Hypothesis
A smaller GBLUP model restricted to genotyped animals, but carrying information from non-genotyped relatives, could replace full single-step GBLUP and cut the size and computational cost of livestock genetic evaluations.
What failed
Absorbing the equations of non-genotyped animals into those of genotyped animals did give solutions equivalent to full ssGBLUP, but the authors judge the model impractical: it pushes pedigree-based additive covariances into the residual covariance matrix, making it dense and hard to invert, and non-genotyped animals' breeding values cannot easily be back-solved from the genotyped ones. The alternative pseudo-phenotype route was itself hard to compute.
Broken assumption
An algebraically equivalent smaller model is also computationally cheaper to run.
Why
The residual covariance matrix stops being diagonal and its inverse is dense, which raises the cost of every downstream multiplication; the conditional structure needed for back-solving is lost.
From the published paper: Nilforooshan et al. Journal of Trial and Error, 2026. ↗CC BY