Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2

The COVID-19 pandemic has initiated an unprecedented worldwide effort to characterize its evolution through the mapping of mutations of the coronavirus SARS-CoV-2. The early identification of mutations that could confer adaptive advantages to the virus, such as higher infectivity or immune evasion, is of paramount importance. However, the large number of currently available genomes precludes the efficient use of phylogeny-based methods. Here we establish a fast and scalable early warning system based on Topological Data Analysis for the identification and surveillance of emerging adaptive mutations in large genomic datasets. Analyzing millions of SARS-CoV-2 genomes from GISAID, we demonstrate that topologically salient mutations are linked with an increase in infectivity or immune escape. We report on emerging potentially adaptive mutations as of January 2022, and pinpoint mutations in Variants of Concern that are likely due to convergent evolution. Our approach can improve the surveillance of mutations of concern, guide experimental studies, and aid vaccine development.