Abstract
Most of the breeding targets are quantitative traits. In exploring the quantitative trait locus (QTL) system of a trait, linkage mapping was established using sparse polymerase chain reaction (PCR) markers. With the genome-wide sequencing technology advanced, genome-wide association study (GWAS) was developed for natural (germplasm) populations using dense genomic markers, which facilitates the identification of the complete QTL system with their multiple alleles on genomic locations. GWAS makes use of the linkage disequilibrium (LD) due to historical saturate recombination and high-density genomic markers to detect QTLs through statistical test for the association between molecular markers and phenotypes. However, due to inbreeding and mixture of source populations, the germplasm population often has complex and unknown structure, which leads to false positives/negatives in GWAS. Various GWAS methods have been proposed to reduce false positives/negatives, including those of the general linear model and the mixed linear model, which focused mainly on finding a handful of major QTLs under single-locus model for major gene cloning and could not detect directly the multiple alleles using bi-allelic single-nucleotide polymorphism (SNP) marker. As a relatively thorough detection of QTLs with their multiple alleles is required for germplasm population, the restricted two-stage multi-locus multi-allele GWAS (RTM-GWAS) procedure was proposed for identifying the QTL system with varying multiple alleles. From the RTM-GWAS results, a QTL-allele matrix is constructed as a compact form of the population genetic constitution, which can be further used for crop genetic and breeding studies, including major gene mining, population evolution, and breeding by genetic design.
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