To determine which of the four models (Equations 2, 4, 6, and the model selection) is optimal, we empirically estimated the FDR for each model over a set of 3,000 genes randomly selected from the set of all genes detected as expressed in the liver samples. For each gene and for each marker we fitted each of the four models to the data. We performed this same analysis on ten separate permutation sets in which each of the 3,000 gene expression trait vectors was permuted such that the correlation structure among the genes was preserved. The FDR for a given LOD score threshold was then computed as the ratio of the mean number of QTL detected in the permuted datasets (the mean taken over the ten permuted datasets) and the total number of QTL detected in the observed 3,000-gene dataset. We then generated ROC-like curves by varying the LOD score threshold, resulting in a range of FDRs (from 0% to more than 50%). To simplify this type of summary, we considered no more than one QTL per chromosome per gene expression trait by considering only the QTL with the max LOD score on each chromosome for each trait. The ROC curves for each of the four models are shown in Figure S1, with the black curve corresponding to Equation 2, the blue curve corresponding to Equation 4, the red curve corresponding to Equation 6, and the green curve corresponding to the model selection procedure.