OPTItree · OPTItree: advanced models, methods, and algorithms for phylogenetic estimation

The OPTItree project seeks to enhance the scalability of mathematical models for computational phylogenetics, ensuring either provable correctness of the inferred phylogeny or certified solution quality. Determining the correct phylogeny is of crucial importance when studying the evolution of bacteria, viruses, and tumoral cells—especially in sensitive scenarios such as pandemics and tumorigenesis. To this end, this project investigates fundamental mathematical properties at the core of computational phylogenetics—a field at the intersection of mathematics, computer science, and molecular biology that develops models and algorithms to infer evolutionary relationships (phylogenies) from inherited traits such as DNA or genomes. These relationships are typically represented by OPTImal tree structures that are solutions to high-dimensional nonlinear optimization problems. Determining these optimal solutions is often very computationally expensive, and this severely limits the size of datasets that can be processed. To overcome this computational bottleneck, existing software relies on heuristic algorithms, which, however, cannot certify the correctness of the inferred trees. OPTItree focuses on a promising exact method based on the balanced minimum evolution criterion, known for its statistical consistency and cutting-edge theoretical foundations. Specifically, the project aims to: (i) provide deeper insight into the polyhedral structure underlying phylogenetic inference, in order to outperform the current state-of-the-art models that are capable of exactly solving only datasets of very small size for real-world applications; and (ii) design tailored approximation algorithms to efficiently find solutions of certified quality, to be used when exact methods cannot be applied.