Cis- vs. trans-eQTL

To discriminate cis- vs. trans-QTL, we compared inferred QTL location to the position of the expressed gene according to the BROAD G. aculeatus genome annotation v. 1.77 (available at http://ftp.ensembl.org/pub/release-77/gtf/gasterosteus_aculeatus/). All positions on the BROAD annotation were recoded to positions on our modified chromosome assemblies. For genes on scaffolds un-anchored to our assembly, we also used information on chromosomal scaffold locations available in the recently published map of Glazer et al. (2015). Any eQTL on a different chromosome from the regulated gene was considered trans. For eQTL on the same chromosome as the gene, we initially considered two alternative threshold distances for an eQTL to be considered trans [> 1 Mb following Grundberg et al. (2012) or > 10 Mb following van Nas et al. (2010)]. For the 1 Mb threshold, we observed strong enrichment of significant trans-eQTL on the same chromosome as the regulated gene, indicating that these were actually mis-identified cis-eQTL; therefore, we selected the conservative 10 Mb threshold. In practice, examination of our results showed that 95% C.I. of eQTL sometimes extended further than this 10 Mb threshold. Considering median 95% C.I. (∼1 Mb), we therefore classified a QTL as trans if the SNP closest to the upper or lower 95% confidence bounds of that QTL was further than 9.5 Mb from the regulated gene. Following Johnsson et al. (2015), we applied a local significance threshold (chromosome-wide P < 0.01) for evaluation of possible cis-QTL and a genome-wide significance threshold (genome-wide P < 0.021, = chromosome-wide threshold of 0.001 * 21 chromosomes) for evaluation of possible trans-QTL. Although this significance threshold is permissive, we considered it acceptable as our aim was to analyze the eQTL distribution across the genome rather than to identify individual QTL-locus associations. Similar significance thresholds have been used for eQTL detection in comparable studies (e.g., Whiteley et al. 2008).

To ask whether the effect of variation in trans-regulatory sites was more often nonadditive than the effect of variation in cis-regulatory sites, we examined the narrow sense heritability (h²) and dominance proportion of genetic variance (d²) estimated for each expression trait by Leder et al. (2015) and provided in the Supplemental Data for that paper.