Recent developments in phylogenetic network reconstruction and beyond

Thursday, June 17 at 02:15am (PDT)
Thursday, June 17 at 10:15am (BST)
Thursday, June 17 06:15pm (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS17" time block.
Note: this minisymposia has multiple sessions. The second session is MS11-EVOP (click here).

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Guillaume Scholz (University of Leipzig, Germany), Katharina Huber (University of East Anglia, United Kingdom)


Phylogenetic is a burgeoning area at the interface between Mathematics (incl Computer Science and Probability Theory) and Molecular Biology concerned with developing mathematical methodology and algorithms to help understand molecular evolution. Although it has been around for some time resulting in numerous deep and beautiful mathematical results the vast amounts of data generated by current sequencing methods have given rise to some exciting new questions. These concern in particular the area of phylogenetic network reconstruction. Such a structure naturally generalises the notion of a phylogenetic tree by allowing for cycles to help accommodate reticulate evolutionary processes such as recombination which is of relevance for understanding virus evolution (e.g. Covid-19). The minisymposium will bring together researcher at various levels of the academic career spectrum to discuss recent developments in phylogenetic network reconstruction and beyond.

Steven Kelk

(Maastricht University, The Netherlands)
"Quantifying the dissimilarity of trees using phylogenetic networks and data reduction"
Purely topological methods for constructing rooted phylogenetic networks often operate by puzzling multiple incongruent trees together in a parsimonious fashion. Early results in this area established a link between the construction of networks and distance measures on pairs, or sets, of trees. In some cases 'pre-network' distance measures turned out to have an unexpected relevance when applied to network construction. Interestingly, it is not only the case that distance measures can help in constructing networks. In this talk I give a brief summary of recent work in which networks are used 'backwards' to establish improved results for the computation of computationally intractable distance measures. I will focus in particular on using networks to develop aggressive kernelization (i.e. data reduction / pre-processing) rules for computation of the NP-hard TBR (Tree Bisection and Reconnect) distance, and present some empirical results demonstrating the impact of these aggressive rules in practice. This is based on ongoing joint work with several authors.

Mike Steel

(University of Canterbury, New Zealand)
"Ranked tree-child networks"
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics. Although these networks have a number of attractive mathematical properties, many combinatorial questions concerning them remain intractable. However, endowing these networks with a biologically-relevant ranking structure yields mathematically tractable objects, which we term ranked tree-child networks (RTCNs). We explain how to derive exact and explicit combinatorial results concerning the enumeration and generation of these networks. We also explore probabilistic questions concerning the properties of RTCNs when they are sampled uniformly at random. These questions include the lengths of random walks between the root and leaves (both from the root to the leaves and from a leaf to the root); the distribution of the number of cherries in the network; and sampling RTCNs conditional on displaying a given tree.

Marc Hellmuth

(Stockholm University, Sweden)
"From modular decomposition trees to rooted median graphs"
The modular decomposition of a symmetric map $deltacolon Xtimes X to Upsilon$ (or, equivalently, a set of symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features of $delta$ in labeled trees. A map $delta$ is explained by a vertex-labeled rooted tree $(T,t)$ if the label $delta(x,y)$ coincides with the label of the last common ancestor of $x$ and $y$ in $T$, i.e., if $delta(x,y)=t(lca(x,y))$. Only maps whose modular decomposition does not contain prime nodes, i.e., the symbolic ultrametrics, can be explained in this manner. Here we consider rooted median graphs as a generalization to (modular decomposition) trees to explain symmetric maps. We first show that every symmetric map can be explained by ``extended'' hypercubes and half-grids. We then derive a a linear-time algorithm that stepwisely resolves prime vertices in the modular decomposition tree to obtain a rooted and labeled median graph that explains a given symmetric map $delta$. We argue that the resulting ``tree-like'' median graphs may be of use in phylogenetics as a model of evolutionary relationships.

Barbara Holland

(University of Tasmania, Australia)
"Modelling convergence and divergence of species in phylogenetic networks"
In a 2018 paper we gave a non-technical introduction to convergence–divergence models, a new modelling approach for phylogenetic data that allows for the usual divergence of lineages after lineage-splitting but also allows for taxa to converge, i.e. become more similar over time. We show that these models are sufficiently flexible that they have some interesting identifiability issues. Specifically, we show many 3-taxon data sets can be equally well explained by supposing violation of the molecular clock due to change in the rate of evolution along different edges, or by keeping the assumption of a constant rate of evolution but instead assuming that evolution is not a purely divergent process. Given the abundance of evidence that evolution is not strictly tree-like, this is an illustration that as phylogeneticists we need to think clearly about the structural form of the models we use. For cases with four taxa, we show that there will be far greater ability to distinguish models with convergence from non-clock-like tree models. This talk will describe the convergence-divergence model and discuss some potential applications.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.