agridat (version 1.8.1)

carmer.density: Maize yield-density model

Description

Maize yield-density model.

source

S G Carmer and J A Jackobs (1965). An Exponential Model for Predicting Optimum Plant Density and Maximum Corn Yield. Agronomy Journal, 57, 241--244

Details

Eight single-cross hybrids were in the experiment--Hy2xOh7 and WF9xC103 were included because it was believed they had optimum yields at relatively high and low popultions. Planted in 1963. Plots were thinned to 2, 4, 6, 8 plants per hill, giving densities 8, 16, 24, 32 thousand plants per acre. Hills were in rows 40 inches apart--one hill = 1/4000 acre. Split-plot design with 5 reps, density is main plot and subplot was hybrid.

Examples

dat <- carmer.density
dat$gen <- factor(dat$gen, levels=c('Hy2x0h7','WF9xC103','R61x187-2',
                             'WF9x38-11','WF9xB14','C103xB14',
                             '0h43xB37','WF9xH60'))
xyplot(yield~pop|gen, dat, pch=16, as.table=TRUE,
       main="carmer.density")

# Separate analysis for each hybrid
# Model: y = x * a * k^x.  Table 1 of Carmer and Jackobs.
out <- data.frame(a=rep(NA,8), k=NA)
preds <- NULL
rownames(out) <- levels(dat$gen)
newdat <- data.frame(pop=seq(2,8,by=.1))
for(i in levels(dat$gen)){
  print(i)
  dati <- subset(dat, gen==i)
  mi <- nls(yield ~ pop * a * k^pop, data=dati, start=list(a=10,k=1))
  out[i, ] <- mi$m$getPars()
  # Predicted values
  pi <- cbind(gen=i, newdat, pred= predict(mi, newdat=newdat))
  preds <- rbind(preds, pi)
}
# Optimum plant density is -1/log(k)
out$pop.opt <- -1/log(out$k)
round(out, 3)

require(latticeExtra)
xyplot(yield~pop|gen, dat, pch=16, as.table=TRUE,
       main="carmer.density models") +
xyplot(pred~pop|gen, preds, col='black', as.table=TRUE,
       type='l')

# A better approach might be to use nlme to fit an overall fixed-effect
# model with random deviations for each hybrid.