An analytical framework to derive the expected precision of genomic selection

Area of Science:

• Quantitative genetics
• Animal breeding
• Genomic selection

Background:

• Existing formulae for genomic estimated breeding values (GEBV) precision rely on simplifying assumptions.
• These assumptions include no linkage disequilibrium, unrelated individuals, and complete genetic control by genotyped loci.
• Previous approximations for GEBV precision were not always clearly defined.

Purpose of the Study:

• To develop a unified framework for deriving equations to predict GEBV precision.
• To establish a method for predicting GEBV precision based on reference population size, heritability, and the number of quantitative trait loci (QTL).

Main Methods:

• Utilized Taylor polynomial expansion to approximate the exact formulation of GEBV precision.
• Employed first and second-order approximations for precision estimation.
• Validated approximations through simulations under defined assumptions.

Main Results:

• First-order approximations improved upon existing GEBV prediction equations.
• Second-order approximations yielded highly accurate GEBV precision estimates compared to simulations.
• The framework allows for generalizations, including multi-trait genomic evaluation.

Conclusions:

• The proposed equations offer a method for a priori comparison of breeding schemes.
• Further refinements are needed for complex, real-world scenarios.
• The framework provides a valuable tool for predicting GEBV precision.