Dispersal-induced instability in complex ecosystems

Abstract

In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors contributing to ecosystem stability or instability continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turing's work on pattern formation with May's random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with trophic structure can become unstable with the introduction of dispersal in space, and we discuss the factors which contribute to this effect. Our work highlights that adding more details to the model of May can give rise to more ways for an ecosystem to become unstable. Making May's simple model more realistic is therefore unlikely to entirely remove the upper bound on complexity.

26+71 pages, 6+14 figures

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• The effect of population abundances on the stability of large random ecosystems
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• Nonlinearity-generated Resilience in Large Complex Systems
• Eigenvalue spectra and stability of directed complex networks
• Spectrum of non-Hermitian deep-Hebbian neural networks
• Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems
• Topological conditions drive stability in meta-ecosystems
• Persistent individual bias in a voter model with quenched disorder
• The Spectral Boundary of Block Structured Random Matrices
• Demographic noise in complex ecological communities
• Stabilization of Microbial Communities by Responsive Phenotypic Switching
• Eigenvalue spectral tails and localization properties of asymmetric networks
• A path integral approach to sparse non-Hermitian random matrices
• Impossible ecologies: Interaction networks and stability of coexistence in ecological communities