COS 152-2 - Constrained higher-order interactions promote coexistence in diverse communities

Abstract: Most ecological models assume that species interact in pairs. In a diverse community, however, it is possible for two or more species to jointly affect the growth of a focal species. Interactions between three or more species, called higher-order interactions, could help to explain how diverse communities assemble and stably coexist. Previous models focused on specific biological scenarios have shown that higher-order interactions can stabilize ecological dynamics, potentially allowing widespread coexistence. More recent theory, however, demonstrated that randomly sampled higher-order interactions in generic ecological models did not enhance opportunities for coexistence. Here, we bridge this apparent gap between specific and generic models. By constraining higher-order interactions to perfectly counter the pairwise interactions that exclude species, we consider an idealized case in which higher-order interactions unambiguously benefit coexistence because they guarantee that there is an equilibrium where all species have positive abundance. Even in this optimistic case, however, stability is far from assured. Using a combination of numerical simulations and analytical theory, we characterize dynamical stability in this system as a function of the statistics of the pairwise interactions that are being turned off. The resulting equilibria are more likely to be stable when the the higher-order interactions counter underlying pairwise interactions that are facilitative, rather than competitive, unlike in the classic pairwise theory. On the other hand, they are less likely to be stable as the underlying pairwise interactions become more variable, which is consistent with results for both pairwise and higher-order interactions. By introducing additional constraints, like tight correlations between the pairwise and higher-order interactions, it is possible to guarantee stable coexistence in diverse systems. Last, we investigate how the values of the equilibrium abundances that the higher-order interactions are constrained to produce impact stability. Our work uncovers a set of patterns in the higher-order interactions that permit coexistence in generic models, thus connecting previously separate theoretical approaches to this topic.