Fusarium infection in wheat varieties — snijders.fusarium • agridat

Infection in wheat by different strains of Fusarium.

Format

A data frame with 204 observations on the following 4 variables.

gen: wheat genotype
strain: fusarium strain
year: year
y: percent infected

Details

The data are the percent of leaf area affected by Fusarium head blight, averaged over 4-5 reps, for 17 winter wheat genotypes.

Van Eeuwijk fit a generalized ammi-2 model to this data. It is a generalized model in the sense that a link function is used, and is a non-linear AMMI model in that there are main effects for variety and year-strain, but additional multiplicative effects for the interactions.

Note, the value for strain F348 in 1988, gen SVP75059-32 should be 28.3 (as shown in VanEeuwijk 1995) and not 38.3 (as shown in Snijders 1991).

Used with permission of Fred van Eeuwijk.

Source

Snijders, CHA and Van Eeuwijk, FA. 1991. Genotype x strain interactions for resistance to Fusarium head blight caused by Fusarium culmorum in winter wheat. Theoretical and Applied Genetics, 81, 239--244. Table 1. https://doi.org/10.1007/BF00215729

References

Fred A van Eeuwijk. 1995. Multiplicative interaction in generalized linear models. Biometrics, 51, 1017-1032. https://doi.org/10.2307/2533001

Examples


library(agridat)

data(snijders.fusarium)
dat <- snijders.fusarium

aggregate(y ~ strain + year, dat, FUN=mean) # Match means in Snijders table 1
#>    strain year         y
#> 1    F329 1986  7.617647
#> 2    F348 1986  8.117647
#> 3     F39 1986 28.000000
#> 4    F436 1986 11.500000
#> 5    F329 1987  2.223529
#> 6    F348 1987  1.441176
#> 7     F39 1987 30.794118
#> 8    F436 1987  8.452941
#> 9    F329 1988  9.247059
#> 10   F348 1988  7.611765
#> 11    F39 1988 14.117647
#> 12   F436 1988 11.276471

dat <- transform(dat, y=y/100, year=factor(year), yrstr=factor(paste0(year,"-",strain)))

# Strain F329 shows little variation across years. F39 shows a lot.
libs(lattice)
dotplot(gen~y|strain, data=dat, group=year,
        main="snijders.fusarium : infection by strain",
        xlab="Fraction infected", ylab="variety",
        auto.key=list(columns=3))

# Logit transform
dat <- transform(dat, logit=log(y/(1-y)))
m1 <- aov(logit ~ yrstr + gen, data=dat) # Match SS in VanEeuwijk table 4
anova(m1)  # Match SS in VanEeuwijk table 4
#> Analysis of Variance Table
#> 
#> Response: logit
#>            Df  Sum Sq Mean Sq F value    Pr(>F)    
#> yrstr      11 224.092 20.3720  39.367 < 2.2e-16 ***
#> gen        16 171.600 10.7250  20.725 < 2.2e-16 ***
#> Residuals 176  91.079  0.5175                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
m2 <- aov(logit ~ year*strain + gen + gen:year + gen:strain, data=dat)
anova(m2) # Match to VanEeuwijk table 5
#> Analysis of Variance Table
#> 
#> Response: logit
#>             Df  Sum Sq Mean Sq  F value    Pr(>F)    
#> year         2  33.890  16.945  50.9711 8.226e-16 ***
#> strain       3 130.246  43.415 130.5964 < 2.2e-16 ***
#> gen         16 171.600  10.725  32.2615 < 2.2e-16 ***
#> year:strain  6  59.957   9.993  30.0593 < 2.2e-16 ***
#> year:gen    32  43.853   1.370   4.1223 4.049e-08 ***
#> strain:gen  48  15.312   0.319   0.9596    0.5541    
#> Residuals   96  31.914   0.332                       
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# \dontrun{

# GLM on untransformed data using logit link, variance mu^2(1-mu)^2
libs(gnm) # for 'wedderburn' family
#> 
#> Attaching package: 'gnm'
#> The following object is masked from 'package:asreml':
#> 
#>     wheat
#> The following object is masked from 'package:lattice':
#> 
#>     barley
m2 <- glm(y ~ yrstr + gen, data=dat, family="wedderburn")
anova(m2) # Main effects match VanEeuwijk table 6
#> Analysis of Deviance Table
#> 
#> Model: wedderburn, link: logit
#> 
#> Response: y
#> 
#> Terms added sequentially (first to last)
#> 
#> 
#>       Df Deviance Resid. Df Resid. Dev
#> NULL                    203     369.44
#> yrstr 11   150.85       192     218.60
#> gen   16   145.27       176      73.33

# Generalized AMMI-2 model. Matches VanEeuwijk table 6
bilin2 <- gnm(y ~ yrstr + gen + instances(Mult(yrstr, gen), 2),
              data=dat, family = wedderburn)
#> Initialising
#> Running start-up iterations..
#> Running main iterations.......................................................
#> Done
# plot(bilin2,1) # Resid vs fitted plot matches VanEeuwijk figure 3c
## anova(bilin2)
##                            Df Deviance Resid. Df Resid. Dev
## NULL                                         203     369.44
## yrstr                      11  150.847       192     218.60
## gen                        16  145.266       176      73.33
## Mult(yrstr, gen, inst = 1) 26   26.128       150      47.20
## Mult(yrstr, gen, inst = 2) 24   19.485       126      27.72

# Manually extract coordinates for biplot
cof <- coef(bilin2)
y1 <- cof[29:40]
g1 <- cof[41:57]
y2 <- cof[58:69]
g2 <- cof[70:86]
g12 <- cbind(g1,g2)
rownames(g12) <- substring(rownames(g12), 29)
y12 <- cbind(y1,y2)
rownames(y12) <- substring(rownames(y12), 31)
g12[,1] <- -1 * g12[,1]
y12[,1] <- -1 * y12[,1]
# GAMMI biplot.  Inner-products of points projected onto
# arrows match VanEeuwijk figure 4.  Slight rotation of graph is ignorable.
biplot(y12, g12, cex=.75, main="snijders.fusarium") # Arrows to genotypes.

# }