A mixed polyploid model for linkage analysis in outcrossing tetraploids using a pseudo-test backcross design

Based on how chromosomes pair at meiosis, the nature of polyploids can be described by bivalent polyploids, multivalent polyploids, and mixed polyploids. In bivalent polyploids, only two chromosomes pair, during which two more similar chromosomes have a higher pairing probability (preferential pairing) than two less similar chromosomes, whereas in multivalent polyploids more than two chromosomes pair at a time, which results in double reduction. Preferential chromosome pairings and double reduction affect the frequencies of gamete formation and, therefore, linkage analysis of polymorphic markers in bivalent and multivalent polyploids, respectively. For mixed polyploids, in which both bivalent and multivalent formations occur simultaneously, linkage analysis is affected by both preferential pairings and double reduction. In this study, we develop a hierarchical maximum likelihood model for discerning gamete genotypes derived from different pairing mechanisms and different formation modes. The first-stage model in the hierarchy is formulated to characterize the relative frequencies of bivalent and multivalent pairing configurations in terms of the preferential pairing factor. The second-stage model is derived to rule out identical gamete genotypes into their different formation modes with relative probabilities determined by the recombination fraction. The first-stage pairing mechanism and second-stage formation mode are integrated to provide the simultaneous maximum likelihood estimates of the preferential pairing factor, the frequency of double reduction, and the recombination fraction, by implementing the EM algorithm. We performed extensive simulation studies to demonstrate the statistical properties of our hierarchical model for linkage analysis in tetraploids. The implications of our model for polyploid linkage mapping are discussed.