Singular-Value Partitioning in Biplot Analysis of Multienvironment Trial Data

TLDR: In this paper, the authors compared four singular-value scaling methods: genotype-focused scaling, environment-focused, symmetric scaling, and equal-space scaling for which-won-where pattern of the MET data.

Abstract: Multienvironment trials (MET) are conducted every year for all major crops throughout the world, and best use of the information contained in MET data for cultivar evaluation and recommendation has been an important issue in plant breeding and agricultural research. A genotype main effect plus genotype × environment interaction (GGE) biplot based on MET data allows visualizing (i) the which-won-where pattern of the MET, (ii) the interrelationship among test environments, and (iii) the ranking of genotypes based on both mean performance and stability. Correct visualization of these aspects, however, requires appropriate singular-value (SV) partitioning between the genotype and environment eigenvectors. This paper compares four SV scaling methods. Genotype-focused scaling partitions the entire SV to the genotype eigenvectors; environment-focused scaling partitions the entire SV to the environment eigenvectors; symmetrical scaling splits the SV symmetrically between the genotype and the environment eigenvectors; and equal-space scaling splits the SV such that genotype markers and environment markers take equal biplot space. It is recommended that the genotype-focused scaling be used in visualizing the interrelationship and comparison among genotypes and the environment-focused scaling be used in visualizing the interrelationship and comparison among environments. All scaling methods are equally valid in visualizing the which-won-where pattern of the MET data, but the symmetric scaling is preferred because it has all properties intermediate between the genotype- and the environment-focused scaling methods.