A Simple Model to Deal with Sire by Treatment Interactions When Sires Are Related

Abstract The assumption that var ( hs ) = I σ hs 2 is not valid when sires are related. A more logical assumption is that the variance is I ⊗ A σ hs 2 . This result is derived from the use of an equivalent multiple-trait model. This procedure was extended to a more complicated model involving treatments and random herds within treatments. A small simulation trial demonstrated that σ hs 2 is underestimated if the I σ hs 2 model is used when the true model should be I ⊗ A σ hs 2 .