Abstract
A new word, phylodynamics, was coined to emphasize the interconnection between phylogenetic properties, as observed for instance in a phylogenetic tree, and the epidemic dynamics of viruses, where selection, mediated by the host immune response, and transmission play a crucial role. The challenges faced when investigating the evolution of RNA viruses call for a virtuous loop of data collection, data analysis and modeling. This already resulted both in the collection of massive sequences databases and in the formulation of hypotheses on the main mechanisms driving qualitative differences observed in the (reconstructed) evolutionary patterns of different RNA viruses. Qualitatively, it has been observed that selection driven by the host immune response induces an uneven survival ability among co-existing strains. As a consequence, the imbalance level of the phylogenetic tree is manifestly more pronounced if compared to the case when the interaction with the host immune system does not play a central role in the evolutive dynamics. While many imbalance metrics have been introduced, reliable methods to discriminate in a quantitative way different level of imbalance are still lacking. In our work, we reconstruct and analyze the phylogenetic trees of six RNA viruses, with a special emphasis on the human Influenza A virus, due to its relevance for vaccine preparation as well as for the theoretical challenges it poses due to its peculiar evolutionary dynamics. We focus in particular on topological properties. We point out the limitation featured by standard imbalance metrics, and we introduce a new methodology with which we assign the correct imbalance level of the phylogenetic trees, in agreement with the phylodynamics of the viruses. Our thorough quantitative analysis allows for a deeper understanding of the evolutionary dynamics of the considered RNA viruses, which is crucial in order to provide a valuable framework for a quantitative assessment of theoretical predictions.