Periodic Environmental Forcing Shapes the Stability of Complex Ecological Networks

Abstract

Environmental variability is a defining feature of natural ecosystems, yet most theories of ecological stability assume static environments. Here, we develop an analytical theory of stability for complex ecological networks subjected to periodic environmental forcing. We show that, in slowly varying environments, ecosystem stability is determined by the time-averaged rightmost spectral edge of the instantaneous interaction matrix, yielding explicit stability criteria for large ecological communities. The theory predicts a universal hierarchy of resilience across ecological interaction topologies and is validated by numerical simulations. Beyond the adiabatic regime, rapid environmental oscillations dynamically stabilize otherwise unstable ecosystems, revealing a high-frequency rescue effect that is absent from static theories. These results extend ecological stability theory beyond autonomous systems and provide a general framework for understanding resilience in fluctuating environments.