  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.
