Strategic interactions often occur in dynamic ecological environments. Further, bi-directional feedbacks between the environment and strategic behavior is common. In social-ecological systems as well as evolutionary-ecological systems the state of the environment can alter the dynamics of competing strategies or types, and vice versa. When such feedbacks are present, the dynamics of strategies and resources must be considered jointly: neither alone can describe the dynamics of the system. We develop a framework for eco-evolutionary game theory that integrates ecological dynamics and evolutionary game dynamics. We seek to address how the explicit inclusion of ecological dynamics alters predictions for outcomes of evolutionary games. When can such feedbacks safely be considered implicitly? What new phenomena can arise only with explicit consideration of these ecological feedbacks?
Results/Conclusions
We provide a complete dynamical analysis for two-strategy games with environmentally dependent payoffs, where the ecological dynamics of the environment are impacted by the strategies employed. We focus on environmental systems governed by renewable resources (e.g. common-pool harvesting) or by decaying resources (e.g. resource acquisition strategies). We find that the explicit inclusion of environmental feedbacks in evolutionary games can give rise to persistent dynamical cycles where they would not be otherwise expected. However, we find that for many regimes, despite feedbacks, such cycling is not possible. In regimes where cycles are possible, we find that they only result when the relative timescale of strategy dynamics is fast relative to ecological dynamics. Our analysis unites dynamical phenomena that occur in settings as diverse as plant nutrient acquisition, human decision-making, and resource harvesting. We discuss the implication of our results for fields including evolution, ecology, and economics.