A plausible explanation for statistical epistasis revealed in genome wide association analyses is the presence of high order linkage disequilibrium (LD) between the genotyped markers tested for interactions and unobserved functional polymorphisms. Based on findings in experimental data, it has been suggested that high order LD might be a common explanation for statistical epistasis inferred between local polymorphisms in the same genomic region. Here, we empirically evaluate how prevalent high order LD is between local, as well as distal, polymorphisms in the genome. This could provide insights into whether we should account for this when interpreting results from genome wide scans for statistical epistasis. An extensive and strong genome wide high order LD was revealed between pairs of markers on the high density 250k SNP-chip and individual markers revealed by whole genome sequencing in the A. thaliana 1001-genomes collection. The high order LD was found to be more prevalent in smaller populations, but present also in samples including several hundred individuals. An empirical example illustrates that high order LD might be an even greater challenge in cases when the genetic architecture is more complex than the common assumption of bi-allelic loci. The example shows how significant statistical epistasis is detected for a pair of markers in high order LD with a complex multi allelic locus. Overall, our study illustrates the importance of considering also other explanations than functional genetic interactions when genome wide statistical epistasis is detected, in particular when the results are obtained in small populations of inbred individuals.

On the relationship between high-order linkage disequilibrium and epistasis