Abundant pollinators are often more generalised than rare pollinators. This could be because abundant species have more chance encounters with potential interaction partners. On the other hand, generalised species could have a competitive advantage over specialists, leading to higher abundance. Determining the direction of the abundance–generalisation relationship is therefore a ‘chicken‐and‐egg’ dilemma. Here we determine the direction of the relationship between abundance and generalisation in plant–hummingbird pollination networks across the Americas. We find evidence that hummingbird pollinators are generalised because they are abundant, and little evidence that hummingbirds are abundant because they are generalised. Additionally, most patterns of species‐level abundance and generalisation were well explained by a null model that assumed interaction neutrality (interaction probabilities defined by species relative abundances). These results suggest that neutral processes play a key role in driving broad patterns of generalisation in animal pollinators across large spatial scales.