FIG. 4.

Example of two binary characters that are not compatible on a phylogenetic tree. Thus the parsimony score of the characters on any phylogenetic tree of six leaves has a cost of three or more. Shown in the figure is a network with one reticulate vertex with softwired and adjusted hardwired scores equal to two. This can be seen by the two dotted edges that allow one substitution each in different characters. While the first character has an additional substitution on the reticulate edge (11, 10), the second character has an additional substitution on the other reticulate edge (7, 10). Thus the two characters choose different optimal spanning trees (whose reticulate edges are shown in different colors with the corresponding character written next to them) inside the network, and the reticulate vertex 10 is not redundant. Hence, the score on this network is better than the score on any tree.