\[
\newcommand{\mY}{\mathbf{Y}}
\newcommand{\mT}{\mathbf{T}}
\newcommand{\mS}{\mathbf{S}}
\newcommand{\mR}{\mathbf{R}}
\newcommand{\vg}{\mathbf{g}}
\newcommand{\E}{\mathrm{E}}
\newcommand{\Var}{\mathrm{Var}}
\newcommand{\Cov}{\mathrm{Cov}}
\]
Abstract
Simulated data with known effects show how well an analysis recovers them, which is useful in teaching, and how often its tests detect effects of a given size, which is the basis for planning an experiment. DiallelSim() draws the data and DiallelPower() estimates the power of the combining-ability tests.
Simulation and the number of replicates
DiallelSim() draws plot data from Griffing’s model with chosen standard deviations of the effects and returns the true effects with the data, so the estimates can be compared with the truth:
s <-
DiallelSim(
Parents = 6
, Method = 1
, Rep = 4
, Env = 1
, Mean = 100
, gca = 5
, sca = 3
, rec = 1
, gcaEnv = 0
, scaEnv = 0
, EnvSD = 0
, Block = 2
, Error = 4
, seed = 123
)
fs <-
Griffing(
y = y
, Rep = Rep
, Cross1 = Cross1
, Cross2 = Cross2
, data = s
, Method = 1
, Model = 1
, Reciprocal = c("combined", "split")[1]
)
round(x = cbind(true = attr(x = s, which = "truth")$gca, estimated = fs$GCA), digits = 2)
true estimated
1 -5.04 -5.01
2 -3.39 -3.14
3 5.56 6.09
4 -1.88 -1.58
5 -1.59 -2.87
6 6.34 6.51
DiallelPower() repeats such simulations to estimate the power of the gca and sca tests for several numbers of replicates, which helps to plan an experiment:
pw <-
DiallelPower(
Parents = 6
, Method = 2
, Rep = 2:5
, Model = 1
, gca = 1
, sca = 1.5
, rec = 0
, Error = 4
, nsim = 200
, alpha = 0.05
, seed = 1
)
pw
Rep Source Power SE
<int> <char> <num> <num>
1: 2 gca 0.320 0.03298485
2: 2 sca 0.115 0.02255826
3: 3 gca 0.425 0.03495533
4: 3 sca 0.270 0.03139267
5: 4 gca 0.605 0.03456696
6: 4 sca 0.340 0.03349627
7: 5 gca 0.665 0.03337477
8: 5 sca 0.370 0.03413942
Summary
DiallelSim() gives data with known effects for teaching and checking; DiallelPower() shows how many replicates detect gca and sca effects of a given size.
References
Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences, 9(4), 463–493.
