Solving the Tree Containment Problem Using Graph Neural Networks

Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for instance, constructed from a DNA fragment showing tree-like evolution) is contained in the given phylogenetic network. In the general case, this is an NP-complete problem. We propose to solve it approximately using Graph Neural Networks. In particular, we propose to combine the given network and the tree and apply a Graph Neural Network to this network-tree graph. This way, we achieve the capability of solving the tree containment instances representing a larger number of species than the instances contained in the training dataset (i.e., our algorithm has the inductive learning ability). Our algorithm demonstrates an accuracy of over $95\%$ in solving the tree containment problem on instances with up to 100 leaves.

Constructing Phylogenetic Networks via Cherry Picking and Machine Learning

Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers of phylogenetic trees or are limited to severely restricted classes of networks. In this paper, we apply the recently-introduced theoretical framework of cherry picking to design a class of efficient heuristics that are guaranteed to produce a network containing each of the input trees, for datasets consisting of binary trees. Some of the heuristics in this framework are based on the design and training of a machine learning model that captures essential information on the structure of the input trees and guides the algorithms towards better solutions. We also propose simple and fast randomised heuristics that prove to be very effective when run multiple times. Unlike the existing exact methods, our heuristics are applicable to datasets of practical size, and the experimental study we conducted on both simulated and real data shows that these solutions are qualitatively good, always within some small constant factor from the optimum. Moreover, our machine-learned heuristics are one of the first applications of machine learning to phylogenetics and show its promise.