A method is provided for constructing an ancestral recombination graph. A value K is received representing K extant units. M non-mixing segments are also received. K vertices V are generated. K lineages for each of M trees are associated with each of the K vertices. An ancestral recombination graph is constructed. To construct the ancestral recombination graph, there is repeated, until only one lineage survives for each of the M trees, a process that includes the following. A tree is randomly selected tree. A first vertex v1 and a second vertex v2 are randomly selected. Two adjoining segments in the M non-mixing segments of the first and second vertices are combined together into a single vertex. A separate vertex is generated for at least one remaining segment in each of the M non-mixing segments of the first and second vertices. The vertices V are updated to be vertices that are non-interior vertices.