This research project investigates probability questions arising in the study of population dynamics and genealogies with multi-species interactions. The latter study is a key to understanding biodiversity in ecosystems, epidemiological spread, heterogeneity of cancer tumors, and the mechanisms underlying many complex systems in nature. This project is the first step towards the development of more refined models that not only address standing questions in virology and ecology, but also catalyze the generation of new mathematical methods. The involvement of undergraduate students in stochastic analysis and simulations will enhance their ability to work at the interface between probability and applied sciences.
The principal investigator aims to design various spatial stochastic models, including nonstandard interacting particle systems, interacting superprocesses, and coupled stochastic partial differential equations on general metric graphs, to contribute to a deeper understanding of the effect of spatial structures and randomness on various population dynamics and their genealogies in different scales of observation. New challenges arise in the study of well-posedness and time asymptotic properties of these models. The project will focus on two research directions. (i) Explore new connections among these models. Outcomes of this research are expected to include scaling limit theorems and duality formulas that rigorously justify the new connections. (ii) Study the long-time behavior of these spatial stochastic models. New probabilistic methods will be developed to compute quantities of interest, such as the asymptotic shape of competition outcome and the propagation speeds of travelling waves on networks.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
