Simulation results supporting Lechón-Alonso et al (2026).

This dataset accompanies the manuscript Tipping points are typical in ecosystems with higher-order interactions. It contains 25 archives of model runs used to map saddle-node (fold) boundaries in growth-rate space across a wide range of community sizes, interaction structures, and dynamical parameterizations. Each archive bundles JSON files describing individual model instances. Per file we provide the model parameters (intrinsic growth rates r, pairwise interactions A, three-body interactions B, equilibrium x*, and the HOI weight α) together with tipping-boundary scan results: for each of 128 perturbation directions in growth-rate space, the critical perturbation δr_crit, the boundary state x_boundary, and a fold/event flag obtained by homotopy continuation. The dataset spans: Standard gLV-HOI banks — 50 random models per community size, sweeping mean pairwise (muA) and HOI (muB) coupling strengths, with sub-banks restricted to all-negative interactions, unique-equilibrium systems, and globally stable systems. Sizes range from n=4 to n=20. Structured/empirical dynamics — banks built from published model families (Aguade, Karatayev FMI/RMI, Lever, Mougi, Stouffer) for n ∈ {4, 6, 8, 9, 10}. Gibbs parameterization — a reference grid of systems (R = A·x + B·x·x) covering three interaction regimes, plus matching boundary-scan banks at n ∈ 4..10 and n=20. The data support reproduction of all figures and statistics in the paper (see accompaning code), and enable further analysis of how community size, interaction sign structure, and HOI strength shape the geometry and fragility of ecological tipping boundaries.