Effect of population abundances on the stability of large random ecosystems

Theo Gibbs, Jacopo Grilli, Tim Rogers, Stefano Allesina

Research output: Contribution to journalArticlepeer-review

48 Citations (SciVal)
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Random matrix theory successfully connects the structure of interactions of large ecological communities to their ability to respond to perturbations. One of the most debated aspects of this approach is that so far studies have neglected the role of population abundances on stability. While species abundances are well studied and empirically accessible, studies on stability have so far failed to incorporate this information. Here we tackle this question by explicitly including population abundances in a random matrix framework. We derive an analytical formula that describes the spectrum of a large community matrix for arbitrary feasible species abundance distributions. The emerging picture is remarkably simple: while population abundances affect the rate to return to equilibrium after a perturbation, the stability of large ecosystems is uniquely determined by the interaction matrix. We confirm this result by showing that the likelihood of having a feasible and unstable solution in the Lotka-Volterra system of equations decreases exponentially with the number of species for stable interaction matrices.

Original languageEnglish
Article number022410
Pages (from-to)1 - 16
Number of pages16
JournalPhysical Review E
Issue number2
Publication statusPublished - 27 Aug 2018

Bibliographical note

23 pages, 12 figures


  • q-bio.PE
  • cond-mat.stat-mech
  • physics.bio-ph

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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