Ecological public goods games in spatially heterogeneous environments

Introduction

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].

Methods

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.

Results

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.

Conclusions 

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.

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Last edited: 02 February 2016