Abstract

A short note about GGE and GGB biplots.

R setup

library("knitr")
knitr::opts_chunk$set(fig.align="center", fig.width=6, fig.height=6)
options(width=90)

An example of a GGE (genotype plus genotype-by-environment) biplot similar to figure 12 of Yan and Tinker (2006).

library(agridat)
## The desplot and gge functions are now in the 'agrifun' package.
data(yan.winterwheat)
dat1 <- yan.winterwheat

library(gge)
m1 <- gge(yield~gen*env, dat1, scale=FALSE)
biplot(m1, title="yan.winterwheat - GGE biplot",
       flip=c(1,0), origin=0, hull=TRUE)

Laffont, Hanafi, and Wright (2007) showed how to partition the sums-of-squares simultaneously along the principal component axes and along ‘G’ and ‘GxE’ axes.

plot(m1, title="yan.winterwheat")

The mosaic plot above shows that the first principal component axis is capturing almost all of the variation between genotypes, so that a projection of the genotype markers onto the first principal component axis is a good overall representation of the rankings of the genotypes.

Laffont, Wright, and Hanafi (2013) presented GGB (genotype plus genotype-by-block of environments) biplots, which are useful to enhance the view of mega-environments consisting of multiple locations.

library(agridat)
data(crossa.wheat)
dat2 <- crossa.wheat

# Define mega-environment groups of locations
dat2$eg <- ifelse(is.element(dat2$loc,
                             c("KN","NB","PA","BJ","IL","TC",
                               "JM","PI","AS","ID","SC","SS",
                               "SJ","MS","MG","MM")), "Grp1", "Grp2")

library(gge)
# Specify env.group as column in data frame
m2 <- gge(yield~gen*loc, dat2, env.group=eg, scale=FALSE)
biplot(m2, title="crossa.wheat - GGB biplot")

References

Laffont, Jean-Louis, Mohamed Hanafi, and Kevin Wright. 2007. “Numerical and Graphical Measures to Facilitate the Interpretation of GGE Biplots.” Cs 47: 990–96. doi:10.2135/cropsci2006.08.0549.

Laffont, Jean-Louis, Kevin Wright, and Mohamed Hanafi. 2013. “Genotype Plus Genotype-by-Block of Environments Biplots.” Crop Science 53 (6): 2332–41. doi:10.2135/cropsci2013.03.0178.

Yan, Weikai, and Nicholas A Tinker. 2006. “Biplot Analysis of Multi-Environment Trial Data: Principles and Applications.” Canadian Journal of Plant Science 86: 623–45. doi:10.4141/P05-169.