Optimal competitors: the balance of attraction and choices of mutualists, like pollinators, drives facilitation and may promote crop pollination.

When two species use the same resource, this typically leads to competition, such as when different plants aim to attract the same mutualist pollinators. However, more flowers may also attract more pollinators to an area, such that one or both 'competitors' actually benefit from the other's presence. For example, it has been argued that strips of wildflowers planted next to crops may attract pollinators who 'spill over' into the crop. Here, we mathematically examine facilitation and competition in consumer attraction. Contrary to previous claims, no accelerating benefits of density on attraction per se are necessary for facilitation. Instead, under very general assumptions, facilitation can be generated by an imbalance between local competition and joint long-distance attraction of consumers; for example, a low presence of highly attractive 'wildflowers' should lead to benefits to a crop. In this mechanism, how pollinator attraction to a patch increases with density of plants is a key factor. Our results generalize to many contexts where local competition may trade off with joint long-distance attraction of consumers, and we show that the exact relationship between competitor density and attraction of consumers can qualitatively shape outcomes, including facilitation or competition.