PT  - JOURNAL ARTICLE
AU  - Andrew R. Tilman
AU  - Joshua Plotkin
AU  - Erol Akçay
TI  - Evolutionary games with environmental feedbacks
AID  - 10.1101/493023
DP  - 2019 Jan 01
TA  - bioRxiv
PG  - 493023
4099  - http://biorxiv.org/content/early/2019/01/17/493023.short
4100  - http://biorxiv.org/content/early/2019/01/17/493023.full
AB  - Strategic interactions often occur in dynamic environments that change according to the behavior of individuals. Feedback between the environment and individual behavior is common in social-ecological systems, evolutionary-ecological systems, and even psychological-economic systems – where the state of the environment alters the dynamics of competing strategies or types, and vice versa. When feedbacks are present, the dynamics of strategies and resources must be considered jointly: neither alone can describe the dynamics of the system. Here we develop a framework for eco-evolutionary game theory that permits the study of strategic dynamics with environmental feedbacks. We provide a complete dynamical analysis for two-strategy games with environmentally dependent payoffs, where the environment is impacted by the strategies employed. The environment in these systems may be governed either as a renewable resource (e.g. common-pool harvesting) or as a decaying resource (e.g. pollution byproducts). We find that for many regimes, despite feedbacks, persistent dynamical cycles are not possible. In regimes where cycling is possible, cycles occur only when the timescale of environmental change is sufficiently slow compared to the timescale of strategic change. We show that a number of prior studies on joint strategic-environmental dynamics, across a range of disciplines, can be understood as special cases of our general analysis. We discuss the implication of our results for fields ranging from ecology to economics.