The feasibility and stability of large complex biological networks: a random matrix approach.

ABSTRACT: In the 70's, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the "circular law" since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the "circular law" does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the

SUBMITTER: Stone L 

PROVIDER: S-EPMC5974107 | biostudies-literature | 2018 May

REPOSITORIES: biostudies-literature