Higher order interactions (HOIs) have been suggested to stabilize diverse ecological communities. However, their role in maintaining species coexistence from the perspective of modern coexistence theory is not known. Here, using generalized Lotka-Volterra model, we derive a general rule for species coexistence modulated by HOIs. We show that where pairwise species interactions fail to promote species coexistence in regions of extreme fitness differences, negative HOIs that intensify pairwise competition, however, can promote coexistence provided that HOIs strengthen intraspecific competition more than interspecific competition. In contrast, positive HOIs that alleviate pairwise competition can stabilize coexistence across a wide range of fitness differences, irrespective of differences in strength of inter- and intraspecific competition. In addition, we extend our three-species analytical result to multispecies communities and show, using simulations, that multispecies coexistence is possible provided that strength of negative intraspecific HOIs is higher than interspecific HOIs. Our work sheds light on the underlying mechanisms through which HOIs can maintain species diversity.

已经提出了更高阶的相互作用（HOI）来稳定多样化的生态群落。然而，从现代共存理论的角度来看，它们在维持物种共存中的作用尚不清楚。在这里，我们使用广义Lotka-Volterra模型，得出了由HOI调制的物种共存的一般规则。我们表明，当成对物种相互作用未能促进极端适应性差异区域中物种共存时，加剧成对竞争的负面HOI可以促进共存，前提是HOI比种间竞争更能增强种内竞争。相比之下，缓解成对竞争的积极HOI可以在广泛的适应性差异中稳定共存，而与种间竞争和种内竞争强度的差异无关。此外，我们将三种物种的分析结果扩展到多物种群落，并通过模拟显示，只要阴性种内HOI的强度高于种间HOI，则多种共存是可能的。我们的工作阐明了HOI可以维持物种多样性的潜在机制。