Ecological communities from random generalised Lotka-Volterra dynamics with non-linear feedback

Abstract

We investigate the outcome of generalised Lotka-Volterra dynamics of ecological communities with random interaction coefficients and non-linear feedback. We show in simulations that the saturation of non-linear feedback stabilises the dynamics. This is confirmed in an analytical generating-functional approach to generalised Lotka-Volterra equations with piecewise linear saturating response. For such systems we are able to derive self-consistent relations governing the stable fixed-point phase, and to carry out a linear stability analysis to predict the onset of unstable behaviour. We investigate in detail the combined effects of the mean, variance and co-variance of the random interaction coefficients, and the saturation value of the non-linear response. We find that stability and diversity increases with the introduction of non-linear feedback, where decreasing the saturation value has a similar effect to decreasing the co-variance. We also find co-operation to no longer have a detrimental effect on stability with non-linear feedback, and the order parameters mean abundance and diversity to be less dependent on the symmetry of interactions with stronger saturation.

arXiv comment48 pages, 11 figures

References in corpus (16)

• Stability Criteria for Complex Ecosystems
• Marginally Stable Equilibria in Critical Ecosystems
• Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems
• Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka-Volterra model of ecosystems
• The effect of population abundances on the stability of large random ecosystems
• Dynamically evolved community size and stability of random Lotka-Volterra ecosystems
• Path integral methods for the dynamics of stochastic and disordered systems
• Matrix Games, Mixed Strategies, and Statistical Mechanics
• Random replicators with asymmetric couplings
• Replica Symmetry Breaking in the Random Replicant Model
• Random replicators with high-order interactions
• Statistical mechanics and stability of a model eco-system
• Rank abundance relations in evolutionary dynamics of random replicators
• Entropy and typical properties of Nash equilibria in two-player games
• Two-population replicator dynamics and number of Nash equilibria in random matrix games
• Dynamics of random replicators with Hebbian interactions

Cited by in corpus (9)

• Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
• Well-mixed Lotka-Volterra model with random strongly competitive interactions
• Generalised Lotka-Volterra model with hierarchical interactions
• Nonlinearity-generated Resilience in Large Complex Systems
• Artificial selection of communities drives the emergence of structured interactions
• Dynamically selected steady states and criticality in non-reciprocal networks
• Competitive exclusion and Hebbian couplings in random generalised Lotka-Volterra systems
• Structured interactions as a stabilizing mechanism for competitive ecosystems
• Invasion and Interaction Determine Population Composition in an Open Evolving System