In (a)–(d) the ranked species tree topology is ( ( ( A , B )
, C )
, ( D , E )
. (a) The ranked gene tree matches the ranked species tree. (b) The (ranked or unranked) gene tree does not match the species tree, and there is an incomplete lineage sorting event (a deep coalescence) because the lineages from species A and B fail to coalesce more recently than s2. (c) The gene tree and species tree have the same unranked topology but have different ranked topologies, as D and E coalesce in the gene tree more recently than A and B, while A and B is the most recent divergence in the species tree. The gene tree in (c) has ranked topology (((A,B)3,C)2,(D,E)4)1. In (c), there are no incomplete lineage sorting events (no deep coalescences); however, there is an extra lineage at time s3 which leads to the gene tree and species tree having different rankings. In (c), all coalescences occur in the most recent possible interval consistent with the ranked gene tree, and we have ℓ1 = 2,ℓ2 = 3,ℓ3 = 5,ℓ4 = 5, and g1 = 2, g2 = 3, g3 = 5, g4 = 5. (d) A gene tree with the same ranked topology as the gene tree in (c) but with coalescences occurring in different intervals.