A Multivalent Pairing Model of Linkage Analysis in Autotetraploids

A Multivalent Pairing Model of Linkage Analysis in Autotetraploids

Samuel S. Wu^a, Rongling Wu^a, Chang-Xing Ma^a,b, Zhao-Bang Zeng^c, Mark C. K. Yang^a, and George Casella^a
^a Department of Statistics, University of Florida, Gainesville, Florida 32611,
^b Department of Statistics, Nankai University, Tianjin 300071, People's Republic of China
^c Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695

Corresponding author: Samuel S. Wu, Division of Biostatistics, P. O. Box 100212, University of Florida, Gainesville, FL 32610., samwu{at}biostat.ufl.edu (E-mail)

Communicating editor: J. B. WALSH

Polyploidy has been recognized as an important step in the evolutionarydiversification of flowering plants and may have a significantimpact on plant breeding. Statistical analyses for linkage mappingin polyploid species can be difficult due to considerable complexitiesin polysomic inheritance. In this article, we develop a novelstatistical method for linkage analysis of polymorphic markersin a full-sib family of autotetraploids. This method is establishedon multivalent pairings of homologous chromosomes at meiosisand can provide a simultaneous maximum-likelihood estimationof the double reduction frequencies of and recombination fractionbetween two markers. The EM algorithm is implemented to providea tractable way for estimating relative proportions of differentmodes of gamete formation that generate identical gamete genotypesdue to multivalent pairings. Extensive simulation studies wereperformed to demonstrate the statistical properties of thismethod. The implications of the new method for understandingthe genome structure and organization of polyploid species arediscussed.

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