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Algorithms for simulation of animal models with multiple traits and with maternal and non-additive genetic effects^*

L.D. Van Vleck

Roman L. Hruska U.S. Meat Anim. Res. Center, ARS, USDA, A218 Animal Sciences, Univ. of Nebraska, Lincoln, NE 68583-0908, USA

ABSTRACT

The Choleski decomposition Lv of the variance-covariance matrix V = L_yL_v' can be used for simulation of genetic values for a population of animals with known numerator and dominance relationship matrices, A and D. If the variances of additive and dominance genetic effects are s_a² and s_d² and va and vd are vectors of order of the number of animals (N) of standard random normal values, then a = L_AVa and d = L_DVd are the vectors of simulated additive and dominance 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. Simulation of the multiple trait analog can be done similarly by taking advantage of the direct product property of G_tN, the genetic covariance matrix for the t traits and N animals. With traits ordered within animal, L_GtN = L_A ⊕ L_G where L_G is the Choleski decomposition of G, the matrix of genetic covariances among the traits and ⊕ is the direct 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.

Keywords: algorithms; simulation; animal models; multiple traits; maternal genetic effects; non-additive genetic effects.

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* Published as Paper No. 9828, Journal Ser., Nebraska Agric. Res. Div., Univ. of Nebraska, Lincoln 68583-0908.