Mutualistic systems can experience abrupt and irreversible regime shifts caused by local or global stressors. Despite decades of efforts to understand ecosystem dynamics and determine whether a tipping point could occur, there are no current approaches to estimate distances (in state/parameter space) to tipping points and compare the distances across various mutualistic systems. Here we develop a general dimension-reduction approach that simultaneously compresses the natural control and state parameters of high-dimensional complex systems and introduces a scaling factor for recovery rates. Our theoretical framework places various systems with entirely different dynamical parameters, network structure and state perturbations on the same scale. More importantly, it compares distances to tipping points across different systems on the basis of data on abundance and topology. By applying the method to 54 real-world mutualistic networks, our analytical results unveil the network characteristics and system parameters that control a system’s resilience. We contribute to the ongoing efforts in developing a general framework for mapping and predicting distance to tipping points of ecological and potentially other systems.

互惠系统可能会经历由局部或全球压力源引起的突然且不可逆转的政权转变。尽管几十年来人们一直在努力了解生态系统动态并确定是否会发生临界点，但目前还没有方法来估计到临界点的距离（在状态/参数空间中）并比较各种互惠系统的距离。在这里，我们开发了一种通用的降维方法，该方法同时压缩高维复杂系统的自然控制和状态参数，并引入恢复率的缩放因子。我们的理论框架将具有完全不同的动力学参数、网络结构和状态扰动的各种系统置于相同的尺度上。更重要的是，它根据丰度和拓扑数据比较不同系统到临界点的距离。通过将该方法应用于 54 个现实世界的互惠网络，我们的分析结果揭示了控制系统弹性的网络特征和系统参数。我们致力于开发一个总体框架，用于绘制和预测生态系统和潜在其他系统的临界点距离。