Partially ordered Reeb graphs, tree decompositions, and phylogenetic networks

Mathematical Biology Seminar
Wednesday, October 9, 2019 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Anastasios Stefanou – Mathematical Biosciences Institute, Ohio State University –
Daniel Cruz

Inspired by the interval decomposition of persistence modules and the extended Newick format of phylogenetic networks, we show that, inside the larger category of partially ordered Reeb graphs, every Reeb graph with n leaves and first Betti number s, is equal to a coproduct of at most 2s trees with (n + s) leaves. An implication of this result, is that Reeb graphs are fixed parameter tractable when the parameter is the first Betti number. We propose partially ordered Reeb graphs as a natural framework for modeling time consistent phylogenetic networks.  We define a notion of interleaving distance on partially ordered Reeb graphs which is analogous to the notion of interleaving distance for ordinary Reeb graphs. This suggests using the interleaving distance as a novel metric for time consistent phylogenetic networks.