DMS-EPSRC Eco-Evolutionary Dynamics of Fluctuating Populations

A fundamental scientific puzzle is understanding the origin of diversity and the evolution of cooperation, which can be understood through understanding the stability of populations composed of competing species. It directly addresses deep societal concerns, such as the maintenance of endangered ecologies, the effective prevention of the loss of biodiversity, and stemming the rise of antimicrobial resistance.

To this end, one must address the coupled eco-evolutionary dynamics of fluctuating populations, namely the interdependence and combined effects of (i) random internal variability in population numbers, composition, and each species’ traits and (ii) sudden, gradual, or repetitive external changes in environmental conditions on the evolution of an ecological system. This transdisciplinary research is situated at the interface of biology, mathematics, physics, statistics, and computer science and will combine a set of advanced theoretical and mathematical tools from these fields that so far have rarely been utilized together.

It will be pursued in an international collaboration, funded jointly through National Science Foundation – Division of Mathematical Sciences and the U.K. Engineering and Physical Sciences Research Council, and provide advanced training for a postdoctoral research fellow at the University of Leeds and a graduate student at Virginia Tech. Conceptual and technical advances in the basic understanding of complex interacting systems in general, and specifically of spontaneous pattern formation under the combined influence of intrinsic noise and environmental variability, are anticipated, and will be disseminated to the scientific community at tailored workshops to be organized alternatingly at Leeds, U.K. and Blacksburg, Virginia.

While population dynamics traditionally ignores fluctuations and considers static and homogeneous environments, demographic noise arising from randomly occurring birth or death events as well as external environmental variations play a crucial role in understanding the eco-evolutionary dynamics of a population in time. The interdependence of external environmental variability and internal demographic noise is poorly understood to date, but it is of eminent importance, for example in microbial communities, which are often subject to sudden and extreme environmental changes.

In particular, modelling populations of varying size and composition subject to changing external factors is crucial to gain a full understanding of the evolution of microbial antibiotic resistance. Standard theoretical techniques, like mean-field approximations or system-size expansions cannot be straightforwardly used, and new mathematical approaches are needed.

A suite of novel theoretical methods, based on and combining evolutionary and nonlinear dynamics, deterministic and stochastic partial differential equations, agent-based computer simulations, and tools from non-equilibrium statistical physics such as dynamical scaling theory, renormalization group approaches to critical phenomena, and mathematical representations of stochastic kinetics in terms of continuum field theories, will be developed. The goal is to design and quantitatively characterize biologically relevant evolutionary models of increasing levels of complexity, which incorporate both switching environmental features and fully account for the underlying stochasticity.

These theoretical advances will be utilized to generate directly testable predictions for laboratory experiments to further explore how demographic noise and environmental variability conjointly influence the emergence of collective features and affect species coexistence and their organization into spatial patterns.

This project is jointly funded by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and the LS-BioTech Venture Fund, and the Division of Materials Research (DMR) through the Condensed Matter and Materials Theory program.

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.