fisher.barley.Rd
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.
yield
yield, bu/ac
gen
genotype/variety, 5 levels
env
environment/location, 2 levels
year
year, 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
#> #>#>#> #>#>#> #>#>#> #># 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))#> Model fitted using the sigma parameterization. #> ASReml 4.1.0 Mon Jan 11 17:08:37 2021 #> LogLik Sigma2 DF wall cpu #> 1 -141.646 1.0 25 17:08:37 0.0 #> 2 -128.547 1.0 25 17:08:37 0.0 #> 3 -114.150 1.0 25 17:08:37 0.0 #> 4 -104.133 1.0 25 17:08:37 0.0 #> 5 -98.582 1.0 25 17:08:37 0.0 #> 6 -96.781 1.0 25 17:08:37 0.0 #> 7 -96.398 1.0 25 17:08:37 0.0 #> 8 -96.355 1.0 25 17:08:37 0.0 #> 9 -96.349 1.0 25 17:08:37 0.0 #> 10 -96.348 1.0 25 17:08:37 0.0#> Warning: Some components changed by more than 1% on the last iteration.#> Model fitted using the sigma parameterization. #> ASReml 4.1.0 Mon Jan 11 17:08:37 2021 #> LogLik Sigma2 DF wall cpu #> 1 -96.3476 1.0 25 17:08:37 0.0 #> 2 -96.3476 1.0 25 17:08:37 0.0#> 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# 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))#> Multi-section model using the sigma parameterization. #> ASReml 4.1.0 Mon Jan 11 17:08:37 2021 #> LogLik Sigma2 DF wall cpu #> 1 -106.401 1.0 25 17:08:37 0.0 (1 restrained) #> 2 -102.077 1.0 25 17:08:37 0.0 #> 3 -100.377 1.0 25 17:08:37 0.0 #> 4 -98.882 1.0 25 17:08:37 0.0 #> 5 -97.150 1.0 25 17:08:37 0.0 #> 6 -96.577 1.0 25 17:08:37 0.0 #> 7 -96.413 1.0 25 17:08:37 0.0 #> 8 -96.363 1.0 25 17:08:37 0.0 #> 9 -96.351 1.0 25 17:08:37 0.0 #> 10 -96.348 1.0 25 17:08:37 0.0 #> 11 -96.348 1.0 25 17:08:37 0.0#> Multi-section model using the sigma parameterization. #> ASReml 4.1.0 Mon Jan 11 17:08:37 2021 #> LogLik Sigma2 DF wall cpu #> 1 -96.3476 1.0 25 17:08:37 0.0 #> 2 -96.3476 1.0 25 17:08:37 0.0#> 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# 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 # }