On ARGs, pedigrees, and genetic relatedness matrices.

Area of Science:

• Genetics
• Computational Biology
• Bioinformatics

Background:

• Genetic relatedness is crucial for population, quantitative, and association studies.
• Existing methods like genotype and pedigree relatedness matrices have limitations.
• Ancestral recombination graph (ARG)-based relatedness offers improved performance but faces computational challenges.

Purpose of the Study:

• To unify diverse definitions of genetic relatedness under a single framework.
• To introduce "branch relatedness" and the "branch genetic relatedness matrix" (BRGM).
• To develop efficient algorithms for computing with BRGM, enabling large-scale genomic analyses.

Main Methods:

• Defined "branch relatedness" using an additive model for quantitative traits.
• Explored the relationship between branch relatedness and pedigree relatedness (kinship) via a case study.
• Derived an efficient algorithm for BRGM-vector products using tree sequence encoding of ARGs, avoiding explicit matrix formation.
• Developed a randomized principal components algorithm for tree sequences scalable to millions of genomes.

Main Results:

• Consolidated various relatedness notions into the concept of branch relatedness.
• Developed an efficient algorithm for computing with the BRGM, leveraging sparse genome encoding via tree sequences.
• Demonstrated scalability to mega-scale genomic datasets with the new algorithms.
• Implemented all algorithms in the open-source tskit Python package.

Conclusions:

• Branch relatedness provides a unifying framework for genetic relatedness.
• Efficient algorithms based on tree sequences enable large-scale computations with BRGM.
• This work facilitates advanced population and quantitative genetics analyses on massive genomic datasets.