Stability of complex communities with environmental feedbacks

The stability of complex ecosystems, which indicates the ability of the system to recover from perturbations, is profoundly influenced by the environment. Recent findings point out that changing environments with the renewal and decay of resources can alter ecological stability by affecting species abundances and interactions. These changes in turn affect the environment, establishing a feedback loop between environments and species. However, studies on ecological stability have primarily been based on static environments, ignoring feedbacks between species and environments. Here, we study ecological stability with environmental feedbacks, considering the co-evolutionary dynamics of species abundances, interactions and environments. We find that environmental feedbacks, while increasing the complexity of ecosystems, generally enhance ecological stability by reducing the noise (variance) of species interaction strengths. Furthermore, we derive stability criteria for multiple interaction types among species and identify the optimal resource stock to promote ecological stability. Our results hold across various realistic scenarios, such as heterogeneous communities, highlighting the significant role of environmental feedbacks on ecological stability.