Many traits that are important to agriculture are quantitative in nature, influenced by multiple genes. Efficient and robust identification and mapping onto genomic positions of those genes is a very important goal in quantitative genetics. Many statistical methods have been proposed and developed to map multiple QTL with epistasis in a variety of populations from crosses of inbred lines. However, crosses of inbred lines are undoable for many species either because of genetic depression caused by endogamy or because of their long life cycles. Instead, crosses of outbreed parents are made and populations with more complex genetic are obtained. In full-sibs each locus in a diploid species can have up to four alleles, leading to segregation patterns as 1:1, 1:2:1, 3:1 and 1:1:1:1. To complicate matters, the linkage phase of markers and QTL are unknown. Nevertheless, in many circumstances methods developed for mapping QTL from inbred line crosses have been used to map QTL populations in full-sibs, resulting in lower power to map QTL, however. Moreover, the majority of methods rely on analyses of each trait separately, ignoring correlation between traits and/or environments. Lin et al. 2003 proposed an univariate method of QTL mapping in full-sibs that combines all segregation patterns of a single QTL, and E Silva (2010) proposed a method of multiple traits multiple intervals mapping (MTMIM) of QTL from inbred line crosses. In this research project, we propose to extend the MTMIM to outbreed crosses to capture information on multiple traits and/or environments, with all segregation patterns. The proposed method will be utilized to map putative QTL affecting traits of industrial and economical interest in sugar-cane. The QTL mapping will shed light into the complex genetic architecture of traits in sugar-cane, and bring benefits to genetic improvement of the species.
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