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Abstract
The increasing number of phenotyped and genotyped animals in genetic evaluations presents significant challenges in delivering routine, accurate breeding values to breeders. Overcoming these challenges requires developing new strategies, methods, and approximations to ensure high-quality predictions while minimizing computational demands. This dissertation addresses key issues, such as developing modeling strategies to account for differences in divergent populations and exploring the use of single-step genomic best linear unbiased prediction (ssGBLUP) as an alternative to traditional multistep methods. With the large number of genotyped animals, particularly in the dairy and beef industries, genomic evaluations have become increasingly complex, necessitating alternative strategies. One such approach is the use of indirect predictions (IP) instead of genomic estimated breeding values (GEBVs), offering a faster method to deliver breeding values for breeders by excluding animals that do not contribute to the evaluation and calculating their IP based on single nucleotide polymorphisms (SNP) effects derived from previous evaluations. Along with IP, methods for efficiently calculating reliabilities—a metric representing the amount of information used to predict breeding values—were also investigated. The computational cost of inverting matrices in the mixed model equations makes it impractical, even without genomic information. This challenge has driven the development of approximation methods to calculate reliabilities. However, complex models can overestimate these approximations, potentially compromising the selection process. Hence, developing correct approximation methods to improve the quality of reliabilities in genetic evaluations is imperative.