Estimating the recovery time of complex ecosystems

Ecosystems are vulnerable to both internal and external perturbations, which can trigger sudden and catastrophic shifts from a stable, functional state to dysfunction, often resulting in biodiversity loss. Here, we explore the efficacy of external interventions in restoring ecosystems from dysfunction to functionality, emphasizing recovery time as a key metric of intervention effectiveness. We propose ecological regulation as a restoration strategy, employing insights from network science and control theory, and introduce recovery time as a measurable indicator. Analytical estimations of recovery time are provided for deterministic and stochastic ecosystems with random interactions, predator–prey interactions, and mixture interactions. Our analysis highlights that recovery time is influenced by several factors: control strength, regulation parameters, and the complexity of ecological networks. Specifically, recovery time decreases with stronger controls but increases with higher regulation parameters and greater network complexity.