**4. Discussion**

The use of allelopathy for weed control has grea<sup>t</sup> potential as a biological control method. Despite this, few genetic studies have examined allelopathy [20] due to the complex challenge of accurately assessing allelopathic interactions in field situations in the presence of natural variability and changing environmental conditions. In this study, an analysis of rice RILs was used to identify QTLs contributing to allelopathic interactions with lettuce, a susceptible receiver plant, in controlled conditions. Six traits were examined, all of which were inhibited in the receiver plant. Inhibition by the different RILs varied widely, and transgressive segregation was observed. Although the cultivation media and growth chamber conditions were well controlled, the conditions in which the receiver plants were cultivated alongside the RILs may produce an inhibitory environment for lettuce growth. Greater inhibition was observed in the non-allelopathic parent ('Nong-an') than in lettuce plants grown in the absence of rice. One possibility is that 'Nong-an' may exhibit low allelopathy, rather than being strictly non-allelopathic [10]. Alternatively, the receiver plant inhibition may have been at least partly due to competition for space. Although it was not possible to completely eliminate the effects of competition in our experimental design, the inhibitory effect of the highly allelopathic parent 'Sathi' was readily apparent, particularly on receiver plant root growth.

Even though we evaluate the allelopathic response with inhibition of weight and length, for the evaluated traits, two main effect additive QTLs for inhibition of root length and inhibition of total length were identified. The locations of both QTLs were identical on the chromosome 8. Because the total length includes the shoot length, this QTL region is mainly for the inhibition of shoot length. The level of explained phenotypic variation for qISL-8 on chromosome 8 was 20.83%. Other previous reports that showed relatively low phenotypic variation explain the value of individual QTL ranging from 5.0% to 11.1%, in general [11]. This relatively low phenotypic variation of values for the individual QTLs is part of the general nature of the allelopathic trait, representing the di fficulty in measuring the allelopathic trait at the individual genotype level. In this study, qISL-8 showed a relatively high value of 20.83%, suggesting it is a possible candidate for further study for cloning genes for the allelopathy. The physical distance of the detected QTL region was 194 Kbp where 31 genes are located (Supplementary Materials Table S2). Among them, 12 genes are unknown or hypothetical proteins, and other proteins were reported to be related with auxin response, dehydration, protein kinase, zinc finger protein, chaperone, peroxidase, and isoamylase. Further study for these candidate genes will be conducted, and the development of near-isogenic lines with each QTL are undergoing. The two digenic epistatic QTLs were detected on identical genomic regions for inhibition rate of shoot length (ISL) and inhibition of total weight (ITW). In addition, PVE and the e ffect of both digenic epistatic QTLs showed ~ 23%. This is possibly the closest related trait between the shoot weight trait and total weight.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4425/11/5/470/s1, Table S1: The 785 SNP markers genotype for 98 RILs. Table S2: The candidate 31 genes located in the detected QTL region on chromosome 8. Figure S1: Linkage map for 12 chromosomes.

**Author Contributions:** Formal analysis, G.-W.C. and Y.L.; investigation, T.-H.H. and G.-W.C.; methodology, I.-M.C. and S.-W.K.; project administration, I.-M.C. and J.L.; resources, I.-M.C. and J.S.; software, Y.L.; supervision, I.-M.C., S.-W.K., J.S., and J.L.; validation, T.-H.H., S.-W.K., and J.L.; visualization, T.-H.H. and J.S.; writing–original draft, T.-H.H.; writing–review and editing, T.-H.H., Y.-J.A., S.-Y.K., S.-H.K. and J.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2017R1E1A1A01075282) and Konkuk University Researcher Fund in 2018.

**Acknowledgments:** This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2017R1E1A1A01075282) and Konkuk University Researcher Fund in 2018.

**Conflicts of Interest:** All of the authors declare that they have no conflicts of interest in this publication.

**Availability of Data and Materials:** The datasets used and/or analyzed during the current study are available from the corresponding author, upon reasonable request.
