abstract
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In crop breeding, we focus on improving yield, quality, resistance, and adaptability traits, which are controlled by a few major genes, modified by a series of polygenes, and regulated by biological small molecules, where there are interactions among genes and between genes and environment. However, it is difficult to identify small genes, gene-by-environment interactions (GEIs), and gene-by-gene interactions (GGIs). Recently, our methodological advances will change this status. First, we established a new three variance component mixed model framework to detect quantitative trait nucleotide (QTN), QTN-by-environment interaction (QEI), and QTN-by-QTN interaction (QQI) and estimate their effects conditional on fully controlling all the possibly polygenic backgrounds. This method named 3VmrMLM. It has been extended into bi-parental segregation populations and genetic mating design populations, in which GCIM-QEI has been established. More small genes identified by these methods may be used to improve the above traits. GEIs across various abiotic stress conditions or various ecological environments may be used to improve the resistance and adaptability traits. GGIs around QQIs may be used to investigate their molecular mechanisms. Then, the numbers of read counts of marker alleles in low and high pools in F2 are used to predict the numbers of read counts of marker genotypes, the two kinds of information was used to construct a new statistic Gw, which is used to detect small and over-dominant genes in F2. This method named dQTG-seq1. If the numbers of marker genotypes are known based on sequencing all the extreme individuals, small and extremely over-dominant genes can be found. This method named dQTG-seq2. This indicates that heterosis genes identified from dQTG-seq2 are available to improve these traits in crop breeding. To popularize the mentioned-above methodologies for mining elite genes, GEIs, and GGIs, we developed R and C++ softwares IIIVmrMLM, R software dQTG.seq, and R software QTL.gCIMapping. We believe that these packages will mine more elite genes that are available in crop breeding.