Methods of Calculating Prediction Error Variance and Prediction Accuracy for Restricted Best Linear Unbiased...

Area of Science:

• Animal Breeding and Genetics
• Quantitative Genetics
• Statistical Genomics

Background:

• Accurate prediction of breeding values (BVs) is crucial for effective animal breeding programs.
• The restricted best linear unbiased prediction (RBLUP) method is widely used but lacks clear formulas for prediction error variance (PEV) and prediction accuracy (PA).
• This ambiguity hinders the precise formulation of breeding plans and prediction of selection response.

Purpose of the Study:

• To derive and clarify the formulas for PEV and PA within the RBLUP framework.
• To develop a practical method for calculating PEV and PA for RBLUP.
• To elucidate the relationship between RBLUP and ordinary best linear unbiased prediction (BLUP).

Main Methods:

• Derivation of PEV and PA formulas from restricted mixed model equations.
• Development of a computational method for easy calculation of PEV and PA under RBLUP.
• Mathematical derivation of the relationship between RBLUP and ordinary BLUP.

Main Results:

• The uniqueness of RBLUP for BVs was proven.
• Novel formulas for PEV and PA in RBLUP were successfully derived.
• An efficient method for calculating RBLUP-based PEV and PA was established.
• The relationship between RBLUP and ordinary BLUP was mathematically defined.

Conclusions:

• The derived formulas and calculation method significantly simplify PEV and PA assessment in RBLUP.
• This advancement facilitates more accurate prediction of selection response, especially when aiming for simultaneous trait improvement.
• The findings enhance the utility of the RBLUP method in practical breeding applications.