Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks

TL;DR

This paper develops a theoretical framework integrating global environmental fluctuations and local feedbacks to understand their combined effects on social dilemma evolution, revealing complex cyclic dynamics in eco-evolutionary systems.

Contribution

It introduces a unified model combining nonlinear global environmental fluctuations with local eco-evolutionary feedbacks, advancing understanding of their joint influence on social dilemma dynamics.

Findings

Emergence of cyclic cooperation and environment dynamics

Interior irregular loops in phase space

Dependence on relative speeds of environmental and strategic changes

Abstract

Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the `eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differs in static and dynamic global environments. In particular, we find the emergence of cyclic evolutions of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Our results provide important insights toward how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments.