Comparing tree shapes: beyond symmetry

This paper describes two types of problems related to tree shapes, as well as algorithms that can be used to solve these problems. The first problem is that of comparing the similarity of the unlabelled shapes instead of merely their degree of balance, in a manner analogous to that routinely used to compare topologies for labelled trees. There are possible practical applications for this comparison, such as determining, based on tree shape similarity alone, whether the taxa in two phylogenies are likely to have a correspondence (e.g. hosts and parasites with high specificity). It is shown that tree balance is insufficient for this task and that standard measures of topological difference (Robinson–Foulds distances, SPR distances or retention indices of the matrices representing the trees, MRPs) can be easily adapted to the problem. The second type of problem is to determine whether taxa of uncertain matching unique to two different phylogenies could correspond to each other (e.g. the same species in larvae and adults of metamorphic animals, fossils known from different body parts). This second problem can be solved by either relabelling taxa in such a way that the number of consensus nodes is maximized, or relabelling taxa in such a way that the sum of the number of steps in the MRP of each tree mapped onto the other is minimum.