For 50 years, ecologists have examined how the number of interactions (links) scales with the number of species in ecological networks. Here, we show that the way the number of links varies when species are sequentially removed from a community is fully defined by a single parameter identifiable from empirical data. We mathematically demonstrate that this parameter is network-specific and connects local stability and robustness, establishing a formal connection between community structure and two prime stability concepts. Importantly, this connection highlights a local stability–robustness trade-off, which is stronger in mutualistic than in trophic networks. Analysis of 435 empirical networks confirmed these results. We finally show how our network-specific approach relates to the classical across-network approach found in literature. Taken together, our results elucidate one of the intricate relationships between network structure and stability in community networks.

50 年来，生态学家一直在研究相互作用（链接）的数量如何与生态网络中的物种数量成比例。在这里，我们表明当物种从社区中按顺序移除时链接数量的变化方式完全由可从经验数据中识别的单个参数定义。我们在数学上证明该参数是特定于网络的，并且连接局部稳定性和稳健性，在社区结构和两个主要稳定性概念之间建立正式联系。重要的是，这种联系突出了局部稳定性-稳健性权衡，这种权衡在互惠网络中比在营养网络中更强。对 435 个实证网络的分析证实了这些结果。我们最终展示了我们的网络特定方法如何与文献中发现的经典跨网络方法相关联。