## 2 Results
### Identification of Epistatic QTLs  
A total of 331 significant epistatic QTLs were detected for GPC, AC, GC, KL, KB, L:B, PTPP, and GYPP at a threshold LOD score \(>\) 5, with PVE ranging from 0.56 to 10.18% (Table S3). At LOD \(>\) 5, we found minor interactions between multiple loci across chromosomes (Figure 5). We detected 28 digenic interactions for GPC. Interestingly, three of these interactions occurred between a significant main-effect QTL (RM562-RM11307) in chromosome 1 for GPC and non-significant loci in other chromosomes. These interactions are represented in the boxplots (Figure 6). Both additive effects were from JAK-686 (Table S3). Similarly, we detected 79 epistatic interactions for AC. Three of these interactions occurred between two significant main-effect QTLs (RM22-A03P09039 and RM562-RM11307) on chromosome 3 and 6, respectively, and non-significant loci in other chromosomes (Figure 7). The influence of additive-by-additive effects of epistatic QTLs was relatively lower com  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Trait**} & \multirow{2}{*}{**Chromosome**} & \multicolumn{2}{c}{**Identified QTLs**} & \multicolumn{2}{c}{**Previously Known QTLs**} \\ \cline{3-6}  & & **Name** & **Physical Position** & **Name** & **Physical Position** & **References** \\ \hline \multirow{9}{*}{Protein content} & 1 & _qPC1.1_ & 4.31–5.05 & _qPC1.1_ & 4.63–4.70 & [20] \\ \cline{2-6}  & 1 & _qPC1.2_ & 14.61–23.92 & _qPr1_ & 12.20–14.63 & [21] \\ \cline{2-6}  & 1 & & _qCPCI.1_ & 0.6–1.1 & [22] \\ \cline{2-6}  & 1 & & _qPC1.1_ & 8.07 & [23] \\ \cline{2-6}  & 1 & & _qRPC-1_ & 11.07 & [11] \\ \cline{2-6}  & 1 & & _qPC-1_ & 25.02–26.19 & [24] \\ \cline{2-6}  & 1 & & _Pro-1_ & 32.09–34.02 & [10] \\ \cline{2-6}  & 1 & & _qPC1_ & 37.88–40.16 & [25] \\ \cline{2-6}  & 1 & & _qPC1.2_ & 39.16–39.23 & [20] \\ \cline{2-6}  & 1 & & _qPC1_ & 40.13–41.16 & [26] \\ \cline{2-6}  & 5 & _qPC5.1_ & 0.59–5.28 & _qPC5_ & 1.94 & [26] \\ \cline{2-6}  & 5 & _qPC5.2_ & 22.28–26.10 & _qPC-5_ & 23.48–24.26 & [27] \\ \cline{2-6}  & 5 & & _qPC5.1_ & 0.53 & [28] \\ \hline \multicolumn{1}{c}{5} & \multicolumn{2}{c}{} \multicolumn{2}{c}{} \multicolumn{2}{c}{} \multicolumn{2}{c}{} \(\sigma\)_GPC5_ & 7.8 & [2] \\ \hline \end{tabular}
\end{table}
Table 3: QTLs identified for grain protein content.  
pared to the individual additive effects of the corresponding QTLs. This could be due to the presence of few individuals with rare loci in the populations. Further, interference from other loci and the limited epistatic variance arising from interactions may also contribute to this effect.  
Figure 5: _Cont._  
Figure 5: Epistatic QTLs for protein, yield, and quality traits in F\({}_{2}\) population by IM-EPI (PC—grain protein content; AC—amylase content; GC—gel consistency; kd—kernel length; kb—kernel breadth; lb—L:B; pptp—productive tillers per plant; gypp—grain yield per plant).  
Figure 6: Box plots illustrating the epistatic interactions for protein content on chromosomes 1A (RM562-RM11307) and 12B (RM27564-A12P02180); 1A (RM562-RM11307) and 1B (RM11307-RM10890); 1A (RM562-RM11307) and 6B (A06P22133-A06P08188) A, JAK-686 allele; B, BPT 5204 allele; H, heterozygous.