Local and extensive fluctuations in sparsely-interacting ecological communities

TL;DR

This paper uncovers a new phase in sparsely-interacting ecological communities where some species fluctuate while others stabilize, revealing complex transition behaviors and the role of interaction graph structures.

Contribution

It introduces a novel phase in sparse ecological networks where fluctuating and fixed species coexist, and characterizes the transition to extensive fluctuations.

Findings

A new phase with coexistence of fixed and fluctuating species.

Fluctuating species are organized around short cycles in the interaction graph.

The number of fluctuating species diverges at the transition point.

Abstract

Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when interactions are sparse, with each species interacting with only several others, has remained largely unexplored. Here we show that a new type of phase appears in the phase diagram, where for the same control parameters different communities may reach either a fixed point or a state where the abundances of a finite subset of species fluctuate, and calculate the probability for each outcome. These fluctuating species are organized around short cycles in the interaction graph, and their abundances undergo large non-linear fluctuations. We characterize the approach from this phase to a phase with extensively many fluctuating species, and show that the probability of fluctuations grows continuously to one as the transition is approached, and that the number of fluctuating species diverges. This is qualitatively distinct from the transition to extensive fluctuations coming from a fixed point phase, which is marked by a loss of linear stability. The differences are traced back to the emergent binary character of the dynamics when far away from short cycles in the local fluctuations phase.