Quantitative analysis of the mode and tempo of virus molecular evolution

Estimating the rate of nucleotide and amino acid substitutions is fundamental to our understanding of how fast species evolve. It also enables us to reconstruct their natural history. The development of sophisticated statistical methods and software in molecular sequencing analysis has made it easier for biologists to test and compare various evolutionary hypotheses and infer evolutionary parameters. However, the use of these software packages as a 'blackbox' without paying close attention to the underlying assumptions can lead to spurious rate estimations across different timescales which often result in erroneous inferences of virus evolutionary histories. In this thesis, I develop quantitative methods to understand biological mechanisms that can alter the molecular evolutionary rate of viruses over time and investigate the implications of having a time-dependent rate of evolution for reconstructing the phylogenetic history of viruses. I also explore alternative methods to estimating the time of origin and reconstructing the evolutionary trajectory of viruses using mobility data, national vital statistics, and serology surveys. I show how three evolutionary processes of rapid within-host evolution during chronic infections, purifying selection, and site saturation can determine the changes in evolutionary rate of viruses over different timescales, from a few weeks to millions of years. I also leverage excess mortality and seroprevalence data to correct for under-reporting of COVID-19-related deaths, reconstruct early transmission dynamics of SARS-CoV-2, and estimate the start of the Iranian epidemic as well its growth rate in the absence of high-quality genome sequence and province-level epidemiological data. This work will build towards the goal of making more accurate estimations of the timescale of phylogenetic histories and the rate at which species evolve. It also further strengthens the conceptual link between phylogenetics, population genetics, and molecular evolution.