Coalescent histories for a gene tree and a species tree with a matching labeled topology G = S = t. (A) A coalescent history. Arrows map the internal nodes of t = ((a, b), ((c, d), (e, f))) to the branches of t. (B) The gene tree topology G = t realized in the matching species tree S = t according to the coalescent history in (A). The mapping in (A) specifies the branches of the species tree (thick lines) where the coalescent events of the gene tree (thin lines) take place.