Dynamics of an ant–plant-pollinator model

•The plant-pollinator interaction is described by a Beddington–DeAngelis formula.•The formula is extended to characterize ant interference.•An ant–plant-pollinator model is derived.•Dynamics of the model demonstrate how the three species can coexist.•Ant interference can lead to extinction of both pollinators and ants.

In this paper, we consider plant-pollinator–ant systems in which plant-pollinator interaction and plant–ant interaction are both mutualistic, but there also exists interference of pollinators by ants. The plant-pollinator interaction can be described by a Beddington–DeAngelis formula, so we extend the formula to characterize plant-pollinator mutualisms, including the interference by ants, and form a plant-pollinator–ant model. Using dynamical systems theory, we show uniform persistence of the model. Moreover, we demonstrate conditions under which boundary equilibria are globally asymptotically stable. The dynamics exhibit mechanisms by which the three species could coexist when ants interfere with pollinators. We define a threshold in ant interference. When ant interference is strong, it can drive plant-pollinator mutualisms to extinction. Furthermore, if the ants depend on pollination mutualism for their persistence, then sufficiently strong ant interference could lead to their own extinction as well. Yet, when ant interference is weak, plant–ant and plant-pollinator mutualisms can promote the persistence of one another.