When can higher-order interactions produce stable coexistence?

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. Most ecological models assume that species interact in pairs, but they often fail to predict the diversity observed in nature. One fascinating explanation for this mismatch is that interactions that only occur among three or more species (called higher-order interactions) are crucial for the maintenance of ecological diversity. Here, we model higher-order interactions that precisely balance pairwise interactions and find that even these model communities are often unstable, except when the higher-order interactions obey additional constraints.image