Comparing related phylogenetic trees

In phylogenetics, several classical distances exist to compare two phylogenetic trees. However, when the evolution in one tree has been influenced by the evolution in the other (e.g. two ecologically linked groups of organisms as hosts and their symbionts), other methods are more appropriate to compare the trees. Among the most used ones, there is phylogenetic tree reconciliation, i.e. mapping of one tree into the other according to certain rules, with a quantification of its quality; we refer to distances based on this concept as reconciliation distances. They bring useful information but are unfortunately NP-hard to be computed. It is then interesting to understand whether a polynomial phylogenetic tree distance is correlated to the reconciliation distances. In this communication we announce a systematic study to compare classical and reconciliation distances and we show that there is not much correlation between them. We then introduce a new distance that is instead correlated with the reconciliation distances and can be computed in polynomial time, hence it represents an efficient alternative to them.