Biplot Analysis of Diallel Data

Diallel crosses have been used in genetic research to determine the inheritance of important traits among a set of genotypes and to identify superior parents for hybrid or cultivar development. Conventional diallel analysis is limited to partitioning the total variation of the data into general combining ability (GCA) of each genotype and specific combining ability (SCA) of each cross. In this paper we formulate a biplot approach for graphical diallel analysis. The biplot is constructed by the first two principal components (PCs) derived from subjecting the tester-centered diallel data to singular value decomposition. It displays the most important entry by tester patterns of the data and allows the following information to be extracted visually: (i) GCA of each genotype; (ii) SCA of each genotype; (iii) groups of parents with similar genetics; and (iv) superior hybrids. In addition, the biplot allows hypotheses to be formulated concerning the genetics of the genotypes. Three published diallel data sets of wheat (Triticum aestivum L.) and maize (Zea mays L.) were used to demonstrate the biplot approach and detailed procedures were provided for constructing and interpreting a biplot.