| Summary: | As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance 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). Classical formalisms have
focused on mapping coalescence and recombination events to the nodes in an ARG. This approach is out of step with some
modern developments, however, which do not represent genetic inheritance in terms of these events or explicitly infer them. We
present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and
show how it generalises these classical treatments and encompasses the outputs of recent methods. We discuss nuances
arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly
growing field.
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