Marginally Stable Equilibria in Critical Ecosystems

Abstract

In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by our numerical studies, shows that for strong and heterogeneous interactions the system displays multiple equilibria which are all marginally stable. This property allows us to obtain general identities between diversity and single species responses, which generalize and saturate May's bound. By connecting the model to systems studied in condensed matter physics, we show that the multiple equilibria regime is analogous to a critical spin-glass phase. This relation provides a new perspective as to why many systems in several different fields appear to be poised at the edge of stability and also suggests new experimental ways to probe marginal stability.

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Cited by in corpus (61)

• Colloquium: Criticality and dynamical scaling in living systems
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• Infinite Ergodic Theory for Heterogeneous Diffusion Processes
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• May's Instability in Large Economies
• Effect of resource dynamics on species packing in diverse ecosystems
• Generalized Lotka-Volterra equations with random, non-reciprocal interactions: the typical number of equilibria
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• Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems
• Hessian spectrum at the global minimum of high-dimensional random landscapes
• Ecological communities from random generalised Lotka-Volterra dynamics with non-linear feedback
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• Local and collective transitions in sparsely-interacting ecological communities
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• Well-mixed Lotka-Volterra model with random strongly competitive interactions
• Generalised Lotka-Volterra model with hierarchical interactions
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• Breakdown of random-matrix universality in persistent Lotka--Volterra communities
• Interactions and migration rescuing ecological diversity
• Nonlinearity-generated Resilience in Large Complex Systems
• Consensus, polarisation and coexistence in a continuous opinion dynamics model with quenched disorder
• Effects of intraspecific cooperative interactions in large ecosystems
• How adaptive immunity constrains the composition and fate of large bacterial populations
• Quenched complexity of equilibria for asymmetric Generalized Lotka-Volterra equations
• Artificial selection of communities drives the emergence of structured interactions
• Dynamical mean-field theory: from ecosystems to reaction networks
• Aging by near-extinctions in many-variable interacting populations
• Stability of large complex systems with heterogeneous relaxation dynamics
• Dynamically selected steady states and criticality in non-reciprocal networks
• Systems of random linear equations and the phase transition in MacArthur's resource-competition model
• Incorporating Heterogeneous Interactions for Ecological Biodiversity
• Breakdown of random matrix universality in Markov models
• Complexity-stability relationships in competitive disordered dynamical systems
• Quantifying the overall effect of biotic interactions on species distributions along environmental gradients
• Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems
• A new spin on optimal portfolios and ecological equilibria
• Competitive exclusion and Hebbian couplings in random generalised Lotka-Volterra systems
• Path-integral solution of MacArthur's resource-competition model for large ecosystems with random species-resources couplings
• Effects of phylogeny on coexistence in model communities
• Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder
• The Spectral Boundary of Block Structured Random Matrices
• Counting equilibria of large complex systems by instability index
• Demographic noise in complex ecological communities
• Progress and open problems in evolutionary dynamics
• Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems
• Searching for long time scales without fine tuning
• A minimal model of pan-immunity maintenance by horizontal gene transfer in the ecological dynamics of bacteria and phages
• Microbiomes Through The Looking Glass: Linking species interactions to dysbiosis through a disordered Lotka-Volterra framework
• Generalized Lotka-Volterra model with sparse interactions: non-Gaussian effects and topological multiple-equilibria phase
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Effective one-dimension reduction of multi-compartment complex systems dynamics
• Critical behavior of a phase transition in the dynamics of interacting populations
• Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities
• Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model
• Mathematical modeling and intuition in microbiology: a perspective
• Minimal model of self-organized clusters with phase transitions in ecological communities
• Emergence of vertical diversity under disturbance
• Random motility regulation as a generic mechanism of community formation