Short communication: Calculating analytical reliabilities for single-step predictions.

Area of Science:

• Quantitative Genetics
• Animal Breeding
• Genomic Prediction

Background:

• Single-step genomic best linear unbiased prediction (ssGBLUP) is a widely used method for genomic prediction.
• Calculating the reliability of genomic predictions, especially with imputed genotypes, presents computational challenges.
• Understanding the contribution of ungenotyped animals to prediction accuracy is crucial for ssGBLUP.

Purpose of the Study:

• To reformulate ssGBLUP into an equivalent marker-oriented model.
• To investigate the theoretical aspects of calculating analytical reliabilities for ssGBLUP.
• To propose approximations for simplifying complex matrix operations in reliability calculations.

Main Methods:

• Reformulation of ssGBLUP into a marker-effect model including imputed genotypes.
• Derivation of prediction error variances for marker effects.
• Development of two approximation methods to reduce computational complexity.
• Implementation framework using standard animal model reliabilities.

Main Results:

• The reformulated marker-oriented model explicitly includes imputed genotypes and accounts for imputation error.
• Marker-oriented models are recommended for reliability calculations as the number of genotyped animals increases.
• Proposed approximations significantly reduce computational complexity while maintaining accuracy for reliability calculations.
• The effectiveness of the approach was demonstrated using Fleckvieh cattle data.

Conclusions:

• The marker-oriented reformulation of ssGBLUP provides a mechanistic understanding of how ungenotyped animals contribute information.
• The proposed approximations offer a computationally efficient way to calculate genomic prediction reliabilities.
• This work provides a valuable framework for implementing and improving ssGBLUP reliability estimations in routine evaluations.