Inference of Phylogenetic Trees from the Knowledge of Rare Evolutionary Events

Rare events have played an increasing role in molecular phylogenetics as potentially homoplasy-poor characters.In this contribution we analyze the phylogenetic information content from a combinatorial point of view by consid-ering the binary relation on the set of taxa defined by the existence of a single event separating two taxa. We showthat the graph-representation of this relation must be a tree. Moreover, we characterize completely the relationshipbetween the tree of such relations and the underlying phylogenetic tree. With directed operations such as tandem-duplication-random-loss events in mind we demonstrate how non-symmetric information constrains the position ofthe root in the partially reconstructed phylogeny.