From linear models to deep learning: statistical advances in genomic selection for animal breeding.

Genomic selection (GS) has revolutionized animal breeding by accelerating genetic gain through genome-wide marker data. As genotyping technologies advance and data dimensionality grows, the statistical foundations of GS are shifting from classical linear frameworks, which assume additive genetic effects, toward advanced computational models that capture complex nonlinear relationships in genomic data. The commercialization of genotyping arrays for livestock and poultry, coupled with steadily declining sequencing costs, has led to an exponential increase in the availability of high-density genomic data. However, challenges persist, including scenarios where the number of genetic markers far exceeds the number of samples with phenotypic data, and the growing complexity of relationships within genomic data. These issues significantly limit the applicability of traditional evaluation models. In parallel, computational power has increased significantly over the last few decades, providing the capacity necessary for highly complex analyses. While traditional linear mixed models provide a robust framework for incorporating biological priors and modeling additive genetic effects, they often rely on simplified assumptions. In contrast, machine learning (ML) and deep learning (DL) algorithms, which do not rely on predefined parametric models, are well-suited to capturing complex nonlinear relationships and offer effective solutions to the aforementioned challenges. This review provides a comprehensive overview of GS methodologies. We first cover the statistical foundations of linear mixed and Bayesian models, and then survey modern ML and DL approaches. We discuss the assumptions, advantages, and limitations of each method and, by comparing the computational efficiency and predictive accuracy of these diverse approaches, aim to provide practical guidance for optimizing genomic evaluation strategies in the era of big data breeding.