Eco-Evolutionary Dynamics of Fluctuating Populations

Eco-Evolutionary Dynamics of Fluctuating Populations | School of Mathematics | University of Leeds

Understanding the origin of species diversity and the evolution of cooperation is a major scientific riddle that resonates with numerous societal concerns, like the rise of antimicrobial resistance or the loss of biodiversity, and is even relevant to epidemiology.

Population dynamics traditionally ignores fluctuations and considers static and homogeneous environments. However, fluctuations arising from randomly occurring birth / death events (demographic noise) and the change of environmental conditions (environmental variability), together with the spatial dispersal of species, play a crucial role in understanding how the size and composition of a population jointly evolve in time, i.e. its eco-evolutionary dynamics.

In this project, we will focus on the ubiquitous situation where the eco-evolutionary dynamics of fluctuating populations is shaped by the coupling of demographic noise and environmental variability (see cartoon). The interdependence of environmental variability and demographic noise is poorly understood but of great importance in microbial communities, which are often subject to sudden and extreme environmental changes.

In particular, modelling population of varying size and composition subject to changing external factors is crucial to understand the evolution of microbial antibiotic resistance. In fact, pharmacodynamics largely focuses on the deterministic description of large well-mixed bacterial populations, but fails to account crucial stochastic effects arising in small communities.

When antibiotics reduce a large population to a very small one but fail to eradicate it, surviving cells may replicate and restore infections, and these survivors are likely to develop antibiotic resistance. Owing to the small population size, the details of the outcome are subject to large fluctuations. This important example clearly illustrates the need for theoretical advances to shed light on extinction and resistance scenarios in fluctuating environments.

This ambitious project aims at carrying out a cutting-edge research programme whose central goal is to develop a suite of theoretical tools that will allow us to describe biologically relevant evolutionary models, and to make testable predictions in laboratory-controlled experiments.

For this joint effort, crucially building on the team's unique complementary expertise, we will adopt a multidisciplinary approach combining various mathematical tools (evolutionary and nonlinear dynamics, statistical physics and critical phenomena, stochastic and field-theoretic methods, partial differential equations), and will consider models of an increasing level of complexity.

Many of the features of our theoretical models, such as switching environments, time-varying population sizes, public good production, etc. can be reproduced in laboratory experiments. This will open the door to a host of exciting possibilities to address theoretical questions of direct biological relevance, and to experimentally test various predictions of our theoretical models.

Publications and outputs

"Evolution of a Fluctuating Population in a Randomly Switching Environment", 
K. Wienand, E. Frey, and M. Mobilia, Phys. Rev. Lett 119,158301 (2017). 

"Eco-Evolutionary Dynamics of a Population with Randomly Switching Carrying Capacity", 
K. Wienand, E. Frey, and M. Mobilia, J. R. Soc. Interface 15, 20180343 (2018). 

 "Population Dynamics in a Changing Environment: Random versus Periodic Switching", 
A. Taitelbaum, R. West, M. Assaf, and M. Mobilia, Phys. Rev. Lett 125,048105 (2020).  

"Fixation properties of rock-paper-scissors games in fluctuating populations", 
R. West and M. Mobilia, J. Theor. Biol. 491, 110135 (2020). 

"Stochastic population dynamics in spatially extended predator-prey systems", 
U. Dobramysl, M. Mobilia, M. Pleimling, and U. C. Täuber, J. Phys. A 51, 063001 (2018).  

 "Cyclic dominance in evolutionary games: A review", 
A. Szolnoki, M. Mobilia, L.-L. Jiang, B. Szczesny, A. M. Rucklidge, and M. Perc, J. R. Soc. Interface 11, 20140735. (2014). 

Hernández-Navarro L, Asker M., and Mobilia M. 
"Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size".
J. Phys. A: Math. Theor. 57, 265003:1-29 (2024)

Swailem M, and Täuber U.C.
"Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations".
Phys. Rev. E 110, 014124 (2024)
DOI: 10.1103/PhysRevE.110.014124

Asker M, Hernández-Navarro L, Rucklidge A. M., and Mobilia M.  
"Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations".
New J. Phys 25, 123010:1-18 (2023)
DOI: 10.1088/1367-2630/ad0d36

Hernández-Navarro L, Asker M, Rucklidge A.M., and Mobilia M. 
"Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance".
J. R. Soc. Interface 20, 20230393:1-13 (2023)
DOI: 10.1098/rsif.2023.0393

Swailem M, and Täuber U.C.
"Lotka-Volterra predator-prey model with periodically varying carrying capacity". 
Phys. Rev. E 107, 064144 (2023)
DOI: 10.1103/physreve.107.064144

Taitelbaum A, West R, Mobilia M, and Assaf M. 
"Evolutionary dynamics in a varying environment: Continuous versus discrete noise".
Phys. Rev. Research 5, L022004:1-7 (2023)
DOI: 10.1103/PhysRevResearch.5.L022004

Yao L, Swailem M, Dobramysl U, and Täuber U.C. 
"Perturbative field-theoretical analysis of three-species cyclic predator-prey models".
J. Phys. A: Math. Theor. 56 225001 (2023).
DOI: 10.1088/1751-8121/acd0e4


Project website