*3.1. Screening of Allelopathy in Rice*

Allelopathic potentials for each RIL were thus represented by the inhibition rates of the six traits. Clear inhibition was detected for all six traits (Figures 2 and 3). Allelopathic di fferences between the parent cultivars were more apparent for height traits than weight traits. For root length, 'Sathi' elicited 62% inhibition, whereas 'Nong-an' elicited only 17% inhibition. For shoot length, 'Sathi' elicited a 57% inhibition rate compared to 30% with 'Nong-an'. Overall, total length inhibition was 62% with 'Sathi' and 22% with 'Nong-an'. The highly allelopathic 'Sathi' cultivar inhibited both root and shoot length by approximately 60%. By contrast, the non-allelopathic 'Nong-an' cultivar elicited stronger inhibition of shoot length (30%) than root length (17%). For root weight, 'Sathi' elicited 40% inhibition and 'Nong-an' elicited 32% inhibition. For shoot weight, 'Sathi' elicited 60% inhibition compared with 42% with 'Nong-an'. Overall, total weight inhibition was 58% with 'Sathi' and 41% with 'Nong-an'. Although di fferences in inhibition between the two parent cultivars were relatively small, RILs exhibited large variations in inhibition for all six traits. Transgressive segregation, where RILs exceeded parental phenotypes, was also observed (Figure 3).

**Figure 2.** Allelopathic effect on growth inhibition of lettuce: ( **A**) lettuces cultivated without rice control; (**B**) lettuces cultivated with rice 'Nong-an'; and ( **C**) lettuces cultivated with rice 'Sathi'.

**Figure 3.** Distribution of growth inhibition rate. (**A**) Inhibition rate of root length, (**B**) inhibition rate of shoot length, (**C**) inhibition rate of total length, (**D**) inhibition rate of root weight, (**E**) inhibition rate of shoot weight, and (**F**) inhibition rate of total weight.

### *3.2. High-Throughput SNP Genotyping and QTL Analysis*

For QTL analysis, 785 polymorphic markers between 'Nong-an' and 'Sathi' were used in constructing a linkage map with 98 RILs (Supplementary Materials Table S1). Among the 247,578 SNP markers used, monomorphic or low-quality markers were eliminated to generate genotypes for 110,770 markers. Additionally, for the generated genotypes for 110,770 markers, binning was carried out for each chromosome, using BIN functionality QTL IciMapping 4.1 to select 2654 markers. Further filtering based on the physical distance (~ 400 kb) was conducted to generate the final 785 markers for the QTL analysis. The markers on the genetic map presented the same ordering presented in the physical map from which the SNP markers were selected, based on the database of IRGSP 1.0. linkage map construct using 98 RIL individuals and 785 markers. Overall, 785 markers were distributed among all 12 rice chromosomes with an average of one marker per 450 kb (Supplementary Materials Figure S1). The number of markers varied from 38 (chromosome 11) to 89 (chromosome 8) with an average of 65.4 per chromosome. The longest length was found in chromosome 1, with 249.5 cM, followed by chromosome 3 with 248.8 cM and by chromosome 12 with 213.2 cM. The linkage map was 2489.75 cM in total length, with the average distance between markers being 3.17 cM. Two main effect-additive QTLs for the allelopathic traits on one chromosome region were detected. One QTL was *qISL-8* (inhibition rate of shoot length), and the other was *qITL-8* (inhibition rate of total length), on chromosome 8, 176.3 cM ~ 177.3 cM (Figure 4). The *qISL-8* showed

an LOD value of 3.38, which explained 20.83% phenotypic variance. The qITL-8 showed an LOD value of 3.24, which explained 14.94% phenotypic variance (Table 1).

**Figure 4.** Detected QTLs (qISL and qITL) region associated with inhibition of growth on chromosome 8: (**A**) the LOD score of DNA markers associate with ISL (inhibition rate of shoot length) and position of qISL-8 on chromosome 8; (**B**) the LOD score of DNA markers associate with ITL (inhibition rate of total length) and position of qITL-8 on chromosome 8. Abbreviations are as follows: ISL—inhibition rate of shoot length; ITL—inhibition rate of total length.

**Table 1.** Quantitative trait loci (QTLs) of allelopathy analyzed by inclusive composite interval mapping.


Abbreviations are as follows: ISL—inhibition rate of shoot length; ITL— inhibition rate of total length; PVE (%)—phenotypic variance explained; Add—estimated additive effect of Nong—an allele for the QTL; CI—confidence interval calculated by one LOD drop from the estimated QTL position.

The phenotype differences were compared between 'Nong-an' allele and 'Sathi' allele on SNP markers C08-70 and C08-71. For the traits of ISL and ITL, the result of the t-test showed significant differences between homozygous alleles of 'Nong-an' and 'Sathi' (Figure 5).

**Figure 5.** Comparison of inhibition ratio between 'Nong-an' and 'Sathi' alleles on SNP markers C08-70 and C08-71 for ISL (inhibition rate of shoot length) and ITL (inhibition rate of total length). Significance was determined by *t*-test. \*\*\* Indicates significance in 0.001 probability level.

Two digenic epistatic QTLs for inhibition rate of shoot weight (ISW) and inhibition rate of total weight (ITW) were also identified on identical genomic regions of chromosomes 1 and 8. The two interacting regions for two digenic epistatic QTLs were located in the interval between markers C01-75 and C01-76 on chromosome 1 and the interval between markers C08-42 and C08-43 on chromosome 8. The two digenic epistatic QTLs showed similar phenotypic variance explained (PVE), which are 23.97% for ISW and 23.29% for ITW. Furthermore, additive-by-additive effects of two digenic epistatic QTLs were −7.06 for ISW and −7.31 for ITW (Table 2).

**Table 2.** Digenic epistatic QTLs of allelopathy analyzed by inclusive composite interval mapping.


Abbreviations are as follows: Chr—chromosome; ISW—inhibition rate of shoot weight; ITW—inhibition rate of total weight; PVE(%)—phenotypic variance explained; Add1—estimated additive effect of first QTL; Add2—estimated additive effect of second QTL; Add by Add—additive by additive epistatic effect of QTL at the two scanning points.
