agridat (version 1.8.1)

john.alpha: Alpha lattice design of spring oats

Description

Alpha lattice design of spring oats

source

John JA, Williams ER. (1995) Cyclic and computer generated designs, Chapman and Hall, London. Page 146.

Details

A spring oats trial grown in Craibstone, near Aberdeen. There were 24 varities in 3 replicates, each consisting of 6 incomplete blocks of 4 plots. Planted in a resolvable alpha design. The plots were laid out in a single line.

References

Piepho, H.P. and M{"o}hring, J. (2007), Computing heritability and selection response from unbalanced plant breeding trials, Genetics, 177, 1881--1888.

Examples

dat <- john.alpha

# RCB (no incomplete block)
m0 <- lm(yield ~ 0 + gen + rep, data=dat)

# Block fixed (intra-block analysis) (bottom of table 7.4 in John)
m1 <- lm(yield ~ 0 + gen + rep + rep:block, dat)
anova(m1)

# Block random (combined inter-intra block analysis)
require(lme4)
m2 <- lmer(yield ~ 0 + gen + rep + (1|rep:block), dat)
anova(m2)
print(VarCorr(m2), comp=c("Variance","Std.Dev."))
## Groups    Name        Variance Std.Dev.
## rep:block (Intercept) 0.061945 0.24889
## Residual              0.085225 0.29193


# Variety means.  John and Williams table 7.5.  Slight, constant
# difference for each method as compared to John and Williams.
means <- data.frame(rcb=coef(m0)[1:24],
                    ib=coef(m1)[1:24],
                    intra=fixef(m2)[1:24])

# Heritability calculation of Piepho & Mohring, Example 1
require(asreml)
m3 <- asreml(yield ~ 1 + rep, data=dat, random=~ gen + rep:block)
sg2 <- summary(m3)$varcomp[1,'component']
vblup <- predict(m3, classify="gen")$pred$avsed ^ 2
m3 <- asreml(yield ~ 1 + gen + rep, data=dat, random = ~ rep:block)
vblue <- predict(m3, classify="gen")$pred$avsed ^ 2
# H^2 = .803
sg2 / (sg2 + vblue/2)
# H^2c = .809
1-(vblup / 2 / sg2)