## 4 Discussion  
Grain number is one of the most important agronomic traits in the determination of rice productivity, which is governed by multiple QTLs with major or minor effect. In the present study, a total of 58 QTLs were detected in three RIL populations, including 22, 17, and 19 for NGP, NSP, and SF, respectively. The individual QTL counted for 1.5% to 22.1% of phenotypic variation. Among 58 QTLs, 15 with various effects shared by two or three populations and eight showed large effects with \(R^{2}\) larger than 10%. When major-effect QTLs were fixed, three minor-effect QTLs for NGP were further detected and validated using secondary segregation populations derived from one RH of the cross TO/IRBB52 under increment homogeneous backgrounds. Among the three minor-effect QTLs for NGP, _qNGP9.1_ and _qNGP12.1_ were stably identified in TI, Ti52-2, ZC9, and ZC12 populations, having the same direction of additive effects and similar value. Moreover, the regions of RM8206\(-\)RM219 containing _qNGP9.1_ and RM511\(-\)RM28313 containing _qNGP12.1_ were previously reported to affect NGP. _qFC9_ and _Gpp12.2_ were detected in the region \begin{table}
\begin{tabular}{c c c c c c c} \hline
**QTL** & **Population** & **Interval** & **LOD** & \(A^{a}\) & \(D^{b}\) & \(R^{2}\) **(\%) \(\epsilon\)** \\ \hline _qNGP5.5_ & ZC5 S12 & RM18927\(-\)RM3321 & 2.72 & \(-\)1.94 & 3.42 & 6.3 \\ _qNGP9.1_ & ZC9 S12 & RM219-RM1896 & 2.22 & \(-\)2.96 & 1.00 & 5.1 \\ _qNGP12.1_ & ZC12 S12 & RM3246-Pita & 9.06 & 5.68 & 0.43 & 16.0 \\ \hline \end{tabular}  
* A, additive effect of replacing a maternal allele with a paternal allele. \({}^{b}\) D, dominance effect. \({}^{c}\)\(R^{2}\), proportion of phenotypic variance explained by the QTL effect.  
\end{table} 
Table 4: QTLs detected for NGP in the ZC5, ZC9, and ZC12 populations. of RM219\(-\)RM342 on chromosome 9 and RG869\(-\)RM277 on chromosome 12, respectively [49; 50]. It proves that _qNGP9.1_ and _qNGP12.1_ are good targets for underlying the genetic basis of grain number. _qNGP5.5_ was a new QTL identified in Ti52-2. This QTL was well verified in ZC5, the direction of allelic effect remaining consistent and \(R^{2}\) increased from 4.9 to 6.3%. Actually, _qNGP5.4_ was detected in TI with an allelic effect in the opposite direction to _qNGP5.5_. Comparing the two loci, we found that _qNGP5.5_ was located in RM18927\(-\)RM3321, while the _qNGP5.4_ was detected in RM274\(-\)RM334. The segregation region of Ti52-2 population covered RM274 but uncovered RM334. In previous studies, two QTLs with opposite allelic direction for grain weight were detected in RM18927\(-\)RM334 [37; 51]. Hence, there might be two tightly linked QTLs with opposite direction of additive effect in the region of RM18927\(-\)RM334. Verification of three minor-effect QTLs was benefited from the fixation of the major-effect QTLs and increment homozygous of genetic background. Along with the background became more homogenous from TI to Ti52-2 then to ZC5, ZC9 and ZC12, the phenotypic variations were getting smaller, and the power of detection of QTLs was further improved. For instance, the standard deviation values and coefficient of variation of NGP and NSP has been decreasing with background became more homogenous (Table 1 and Table S2). Out of the 12 QTLs for NGP detected in TI, only _qNGP4_, _qNGP5.4_, _qNGP9.1_ and _qNGP12.1_ were located in the segregation region of Ti52-2. Except _qNGP4_ with the smallest \(R^{2}\), other three QTLs were detected in Ti52-2. In addition, two more QTLs _qNGP3.3_ and _qNGP5.5_ were detected in Ti52-2. These results supported that RHs are efficient materials in the establishment of NILs and secondary mapping populations for QTL validation and fine-mapping especially for minor-effect QTLs. Interestingly, among the five QTLs for NGP identified in Ti52-2, _qNGP3.3_, _qNGP5.5_, and _qNGP12.1_ were located in the same regions with _qNSP3.2_, _qNSP5.4_, and _qNSP12_, respectively. The regions of _qNGP6.1_ and _qNGP9.1_ showed the same intervals with _qSF6.1_ and _qSF9.2_.