Eco-evolutionary dynamics of cooperation in the presence of policing

TL;DR

This paper develops an eco-evolutionary model combining cooperation, defection, and punishment strategies within a population, revealing complex dynamics including stable states, oscillations, and novel cyclic dominance routes influenced by ecological factors.

Contribution

It introduces a new eco-evolutionary framework integrating ecological space and punishment strategies in the Prisoner's Dilemma, uncovering complex dynamics and novel cyclic dominance mechanisms.

Findings

Cooperators, defectors, and punishers can coexist in various stable or oscillating states.

Oscillations are driven by cyclic dominance among strategies.

A new route to cyclic dominance via inverse Hopf bifurcation was identified.

Abstract

Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.