Estimation of the risk that epistatic pairs identified in the GWA analysis are due to high-order LD to unobserved functional variants (“apparent epistasis”).

1Locus detected as part of epistatic pair named as Chromosome_PositionInBp; r2mean: mean high-order LD between epistatic pseudo-marker and genome-wide sequence variants ± standard error; r2max: maximum high-order LD between epistatic pseudo-marker and genome-wide sequence variants ± standard error; P(r2max > 0.8): probability of observing a high-order LD larger then 0.8 in a random sample of 93 accessions with MAFPM for the epistatic pseudo-marker; MAFPM: minor-allele frequency for the epistatic pseudo-marker, i.e. the frequency of the minor-allele double-homozygote for the epistatic pair.
Using the whole-genome re-sequencing data from the reference 1001 Genomes A. thaliana collection, we estimated the high-order LD (r2) between the four pseudo-markers representing our epistatic pairs and all sequencing variants that were not genotyped in our GWA analysis. A bootstrap approach was used to estimate the mean and max r2 between the epistatic pseudo-markers and all the genome-wide sequencing-variants. The risk that an association might be due to “apparent epistasis” was calculated as the risk of observing an r2max > 0.8 in this analysis.