Abstract
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.
Highlights
IntroductionWhile large temporal variations are widespread in natural populations [1, 2], it is difficult to ascertain how much they are caused by external perturbations, or by the ecosystem’s internal dynamics, see e.g. [3, 4]
Large abundance fluctuations are well-documented in natural populations
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
Summary
While large temporal variations are widespread in natural populations [1, 2], it is difficult to ascertain how much they are caused by external perturbations, or by the ecosystem’s internal dynamics, see e.g. [3, 4]. While large temporal variations are widespread in natural populations [1, 2], it is difficult to ascertain how much they are caused by external perturbations, or by the ecosystem’s internal dynamics, see e.g. Some authors have even proposed that fluctuations driven by interactions are generally too rare or short-lived to matter, since they can be self-defeating: dynamics that create large erratic variations lead to extinctions, leaving only species whose interactions are less destabilizing, until an equilibrium is reached [9, 10]. We go past both the equilibrium [8, 11] or few-species starting points [5,6,7], to look directly at the dynamics of high-diversity communities in a spatially extended systems
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