You have to fit an appropriate model that allows you to fit the
interaction between random effects and treatments/populations. Basically
you need to test for the interaction between fixed and random effects.
Your sire/dam model makes this tricky because it will involve
genotype by 'environment' interactions as well as other interactions.
So you might want to consider an animal model.
The easiest case is just the model where you just fit sire
and the sire by treatment as random effects (or animal). It is necessary
to define the appropriate variance/covariance structures. Then somehow
find the appropriate test of the sire by treatment variance. If you do a
likelihood ratio test with the basic sire model, it will be a mixture
of Chi-square distributions with different degrees of freedom.
The effect of dam nested within sire brings in issues about your
assumptions (dominance and maternal effects) and model. If there is a
genotype by treatment interaction then it is present in both the sire
by treatment and dam by treatment interactions. The problems arise if
there are other reasons for this interaction than the genotype.
The problem with treating treatments as different traits is that you have
to fit a constrained matrix to the random effects. It is not clear to me
what the appropriate covariance matrices should be.
> I wonder if it is possible to test if genetic covariances (or rather
> genetic covariance matrices) differ between two treatments (or
> populations). For example, a model that looks like TRA TRB TRC TRD ~ Trait
> Tr.Group !r Tr.Sire Tr.Sire.Dam for two different populations (Group is
> not the population factor). What I then would like to test is if Tr.Sire
> differs between the Pops. Any suggestions on how to do this with ASREML?
> One idea could be to incorporate the Pop factor in some way and test the
> differences in likelihood between a model were Pop (and its interaction
> with Tr.Sire) was constrained to be equal and alternatively free, but how
> to do this?
> Best regards,
> Patrik Waldmann
> University of Oulu
> Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml
Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml