[DMO] Mark Jones: Reconstructing phylogenetic networks from DNA under Markov models of evolution

13 October 2023 14:00 till 15:00 - Location: Timmanzaal LB01.170 | Add to my calendar

In this talk, I will discuss the new research project that Leo van Iersel, Niels Holtgrefe and I are starting on (along with Steven Kelk and Martin Frohn at the university of Maastricht).

In phylogenetics, the primary goal is to infer the evolutionary history of a set of species, given access only to the DNA data of their present-day successors. Mathematically speaking, we wish to reconstruct an unknown directed acyclic graph (the phylogenetic network), given a sequence of vectors that map each leaf to one of 4 states {A,C,G,T} (the DNA data). Such data is generated under a certain probabilistic model, that assumes genetic data is inherited from one's parents with some (unknown) probability of mutation.

Using algebraic invariants, it is possible to show that, at least for some classes of network, it is possible to reconstruct the network topology with extremely high confidence (in the sense that almost every possible output from a given network is vanishingly improbably for any other network). Algebraic statistics thus presents a powerful tool for network reconstruction. However finding these invariants is very time-consuming, and only practical for very small networks.
On the other hand, graph theory techniques developed by Leo and others allow us to reconstruct the network from its smaller subnetworks, without saying anything about how to find those smaller networks. Our aim is to combine these algebraic and graph theoretical approaches, in order to prove reconstructibility results for much larger classes of phylogenetic networks.

I'll give an overview of the central problem, the algebraic and combinatorial techniques involved, the results we have so far and future goals.