Most ecological models are based on the assumption that species interact in pairs. Diverse communities, however, can have higher-order interactions, in which two or more species jointly impact the growth of a third species. A pitfall of the common pairwise approach is that it misses the higher-order interactions potentially responsible for maintaining natural diversity. Here, we explore the stability properties of systems where higher-order interactions guarantee that a specified set of abundances is a feasible equilibrium of the dynamics. Even these higher-order interactions which lead to equilibria do not necessarily produce stable coexistence. Instead, these systems are more likely to be stable when the pairwise interactions are weak or facilitative. Correlations between the pairwise and higher-order interactions, however, do permit robust coexistence even in diverse systems. Our work not only reveals the challenges in generating stable coexistence through higher-order interactions but also uncovers interaction patterns that can enable diversity.

中文翻译：

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高阶相互作用什么时候才能产生稳定共存？


大多数生态模型都基于物种成对相互作用的假设。然而，不同的群落可以产生更高阶的相互作用，其中两个或多个物种共同影响第三个物种的生长。常见的成对方法的一个缺陷是它错过了可能负责维持自然多样性的高阶相互作用。在这里，我们探索系统的稳定性特性，其中高阶相互作用保证一组指定的丰度是动力学的可行平衡。即使这些导致平衡的高阶相互作用也不一定会产生稳定的共存。相反，当成对相互作用较弱或有促进作用时，这些系统更有可能保持稳定。然而，成对和高阶相互作用之间的相关性确实允许即使在不同的系统中也能稳健地共存。我们的工作不仅揭示了通过高阶交互产生稳定共存的挑战，而且还揭示了可以实现多样性的交互模式。