We start with a simpler reduced model to estimate genetic variance due to GCA effects. Unlike half-sib family data we saw in Chapter 4, writing the GCA effect for diallels is trickier, because the same parents are used as both female and male. We are going to model the parental GCA effects as identical whether they are transmitted through the male or female side of the parent. So, a progeny from parent A is modeled as having the GCA effect of parent A whether A was its male or female parent. We accomplish this restriction on the model by ‘overlaying’ the design matrix Z for males and female parents in the linear mixed model. This will estimate one common GCA variance and one GCA estimate for each parent regardless of how the parents were used.
The reduced linear model ignoring SCA effects is: