An improved method for predicting local stability of microbial communities with competitive and mutualistic interactions

The local stability of microbial communities, defined as their ability to return to a steady state after small perturbations, is critical for maintaining ecosystem functions and human health. However, most existing studies focus on the structural properties of species interaction matrices, paying less attention to the role of species abundances in determining community local stability. In this study, we combine mean-field dimension reduction with spectral analysis to delve into the issue. This approach calculates species’ equilibrium abundances using the dimension reduction framework, then constructs a density-dependent Jacobian matrix from these obtained data, and employs spectral analysis to predict the eigenvalue distribution for assessing local stability. Experiments on local stability prediction conducted on real microbial communities and network models demonstrate that mutualistic interactions promote community stability, whereas high interaction strength, species diversity, and connectivity tend to destabilize communities. Furthermore, we also explore the correlation between local stability and species abundance at equilibrium. Our work provides accurate predictions of the local stability of the communities within the feasible parameter ranges, offering insights for constructing stable microbial communities and for developing protective measures.