%0 Journal Article
%T EM Algorithm for Mapping Quantitative Trait Loci in Multivalent Tetraploids
%A Jiahan Li
%A Kiranmoy Das
%A Guifang Fu
%A Chunfa Tong
%A Yao Li
%A Christian Tobias
%A Rongling Wu
%J International Journal of Plant Genomics
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/216547
%X Multivalent tetraploids that include many plant species, such as potato, sugarcane, and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in multivalent tetraploids is challenged by their unique cytogenetic properties, such as double reduction. We develop a statistical method for mapping multivalent tetraploid QTLs by considering these cytogenetic properties. This method is built in the mixture model-based framework and implemented with the EM algorithm. The method allows the simultaneous estimation of QTL positions, QTL effects, the chromosomal pairing factor, and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We used simulated data to examine the statistical properties of the method and validate its utilization. The new method and its software will provide a useful tool for QTL mapping in multivalent tetraploids that undergo double reduction. 1. Introduction Genetic analysis in polyploids has received considerable interest in recent years because of the biological and economic importance [1¨C3]. Genetic linkage maps constructed from molecular markers have been published for several major polyploids [4¨C10]. Statistical models for linkage analysis and map construction that consider unique biological properties of polyploids have been developed [11¨C14]. For bivalent polyploids, Wu et al. [15, 16] incorporated the so-called chromosomal pairing preference [17] into the linkage analysis framework, to increase the biological relevance of linkage mapping models. There have been several statistical models developed to map quantitative trait loci (QTLs) in bivalent polyploids [18, 19]. There is also a group of polyploids, called multivalent polyploids, in which chromosomes pair among more than two homologous copies at meiosis, rather than only two copies as like in bivalent polyploids. The origin of multivalent polyploids is mostly from the duplication of similar genomes and, for this reason, they are called autopolyploids [20, 21]. The consequence of multivalent pairing in autopolyploids is the occurrence of double reduction, that is, two sister chromatids of a chromosome sort into the same gamete [22]. Fisher [23] proposed a conceptual model for characterizing the individual probabilities of 11 different modes of gamete formation for a quadrivalent polyploid in terms of the recombination fraction between two different loci and their double reductions. Wu et al. [24] used Fisher's model to derive the EM algorithm for the
%U http://www.hindawi.com/journals/ijpg/2010/216547/