On ARGs, pedigrees, and genetic relatedness matrices.

Area of Science:

• Genetics
• Computational Biology
• Bioinformatics

Background:

• Genetic relatedness is crucial for population, quantitative, and association genetics studies.
• Genetic Relatedness Matrices (GRMs) store pairwise relatedness but face computational challenges (quadratic time/space complexity).
• Existing GRMs include pedigree, genotype, and Ancestral Recombination Graph (ARG)-based definitions, with ARG-GRMs showing improved population structure capture.

Purpose of the Study:

• To unify diverse definitions of genetic relatedness under a single framework, introducing "branch relatedness" and the "branch GRM".
• To develop efficient computational methods for large-scale GRM operations, particularly for ARG-based relatedness.
• To enable scalable analysis of genomic datasets, including millions of individuals.

Main Methods:

• Introduced "branch relatedness" and the "branch GRM" using an additive model for quantitative traits.
• Developed an efficient algorithm to compute products involving the branch GRM and a vector without explicit GRM formation, leveraging tree sequence encoding of ARGs.
• Implemented a randomized principal components algorithm for tree sequences, scalable to millions of genomes.

Main Results:

• Demonstrated the relationship between branch relatedness and pedigree relatedness through a French-Canadian cohort case study.
• The derived algorithm significantly reduces computational complexity for branch GRM operations.
• The randomized principal components algorithm effectively scales to mega-scale genomic datasets.

Conclusions:

• Consolidated various genetic relatedness concepts into the unified "branch relatedness" framework.
• Leveraging ARG tree sequence encoding provides efficient, scalable algorithms for branch GRM computations.
• Enabled large-scale genomic analyses previously intractable due to computational limitations.