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

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 of ecological time-series data of plankton abundances. Fluctuations in ecosystems and other large dynamical systems are driven by intrinsic and extrinsic noise and contain hidden information which is difficult to extract. Here, the authors derive analytical characterizations of fluctuations in random interacting systems, allowing inference of network properties from time series data.

Automated summary

Understanding the relation between complexity and stability in large dynamical systems, like ecosystems, is a key question in complexity theory. Most theories focus on linear stability around equilibrium points, but stability has other meanings in empirical ecological literature. By applying random matrix theory, analytical predictions for fluctuation spectra of complex ecological networks can be derived, revealing distinct signatures in fluctuation spectrum based on network structures. The theory can be applied to analyze ecological time-series data, extracting hidden information from fluctuations driven by intrinsic and extrinsic noise.