Overview of Genomic Prediction Methods and the Associated Assumptions on the Variance of Marker Effect, and on the Architecture of the Target Trait.

Genomic selection (GS) is a methodology that revolutionized the process of breeding improved genetic materials in plant and animal breeding programs. It uses predicted genomic values of the potential of untested/unobserved genotypes as surrogates of phenotypes during the selection process. Such that the predicted genomic values are obtained using exclusively the marker profiles of the untested genotypes, and these potentially can be used by breeders for screening the genotypes to be advanced in the breeding pipeline, to identify potential parents for next improvement cycles, or to find optimal crosses for targeting genotypes among others. Conceptually, GS initially requires a set of genotypes with both molecular marker information and phenotypic data for model calibration and then the performance of untested genotypes is predicted using their marker profiles only. Hence, it is expected that breeders would look at these values in order to conduct selections. Even though the concept of GS seems trivial, due to the high dimensional nature of the data delivered from modern sequencing technologies where the number of molecular markers (p) excess by far the number of data points available for model fitting (n; p ≫ n) a complete renovated set of prediction models was needed to cope with this challenge. In this chapter, we provide a conceptual framework for comparing statistical models to overcome the "large p, small n problem." Given the very large diversity of GS models only the most popular are presented here; mainly we focused on linear regression-based models and nonparametric models that predict the genetic estimated breeding values (GEBV) in a single environment considering a single trait only, mainly in the context of plant breeding.