Predictions of the accuracy of genomic prediction: connecting R(2), selection index theory, and Fisher information

BACKGROUND: Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) when combining information sources have been developed based on selection index theory (SIT) and on Fisher information (FI). These two approaches have resulted in slightly different results when considering the combination of pedigree and genomic information. Here, we clarify this apparent contradiction, both for the combination of pedigree and genomic information and for the combination of subpopulations into a joint reference population. RESULTS: First, we show that existing expressions for the squared accuracy of GEBV can be understood as a proportion of the variance explained. Next, we show that the apparent discrepancy that has been observed between accuracies based on SIT vs. FI originated from two sources. First, the FI referred to the genetic component that is captured by the marker genotypes, rather than the full genetic component. Second, the common SIT-based derivations did not account for the increase in the accuracy of GEBV due to a reduction of the residual variance when combining information sources. The SIT and FI approaches are equivalent when these sources are accounted for. CONCLUSIONS: The squared accuracy of GEBV can be understood as a proportion of the variance explained. The SIT and FI approaches for combining information for GEBV are equivalent and provide identical accuracies when the underlying assumptions are equivalent.