There is increasing interest in the role that evolution may play in current and future pandemics, but there is often also considerable confusion about the actual evolutionary predictions. This may be, in part, due to a historical separation of evolutionary and medical fields, but there is a large, somewhat nuanced body of evidence-supported theory on the evolution of infectious disease. In this review, we synthesize this evolutionary theory in order to provide a framework for clearer understanding of the key principles. Specifically, we discuss the selection acting on zoonotic pathogens' transmission rates and virulence at spillover and during emergence. We explain how the direction and strength of selection during epidemics of emerging zoonotic disease can be understood by a three Ts framework: trade-offs, transmission, and time scales. Virulence and transmission rate may trade-off, but transmission rate is likely to be favoured by selection early in emergence, particularly if maladapted zoonotic pathogens have ‘no-cost’ transmission rate improving mutations available to them. Additionally, the optimal virulence and transmission rates can shift with the time scale of the epidemic. Predicting pathogen evolution, therefore, depends on understanding both the trade-offs of transmission-improving mutations and the time scales of selection.

When novel zoonotic diseases like Sars-CoV-2 emerge, they are likely to be poorly adapted to humans. Effective control measures will suppress transmission before significant evolution can occur, but extended transmission in human populations allows time for selection pressures to act. In this review, we discuss these selection pressures with the aim of better understanding the factors shaping both transmission and virulence in zoonotic pathogens as they become established. We discuss how selection pressures during epidemics of emerging zoonotic disease are determined by the three Ts: trade-offs, transmission, and time scales. In short, virulence and transmission may trade-off, but transmission is likely to be favored by selection early in emergence. However, the relative selection pressures on transmission and virulence shift depending on the time scale of the epidemic. Predicting pathogen evolution in zoonoses therefore depends critically on understanding both the trade-offs of transmission-improving mutations and the time scales of selection.