A note on the application of diallel crosses for the analysis of genetic variation in natural populations.

The complete diallel cross among homozygous lines can be a useful tool to analyze the genetic architecture of natural populations. However, it represents the natural population only approximately, in particular if the number of lines is small and the analyzed traits exhibit inbreeding depression or other forms of directional dominance. Some incorrect expected mean squares that can be found in the literature suggest tests for genetic variance components that can be misleading under such circumstances. Expected mean squares for a factorial analysis and for a modified Hayman analysis are presented and the effect of the number of lines and directional dominance is discussed.