Computing procedures for genetic evaluation including phenotypic, full pedigree, and genomic information.

Area of Science:

• Animal Breeding and Genetics
• Quantitative Genetics
• Bioinformatics

Background:

• Current genomic evaluations often use multi-step procedures, leading to potential biases and errors.
• A single-step approach requires modifying the numerator relationship matrix (A) to H = A + A(Delta), but calculating H(-1) is computationally challenging for large pedigrees.

Purpose of the Study:

• To develop and evaluate an alternative mixed model equation formulation that avoids direct inversion of the H matrix.
• To enable efficient incorporation of genomic information into existing evaluations using modified relationship matrices.

Main Methods:

• Reformulated mixed model equations to use an alternative form applicable to singular H matrices.
• Employed conjugate gradient techniques (symmetric and nonsymmetric solvers) for equation solving.
• Analyzed 10.2 million Holstein scores using a repeatability model with simulated A(Delta).

Main Results:

• The alternative equations, when solved with nonsymmetric solvers, showed slightly better convergence than symmetric solvers for original equations, but at double the time per round.
• Convergence rates for alternative equations were lower (2-3 times) compared to original equations, depending on the size of A(Delta).
• The proposed methodology allows upgrading existing evaluations by incorporating genomic information expressed as modifications to the numerator relationship matrix.

Conclusions:

• The developed methodology provides a feasible approach for single-step genomic evaluations, especially when genomic information modifies the numerator relationship matrix.
• This method can help reduce biases and errors associated with traditional multi-step genomic evaluation procedures.
• Further research can explore generalizations to more complex genetic models.