Control of ecological networks: Abundance control or ecological regulation?

Complex ecosystems often exhibit a tipping point around which a small perturbation can lead to the loss of the basic functionality of ecosystems. It is challenging to develop a control strategy to bring ecosystems to the desired stable states. Typically, two methods are employed to restore the functionality of ecosystems: abundance control and ecological regulation. Abundance control involves directly managing species abundance through methods such as trapping, shooting, or poisoning. On the other hand, ecological regulation is a strategy for ecosystems to self-regulate through environment improvement. To enhance the effectiveness of ecosystem recovery, we propose adaptive regulation by combining the two control strategies from mathematical and network science perspectives. Criteria for controlling ecosystems to reach equilibrium with or without noise perturbation are established. The time and energy costs of restoring an ecosystem to equilibrium often determine the choice of control strategy, thus, we estimate the control costs. Furthermore, we observe that the regulation parameter in adaptive regulation affects both time and energy costs, with a trade-off existing between them. By optimizing the regulation parameter based on a performance index with fixed weights for time and energy costs, we can minimize the total cost. Moreover, we discuss the impact of the complexity of ecological networks on control costs, where the more complex the networks, the higher the costs. We provide corresponding theoretical analyses for random networks, predator-prey networks, and mixture networks.