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

Yvonne Krumbeck, Qian Yang, George William Albert Constable, Tim Rogers

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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.
Original languageEnglish
Article number3625 (2021)
Number of pages14
JournalNature Communications
Publication statusPublished - 15 Jun 2021

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