Spatial interactions and eco-evolutionary games

Abstract

Organisms compete for limited resources to reproduce. Reproduction depends on behaviors that are modified by abiotic and biotic factors, including the behavior of other organisms. This thesis adopts and extends evolutionary game theory to understand the coupled dynamics of individual behavior and resources. In doing so, the work is motivated by the example of the Tragedy of the Commons introduced by Garret Hardin in which individuals, each acting in their own self-interest, overuse resources and lead to the collapse of the commons. Although Hardin claimed that the TOC is inevitable, there are many examples from ecology to economics that offer alternative outcomes. An explanation for this gap was recently proposed in a mean-field model of evolutionary games coupled to environmental feedback in which depletion of resources can change individual behavior, thus leading to the aversion of the tragedy. This thesis extends this continuous model of game-environment feedback to address three motivating questions: 1) How does demographic noise and spatial interactions shape the spatiotemporal dynamics of the system, 2) How does the relative speed of strategy and environment dynamics affect TOC, 3) What new insights can we learn regarding public good production in microbial systems when game and environment are reciprocally coupled. Our approach to answer these questions leverages a derivation of individual-based game rules that can recapitulate feedback given both demographic noise and spatially explicit interactions. These games rules recapitulate the mean-field model in the large system limit. Individual-based simulations of the game yield multiple findings. First, spatial and non-spatial simulations give different population dynamics with the same simulation parameter sets, suggesting that spatial interactions can shift regimes where TOCs occur. Second, the spatially explicit system shows coherent spatial-temporal patterns, including the expansion of clusters of resources and strategies. Additional findings highlight the role of diffusivity and time-scales in modulating the coupled fates of behaviors and environment. Overall, the work helps identify consequences of the mutual feedback between behavior and environmental resources in finite-sized populations.