MS03 - ECOP-10 Part 2 of 2

Applications of Evolutionary Game Theory and Related Frameworks: From Cells to Societies (Part 2)

Tuesday, July 15 at 10:20am in Salon 2

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Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Daniel Cooney (University of Illinois Urbana-Champaign), Olivia Chu (Bryn Mawr College) and Alex McAvoy (University of North Carolina, Chapel Hill)

Description:

Evolutionary game theory is a mathematical framework that describes how traits or behaviors can spread through populations, modeling frequency-dependent selection due to either natural selection or social imitation. Models of evolutionary games have found use in modeling biological and social systems in applications ranging from the study of adaptive cancer therapies to understanding the emergence of cooperative social norms in human populations. In this session, we aim to bring together researchers working on evolutionary game theory and related modeling frameworks for emergent phenomena arising from social interactions in populations, exploring a range of scientific applications across levels of biological organization and building a common understanding of mathematical approaches that can be used to explore evolutionary dynamics across a range of spatial and temporal scales.

Room assignment: Salon 2

Emerson Arehart

Princeton University

"Modeling socio-ecological systems on the frontier: A case study from the Amazon River basin"

TBD

Haihui Cheng

University of Alberta

"Evolution of cooperation in spatio-temporal evolutionary games with public goods feedback"

In biology, evolutionary game-theoretical models often arise in which players' strategies impact the state of the environment, driving feedback between strategy and the surroundings. In this case, cooperative interactions can be applied to studying ecological systems, animal or microorganism populations, and cells producing or actively extracting a growth resource from their environment. We consider the framework of eco-evolutionary game theory with replicator dynamics and growth-limiting public goods extracted by population members from some external source. It is known that the two sub-populations of cooperators and defectors can develop spatio-temporal patterns that enable long-term coexistence in the shared environment. To investigate this phenomenon and unveil the mechanisms that sustain cooperation, we analyze two eco-evolutionary models: a well-mixed environment and a heterogeneous model with spatial diffusion. In the latter, we integrate spatial diffusion into replicator dynamics. Our findings reveal rich strategy dynamics, including bistability and bifurcations, in the temporal system and spatial stability, as well as Turing instability, Turing-Hopf bifurcations, and chaos in the diffusion system. The results indicate that effective mechanisms to promote cooperation include increasing the player density, decreasing the relative timescale, controlling the density of initial cooperators, improving the diffusion rate of the public goods, lowering the diffusion rate of the cooperators, and enhancing the payoffs to the cooperators. We provide the conditions for the existence, stability, and occurrence of bifurcations in both systems. Our analysis can be applied to dynamic phenomena in fields as diverse as human decision-making, microorganism growth factors secretion, and group hunting.

Daniel Cooney

University of Illinois Urbana-Champaign

"Spatial Pattern Formation and the Evolution of Cooperative Behavior"

Social dilemmas featuring tension between the individual incentive to cheat and a collective goal to maintain cooperative behavior arise across a range of natural and social systems, from the origins of multicellular life to the sustainable manage of shared natural resources. Evolutionary game theory provides a helpful analytical framework for describing this conflict between individual and collective interests, allowing for the exploration of mechanisms that can allow for the emergence and stability of cooperative behaviors. Work on spatial models of evolutionary games have shown that localized game-theoretic interactions can promote cooperation for games in which cheating prevails in well-mixed populations, but that spatial diffusion of individuals and common resources can also hurt the ability to maintain aggregates of cooperative individuals. In this presentation, we will discuss several PDE models for evolutionary games featuring diffusion of individuals and environmental resources as well as directed motion towards either increasing payoff or increasing levels of natural resources. We show that biased motion towards increasing payoff or resource quality can promote the formation of spatial patterns featuring regions with greater population density and increased average payoffs and environmental quality in regions in which cooperators have aggregated. However, by measuring the average payoff of the population or the average level of environmental quality across the population, we see that these pattern-forming mechanisms can actually decrease the overall success of the population, relative to the equilibrium outcome in the absence of spatial motion. This suggests that payoff-driven and environmental-driven motion can produce a kind of spatial social dilemma, in which biased motions towards more beneficial regions can produce emergent patterns featuring a worse overall environment for the population. This project is based on joint work with Seokhwan Moon (Pohang Institute of Science and Technology), Chenning Xu (California Institute of Technology), and Tianyong Yao (University of Michigan).

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Annual Meeting for the Society for Mathematical Biology, 2025.