A variant-dependent molecular clock with anomalous diffusion models SARS-CoV-2 evolution in humans

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 120; no. 30; p. e2303578120
• Main Authors: Goiriz, Lucas, Ruiz, Raúl, Garibo-I-Orts, Òscar, Conejero, J Alberto, Rodrigo, Guillermo
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 25.07.2023
• Series: Brief Report
• Subjects: Biological Sciences; Coronaviruses; Diffusion rate; Evolution; Gene sequencing; Genomes; Mathematical models; Pandemics; Public health; Severe acute respiratory syndrome coronavirus 2; Stochastic processes; Stochasticity; Time dependence; Viral diseases; whole genome sequencing; stochastic process; anomalous diffusion; dynamic systems; virus evolution rate
• DOI: 10.1073/pnas.2303578120
• ISSN: 0027-8424

The evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in humans has been monitored at an unprecedented level due to the public health crisis, yet the stochastic dynamics underlying such a process is dubious. Here, considering the number of acquired mutations as the displacement of the viral particle from the origin, we performed biostatistical analyses from numerous whole genome sequences on the basis of a time-dependent probabilistic mathematical model. We showed that a model with a constant variant-dependent evolution rate and nonlinear mutational variance with time (i.e., anomalous diffusion) explained the SARS-CoV-2 evolutionary motion in humans during the first 120 wk of the pandemic in the United Kingdom. In particular, we found subdiffusion patterns for the Primal, Alpha, and Omicron variants but a weak superdiffusion pattern for the Delta variant. Our findings indicate that non-Brownian evolutionary motions occur in nature, thereby providing insight for viral phylodynamics.