(click to copy)


Eco-evolutionary dynamics of cooperation in the presence of policing

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.


S. Chowdhury, S. Kundu, J. Banerjee, M. Perc, D. Ghosh, Eco-evolutionary dynamics of cooperation in the presence of policing, Journal of Theoretical Biology 518(7) (2021) 110606.

Matjaz Perc

0 Pages 0 Press 0 News 0 Events 0 Projects 0 Publications 0 Person 0 Visualisation 0 Art


CSH Newsletter

Choose your preference
Data Protection*