# Can endogenous fluctuations persist in high-diversity ecosystems?

## TL;DR

This paper develops a theoretical framework to understand how high-diversity, spatially-extended ecosystems can sustain persistent endogenous chaotic fluctuations, which promote biodiversity and differ from well-mixed systems.

## Contribution

It introduces a dynamical mean-field theory to predict conditions for endogenous fluctuations and explores their implications for biodiversity and ecosystem dynamics.

## Key findings

- Endogenous fluctuations can persist for long times in high-diversity systems.
- Fluctuation amplitude is closely linked to species diversity.
- Spatial extension influences the nature and persistence of fluctuations.

## Abstract

When can complex ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where species abundances keep fluctuating without going to extinction? We show that high-diversity spatially-extended systems, in which conditions vary somewhat between spatial locations, 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 the 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.