The calculation of exact reliabilities involving the inversion of mixed model equations poses a heavy computational challenge when the system of equations is large. This has prompted the development of different approximation methods. We give an overview of the various methods and computational approaches in calculating reliability from the era before the animal model to the era of single-step genomic models. The different methods are discussed in terms of modeling, development, and applicability in large dairy cattle populations. The paper also describes the problems faced in reliability computation. Many details dispersed throughout the literature are presented in this paper. It is clear that a universal solution applicable to every model and input data may not be possible, but we point out several efficient and accurate algorithms developed recently for a variety of very large genomic evaluations.
Keywords: dairy cattle; estimated breeding values; reliability computation; single-step genomic models.
The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).