Scholars have characterized academic communities of faculty, administration, and students in U.S. universities as "organized anarchies." In contrast, we offer evidence that the community structures of two representative public university systems are notably systematic by applying empirical phase-diagram techniques from the nonlinear dynamics literature to reconstruct low-dimensional deterministic behavior from historic data on the coevolution of faculty, administration, and student populations in each system. Ecological community models, fit with population data for each university, reproduce the essence of this behavior. The models offer novel explanations of how university resources obtained from enrollments and other sources are systematically partitioned among faculty, administration, and student populations interacting in shifting and well-defined community roles. This work offers empirical evidence that ecological principles, typically reserved for characterizing nonhuman interactions in biological systems, can shed light on human interactions in social systems.