A heritability-adjusted GGE biplot for test environment evaluation

TLDR: It is demonstrated that the vector length of an environment in the HA-GGE biplot approximates the square root heritability within the environment and that the cosine of the angle between the vectors of two environments approximate the genetic correlation between them.

Abstract: Test environment evaluation has become an increasingly important issue in plant breeding. In the context of indirect selection, a test environment can be characterized by two parameters: the heritability in the test environment and its genetic correlation with the target environment. In the context of GGE biplot analysis, a test environment is similarly characterized by two parameters: its discrimination power and its similarity with other environments. This paper investigates the relationships between GGE biplots based on different data scaling methods and the theory of indirect selection, and introduces a heritability-adjusted (HA) GGE biplot. We demonstrate that the vector length of an environment in the HA-GGE biplot approximates the square root heritability (\( \sqrt H \)) within the environment and that the cosine of the angle between the vectors of two environments approximates the genetic correlation (r) between them. Moreover, projections of vectors of test environments onto that of a target environment approximate values of \( r\sqrt H \), which are proportional to the predicted genetic gain expected in the target environment from indirect selection in the test environments at a constant selection intensity. Thus, the HA-GGE biplot graphically displays the relative utility of environments in terms of selection response. Therefore, the HA-GGE biplot is the preferred GGE biplot for test environment evaluation. It is also the appropriate GGE biplot for genotype evaluation because it weights information from the different environments proportional to their within-environment square root heritability. Approximation of the HA-GGE biplot by other types of GGE biplots was discussed.