Andreas Dress - Cluster analysis and phylogenetic nets

Over the past fifteen or twenty years, it has become evident that phylogenetic relationships cannot always be represented appropriately by one single phylogenetic tree--sometimes because too many trees look almost equally plausible, sometimes just because of reticulated evolution.

To deal with data that do not support a single tree, standard tree-building methods have to be replaced by methods that allow for reticulation and, hence, construct (if necessary) rather nets than trees. A good starting point for developing such a method is the observation that Isbell's construction of injective hulls of metric spaces leads to trees if and only if one applies it to metrics that fit isometrically into (R-)trees, and leads to delta-hyperbolic, contractible, polyhedral cell complexes of higher dimension if this is not the case.

For this reason, Isbell's construction has been analysed and, actulally, scrutinized within the context of ``overlapping'' clustering for more than ten years by now, resulting in quite a few publications dealing with various aspects of this construction.

In the lecture, the basic definitions will be reviewed, new results (many of which have been obtained jointly with Katharina Huber and Vincent Moulton) will explained, and consequences for phylogenetic analysis will be discussed.