Workbench for Ancestral Recombination Graph Summation

The Ancestral Recombination Graph (ARG) is the graph that describes the relationship of a set of homologous sequences subject to recombination.  It was first introduced by Griffiths (1981) and Hudson (1983). The two basic events in an ARG are coalescent and recombination events. An evolutionary history can be translated into an ARG by starting in the present and going backwards in time until all positions of the sequences have found one single ancestor. Going back in time, sequences encounter coalescences and recombinations. Coalescent events will merge sequences that are identical, reducing the sample size by one.  Recombinations will redistribute a single sequence to two sequences, where one sequence will carry the material to the left of the recombination point and the other the material to the right of that point. In most analysis the ARG ignores that sequences are in individuals and thus describes a population of sequences, not of individuals with sequences.