Were, A: the

additive genetic relationship matrix; [[sigma].sup.2.sub.a11], [[sigma].sup.2.sub.a12], [[sigma].sup.2.sub.a21], [[sigma].sup.2.sub.a22], are additive genetic (co)variances for the traits under consideration; [[sigma].sup.2.sub.e11], [[sigma].sup.2.sub.e12], [[sigma].sup.2.sub.e21], [[sigma].sup.2.sub.e22] are residual (co)variances for the traits; and I is the identity matrix.

The model of MBLUP: (Eq.) where y is vector of trait phenotype value, v is random rector of QLT allelic effects with mean 0 and variance-covariance matrix (Eq.) (G is the gametic relationship matrix at the QTL, (Eq.) is the QTL allelic variance ), u is the random rector of breeding values with mean 0 and variance-covariance matrix (Eq.) (A is the

additive genetic relationship matrix, (Eq.) is the additive genetic variance), e is rector of residual effects with mean 0 and variance-covariance matrix (Eq.) (I is a rector of one's ), W and Z are the incidence matrices of v and u.

where [F.sub.i] is the inbreeding coefficient of individual i, [a.sub.ii] is the

additive genetic relationship between individual i and itself.

The terms [r'.sub.a] [bar.[A.sub.t+1(a,a)]][r.sub.a] and [r'.sub.a] [bar.[A.sub.t+1(a,b)]][r.sub.b] are influenced by selection in year t, where the former represents the average

additive genetic relationship among new progenies, and the second term represents the average

additive genetic relationship between new progenies and other older animals (age class 2 to q).

Where, I is the identity matrix, [[sigma].sup.2.sub.s] and [[sigma].sub.h.sup.2] is the variance of the random sy and htm effect, respectively, A is the matrix of

additive genetic relationships among animals, [cross product] is the Kronecker product, P and G are covariance matrices for permanent environmental and additive genetic effects, respectively, R is the diagonal matrix of the form I[[sigma].sub.3.sup.2], and [sigma].sub.3.sup.2] is the residual variance.