A Pseudo-Absorption Strategy for Solving Animal Model Equations for Large Data Files

¹ Station de Génétique Quantitative et Appliquée, C.R.J. Institut National de la Recherche Agronomique, F-78350 Jouy-en-Josas, France

Iterative Gauss-Seidel or Jacobi methods have been extensively used worldwide to solve mixed model equations arising in genetic evaluation, but convergence rates have been very low and central memory requirements high for most applications of animal models with large data files. A new computing algorithm is proposed that is especially adapted to dairy cattle evaluation using all lactations, with group effects for unknown parents only, and without stringent limitations on the number of fixed effects included in the model. The iterative procedure takes advantage of the known structure of the coefficient matrix after absorption of permanent environmental effects. The proposed strategy, although more complex to implement than classical iterative methods, does not require computers with extremely large central memory and appears to have a satisfactory convergence rate. The method is illustrated by a numerical example dealing with milk yield evaluation of the Normande breed (2,019,137 females).