GBLUP

GBLUP, or Genomic Best Linear Unbiased Prediction, is a statistical approach used to predict genetic merit in individuals using dense genome-wide marker data. It extends the classical BLUP framework by incorporating information about realized relationships derived from molecular markers rather than relying solely on a pedigree-based relationship matrix.

GBLUP fits a linear mixed model where observed phenotypes are modeled as the sum of fixed effects, additive genetic effects, and residual error. The additive genetic effects are assumed to follow a multivariate normal distribution with variance proportional to a genomic relationship matrix G, instead of the pedigree-based numerator relationship matrix A. The model is typically written as y = Xb + Zu + e, with u ~ N(0, Gσ_g^2) and e ~ N(0, Iσ_e^2).

Construction of G commonly uses SNP genotype data. A widely used formulation is VanRaden's method: G = (M − P)(M − P)' / sum 2p_i(1 − p_i), where M is the centered genotype matrix and p_i is the allele frequency at marker i. Other variants and scaling schemes exist.

Applications and advantages: GBLUP enables genomic selection by providing genomic estimated breeding values (GEBVs). It captures realized relatedness, can operate without complete pedigree data, and often increases accuracy for young or low-heritability traits. It is widely used in animal and plant breeding and in research.

Limitations and considerations: GBLUP assumes additive genetic effects and relies on marker density, reference population size, and marker quality. Population structure and non-additive effects can bias estimates. Computationally, large datasets require efficient software and high-performance hardware, though specialized tools exist (e.g., BLUPF90, Sommer, BGLR).