Technical note: Acceleration of sparse operations for average-information REML analyses with supernodal methods and...

Area of Science:

• Animal Breeding and Genetics
• Computational Biology
• Quantitative Genetics

Background:

• Average-information REML (Restricted Maximum Likelihood) is crucial for genetic parameter estimation in animal breeding.
• Existing software often faces computational bottlenecks, limiting analysis of large datasets.
• Efficient mixed-model equation solving is essential for genomic evaluations.

Purpose of the Study:

• To identify and resolve computational bottlenecks in average-information REML software.
• To enhance the efficiency of setting up and solving mixed-model equations.
• To improve the performance of sparse matrix operations in genetic analyses.

Main Methods:

• Implemented a hash table with a faster hash function for sparse matrix storage.
• Optimized sparse matrix structures for trace calculations.
• Replaced the traditional FSPAK sparse matrix package with the supernodal YAMS package.
• Tested refinements on 23 diverse animal models (single-trait, multiple-trait, maternal, random regression) using phenotypic and genomic data.

Main Results:

• Mixed-model equation setup completed successfully for all analyses.
• Hash format accelerated trace calculations up to 67 times faster, especially with genomic data.
• The YAMS package was on average over 10 times faster than FSPAK.
• YAMS demonstrated greater advantages for large datasets and complex models, including genomic effects.

Conclusions:

• Refinements effectively removed computational bottlenecks in average-information REML programs.
• The new methods significantly improve the speed and scalability of genetic analyses.
• These improvements are applicable to general average-information REML software for animal breeding and genetics.