Department of Ecology and Evolutionary Biology, Princeton University, United States
A central assumption in most ecological models is that the interactions in a community operate only between pairs of species. However, the interaction between two species may be fundamentally changed by the presence of others. Although interactions among three or more species, called higher-order interactions, have the potential to modify our theoretical understanding of coexistence, ecologists lack clear expectations for how these interactions shape community structure. Part of the challenge is that theoreticians have limited analytical tools to characterize the complex ecological dynamics emerging from communities with higher-order interactions. We derived analytical predictions for how the variability and strength of higher-order interactions affect species coexistence using a theoretical technique from statistical physics. We then confirmed our predictions with extensive numerical simulations. Because our model communities contained many species, our theory used only the mean and variance of the pairwise and higher-order interactions, rather than their exact values, to understand the macroecological properties of the assembled community.
We found that, as higher-order interaction strengths become more variable across species, fewer species coexist, echoing the behavior of pairwise models. If the average strength of inter-specific higher-order interactions was too competitive relative to self-regulation, coexistence was destabilized, but coexistence was also lost when these interactions were too weak and mutualistic effects became prevalent. Last, we showed that more species rich communities structured by higher-order interactions lose species more readily than their species poor counterparts, generalizing classic results for community stability. Our work provides needed theoretical expectations for how higher-order interactions impact species coexistence in diverse communities. From an empirical perspective, because our predictive framework only requires the statistics of the interactions, it can be parameterized using significantly fewer experiments than if every interaction needed to be measured precisely. Our theory therefore provides empiricists a null expectation for the influence of higher-order interactions on species coexistence. More generally, our work will stimulate future experimental and theoretical investigations of how pairwise and higher-order interactions jointly shape the macroecological patterns observed in nature.