A Bivalent Polyploid Model for Linkage Analysis in Outcrossing Tetraploids

Polyploids can be classified as either allopolyploids or autopolyploids based on their presumed origins. From a perspective of linkage analysis, however, the nature of polyploids can be better described as bivalent polyploids, in which two chromosomes pair at meiosis, multivalent polyploids, in which more than two chromosomes pair, and general polyploids, in which bivalent and multivalent formations occur simultaneously. In this paper, we develop a statistical method for linkage analysis of polymorphic markers in bivalent polyploids. This method takes into account a unique cytological pairing mechanism for the formation of diploid gametes in tetraploids - preferential bivalent pairings at meiosis during which two homologous chromosomes pair with a higher probability than two homoeologous chromosomes. The higher frequency of homologous over homoeologous pairing, defined as the preferential pairing factor, affects the segregation patterns and linkage analysis of different genes on the same chromosome. A maximum likelihood method implemented with the EM algorithm is proposed to simultaneously estimate linkage and parental linkage phases over a pair of markers from any possible marker cross type between two outbred bivalent tetraploid parents demonstrating preferential bivalent pairings. Simulation studies display that the method can be well used to estimate the recombination fraction between different marker types and the preferential pairing factor typical of bivalent tetraploids. The implications of this method for current genome projects in polyploid species are discussed.