Approximating reliabilities of indirect predictions using single nucleotide polymorphism effects from large single-step genomic best linear unbiased predictor evaluations

Reliability (REL) is a metric used to assess how accurately breeding values are predicted. Calculating theoretical REL requires the prediction error variance from the inverse of the coefficient matrix of the mixed model equations, which is computationally intensive for large populations or complex models. In such cases, REL are approximated. In routine genetic evaluations it is not feasible to evaluate animals received between evaluation cycles. As an interim solution, these individuals would rely on indirect predictions (IP) based on SNP effects, and their associated reliability approximated based on the variance of estimated SNP effects. This study aimed to approximate IP reliabilities when SNP effects are estimated from multi- and single-breed single-step genomic evaluations. Two reliability approximations were compared: (1) REL_IP, based on an approximated prediction error covariance (PEC) of estimated SNP effects, and (2) REL_GEBV, a benchmark REL calculated in routine genetic evaluations. In the multibreed analysis, the regression slope of REL_GEBV on REL_IP was ∼1, and the intercept was equal to zero for Holstein (HO). For Jersey (JE), slopes were 0.60 (males) and 0.78 (females), and intercepts were 0.32 (males) and 0.15 (females). For Brown Swiss (BS), slopes were 0.88 (males) and 0.82 (females), and intercepts were 0.03 (males) and 0.08 (females). Correlations between both reliabilities were higher than 0.96 for HO and BS, 0.79 (males) and 0.69 (females) for JE. In the single-breed analysis, JE showed no dispersion issues, with slopes of 1 and intercepts of zero, and correlations equal to 0.99 for both sexes. For BS, reliabilities were slightly under-dispersed, with slopes of 1.14 (males) and 1.08 (females). Additionally, single-breed evaluations yielded more consistent reliability averages within each breed. In contrast, multibreed evaluation showed that dominant breeds disproportionately influenced reliability estimates of smaller breeds, highlighting the importance of approximating the PEC within-breed to avoid biased reliability estimates.