Multi-environment trial of maize, half diallel

Half diallel of maize

data("lonnquist.maize")

Format

A data frame with 78 observations on the following 3 variables.

p1

parent 1 factor

p2

parent 2 factor

yield

yield

Details

Twelve hybrids were selfed/crossed in a half-diallel design. The data here are means adjusted for block effects. Original experiment was 3 reps at 2 locations in 2 years.

Source

J. H. Lonnquist, C. O. Gardner. (1961) Heterosis in Intervarietal Crosses in Maize and Its Implication in Breeding Procedures. Crop Science, 1, 179-183. Table 1.

References

Mohring, Melchinger, Piepho. (2011). REML-Based Diallel Analysis. Crop Science, 51, 470-478. https://doi.org/10.2135/cropsci2010.05.0272

C. O. Gardner and S. A. Eberhart. 1966. Analysis and Interpretation of the Variety Cross Diallel and Related Populations. Biometrics, 22, 439-452. https://doi.org/10.2307/2528181

Examples

# \dontrun{

  library(agridat)
  data(lonnquist.maize)
  dat <- lonnquist.maize
  dat <- transform(dat,
                   p1=factor(p1,
                             levels=c("C","L","M","H","G","P","B","RM","N","K","R2","K2")),
                   p2=factor(p2,
                             levels=c("C","L","M","H","G","P","B","RM","N","K","R2","K2")))
  
  libs(lattice)
  redblue <- colorRampPalette(c("firebrick", "lightgray", "#375997"))
  levelplot(yield ~ p1*p2, dat, col.regions=redblue,
            main="lonnquist.maize - yield of diallel cross")



  # Calculate the F1 means in Lonnquist, table 1
  # libs(reshape2)
  # mat <- acast(dat, p1~p2)
  # mat[upper.tri(mat)] <- t(mat)[upper.tri(mat)] # make symmetric
  # diag(mat) <- NA
  # round(rowMeans(mat, na.rm=TRUE),1)
  ##    C     L     M     H     G     P     B    RM     N     K    R2    K2
  ## 94.8  89.2  95.0  96.4  95.3  95.2  97.3  93.7  95.0  94.0  98.9 102.4


  # Griffings method
  # https://www.statforbiology.com/2021/stat_met_diallel_griffing/
  # libs(lmDiallel)
  # dat2 <- lonnquist.maize
  # dat2 <- subset(dat2,
  #                is.element(p1, c("M","H","G","B","K","K2")) &
  #                is.element(p2, c("M","H","G","B","K","K2")))
  # dat2 <- droplevels(dat2)
  # dmod1 <- lm(yield ~ GCA(p1, p2) + tSCA(p1, p2),
  #             data = dat2)
  # dmod2 <- lm.diallel(yield ~ p1 + p2, 
  #                     data = dat2, fct = "GRIFFING2")
  # anova.diallel(dmod1, MSE=7.1, dfr=60)
  ## Response: yield
  ##              Df Sum Sq Mean Sq F value    Pr(>F)    
  ## GCA(p1, p2)   5 234.23  46.846  6.5980 5.923e-05 ***
  ## tSCA(p1, p2) 15 238.94  15.929  2.2436   0.01411 *  
  ## Residuals    60          7.100                      

  
  # ----------

  # asreml4
  # Mohring 2011 used 6 varieties to calculate GCA & SCA
  # Matches Table 3, column 2
  d2 <- subset(dat, is.element(p1, c("M","H","G","B","K","K2")) &
                      is.element(p2, c("M","H","G","B","K","K2")))
  d2 <- droplevels(d2)
  libs(asreml,lucid)
  m2 <- asreml(yield~ 1, data=d2, random = ~ p1 + and(p2))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Fri Dec 17 15:17:47 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -42.1442       18.4535     20 15:17:47    0.0
#>  2      -42.0279       17.6444     20 15:17:47    0.0
#>  3      -41.9054       16.2198     20 15:17:47    0.0
#>  4      -41.9007       15.9433     20 15:17:47    0.0
  # vc(m2)
  ##     effect component std.error z.ratio      con
  ##  p1!p1.var     3.865     3.774     1   Positive
  ## R!variance    15.93      5.817     2.7 Positive
  
  # Calculate GCA effects
  m3 <- asreml(yield~ p1 + and(p2), data=d2)
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Fri Dec 17 15:17:47 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -34.0862       15.9294     15 15:17:47    0.0
  coef(m3)$fixed-1.462
#>               effect
#> p1_M        -1.46200
#> p1_H        -0.19950
#> p1_G        -2.16200
#> p1_B         1.48800
#> p1_K        -1.78700
#> p1_K2        4.12550
#> (Intercept) 91.77014
  # Matches Gardner 1966, Table 5, Griffing method

# }