Population Ecology

, Volume 57, Issue 1, pp 63–75 | Cite as

The stability–complexity relationship at age 40: a random matrix perspective

Special Feature: Review Unravelling ecological networks

Abstract

Since the work of Robert May in 1972, the local asymptotic stability of large ecological systems has been a focus of theoretical ecology. Here we review May’s work in the light of random matrix theory, the field of mathematics devoted to the study of large matrices whose coefficients are randomly sampled from distributions with given characteristics. We show how May’s celebrated “stability criterion” can be derived using random matrix theory, and how extensions of the so-called circular law for the limiting distribution of the eigenvalues of large random matrix can further our understanding of ecological systems. Our goal is to present the more technical material in an accessible way, and to provide pointers to the primary mathematical literature on this subject. We conclude by enumerating a number of challenges, whose solution is going to greatly improve our ability to predict the stability of large ecological networks.

Keywords

Complexity Eigenvalue Food web Random matrix Stability 

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Copyright information

© The Society of Population Ecology and Springer Japan 2015

Authors and Affiliations

  1. 1.Department of Ecology and EvolutionUniversity of ChicagoChicagoUSA
  2. 2.Computation InstituteUniversity of ChicagoChicagoUSA

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