Fluctuation spectra of large random dynamical systems reveal hidden structure in ecological networks

TL;DR

This paper uses random matrix theory to analyze fluctuation spectra in ecological networks, revealing how network structure influences temporal stability and applying the theory to real plankton data.

Contribution

It introduces a novel analytical framework linking network structure to fluctuation spectra in ecological systems, extending stability analysis beyond equilibrium points.

Findings

Different network structures produce distinct fluctuation signatures

The theory accurately predicts fluctuation spectra in ecological time series

Application to plankton data demonstrates practical relevance

Abstract

Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of `stability' in fact has other uses in the empirical ecological literature. The important notion of `temporal stability' describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. We show that different network structures leave distinct signatures in the spectrum of fluctuations, and demonstrate the application of our theory to the analysis ecological timeseries data of plankton abundances.