Hi,
The competition model is one of the "genetic" models and
it works with a pedigree only.
Unfortunately, it can't be replicated using generic components because while you can have two generic components, they are assumed independent, whereas the competition model is a bi-variate joint model.
You could nevertheless do it, using a generic model for the direct genetic effect (incidence= indicator matrix for the genotypes, covariance: G matrix) and a second generic model for the indirect genetic effect (incidence= competition matrix, covariance: G matrix). It is not optimal, but you could assess the empirical correlation between the components empirically by looking at the corresponding breeding values.
Hope it helps
ƒacu.-
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