Wheat yield in South Australia with serpentine row/col effects

An RCB experiment of wheat in South Australia, with strong spatial variation and serpentine row/column effects.

Format

A data frame with 330 observations on the following 5 variables.

col

column

row

row

rep

replicate factor, 3 levels

gen

wheat variety, 108 levels

yield

yield

Details

A randomized complete block experiment. There are 108 varieties in 3 reps. Plots are 6 meters long, 0.75 meters wide, trimmed to 4.2 meters lengths before harvest. Trimming was done by spraying the wheat with herbicide. The sprayer travelled in a serpentine pattern up and down columns. The trial was sown in a serpentine manner with a planter that seeds three rows at a time (Left, Middle, Right).

Field width 15 columns * 6 m = 90 m

Field length 22 plots * .75 m = 16.5 m

Used with permission of Arthur Gilmour, in turn with permission from Gil Hollamby.

Source

Arthur R Gilmour and Brian R Cullis and Arunas P Verbyla, 1997. Accounting for natural and extraneous variation in the analysis of field experiments. Journal of Agric Biol Env Statistics, 2, 269-293.

References

N. W. Galwey. 2014. Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance. Table 10.9

Examples

if (FALSE) { # \dontrun{

  library(agridat)
  data(gilmour.serpentine)
  dat <- gilmour.serpentine

  libs(desplot)
  desplot(dat, yield~ col*row,
          num=gen, show.key=FALSE, out1=rep,
          aspect = 16.5/90, # true aspect
          main="gilmour.serpentine")


  # Extreme field trend.  Blocking insufficient--needs a spline/smoother
  # xyplot(yield~col, data=dat, main="gilmour.serpentine")

  if(require("asreml", quietly=TRUE)) {
  
    libs(asreml,lucid)
    
    dat <- transform(dat, rowf=factor(row), colf=factor(10*(col-8)))
    dat <- dat[order(dat$rowf, dat$colf), ] # Sort order needed by asreml
    
    # RCB
    m0 <- asreml(yield ~ gen, data=dat, random=~rep)
    
    # Add AR1 x AR1
    m1 <- asreml(yield ~ gen, data=dat,
                 resid = ~ar1(rowf):ar1(colf))
    
    # Add spline
    m2 <- asreml(yield ~ gen + col, data=dat,
                 random= ~ spl(col) + colf,
                 resid = ~ar1(rowf):ar1(colf))
  
    # Figure 4 shows serpentine spraying
    p2 <- predict(m2, data=dat, classify="colf")$pvals
    plot(p2$predicted, type='b', xlab="column number", ylab="BLUP")
  
    # Define column code (due to serpentine spraying)
    # Rhelp doesn't like double-percent modulus symbol, so compute by hand
    dat <- transform(dat, colcode = factor(dat$col-floor((dat$col-1)/4)*4 -1))
    
    m3 <- asreml(yield ~ gen + lin(colf) + colcode, data=dat,
                 random= ~ colf + rowf + spl(colf),
                 resid = ~ar1(rowf):ar1(colf))
  
    # Figure 6 shows serpentine row effects
    p3 <- predict(m3, data=dat, classify="rowf")$pvals
    plot(p3$predicted, type='l', xlab="row number", ylab="BLUP")
    text(1:22, p3$predicted, c('L','L','M','R','R','M','L','L',
                               'M','R','R','M','L','L','M','R','R','M','L','L','M','R'))
    
    # Define row code (due to serpentine planting). 1=middle, 2=left/right
    dat <- transform(dat, rowcode = factor(row))
    levels(dat$rowcode) <- c('2','2','1','2','2','1','2','2','1',
                             '2','2','1','2','2','1','2','2','1','2','2','1','2')
    
    m6 <- asreml(yield ~ gen + lin(colf) + colcode +rowcode, data=dat,
                 random= ~ colf + rowf + spl(col),
                 resid = ~ar1(rowf):ar1(colf))
    plot(varioGram(m6), xlim=c(0:17), ylim=c(0,11), zlim=c(0,4000),
         main="gilmour.serpentine")
  }
  
} # }