Simulate diallel data

DiallelSim() simulates plot data of a diallel in randomized complete blocks, in one or several environments, from Griffing's model with random effects. It serves teaching (data with known effects) and the planning of experiments (see DiallelPower).

Usage

DiallelSim(
  Parents,
  Method,
  Rep,
  Env = 1,
  Mean = 0,
  gca,
  sca,
  rec = 0,
  gcaEnv = 0,
  scaEnv = 0,
  EnvSD = 0,
  Block = 0,
  Error,
  seed = NULL
)

Arguments

Parents: number of parents $P \geq 3$.
Method: Griffing's method, 1 to 4: which crosses are grown.
Rep: number of replicates (blocks) per environment.
Env: number of environments (default 1; the column Env is added when it is larger).
Mean: overall mean $\mu$.
gca, sca, rec: standard deviations of the gca, sca and reciprocal effects.
gcaEnv, scaEnv: standard deviations of the gca $\times$ environment and sca $\times$ environment effects (default 0).
EnvSD: standard deviation of the environment effects (default 0).
Block: standard deviation of the block effects (default 0).
Error: standard deviation of the plot errors $\sigma$.
seed: seed of the random numbers, or NULL (default) to leave the generator as it is.

Value

A data.frame with columns Cross1, Cross2, Rep, y (and Env), with the attribute "truth": a list with gca (vector), sca and rec (matrices) and Mean.

Details

The response of the plot of cross $i \times j$ in block $k$ of environment $e$ is $$y_{ijke} = \mu + g_i + g_j + s_{ij} + r_{ij} + \eta_e + (gE)_{ie} + (gE)_{je} + (sE)_{ije} + b_{ke} + \varepsilon_{ijke},$$ with independent normal effects of standard deviations gca, sca ($s_{ij} = s_{ji}$), rec ($r_{ij} = -r_{ji}$, Methods 1 and 3), gcaEnv, scaEnv, Block and Error; environment effects $\eta_e$ have standard deviation EnvSD. The gca, environment and block effects are centred to sum to zero and the sca effects to zero row and column sums over the full $P \times P$ table (Griffing's constraints of Methods 1 and 2). The true effects are returned as the attribute "truth".

Author

Muhammad Yaseen (myaseen208@gmail.com)

Examples

d <-
  DiallelSim(
      Parents = 6
    , Method  = 1
    , Rep     = 3
    , Env     = 1
    , Mean    = 100
    , gca     = 5
    , sca     = 3
    , rec     = 1
    , gcaEnv  = 0
    , scaEnv  = 0
    , EnvSD   = 0
    , Block   = 2
    , Error   = 4
    , seed    = 123
    )
head(d)
#>   Cross1 Cross2 Rep         y
#> 1      1      1   1  91.31074
#> 2      1      2   1  92.49970
#> 3      1      3   1 104.10394
#> 4      1      4   1  90.53502
#> 5      1      5   1  94.83385
#> 6      1      6   1 108.32714
attr(x = d, which = "truth")$gca
#>         1         2         3         4         5         6 
#> -5.038142 -3.386651  5.557778 -1.883222 -1.589325  6.339561 
fit <-
  Griffing(
      y          = y
    , Rep        = Rep
    , Cross1     = Cross1
    , Cross2     = Cross2
    , data       = d
    , Method     = 1
    , Model      = 1
    , Reciprocal = c("combined", "split")[1]
    )
cbind(true = attr(x = d, which = "truth")$gca, estimated = fit$GCA)
#>        true estimated
#> 1 -5.038142 -5.419897
#> 2 -3.386651 -2.793203
#> 3  5.557778  5.586346
#> 4 -1.883222 -1.615612
#> 5 -1.589325 -2.148496
#> 6  6.339561  6.390862