A general and efficient representation of ancestral recombination graphs

Abstract

As a result of recombination, adjacent nucleotides can have different paths of genetic inheri-tance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). New developments have made it possible to infer ARGs at scale, enabling many new applications in population and statistical genetics. This rapid progress, however, has led to a substantial gap opening between theory and practice. Standard mathematical formalisms, based on exhaustively detailing the “events” that occur in the history of a sample, are insufficient to describe the outputs of current methods. Moreover, we argue that the underlying assumption that all events can be known and precisely estimated is fundamentally unsuited to the realities of modern, population-scale datasets. We propose an alternative mathematical formulation that encompasses the outputs of recent methods and can capture the full richness of modern large-scale datasets. By defining this ARG encoding in terms of specific genomes and their intervals of genetic inheritance, we avoid the need to exhaustively list (and estimate)allevents. The effects of multiple events can be aggregated in different ways, providing a natural way to express many forms of approximate and partial knowledge about the recombinant ancestry of a sample.

Inferring the geographic history of recombinant lineages using the full ancestral recombination graph

“…An ARG is graphical representation of the genealogical history of a set of sample genomes that may have undergone recombination in the past (Wong et al, 2023). As the history of the samples at each site can be depicted as a tree, an ARG weaves together these histories based upon their shared structure to represent the history of the samples across the entire genome.…”

“…We estimated the locations of these ancestors using our method (applied using six different window sizes) and compared to the averaging-up approach (Wohns et al, 2022). For the averaging-up method, we first simplified our ARG to its corresponding succinct tree sequence (Kelleher et al, 2018;Wong et al, 2023). We first calculated the error between estimates of the most likely location of an ancestor and its true location (Figure 6A).…”

“…It is commonly displayed as 1) a sequence of trees with each tree representing the history of a continuous block of the genome or 2) a single directed acyclic graph with annotated edges corresponding to their genomic intervals (see Fig 5A for an example of each). While the two representations can be interchangeable, tree sequences often lack the recombination events that tie the trees together and are further simplified, removing this equivalency (Wong et al, 2023). ARGs are an incredibly rich source of information about the history of the sample (Harris, 2019;Hejase et al, 2020;Lewanski et al, 2023).…”

A geographic history of human genetic ancestry

“…Although such detailed pedigree information is rarely available (but see Aguillon et al (2017) and Anderson-Trocmé et al (2023)), it nevertheless is possible to learn about the pedigree ancestors that are shared among individuals in a sample. This is because genetic relationships between samples, as well as the identities of the shared ancestors via whom they are related, are encoded in an interwoven collection of gene genealogies called an ancestral recombination graph (ARG) (Griffiths and Marjoram, 1997; Lewanski et al, 2024; Wong et al, 2023).…”

“…Our method, called (geographic ancestor inference algorithm), efficiently infers the geographic locations of the shared ancestors of a modern, georeferenced sample. We apply to a tree sequence of humans sampled in Europe, Asia, the Middle East, and Africa (Wong et al, 2023), and are able to reconstruct the geographic history of human ancestry over the last two million years.…”