Mutualisms are prevalent in nature, even though mean-field models predict that mutualists should be displaced by cheaters. Many complex behaviors (quorum sensing, policing, kin selection, multi-level selection) have been suggested as explanations for the robustness of mutualism. Here we invoke a simpler mechanism: spatially explicit population dynamics. We use a stochastic spatial model (i.e. cellular automata) to analyze a three species community - two obligate mutualists and one cheater - in which species compete for sites. Mutualist birth rates depends on their maximum birth rate, the fraction of nearby empty sites, and amount of benefit it gains from nearby mutualist partners. Cheater growth rates are similar, except that cheaters a have higher maximum birth rate, and the mutualist benefit is proportional the rarer mutualist (following Liebig’s law of the minimum). The equations for growth on the global scale are unavailable, and thus we use simulations. Specifically, we test how the dispersal distance of progeny and the diffusion distance of mutualistic benefits affects the robustness of mutualists to invasions and displacement by cheaters.
We discovered two novel ways that mutualists can be robust to cheaters. Both mechanisms operate by segregating mutualistic benefits in space, ensuring that cheaters don’t have access to the benefits from both mutualists. First, when dispersal distance is low and mutualistic benefits diffuse over long distances, mutualists can build up locally and diffuse their benefits to their mutualistic partners. The emergent patterns are spatially and temporally stable (i.e. Turing-like patterns). Secondly, when dispersal distance is high and mutualistic benefits diffuse short differences, mutualistic benefits become randomly distributed, making it unlikely that cheaters will encounter benefits from both mutualists. The first mechanism (high benefit diffusion) relies on large-scale variation which emerges from self-organized spatial structure. The second mechanism (high dispersal) relies on small-scale variation and local interactions. It is interesting to note that when both dispersal distance and benefit diffusion are low, we recover the previously-known result that multi-level selection can drive mutualism robustness. Our two novel mechanisms are fundamentally different from multi-level selection – whereas multi-level selection requires the mutualists to occasionally escape the cheaters and rapidly proliferate in a few locations, our mechanisms boost mutualist birth rates across the landscape.