Exploiting Low-Rank Structure in Genomic Relationship Matrices for Computationally Efficient Optimum Contribution Selection

Abstract

Motivation Optimum contribution selection (OCS) maximizes genetic gain under a constraint on relatedness. Genomic relationship matrices are dense, so the quadratic term costs O(n3) operations, and existing OCS software assumes pedigree sparsity. Results We replace the relationship matrix by its leading eigen-pairs, computed by randomized SVD, and solve OCS in factorized form. On Norway spruce population (n = 5,525), ranks 10–30 kept the exact objective within 1% of the optimum at 110– 330-fold speedups; on the QTL-MAS 2010 (n = 3,226), ranks up to 100 were needed (24–211-fold). The required rank rises as the diversity constraint loosens. Gain alone is a misleading accuracy check, since coancestry exceeded the optimum by up to 28%, so we choose the rank on the exact objective, which can be checked without a dense solve. The speedup comes from computing only the leading eigenpairs. We extend the factorization to robust OCS (18-fold). Availability and implementation Julia implementation, and examples are available at https://github.com/jonhar97/fastocs under the MIT license (archived at Zenodo, DOI 10.5281/zenodo.23214804). Contact jon.ahlinder@skogforsk.se Supplementary information Supplementary data are available at Bioinformatics online.