Species Coexistence and Extinction Resulting from Higher-Order Lotka-Volterra Two-Faction Competition

It is known that the effect of species' density on species' growth is non-additive in real ecological systems. This challenges the conventional Lotka-Volterra model, where the interactions are always pairwise and their effects are additive. To address this challenge, we introduce HOIs (Higher-Order Interactions) and are able to capture, for example, the indirect effect of one species on a second one correlating to a third species. Towards this end, we propose a purely cooperative higher-order Lotka-Volterra model and a higher-order Lotka-Volterra two-faction competition model. By utilizing the theory of monotone systems, we provide stability conditions for both models. The stability analysis further shows that small HOIs usually promote the coexistence of all species, while the extinction of some species is usually caused by a huge difference among the higher-order competitive terms. Finally, illustrative numerical examples are provided to highlight our contributions.