Competition experiment in beans with height measurements

data("besag.beans")

Format

A data frame with 152 observations on the following 6 variables.

gen: genotype / variety
height: plot height, cm
yield: plot yield, g
row: row / block
rep: replicate factor
col: column

Details

Field beans of regular height were grown beside shorter varieties. In each block, each variety occurred once as a left-side neighbor and once as a right-side neighbor of every variety (including itself). Border plots were placed at the ends of each block. Each block with 38 adjacent plots. Each plot was one row, 3 meters long with 50 cm spacing between rows. No gaps between plots. Spacing between plants was 6.7 cm. Four blocks (rows) were used, each with six replicates.

Plot yield and height was recorded.

Kempton and Lockwood used models that adjusted yield according to the difference in height of neighboring plots.

Field length: 4 plots * 3m = 12m

Field width: 38 plots * 0.5 m = 19m

Source

Julian Besag and Rob Kempton (1986). Statistical Analysis of Field Experiments Using Neighbouring Plots. Biometrics, 42, 231-251. Table 6. https://doi.org/10.2307/2531047

References

Kempton, RA and Lockwood, G. (1984). Inter-plot competition in variety trials of field beans (Vicia faba L.). The Journal of Agricultural Science, 103, 293--302.

Examples

# \dontrun{

library(agridat)

data(besag.beans)
dat = besag.beans

libs(desplot)
desplot(dat, yield ~ col*row,
        aspect=12/19, out1=row, out2=rep, num=gen, cex=1, # true aspect
        main="besag.beans")


libs(reshape2)
# Add a covariate = excess height of neighbors
mat <- acast(dat, row~col, value.var='height')
mat2 <- matrix(NA, nrow=4, ncol=38)
mat2[,2:37] <- (mat[,1:36] + mat[,3:38] - 2*mat[,2:37])
dat2 <- melt(mat2)
colnames(dat2) <- c('row','col','cov')
dat <- merge(dat, dat2)
  
# Drop border plots
dat <- subset(dat, rep != 'R0')
  
libs(lattice)
# Plot yield vs neighbors height advantage
xyplot(yield~cov, data=dat, group=gen,
       main="besag.beans",
       xlab="Mean excess heights of neighbor plots",
       auto.key=list(columns=3))
  
# Trial mean.
mean(dat$yield) # 391 matches Kempton table 3
#> [1] 390.9722
  
# Mean excess height of neighbors for each genotype
# tapply(dat$cov, dat$gen, mean)/2 # Matches Kempton table 4

# Variety means, matches Kempton table 4 mean yield
m1 <- lm(yield ~ -1 + gen, dat)
coef(m1)
#>   genDwarf   genMaris genMetissa  genMinica  genStella genTopless 
#>   318.7500   434.1667   387.7083   456.2500   469.5833   279.3750 

# Full model used by Kempton, eqn 5.  Not perfectly clear.
# Appears to include rep term, perhaps within block
dat$blk <- factor(dat$row)
dat$blkrep <- factor(paste(dat$blk, dat$rep))
m2 <- lm(yield ~ -1 + gen + blkrep + cov, data=dat)
coef(m2) # slope 'cov' = -.72, while Kempton says -.79
#>    genDwarf    genMaris  genMetissa   genMinica   genStella  genTopless 
#> 271.9249148 304.9869194 314.3474168 362.8740025 331.7998182 186.9650396 
#>  blkrep1 R2  blkrep1 R3  blkrep1 R4  blkrep1 R5  blkrep1 R6  blkrep2 R1 
#>   9.6257870  90.1207546 130.3503148 153.5628935 133.5867917  74.2635231 
#>  blkrep2 R2  blkrep2 R3  blkrep2 R4  blkrep2 R5  blkrep2 R6  blkrep3 R1 
#>  61.9201251  92.8503148 134.6257870 188.8163519  98.6716990  44.1666667 
#>  blkrep3 R2  blkrep3 R3  blkrep3 R4  blkrep3 R5  blkrep3 R6  blkrep4 R1 
#>  69.0339629 119.5169815  94.8792454 165.7974860  89.6616343  74.3962268 
#>  blkrep4 R2  blkrep4 R3  blkrep4 R4  blkrep4 R5  blkrep4 R6         cov 
#>  53.5509444  71.5578612  96.0150970 152.1855326  93.3094351  -0.7245278 

# }