An analytical approach to sire-by-year interactions in direct and maternal genetic evaluation

The negative direct-maternal genetic correlation (r(dm)) for weaning weight is inflated when data are analyzed with model ignoring sire-by-year interactions (SY). An analytical study investigating the consequences of ignoring SY was undertaken. The inflation of negative correlation could be due to a functional relationship of design matrices for additive direct and maternal genetic effects to that for sire effects within which SY effects were nested. It was proven that the maternal genetic variance was inflated by the amount of reduction for sire variance; the direct genetic variance was inflated by four times the change for maternal genetic variance; and the direct-maternal genetic covariance was deflated by twice the change for maternal genetic variance. The findings were agreed to the results in previous studies.