How spatial structure and neighbor uncertainty promote mutualists and weaken black queen effects

The ubiquity of cooperative cross-feeding (a resource-exchange mutualism) raises two related questions: Why is cross-feeding favored over self-sufficiency, and how are cross-feeders protected from non-producing cheaters? The Black Queen Hypothesis suggests that if leaky resources are costly, then there should be selection for either gene loss or self-sufficiency, but selection against mutualistic inter-dependency. Localized interactions have been shown to protect mutualists against cheaters, though their effects in the presence of self-sufficient organisms are not well understood. Here we develop a stochastic spatial model to examine how spatial effects alter the predictions of the Black Queen Hypothesis. Microbes need two essential resources to reproduce, which they can produce themselves (at a cost) or take up from neighbors. Additionally, microbes need empty sites to give birth into. Under well mixed mean-field conditions, the cross-feeders will always be displaced by a non-producer and a self-sufficient microbe. However, localized interactions have two effects that favor production. First, a microbe that interacts with a small number of neighbors will not always receive the essential resources it needs; this effect slightly harms cross-feeders but greatly harms non-producers. Second, microbes tend to displace other microbes that produce resources they need; this effect also slightly harms cross-feeders but greatly harms non-producers. Our work therefore suggests localized interactions produce an accelerating cost of non-production. Thus, the right trade-off between the cost of producing resources and the cost of sometimes being resource-limited can favor mutualistic inter-dependence over both self-sufficiency and non-production.