Modification speed alters stability of ecological higher-order interaction networks

Higher-order interactions (HOIs) have the potential to greatly increase our understanding of ecological interaction networks beyond what is possible with established models that usually consider only pairwise interactions between organisms. While equilibrium values of such HOI-based models have been studied, the dynamics of these models and the stability of their equilibria remain underexplored. Here we present a novel investigation on the effect of the onset speed of a higher-order interaction. In particular, we study the stability of the equilibrium of all configurations of a three-species interaction network, including transitive as well as intransitive ones. We show that the HOI onset speed has a dramatic effect on the evolution and stability of the ecological network, with significant structural changes compared to commonly used HOI extensions or pairwise networks. Changes in the HOI onset speed from fast to slow can reverse the stability of the interaction network. The evolution of the system also affects the equilibrium that will be reached, influenced by the HOI onset speed. This implies that the HOI onset speed is an important determinant in the dynamics of ecological systems, and including it in models of ecological networks can improve our understanding thereof.