Multi-environment trial of 5 barley varieties, 6 locations, 2 years

Usage

data("fisher.barley")

Format

A data frame with 60 observations on the following 4 variables.

yield: yield, bu/ac
gen: genotype/variety, 5 levels
env: environment/location, 2 levels
year: year, 1931/1932

Details

Trials of 5 varieties of barley were conducted at 6 stations in Minnesota during the years 1931-1932.

This is a subset of Immer's barley data. The yield values here are totals of 3 reps (Immer gave the average yield of 3 reps).

Source

Ronald Fisher (1935). The Design of Experiments.

References

George Fernandez (1991). Analysis of Genotype x Environment Interaction by Stability Estimates. Hort Science, 26, 947-950.

F. Yates & W. G. Cochran (1938). The Analysis of Groups of Experiments. Journal of Agricultural Science, 28, 556-580, table 1. https://doi.org/10.1017/S0021859600050978

G. K. Shukla, 1972. Some statistical aspects of partitioning of genotype-environmental components of variability. Heredity, 29, 237-245. Table 1. https://doi.org/10.1038/hdy.1972.87

Examples

if (FALSE) { # \dontrun{

  library(agridat)
  data(fisher.barley)
  dat <- fisher.barley

  libs(dplyr,lattice)
  # Yates 1938 figure 1. Regression on env mean
  # Sum years within loc
  dat2 <- aggregate(yield ~ gen + env, data=dat, FUN=sum)
  # Avg within env
  emn <- aggregate(yield ~ env, data=dat2, FUN=mean)
  dat2$envmn <- emn$yield[match(dat2$env, emn$env)]
  xyplot(yield ~ envmn, dat2, group=gen, type=c('p','r'),
         main="fisher.barley - stability regression",
         xlab="Environment total", ylab="Variety mean",
         auto.key=list(columns=3))


  # calculate stability according to the sum-of-squares approach used by
  # Shukla (1972), eqn 11. match to Shukla, Table 4, M.S. column
  # also matches fernandez, table 3, stabvar column
  libs(dplyr)
  dat2 <- dat
  dat2 <- group_by(dat2, gen,env)
  dat2 <- summarize(dat2, yield=sum(yield)) # means across years
  dat2 <- group_by(dat2, env)
  dat2 <- mutate(dat2, envmn=mean(yield)) # env means
  dat2 <- group_by(dat2, gen)
  dat2 <- mutate(dat2, genmn=mean(yield)) # gen means
  dat2 <- ungroup(dat2)
  dat2 <- mutate(dat2, grandmn=mean(yield)) # grand mean
  # correction factor overall
  dat2 <- mutate(dat2, cf = sum((yield - genmn - envmn + grandmn)^2))
  t=5; s=6 # t genotypes, s environments
  dat2 <- group_by(dat2, gen)
  dat2 <- mutate(dat2, ss=sum((yield-genmn-envmn+grandmn)^2))
  # divide by 6 to scale down to plot-level
  dat2 <- mutate(dat2, sig2i = 1/((s-1)*(t-1)*(t-2)) * (t*(t-1)*ss-cf)/6)
  dat2[!duplicated(dat2$gen),c('gen','sig2i')]    
  ##       <chr>     <dbl>
  ## 1 Manchuria  25.87912
  ## 2  Peatland  75.68001
  ## 3  Svansota  19.59984
  ## 4     Trebi 225.52866
  ## 5    Velvet  22.73051

  if(require("asreml", quietly=TRUE)) {
    # mixed model approach gives similar results (but not identical)
    libs(asreml,lucid)

    dat2 <- dat
    dat2 <- dplyr::group_by(dat2, gen,env)
    dat2 <- dplyr::summarize(dat2, yield=sum(yield)) # means across years
    dat2 <- dplyr::arrange(dat2, gen)
    
    # G-side
    m1g <- asreml(yield ~ gen, data=dat2,
                  random = ~ env + at(gen):units,
                  family=asr_gaussian(dispersion=1.0))
    m1g <- update(m1g)
    summary(m1g)$varcomp[-1,1:2]/6
    #                            component std.error
    # at(gen, Manchuria):units  33.8145031  27.22721
    # at(gen, Peatland):units   70.4489092  50.52680
    # at(gen, Svansota):units   25.2728568  21.92919
    # at(gen, Trebi):units     231.6981702 150.80464
    # at(gen, Velvet):units     13.9325646  16.58571
    # units!R                    0.1666667        NA
    
    # R-side estimates = G-side estimate + 0.1666 (resid variance)
    m1r <- asreml(yield ~ gen, data=dat2,
                  random = ~ env,
                  residual = ~ dsum( ~ units|gen))
    m1r <- update(m1r)
    summary(m1r)$varcomp[-1,1:2]/6
    #                     component std.error
    # gen_Manchuria!R  34.00058  27.24871
    # gen_Peatland!R   70.65501  50.58925
    # gen_Svansota!R   25.42022  21.88606
    # gen_Trebi!R     231.85846 150.78756
    # gen_Velvet!R     14.08405  16.55558
  }
  
} # }