Gagnon-Bartsch and Speed 2012). However, these methods generally cannot distinguish trans-eQTL hotspots ...