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

Abstract

The assumption that var(hs) = IOns is not valid when sires are related. A more logical assumption is that the variance is [I O A] O~s. 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 O~s is underestimated if the IOns model is used when the true model should be I1 Q A] O~s.