AbstractPlant-breeding programs are designed and operated over multiple cycles to systematically change the genetic makeup of plants to achieve improved trait performance for a Target Population of Environments (TPE). Within each cycle, selection applied to the standing genetic variation within a structured reference population of genotypes (RPG) is the primary mechanism by which breeding programs make the desired genetic changes. Selection operates to change the frequencies of the alleles of the genes controlling trait variation within the RPG. The structure of the RPG and the TPE has important implications for the design of optimal breeding strategies. The breeder’s equation, together with the quantitative genetic theory behind the equation, informs many of the principles for design of breeding programs. The breeder’s equation can take many forms depending on the details of the breeding strategy. Through the genetic changes achieved by selection, the cultivated varieties of crops (cultivars) are improved for use in agriculture. From a breeding perspective, selection for specific trait combinations requires a quantitative link between the effects of the alleles of the genes impacted by selection and the trait phenotypes of plants and their breeding value. This gene-to-phenotype link function provides the G2P map for one to many traits. For complex traits controlled by many genes, the infinitesimal model for trait genetic variation is the dominant G2P model of quantitative genetics. Here we consider motivations and potential benefits of using the hierarchical structure of crop models as CGM-G2P trait link functions in combination with the infinitesimal model for the design and optimization of selection in breeding programs.