Gene tree and species trees. An example of an unrooted gene tree G with three multifurcations and a species tree S. The gene tree G is depicted with a star topology, and it has one star of type M2 and three stars of type M1. Every edge e of G is decorated with the duplication cost D(G
, S) (note that the rooting G
is not refined). Observe, that the optimal edge (empty edge) is adjacent to a leaf labelled by a. Rooting at this edge yields the duplication cost 0.