Multi-environment trial of 5 barley varieties, 6 locations, 2 years
Multi-environment trial of 5 barley varieties, 6 locations, 2 years
data("fisher.barley")A data frame with 60 observations on the following 4 variables.
yieldyield, bu/ac
gengenotype/variety, 5 levels
envenvironment/location, 2 levels
yearyear, 1931/1932
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).
Ronald Fisher (1935). The Design of Experiments.
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
## Not run:
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))
if(0){
# 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$gen),c('gen','sig2i')]
## <chr> <dbl>
## 1 Manchuria 25.87912
## 2 Peatland 75.68001
## 3 Svansota 19.59984
## 4 Trebi 225.52866
## 5 Velvet 22.73051
}
libs(asreml,lucid) # asreml3
# mixed model approach gives similar results (but not identical)
dat2 <- dat
dat2 <- dplyr::group_by(dat2, gen,env)
dat2 <- dplyr::summarize(dat2, yield=sum(yield)) # means across years
dat2 <- dat2[order(dat2$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
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