Spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities
Classical ecological models predict that diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. We revisit this long-standing problem by extending the generalized Lotka-Volterra model to include both spatial structure and environmental fluctuations across space and time. We find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that together they permit arbitrarily many species to stably coexist in a sufficiently large system, despite strongly disordered competitive interactions. We analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives power-law abundance fluctuations, leading to an anomalous scaling of moments known empirically as Taylor's law. At the metacommunity level, this manifests as an emergent sublinear self-inhibition that stabilizes diversity and renders the interaction disorder irrelevant in the high-diversity limit. Spatiotemporal noise thus provides a novel resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist.