Multi-environment trial of wheat susceptibile to powdery mildew

Resistance of wheat to powdery mildew

data("lillemo.wheat")

Format

A data frame with 408 observations on the following 4 variables.

gen: genotype, 24 levels
env: environrment, 13 levels
score: score
scale: scale used for score

Details

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.

Source

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

References

None.

Examples


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")

# ----------------------------------------------------------------------------

# \dontrun{
  # 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)
#>      Bj03      Bj05      CA03      Ba04      Ma04      Kh06      Gl05      BT06 
#>  3.750000  4.729167  1.854167  4.362500  5.208333 17.875000 16.479167 14.708333 
#>      Ch04      Ce04      Ha03      Ha04      Ha05      Ha07      Aa03      Aa04 
#>  4.750000  4.416667 14.504167 18.416667 21.354167 16.270833 23.012500 12.833333 
#>      Aa05 
#> 24.062500 
  
  # 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)
#>  G01  G02  G03  G04  G05  G06  G07  G08  G09  G10  G11  G12  G13  G14  G15  G16 
#> 3.24 2.40 2.96 3.05 3.76 3.38 3.74 4.66 2.34 2.64 3.97 4.61 4.47 4.85 3.83 2.95 
#>  G17  G18  G19  G20  G21  G22  G23  G24 
#> 3.45 4.61 3.34 4.08 2.91 3.79 7.72 7.46 

  # 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)
#> 1: 337.6127
#> 2: 325.4158
#> Final: 324.2539
  # 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
#>     MeanRank    S1     S2
#> G01    12.00  7.01  36.12
#> G02    14.53  9.66  71.51
#> G03    13.29  7.59  41.72
#> G04    14.06  9.51  68.93
#> G05    11.00  7.26  38.50
#> G06    13.47  3.99  12.39
#> G07    12.29  6.66  33.22
#> G08    10.06  9.18  65.68
#> G09    14.47  7.21  38.01
#> G10    14.00  6.47  31.00
#> G11    10.88  7.47  41.74
#> G12    10.82  7.29  40.53
#> G13    10.88  8.97  62.49
#> G14    11.18  8.69  55.65
#> G15    13.12  7.34  39.99
#> G16    13.88  6.00  27.74
#> G17    11.88  6.97  35.74
#> G18    10.94  6.37  31.81
#> G19    14.24  5.40  21.32
#> G20    11.06  7.87  46.43
#> G21    14.88  7.96  48.99
#> G22    11.35  9.00  59.87
#> G23    13.00 11.85 117.12
#> G24    12.71 11.29 102.22
  
  # I do not think phenability package gives correct values for S1
  # libs(phenability)
  # nahu(datm)
  
# }