Periodic Environmental Forcing Shapes the Stability of Complex Ecological Networks
Abstract
Environmental variability is a defining feature of natural ecosystems, yet many theories of ecological stability assume static environments. Here, we develop an analytical framework for local stability in complex ecological communities subjected to periodic environmental forcing. We show that, in slowly varying environments and under a large-system approximation, the maximal Lyapunov exponent can be approximated by the time-averaged rightmost spectral edge of the instantaneous interaction matrix, yielding explicit stability criteria for large ecological communities. Within the random-matrix interaction ensembles considered here, our minimal theoretical framework predicts a topology-dependent ordering of local perturbation stability under periodic temporal modulation in high-dimensional ecological networks, which is supported 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.