Supertree Algorithms for Nested Taxa

Most supertree algorithms combine collections of rooted phylogenetic trees with overlapping leaf sets into a single rooted phylogenetic tree. It is implicit in all these algorithms that the leaves of the rooted phylogenetic trees in the input collection, as a whole, represent non-nested taxa. Thus, for example, the “domestic dog” and “mammal” cannot be represented by two distinct leaves in such a collection because the former is nested inside the latter. In practice, however, one often wants to combine rooted trees in which taxa are nested. In other words, to combine rooted trees in which the leaves as well as some of the interior vertices are labeled. These interior labels represent taxa at a level higher than that of their descendants (e.g., families versus genera, or genera versus species). Moreover, it could happen that a leaf of one of the input trees represents a taxon that is represented by an interior label of another tree. In this chapter, we describe two supertree algorithms for combining rooted trees in which the leaves as well as some of the interior vertices are labeled. Called “rooted semi-labeled trees”, these trees are more general than rooted phylogenetic trees in that not only are their leaves labeled, but some of their interior vertices might be as well. Both algorithms are polynomial-time in the size of the input and are motivated by a problem posed by Page in an earlier chapter called “Taxonomy, Supertrees, and the Tree of Life”.