ALGORITHMS FOR SIMULATION OF ANIMAL-MODELS WITH MULTIPLE TRAITS AND WITH MATERNAL AND NONADDITIVE GENETIC-EFFECTS

The Choleski decomposition L(v) of the variance-covariance matrix V = L(v)L(v), can be used for simulation of genetic values for a populatio n of animals with known numerator and dominance relationship matrices, A and D. If the variances of additive and dominance genetic effects a re sigma(a)2 and sigma(d)3 and v(a) and v(d) are vectors of order of t he number of animals (N) of standard random normal values, then a = L( A)v(a) and d = L(D)v(d) are the vectors of simulated additive and domi nance genetic values for the N animals. The calculations to accumulate elements of a or d can be done one random normal value at a time. Sim ulation of the multiple trait analog can be done similarly by taking a dvantage of the direct product property of G(tN), the genetic covarian ce matrix for the t traits and N animals. With traits ordered within a nimal, L(GtN) = L(A) x L(G) where L(G) is the Choleski decomposition o f G, the matrix of genetic covariances among the traits and x is the d irect product operator. The pattern of accumulating the genetic values is such that the accumulation can be done sequentially, one vector of order, t, of standard random normal values at a time.