BLUPs

BLUPs, or Best Linear Unbiased Predictors, are statistical estimates of random effects in linear mixed models. In quantitative genetics and breeding programs, they are used to predict breeding values—the additive genetic merit of individuals—while accounting for fixed effects such as environment or management. BLUPs are obtained by combining information from relatives and performance data to separate genetic and non-genetic sources of variation.

The defining properties of BLUPs are that they are linear, unbiased, and have minimum mean squared error among all linear unbiased predictors, given specified variance components. In practice, the estimation relies on Henderson’s mixed-model equations, which combine data on individuals, their relationships, and the structure of fixed and random effects. Random effects often represent additive genetic merit, while fixed effects capture systematic factors.

BLUPs can be implemented with different relationship matrices. Pedigree-based BLUP (PBLUP) uses the expected relationships from pedigree data, whereas genomic BLUP (GBLUP) uses genomic relationships derived from marker data, potentially improving accuracy when pedigrees are incomplete. The two approaches are commonly distinguished as PBLUP and GBLUP; genomic methods are increasingly standard in modern breeding programs.

Applications include estimation of breeding values for selection decisions in animals and crops, evaluation of genetic merit across herds or fields, and more complex models that incorporate maternal effects, permanent environments, or genotype-by-environment interactions. Limitations include reliance on correct variance components and model assumptions (linearity, normality) and potential bias if non-additive effects or poorly specified structures are present. BLUPs remain a central tool for extracting additive genetic information from phenotypic and relational data.