Fast3VmrMLM enables statistically powerful and computationally efficient large-scale marker-pair epistasis GWAS in sizable populations.

Identifying marker-pair epistasis in genome-wide association studies remains challenging due to computational burden and statistically underpowered. Hence, we developed a big-data algorithm, Fast3VmrMLM, that integrates a genome-wide pairwise scanning plus machine-learning framework with seven big-data techniques. Fast3VmrMLM considers all possible genetic effects while controlling for all polygenic backgrounds, substantially improving power of identifying epistasis. To broaden its utility, we extended three modules: Fast3VmrMLM-Hap for haplotype-by-haplotype interactions, Fast3VmrMLM-NCII for breeding populations with inferred genotypes, and Fast3VmrMLM-mQTL for molecular QTL interactions. Simulation studies demonstrated a high power (68.33%), a low false-positive rate (0.0056‱), and a high F1 score (0.70). For epistasis detection among half a million markers in 1000 individuals, Fast3VmrMLM finished the analysis in 7.23 hours using 30 server threads, outperforming plink, FaST-LMM, REMMA, Next-Gen GWAS, and 3VmrMLM. In analyzing rice real-datasets (1439, 3K and 18K accessions), the new methods and genetic network identified 58 gene-by-gene interactions (GGIs) with experimental evidence and 219 candidate GGIs supported by bioinformatics, with an average runtime of 0.26, 0.91, and 5.45 hours per trait, respectively. Some GGIs fall within previously reported high-order interactions. In a soybean structural variant dataset, Fast3VmrMLM-mQTL identified five candidate GGIs. By integrating genes, gene-by-environment interactions, and GGIs into a genetic network, we prioritized twenty-four key genes for rice yield-related traits. Furthermore, we identified 21 (51) superior gene pairs (genes) haplotypes and 93 lines for early-heading breeding in 18K rice dataset. Collectively, Fast3VmrMLM works well even in some challenging scenarios and offers a powerful tool for epistasis discovery and breeding by design.