Phylodynamic inference for emerging viruses using segregating sites

Epidemiological models are commonly fit to case data to estimate model parameters and to infer unobserved disease dynamics. More recently, epidemiological models have also been fit to viral sequence data using phylodynamic inference approaches that generally rely on the reconstruction of viral phylogenies. However, especially early on in an expanding viral population, phylogenetic uncertainty can be substantial and methods that require integration over this uncertainty can be computationally intensive. Here, we present an alternative approach to phylodynamic inference that circumvents the need for phylogenetic tree reconstruction. Our "tree-free" approach instead relies on quantifying the number of segregating sites observed in sets of sequences over time and using this trajectory of segregating sites to infer epidemiological parameters within a Sequential Monte Carlo (SMC) framework. Using forward simulations, we first show that epidemiological parameters and processes leave characteristic signatures in segregating site trajectories, demonstrating that these trajectories have the potential to be used for phylodynamic inference. We then show using mock data that our proposed approach accurately recovers key epidemiological quantities such as the basic reproduction number and the timing of the index case. Finally, we apply our approach to SARS-CoV-2 sequence data from France, estimating a reproductive number of approximately 2.2 and an introduction time of mid-January 2021, consistent with estimates from epidemiological surveillance data. Our findings indicate that "tree-free?" phylodynamic inference approaches that rely on simple population genetic summary statistics can play an important role in estimating epidemiological parameters and reconstructing infectious disease dynamics, especially early on in an epidemic.