Self-organized critical dynamics of RNA virus evolution

RNA virus (e.g., SARS-CoV-2) evolves in a complex manner. Studying RNA virus evolution is vital for understanding molecular evolution and medicine development. Scientists lack, however, general frameworks to characterize the dynamics of RNA virus evolution directly from empirical data and identify potential physical laws. To fill this gap, we present a theory to characterize the RNA virus evolution as a physical system with absorbing states and avalanche behaviors. This approach maps accessible biological data (e.g., phylogenetic tree and infection) to a general stochastic process of RNA virus infection and evolution, enabling researchers to verify potential self-organized criticality underlying RNA virus evolution. We apply our framework to SARS-CoV-2, the virus accounting for the global epidemic of COVID-19. We find that SARS-CoV-2 exhibits scale-invariant avalanches as mean-field theory predictions. The observed scaling relation, universal collapse, and slowly decaying auto-correlation suggest a self-organized critical dynamics of SARS-CoV-2 evolution. Interestingly, the lineages that emerge from critical evolution processes coincidentally match with threatening lineages of SARS-CoV-2 (e.g., the Delta virus). We anticipate our approach to be a general formalism to portray RNA virus evolution and help identify potential virus lineages to be concerned.