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Savannas are characterized by the coexistence of trees and flammable grasses. Yet, tree-grass coexistence has been labeled as paradoxical-how do these two functional groups coexist over such an extensive area, despite being generally predisposed to excluding each other? For instance, many trees develop dense canopies that limit grass growth, and many grasses facilitate frequent/intense fires, increasing tree mortality. This study revisits tree-grass coexistence with a model of hierarchical competition between pyrogenic grasses, 'forest trees' adapted to closed-canopy competition, and 'savanna trees' that are inferior competitors in closed-canopy communities, but more resistant to fire. The assumptions of this model are supported by empirical observations, including a systematic review of savanna and forest tree community composition reported here. In general, the model simulations show that when savanna trees exert weaker competitive effects on grasses, a self-reinforcing grass community is maintained, which limits forest tree expansion while still allowing savanna trees to persist (albeit as a subdominant to grasses). When savanna trees exert strong competitive effects on grasses, savanna trees cover increases initially, but as grasses decline their inhibitory effect on forest trees weakens, allowing forest trees to expand and exclude grasses and savanna trees. Rather than paradoxical, these results suggest that having weaker competitive effects on grasses may be advantageous for savanna trees, leading to greater long-term abundance and stability. We label this the 'enemy of my enemy hypothesis,' which might apply to species coexistence in communities defined by hierarchical competition or with species capable of generating strong ecological feedbacks. [ABSTRACT FROM AUTHOR]