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Some concepts
What is a biplot
The concept of biplot was first
developed by Gabriel (1971).
It is a scatter plot that graphically displays both the entries (e.g.,
cultivars) and the testers (e.g., environments) of a two-way data. In breeding
and genetics data, testers can also be traits, genetic markers, etc. When the
two-way data is subjected to singular value decomposition, it is decomposed
into three matrices: the singular value matrix, the entry eigenvector matrix,
and the tester eigenvector matrix. The singular value matrix is a diagonal
matrix, and can be somehow partitioned into the entry and tester eigenvector
matrices. After singular values are partitioned, the positions of the entries
in the biplot is defined by the entry eigenvector matrix and those of the
testers by the tester eigenvector matrix.
Properties of a
biplot
A
biplot graphically displays the two-way data and allows visualization of:
-
the
interrelationship among the entries
(e.g., genotypes),
-
the
interrelationship among testers (e.g., environments), and
-
the
interaction between entries and testers.
See References for more
in-depth information.
What is GGE
GGE stands
for genotype main effect (G) plus genotype by environment interaction (GE),
which is the only source of variation that is relevant to cultivar evaluation.
Mathematically, GGE is the genotype by environment data matrix after the
environment means are subtracted.
What is GGE biplot
A GGE
biplot is a biplot that displays the GGE of a genotype by environment two-way
data. The GGE biplot methodology originates from graphical analysis of
multi-environment variety trials (MET) data, but is equally applicable to all
other types of two-way data.
What are entries
and testers
Entry
and tester are the two factors in a two-way data. Entry is the factor to be
tested, and tester is the factor used to test. An entry is a level of the
entry factor, and a tester is a level of the tester factor. In genotype by
environment data, genotypes are entries and environments are testers. In
genotype by trait data, genotypes are entries and traits are testers. In
genotype by genetic marker data, genotypes are entries and markers are
testers. In convention, entries are presented as rows, and testers as columns
in a data matrix.
Here
is a biplot generated by
GGEbiplot. It has 18 cultivars (in blue) and 9 environments (in red).
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