A Bivalent Polyploid Model for Mapping Quantitative Trait Loci in Outcrossing Tetraploids

Two major aspects have made the genetic and genomic study of polyploids extremely difficult. First, increased allelic or nonallelic combinations due to multiple alleles result in complex gene actions and interactions for quantitative trait loci (QTL) in polyploids. Second, meiotic configurations in polyploids undergo a complex biological process including either bivalent or multivalent formation, or both. For bivalent polyploids, different degrees of preferential chromosome pairings may occur during meiosis. In this article, we develop a maximum-likelihood-based model for mapping QTL in tetraploids by considering the quantitative inheritance and meiotic mechanism of bivalent polyploids. This bivalent polyploid model is implemented with the EM algorithm to simultaneously estimate QTL position, QTL effects, and QTL-marker linkage phases by incorporating the impact of a cytological parameter determining bivalent chromosome pairings (the preferential pairing factor). Simulation studies are performed to investigate the performance and robustness of our statistical method for parameter estimation. The implication and extension of the bivalent polyploid model are discussed.