Uumarrty and the Nash Score: a Game-theoretic, Agent-based Framework for Understanding Evolutionary Stability in Behavioral Traits

This paper introduces a new simulation framework for testing hypotheses relating to behavior strategies in predator-prey systems. To this end, we present two tools for simulating and analyzing behavioral trait dynamics: The Nash Score, a novel metric for evaluating evolutionary stability, and Uumarrty, an agent-based framework for simulating predator-prey interactions using game theory. These tools provide an approach for assessing the temporal co-evolution of behavioral traits within agent-based models, with a particular focus on predator-prey dynamics, though the framework is generalizable to other ecological interactions. The Nash Score functions as an analog to the Evolutionarily Stable Strategy (ESS) from classical game theory, offering a quantitative index to assess the relative stability and resilience of behavioral traits under selection. We demonstrate the utility of these tools through a case study on the microhabitat preferences of kangaroo rats and rattlesnakes. Specifically, we explore the emergence and stability of optimal strategies across scenarios with: (1) heterogeneous energy yields among microhabitats, (2) differential strike success rates by microhabitat, and (3) the presence of a specialist predator. Our results highlight how microhabitat specialist predators can drive other predators in the system to specialize due to outcompeting generalists at a given population frequency; leading to behavioral strategy stability in the system. Our case studies also show how behavioral trait dynamics can greatly vary depending on if you treat the trait as a pure strategy versus a mixed strategy. Collectively, this framework enhances our ability to explore ecological and evolutionary responses to environmental change, supporting more robust and comparable simulation-based research in eco-evolutionary dynamics.