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Marc Duran-Sala, Sandro Meloni and Violeta Calleja-Solanas, arRxiv 2025.01.15.XXXXX

# Abstract
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species—higher-order interactions—which recent theory suggests can by themselves stabilize communities. However, ecological communities exhibit both pairwise and higher-order interactions, and how their interplay governs stability and coexistence remains unknown. This work addresses this gap by analyzing a model of competitive communities that incorporates a proportion of pairwise and higher-order interactions. Using empirical data, numerical simulations, and analytical methods, we show that higher-order interactions alone cannot guarantee coexistence. We find that, while a small fraction of higher-order interactions can stabilize dynamics in communities of identical species, this effect disappears under more realistic conditions—such as heterogeneity in birth and death rates, empirically derived rates, or explicit interaction structures. Our results challenge the prevailing view of higher-order interactions as a universal stabilizing mechanism, providing quantitative evidence of the joint importance of both pairwise and higher-order interactions, together with network structure and species parameters, for understanding ecological stability.