A method to obtain exact single-step GBLUP for non-genotyped descendants when the genomic relationship matrix of ancestors is not available

BACKGROUND: Single-step genomic best linear unbiased prediction (GBLUP) involves a joint analysis of individuals with genotype information, and their ancestors, descendants, or contemporaries, without recorded genotypes. Livestock applications typically represent populations with fewer individuals with genotypes relative to the number not genotyped. Most breeding programmes are structured, consisting of a nucleus tier in which selection drives genetic gains that are propagated through descendants that represent parents in multiplier and commercial tiers. In some cases, the genotypes in the nucleus tier are proprietary to a breeding company, and not publicly available for a whole industry analysis. Bayesian inference involves combining a defined description of prior information with new information to generate a posterior distribution that contains all available information on parameters of interest. A natural extension of Bayesian analysis would be to use information from the posterior distribution to define the prior distribution in a subsequent analysis. METHODS: We derive the mixed model equations for inference on breeding values for non genotyped individuals in that subset of the population that is of current interest, using only data on the performance of current individuals and their immediate pedigree, along with prior information defined from the posterior distribution of an external BLUP or single-step GBLUP analysis of the ancestors of the current population. DISCUSSION: Identical estimates of breeding values and their prediction error covariances for current animals of interest in the multiplier or commercial tier can be obtained without requiring neither the genomic relationship matrix nor genotypes of any of their ancestors in the nucleus tier, as can be obtained from a single analysis using pedigree, performance, and genomic information from all tiers. The Bayesian analysis of the current population does not require explicit information on unselected genotyped animals in the external population. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12711-022-00759-x.