Abstract

Computations in Animal Breeding

Ignacy Misztal, (University of Georgia), ` ignacy@uga.edu`, and

Romdhane Rekaya, (University of Georgia), ` rrelkaya@uga.edu`

**Abstract**

Most farm animals are selected for reproduction so that subsequent generations are more profitable. Information for selection includes field generated records such as weights measured at different ages, milk yields, or category of calving difficulty. Additional information is provided by pedigrees and recently by molecular markers. Statistical techniques, mainly related to mixed models, are used to separate genetic and environmental effects. System of equations may be very large. With animal populations of over 20 million and a few equations per animal, the total number of equations can exceed 100 million; however, the left hand side is usually very sparse. Two major types of computations are performed: estimation of variance components, which determine heritabilities and genetic and non-genetic relationships among various traits, and solving equations. Estimation of variance components is done either using likelihood based methods like REML, or Bayesian methods via Markov Chains. Finite methods used in computing involve sparse matrix factorization and inverse. Iterative methods involved mainly block SOR and Jacobi because of small memory requirements, although recently preconditioned conjugate gradient techniques are becoming more popular. Iterative strategies with a large number of equations are implemented matrix-free, where in each round of iteration; coefficients of the left hand side are recreated from the data. An entirely new set of problems in animal breeding arises from analysis of molecular data. System of equations become larger and less sparse. Another challenge facing animal breeders is the handling, mining and analysis of chip (microarray) data. Such data consist of the expression profiles of thousand of genes for potentially large animal populations.

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