where, At denotes the matrix of additive genetic relationship among animals in year t; [c.
Inbreeding increases on average within new progenies equal half the increase of the average additive genetic relationship among selected parents (Falconer and Mackay, 1996).
Combining equation (3), (4), (5) and (6) yields a restriction on the average additive genetic relationship in a population with different lifetimes between sire and dam:
As described by Meuwissen and Sonesson (1998), this paper also controls the increase of average additive genetic relationship for parents selected by constraining the r'[bar.
t+1]] is a matrix with the average additive genetic relationships within age classes on the diagonals and between age classes on the off-diagonals.