Multi-environment trial of wheat susceptibile to powdery mildew
Resistance of wheat to powdery mildew
data("lillemo.wheat")A data frame with 408 observations on the following 4 variables.
gengenotype, 24 levels
envenvironrment, 13 levels
scorescore
scalescale used for score
The data are means across reps of the original scores. Lower scores indicate better resistance to mildew.
Each location used one of four different measurement scales for scoring resistance to powdery mildew: 0-5 scale, 1-9 scale, 0-9 scale, percent.
Environment codes consist of two letters for the location name and two digits for the year of testing. Location names: CA=Cruz Alta, Brazil. Ba= Bawburgh, UK. Aa=As, Norway. Ha=Hamar, Norway. Ch=Choryn, Poland. Ce=Cerekwica, Poland. Ma=Martonvasar, Hungary. Kh=Kharkiv, Ukraine. BT=Bila Tserkva, Ukraine. Gl=Glevakha, Ukraine. Bj=Beijing, China.
Note, Lillemo et al. did not remove genotype effects as is customary when calculating Huehn's non-parametric stability statistics.
In the examples below, the results do not quite match the results of Lillemo. This could easily be the result of the original data table being rounded to 1 decimal place. For example, environment 'Aa03' had 3 reps and so the mean for genotype 1 was probably 16.333, not 16.3.
Used with permission of Morten Lillemo.
Electronic data supplied by Miroslav Zoric.
Morten Lillemo, Ravi Sing, Maarten van Ginkel. (2011). Identification of Stable Resistance to Powdery Mildew in Wheat Based on Parametric and Nonparametric Methods Crop Sci. 50:478-485. https://doi.org/10.2135/cropsci2009.03.0116
None.
library(agridat)
data(lillemo.wheat)
dat <- lillemo.wheat
# Change factor levels to match Lillemo
dat$env <- as.character(dat$env)
dat$env <- factor(dat$env,
levels=c("Bj03","Bj05","CA03","Ba04","Ma04",
"Kh06","Gl05","BT06","Ch04","Ce04",
"Ha03","Ha04","Ha05","Ha07","Aa03","Aa04","Aa05"))
# Interesting look at different measurement scales by environment
libs(lattice)
qqmath(~score|env, dat, group=scale,
as.table=TRUE, scales=list(y=list(relation="free")),
auto.key=list(columns=4),
main="lillemo.wheat - QQ plots by environment")
# ----------------------------------------------------------------------------
## Not run:
# Change data to matrix format
libs(reshape2)
datm <- acast(dat, gen~env, value.var='score')
# Environment means. Matches Lillemo Table 3
apply(datm, 2, mean)
# Two different transforms within envts to approximate 0-9 scale
datt <- datm
datt[,"CA03"] <- 1.8 * datt[,"CA03"]
ix <- c("Ba04","Kh06","Gl05","BT06","Ha03","Ha04","Ha05","Ha07","Aa03","Aa04","Aa05")
datt[,ix] <- apply(datt[,ix],2,sqrt)
# Genotype means of transformed data. Matches Lillemo table 3.
round(rowMeans(datt),2)
# Biplot of transformed data like Lillemo Fig 2
libs(gge)
biplot(gge(datt, scale=FALSE), main="lillemo.wheat")
# Median polish of transformed table
m1 <- medpolish(datt)
# Half-normal prob plot like Fig 1
# libs(faraway)
# halfnorm(abs(as.vector(m1$resid)))
# Nonparametric stability statistics. Lillemo Table 4.
huehn <- function(mat){
# Gen in rows, Env in cols
nenv <- ncol(mat)
# Corrected yield. Remove genotype effects
# Remove the following line to match Table 4 of Lillemo
mat <- sweep(mat, 1, rowMeans(mat)) + mean(mat)
# Ranks in each environment
rmat <- apply(mat, 2, rank)
# Mean genotype rank across envts
MeanRank <- apply(rmat, 1, mean)
# Huehn S1
gfun <- function(x){
oo <- outer(x,x,"-")
sum(abs(oo)) # sum of all absolute pairwise differences
}
S1 <- apply(rmat, 1, gfun)/(nenv*(nenv-1))
# Huehn S2
S2 <- apply((rmat-MeanRank)^2,1,sum)/(nenv-1)
out <- data.frame(MeanRank,S1,S2)
rownames(out) <- rownames(mat)
return(out)
}
round(huehn(datm),2) # Matches table 4
# I do not think phenability package gives correct values for S1
# libs(phenability)
# nahu(datm)
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