Limits of epistatic models displaying no marginal effects

The completed map of the Human Genome increases the power of association and measured genotype studies. While available SNPs may suffice for a genome scan, disequilibrium studies may not readily explain the genetic mechanisms of complex diseases. Since there are many fewer human genes than proteins, it seems likely that epistatic interactions play an important role in complex diseases. To understand how large a role interactions might play, we examined models in which all genetic variation is due to epistatic interactions, with no additive or dominance contribution from any single locus. We examined the limits of disease models involving 2, 3, and 4 loci and found that in each case, models with no single-locus additive or dominance variance can represent qualitative traits with 100% heritability. Models involving 2 loci can reach 50% heritability for disease prevalences above 20%. Models involving 3 and 4 loci can reach 50% heritablity for prevalences above 5% and 2% respectively. Thus, it is plausible to expect that some/many contributing genes for complex diseases will not be detectable in a disequiblibrium genome scan, no matter how densely placed or polymorphic the markers or how large the sample. Instead, more sophisticated techniques will be required.