Lysine is an essential amino acid that cannot be synthesized in humans. Rice is a global staple food for humans but has a rather low lysine content. Identification of the quantitative trait nucleotides (QTNs) and genes underlying lysine content is crucial to increase lysine accumulation. In this study, five grain and three leaf lysine content datasets and 4,630,367 single nucleotide polymorphisms (SNPs) of 387 rice accessions were used to perform a genome-wide association study (GWAS) by ten statistical models. A total of 248 and 71 common QTNs associated with grain/leaf lysine content were identified. The accuracy of genomic selection/prediction RR-BLUP models was up to 0.85, and the significant correlation between the number of favorable alleles per accession and lysine content was up to 0.71, which validated the reliability and additive effects of these QTNs. Several key genes were uncovered for fine-tuning lysine accumulation. Additionally, 20 and 30 QTN-by-environment interactions (QEIs) were detected in grains/leaves. The QEI-sf0111954416 candidate gene LOC_Os01g21380 putatively accounted for gene-by-environment interaction was identified in grains. These findings suggested the application of multi-model GWAS facilitates a better understanding of lysine accumulation in rice. The identified QTNs and genes hold the potential for lysine-rich rice with a normal phenotype.

Rice (Oryza sativa L.) is a globally important food source providing carbohydrates, amino acids, and dietary fiber for humans and livestock. The branched-chain amino acid (BCAA) level is a complex trait related to the nutrient quality of rice. However, the genetic mechanism underlying the BCAA (valine, leucine, and isoleucine) accumulation in rice grains remains largely unclear. In this study, the grain BCAA contents and 239,055 SNPs of a diverse panel containing 422 rice accessions were adopted to perform a genome-wide association study (GWAS) using a recently proposed 3VmrMLM model. A total of 357 BCAA-content-associated main-effect quantitative trait nucleotides (QTNs) were identified from 15 datasets (12 BCAA content datasets and 3 BLUP datasets of BCAA). Furthermore, the allelic variation of two novel candidate genes, LOC_Os01g52530 and LOC_Os06g15420, responsible for the isoleucine (Ile) content alteration were identified. To reveal the genetic basis of the potential interactions between the gene and environmental factor, 53 QTN-by-environment interactions (QEIs) were detected using the 3VmrMLM model. The LOC_Os03g24460, LOC_Os01g55590, and LOC_Os12g31820 were considered as the candidate genes potentially contributing to the valine (Val), leucine (Leu), and isoleucine (Ile) accumulations, respectively. Additionally, 10 QTN-by-QTN interactions (QQIs) were detected using the 3VmrMLM model, which were putative gene-by-gene interactions related to the Leu and Ile contents. Taken together, these findings suggest that the implementation of the 3VmrMLM model in a GWAS may provide new insights into the deeper understanding of BCAA accumulation in rice grains. The identified QTNs/QEIs/QQIs serve as potential targets for the genetic improvement of rice with high BCAA levels.

This paper is concerned with a population dynamic model with delay. In this work, by rewriting the equation and using the Ikehara's theorem, we show the exact asymptotic behavior of the profile as xi ->-infinity for critical speed.