Seasonal influenza and SARS-CoV-2 (coronaviruses) repeatedly avoid the human immune system and circulate in the human population because they evolve rapidly due to mutations. Quantitative elucidation of viral evolutionary dynamics is extremely important for vaccine development and public health interventions. Theoretical methods based on phylogenetic trees suffer from low temporal resolution and do not scale well with large data size.

Here, we develop a new theoretical method to systematically analyze the evolutionary dynamics of viruses from gene time series data. Since this method can handle large data sizes with high temporal resolution, it can analyze high-density data of coronaviruses. By applying this method, we find, for example, that beneficial mutations are qualitatively changing evolutionary dynamics and how geographic structure affects patterns of infection spread.