Determinants of Structural Stability in Complex Ecological and Biological Networks: the Google Matrix Approach Determinants of stability in biological and ecological networks: the Google matrix approach

TL;DR

This paper extends Mays' random-matrix approach to large ecological networks using a Google matrix reduction, revealing how network topology influences stability and feasibility of species coexistence.

Contribution

It introduces a Google matrix-based reduction scheme to analyze stability in complex ecological networks, linking topology to stability and feasibility.

Findings

Network connectance significantly affects stability.

Feasibility constraints are more restrictive than stability constraints.

The Google matrix approach provides a practical stability index.

Abstract

Mays celebrated theoretical work of the 70s contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here Mays random-matrix modelling approach is generalized to realistic large-scale webs of species interactions, be they structured by networks of competition, mutualism or both. Simple relationships are found to govern these otherwise intractable models, and control the parameter ranges for which biological systems are stable and feasible. Our analysis of model and real empirical networks is only achievable upon introducing a simplifying Google-matrix reduction scheme, which in the process, yields a practical ecological eigenvalue stability index. These results provide an understanding on how network topology, especially connectance, influences species stable coexistence. Constraints controlling feasibility (positive equilibrium populations) in these systems, are found more restrictive than those controlling stability, helping explain the enigma of why many classes of feasible ecological models are nearly always stable.