Higher-order interactions as stabilising mechanism for competitive communities

Ecological communities, like many other complex systems, continue to intrigue researchers to find a way to explain how the biodiversity observed in nature is maintained. This raises a fundamental question: what sustains the stability and the coexistence of species in these ecosystems? Ecological models have largely rested on the premise that species primarily en- gage in pairwise interactions. Yet, in ecological systems, interactions can often occur in groups of three or more individuals. That is why, in this master’s thesis, we will study a model for competitive community, exploring how higher-order interactions together with different net- work structures, affect species coexistence and the stability of ecological dynamics. Relying on numerical simulations of the system’s dynamics, we investigate structured communities and non-spatially structured communities, in addition to well-mixed populations, along with some theoretical derivations using a mean-field approximation. Our findings reveal that, network topology and interaction range, together with the presence of higher-order interactions, play pivotal roles in the emergence of coexistence and stability of multi-species competitive communities. For example, we find that for well-mixed populations, when species present the same physiological rates (e.g. birth and death rates), even a small fraction of higher-order interactions are able to stabilise the dynamics. Instead, when physiological rates are different between species, their relative variance dictates the critical fraction of higher-order interactions needed to achieve stable coexistence. These discoveries represent a step forward in our understanding of ecological dynamics and open up promising avenues for future research.