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. 2020 Apr 30;10:7320. doi: 10.1038/s41598-020-64107-z

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Al tolerance (RNRG means and standard deviations) for F_2:3 progeny showing combinations of alleles at pairs of epistatic QTLs. Progeny homozygous for the allele donated by the Al-sensitive parent, SCH3, are shown in B (blue dot), whereas progeny homozygous for the Al-tolerant parent, 203B-14, are shown in A (red triangle). Means for heterozygous (H) progeny are also shown (green square). Interaction between QTLs (a) qALT8.05 × qALT1.09, (b) qALT8.05 × qALT9.01, (c) qALT10.02 × qALT1.09 and (d) qALT9.01 × qALT1.09.