snijders.fusarium {agridat} | R Documentation

## Fusarium infection in wheat varieties

### Description

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).

### 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. http://doi.org/10.1007/BF00215729

Used with permission of Fred van Eeuwijk.

### References

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

### Examples

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

    aggregate(y ~ strain + year, dat, FUN=mean) # Match means in Snijders table 1

    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.
    require(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
    m2 <- aov(logit ~ year*strain + gen + gen:year + gen:strain, data=dat)
    anova(m2) # Match to VanEeuwijk table 5

    ## Not run:

    # GLM on untransformed data using logit link, variance mu^2(1-mu)^2
    require(gnm) # for 'wedderburn' family
    m2 <- glm(y ~ yrstr + gen, data=dat, family="wedderburn")
    anova(m2) # Main effects match VanEeuwijk table 6

    # Generalized AMMI-2 model. Matches VanEeuwijk table 6
    bilin2 <- gnm(y ~ yrstr + gen + instances(Mult(yrstr, gen), 2),
                  data=dat, family = wedderburn)
    # 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.

    ## End(Not run)

[Package agridat version 1.16 Index]