Extension of the reduced animal model to single-step methods.

For a few decades, animal models (AMs) in the form of best linear unbiased prediction (BLUP) have been used for the genetic evaluation of animals. An equation system is set in the order of all the effects in the model, including all the animals in the pedigree. Solving these large equation systems has been a challenge. Reduced AM (RAM) was introduced in 1980, which allowed setting up equations for parents instead of all animals. That greatly reduced the number of equations to be solved. The RAM is followed by a back-solving step, in which progenies' breeding values are obtained conditional on parental breeding values. Initially, pedigree information was utilized to model genetic relationships between animals. With the availability of genomic information, genomic BLUP (GBLUP), single-step GBLUP (ssGBLUP), and single-step marker models were developed. Single-step methods utilize pedigree and genomic information for simultaneous genetic evaluation of genotyped and nongenotyped animals. There has been a shortage of studies on RAM development for genetic evaluation models utilizing genomic information. This study extended the concept of RAM from BLUP to the single-step methods. Using example data, three RAMs were described for ssGBLUP. The order of animal equations was reduced from the total number of animals to (1) genotyped animals and nongenotyped parents, (2) genotyped animals and nongenotyped phenotyped animals, and (3) genotyped animals and nongenotyped parents of phenotyped nongenotyped nonparents. Solutions for the remaining animals are obtained following a back-solving step. All the RAMs produced identical results to the full ssGBLUP. Advances in computational hardware have alleviated many computational limitations, but, on the other hand, the size of data is growing rapidly by the number of animals, traits, phenotypes, genotypes, and genotype density. There is an opportunity for a RAM comeback for the single-step methods to reduce the computational demands by reducing the number of equations.