Project Summary / Abstract Population dynamics are central to many pressing problems in biomedicine. Whether we look at epidemics, microbiome, or cancer, we need to understand how populations grow, spread, and evolve. The outcome of these processes is largely controlled by ecological and genetic diversity of the population. Moreover, the patterns of diversity are often the only available cues about the factors that drive population dynamics. Although a lot of effort went into characterizing the diversity of stationary populations (both well-mixed and spatially structured) the understanding of evolutionary processes in growing populations is much more limited. Our recent work found that seemingly innocuous changes in the growth dynamics can fundamentally alter how populations evolve during spatial expansions. To understand such phenomena, we developed powerful theoretical tools, which lead to the discovery of hidden universality classes in the standard reaction-diffusion models of population genetics. Preliminary data strongly supports the hypothesis that each universality class has a unique structure of genealogies. Moreover, neutral evolution in some spatially expanding populations seems to produce genealogies identical to those in rapidly-adapting well-mixed populations, which suggests that some common signatures of selection need to be revisited. The first aim is to develop this theory further and test it in numerical simulations. The second aim is to examine how the universal behavior of genealogies is affected by common biophysical process, which are neglected in standard one-component reaction-diffusion models. Specifically, we will extend our theory of evolutionary dynamics to include the influence of mechanical pressure, nutrient diffusion, and movement in response to environmental gradients. The third aim is focused on establishing a connection between genetic diversity and growth instabilities that produce typical population morphologies. Taken together, these lines of research will lay the groundwork to interpret spatially-resolved genetic data and use it to predict and control the course of evolution. Such capabilities are essential for our fight against cancer, antibiotic resistance, and epidemics. The mathematical innovations developed in the course of this work should also be useful across a wide set of applications because reaction- diffusion models find numerous uses in chemistry, biology, and medicine.