Submitted to: Meeting Abstract
Publication Type: Abstract Only
Publication Acceptance Date: 5/21/2008
Publication Date: 8/11/2008
Citation: Thallman, R.M. 2008. Challenges and opportunities in variance component estimation for animal breeding [abstract]. In: Proceedings of the Canadian Society of Animal Science Kennedy Conference on Quantitative Genetics and Animal Breeding, the Charles R. Henderson Lectureship in Statistics & Animal Breeding, August 11-12, 2008, Guelph, Ontario, Canada. 2008 CDROM.
Technical Abstract: There have been many advances in variance component estimation (VCE), both in theory and in software, since Dr. Henderson introduced Henderson’s Methods 1, 2, and 3 in 1953. However, many challenges in modern animal breeding are not addressed adequately by current algorithms and software. Examples include VCE from field data sets with tens or hundreds of millions of equations and VCE in models with many (co)variance parameters to be estimated (e.g., multiple trait models with more than 10 traits, whole genome selection, and microarray analyses). Opportunities to meet these challenges exist in the form of combining algorithms that have different properties (e.g., begin analyses with very fast approximate algorithms and finish them with relatively few rounds of algorithms that are exact, but with much greater computational effort per round). Approximate algorithms for which the degree of approximation can be progressively decreased (at the expense of computational effort) as the algorithm converges would be quite useful. A Monte Carlo (MC) algorithm with this property will be described. The MC algorithm approximates quantities of the form tr(A-1Cij) where tr is the trace operator, A-1 is the inverse numerator relationship matrix and Cij is an appropriate block of Henderson’s Mixed Model Equations (MME). Briefly, a set of observations with structure (design matrices) identical to the real data are simulated using the values of the variance components upon which tr(A-1Cij) is conditional and the MME are solved using right hand sides formed from the simulated observations. Quadratic forms of the solutions are set equal to their expected values to obtain approximate expressions for tr(A-1Cij). Average information approaches can enhance the MC algorithm and vice versa. A number of unexploited tools are available from which to design software that should meet current and future needs of animal breeders and quantitative geneticists.