Abstract

Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. One approach requires us to construct a phylogenetic network such that, for each cluster (i.e. clade) that is present in at least one input gene tree, at least one tree embedded in the network contains that cluster. This is often called the softwired cluster approach. Motivated by parsimony we might wish to construct such a network using as few reticulations as possible, or minimizing the maximum number of reticulations used in any “tangled” region of the network (known as the level of the network).

In this talk we present a number of new algorithmic results, both positive and negative, which emphasize the curious mathematical structure of the softwired cluster model. We also describe the relationship between our results and other recent results in constructing rooted phylogenetic networks. We conclude with a number of intruiging open questions.

This talk will be given by Steven Kelk, based on forthcoming joint work between Steven Kelk, Celine Scornavacca and Leo van Iersel.