Complex interactions can create persistent fluctuations in high-diversity ecosystems.

When can ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where many species populations fluctuate without going to extinction? We show that high-diversity spatially heterogeneous systems can exhibit chaotic dynamics which persist for extremely long times. We develop a theoretical framework, based on dynamical mean-field theory, to quantify the conditions under which these fluctuating states exist, and predict their properties. We uncover parallels with the persistence of externally-perturbed ecosystems, such as the role of perturbation strength, synchrony and correlation time. But uniquely to endogenous fluctuations, these properties arise from the species dynamics themselves, creating feedback loops between perturbation and response. A key result is that fluctuation amplitude and species diversity are tightly linked: in particular, fluctuations enable dramatically more species to coexist than at equilibrium in the very same system. Our findings highlight crucial differences between well-mixed and spatially-extended systems, with implications for experiments and their ability to reproduce natural dynamics. They shed light on the maintenance of biodiversity, and the strength and synchrony of fluctuations observed in natural systems. Author summary Large abundance fluctuations are well-documented in natural populations. Yet, it is still not known to what extent these fluctuations stem from multi-species interactions, rather than environmental perturbations or demographic processes. There have been long-standing debates on these issues, questioning even the possibility of interaction-driven fluctuations, as they might induce species extinctions until equilibrium is reached. The situation is all the more challenging and richer in complex high-dimensional settings (many interacting species, many niches, etc.), which feature qualitatively new phenomena, and where theory is still lacking. Here we show that high-diversity metacommunities can persist in dynamically-fluctuating states for extremely long periods of time without extinctions, and with a diversity well above that attained at equilibrium. We describe the quantitative conditions for these endogenous fluctuations, and the key fingerprints which would distinguish them from external perturbations. We establish a theoretical framework for the many-species dynamics, derived from statistical physics of out-of-equilibrium systems. These settings present unique challenges, and observed behaviors may be counter-intuitive, making specialized theoretical techniques an indispensable tool. Our theory exactly maps the many-species problem to that of a single representative species (metapopulation). This allows us to draw connections with existing theory on perturbed metapopulations, while accounting for unique properties of endogenous feedbacks at high diversity.