  Statistical Physics has proved essential to analyze multi-agent environments.
Motivated by the empirical observation of various non-equilibrium features in
Barro Colorado and other ecological systems, we analyze a plant-species
abundance model, presenting analytical evidence of scale-invariant plant
clusters and non-trivial emergent modular correlations. Such first theoretical
confirmation of a scale-invariant region, based on percolation processes,
reproduces the key features in actual ecological ecosystems and can confer the
most stable equilibrium for ecosystems with vast biodiversity.
