Ecological public goods games in spatially heterogeneous environments

Jaideep Joshi, of the Indian Institute of Science, examined the evolutionary conditions under which a “tragedy of the commons” can be averted.

Jaideep Joshi

Jaideep Joshi


Public goods that are freely accessible to everyone are at risk of over-exploitation by selfish consumers: a phenomenon called “the tragedy of commons” [1]. Space plays a crucial role in the dynamics of ecological public goods, as consumers can harvest resources from their present locations and disperse them to new locations when local resource levels drop. In such a situation, as the benefits of harvesting are offset by costs of dispersal, two strategies could potentially arise: the milker strategy, with low consumption and low dispersal, and the killer strategy, with high consumption and high dispersal. We explored the coevolution of harvesting rate and dispersal distance of consumers, using the milker-killer framework [2].


We modeled consumer and resource populations on a continuous two-dimensional space. The resource grows logistically with a spatially varying growth rate (and/or carrying capacity). Consumers exploit the resource in their neighborhood at an individual specific consumption rate and disperse to other sites, when local conditions become adverse, at an individual specific dispersal rate. Both the resource exploitation rate and the dispersal distance can evolve over time through imitation of successful individuals.


In a homogeneous environment, we find that when the benefits from harvesting (b) are low, the dispersal costs (c) prevent individuals from over-exploiting the local resource, giving rise to a stable milker strategy. As b is increased, evolutionary branching occurs, leading to co-existence of distinct milker and killer strategies. For moderate values of b, the milker strategy goes extinct after some time, leading to the tragedy of commons. But as b is increased further, both strategies remain stable. When b is very high, the killer branch goes extinct, as the resource is severely depleted. In a heterogeneous environment, where the resource growth rate varies across space, we find similar dynamics. However, if individuals are only able to imitate the nearest neighbors, rather than the globally fittest individuals, then the amount of heterogeneity determines whether or not branching occurs.


We show that space plays a crucial role in the dynamics of ecological public goods, leading to a variety of evolutionary outcomes, ranging from the pure milker strategies to ever changing mixed strategies.


[1] Hardin G (1968). The Tragedy of the Commons. Science 162: 1243–1248

[2] Baalen M, & Sabelis MW (1995). The Milker-Killer Dilemma in Spatially Structured Predator-Prey Interactions. Oikos 74: 391–400


Åke Brännström, Evolution and Ecology Program, IIASA


Jaideep Joshi, of the Indian Institute of Science, is a citizen of India. He was funded by the IIASA Indian National Member Organization and worked in the Evolution and Ecology Program during the YSSP.

Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.

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Last edited: 02 February 2016

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