Hill numbers at the edge of a pandemic: rapid SARS-COV2 surveillance using clinical, pooled, or wastewater sequence as a sensor for population change

The COVID-19 pandemic has highlighted the critical role of genomic surveillance for guiding policy and control strategies. Timeliness is key, but rapid deployment of existing surveillance is difficult because most approaches are based on sequence alignment and phylogeny. Millions of SARS-CoV-2 genomes have been assembled, the largest collection of sequence data in history. Phylogenetic methods are ill equipped to handle this sheer scale. We introduce a pan-genomic measure that examines the information diversity of a k-mer library drawn from a country’s complete set of clinical, pooled, or wastewater sequence. Quantifying diversity is central to ecology. Studies that measure the diversity of various environments increasingly use the concept of Hill numbers, or the effective number of species in a sample, to provide a simple metric for comparing species diversity across environments. The more diverse the sample, the higher the Hill number. We adopt this ecological approach and consider each k-mer an individual and each genome a transect in the pan-genome of the species. Applying Hill numbers in this way allows us to summarize the temporal trajectory of pandemic variants by collapsing each day’s assemblies into genomic equivalents. For pooled or wastewater sequence, we instead compare sets of days represented by survey sequence divorced from individual infections. We do both calculations quickly, without alignment or trees, using modern genome sketching techniques to accommodate millions of genomes or terabases of raw sequence in one condensed view of pandemic dynamics. Using data from the UK, USA, and South Africa, we trace the ascendance of new variants of concern as they emerge in local populations. Using data from San Diego wastewater, we monitor these same population changes from raw, unassembled sequence. This history of emerging variants senses all available data as it is sequenced, intimating variant sweeps to dominance or declines to extinction at the leading edge of the COVID19 pandemic. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study did not receive any funding ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced are available online at: https://www.cogconsortium.uk https://www.gisaid.org