Student AIM Seminar: Spatial Pattern Formation in Eco-Evolutionary Games with Environment-Driven Motion

The sustainable management of common resources often leads to a social dilemma known as the tragedy of the commons: individuals benefit from rapid extraction of resources, while communities as a whole benefit from more sustainable extraction strategies. In this talk, we explore a PDE model of evolutionary game theory with environmental feedback, describing how the spatial distribution of resource extraction strategies and environmental resources evolve due to reaction terms describing eco-evolutionary game-theoretic dynamics and spatial terms describing diffusion of environmental resources and directed motion of resource harvesters towards regions of greater environmental quality. Through linear stability, we show that this biased motion towards higher-quality environments can lead to spatial patterns in the distribution of extraction strategies, creating local regions with improved environmental quality and increase payoff for resource extractors. However, by measuring the average payoff and environmental quality across the spatial domain, we see that this pattern-forming mechanism can actually decrease the overall success of the population relative to the equilibrium outcome in the absence of spatial motion. This suggests that environmental-driven motion can produce a spatial social dilemma, in which biased motion towards more beneficial regions can produce emergent patterns featuring a worse overall environment for the population.