Fig. 2

Next-Gen GWAS retrieves simulated epistatic interactions. Var1 (x-axis) and Var2 (y-axis) are a series of 100 SNPs. The triangle corresponds to SNP combinations when the diagonal contains simple SNP effects. Z-axis reports NGG estimated \(\widehat{\theta }\) values of simple SNPs (diagonal) and combinations (rest of the triangle). Purple points correspond to simulated support of simple (diagonal) and epistatic signals (in the triangle). The sample size is 5000. A and B Genotype and phenotype data are simulated using specific and modulable parameters (see Additional file 1. Material for details on the simulation). Random noise is added. NGG retrieves the 5 simulated signals (purple) including the pure epistatic effects (outside of the diagonal). C and D Phenotype data only have been simulated while genotypes are from the Arabidopsis genome (SNPs are sampled from X matrix). Again epistatic interactions (purple points) are retrieved by NGG. E and F report heatmaps for Recall and % of recovery in an analysis of 1000 × 1000 SNP interactions (0.5 M interactions) where 10 non-null signals have been simulated. Recall in E is calculated for the top 10 stronger signals. The percent of true signal recovery in F is calculated for the top 100 signals. We have found that NGG is quite resilient to noise in the data (on phenotypes Additional file 1: Fig. 1) and the power of NGG increases quickly with the number of individuals and for stronger heritabilities