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

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.

arXiv comment17 pages, 7 figures, revised submission, added sections on data application and expanding notion of temporal stability

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Cited by in corpus (4)

• Stability of large complex systems with heterogeneous relaxation dynamics
• Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures
• Mean-field theory of vector spin models on networks with arbitrary degree distributions
• Resistance distance distribution in large sparse random graphs